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North American Review of Finance Volume 13 (4)

North American Review of Finance Volume 12, Number 4


North American Review of Finance Volume 13, Number 4

Articles Investor Overconfidence: An Examination of Individual Traders on the Tunisian Stock Market Salma Zaiane…………..……………………………………………….…….……..….…….1 - 13 The Effect of Foreign Aid on Real Exchange Rate in Ghana Peter Arhenful……………………………………………………..............................14 – 32 Interbank Exposures and Risk of Contagion in Crises: Evidence from Finland in the 1990s and the 2000s Mervi Toivanen………………………………………………………………………..…..33 – 53 Further Evidence of Deficiencies in Classical Finance Erhard Reschenhofer and Kevin Windisch…………..…………………………..54 - 79

Copyright © 2013 by North American Academic Journals


Investor overconfidence: An Examination Of Individual Traders On The Tunisian Stock Market

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Salma Zaiane1

Abstract

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The aim of this paper is to investigate individual overconfidence on the Tunisian stock market. This was achieved by administrating a questionnaire and by collecting empirical evidence about Tunisian individual investors. The survey is for exploratory purpose and it is based on multiple factorial correspondence analyses. The results reveal that Tunisian investors suffer from the overconfidence bias. In fact, they are confident about their intuition; they consider themselves lucky and trade aggressively. Besides, they use different sources of information when they choose their stocks.

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1 Introduction

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JEL Classification numbers: G11, G12. Keywords: behavioural finance, overconfidence bias, individual investors, questionnaire, multiple factorial correspondence analysis.

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The scandals that have occurred in recent years and the crashes and successive financial crises that characterize modern economies, including the current financial meltdown from the subprimes, lead us to question the functioning of financial markets. Researchers try to understand the attitudes of investors, often influenced by mental routines, errors in judgments or even emotional factors. Obviously, this leads one to doubt the efficiency of financial markets, that is to say, their ability to control the policies of the firms and to allocate the capital optimally. Kahneman and Tversky (1979) propose an alternative study focusing on behavioral evidence in total opposition to the rationality of investors which follows the theory of financial markets. Indeed, investors are not fully rational and their demand for risky financial assets is affected by their beliefs or their feelings, which are clearly not justified by economic fundamentals. They are thus prey to several biases that affect their logical reasoning, and push them to commit errors in thinking.

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Assistant professor at the Faculty of Economics and Management Sciences of Tunis.

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Empirical work and recent experimental research have confirmed that the errors of judgments made by individuals affect the behavior of security prices on financial markets. In fact, investors do not necessarily follow objective notions of financial loss or gain calculated mathematically. A key way, in which investors are victims, is the overconfidence bias. Indeed, they are tempted to overestimate the quality of information they have and their ability to interpret it. These features give them an illusion of control over the evolution of markets and distort their perception of risk, sometimes even encouraging them to take more risks. In this paper, we seek to better understand the human behavior that governs the dynamics of financial markets, studied through investor overconfidence on the Tunisian stock market. For that purpose, we use a questionnaire developed and administered to a Tunisian sample of individual investors. The rest of the paper is organized as follows: Section II presents a review of the literature of the overconfidence bias, and Section III presents the assumptions of our work. Empirical validation is described in Section IV and Section V is devoted to present the empirical results and their interpretation. Finally, Section VI contains the summary and the conclusion.

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2 Literature Review

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Overconfidence bias is often regarded as the most prevalent judgment bias (Langer et al., 2010). It stems from the study of the calibration of subjective probabilities. This reflects how the confidence in an event corresponds to its actual probability of occurrence. In the psychological literature, there is no precise definition of overconfidence. In financial literature there are several findings that are often summarized under the concept of overconfidence: miscalibration, the better than average effect, illusion of control, and unrealistic optimism. - Miscalibration: It refers to the difference between the accuracy rate and the probability assigned (that a given answer is correct). This arises when the confidence interval around the investor’s private signal is tighter than it is in reality. This can be thought of as an irrational shift in perceived variance. According to Ben-David et al. (2010), miscalibrated people are those who overestimate the precision of their own forecasts, or underestimate the variance of risky processes; in other words, their subjective probability distributions are too narrow. Studies that analyze assessments of uncertain quantities using the fractile method usually find that people’s probability distributions are too tight (Lichtenstein et al., 1982), i.e. when subjects are asked to state a 90% confidence interval for some uncertain quantities, the percentage of true values that fall outside the interval, is higher than 10% (the percentage of surprises of a perfectly calibrated person). - Better than the average effect: Psychological research has established that, in general, people tend to have an unrealistically positive view of themselves. In fact, most of us, when comparing ourselves to a group (of co-student, co-workers, random participants), believe to be superior to an average representative of that group in various fields. A well known study of better than average effect carried out by Svenson (1981) demonstrated that, while comparing themselves with others, people generally believe themselves to be more skilful and less risky drivers than an average driver, without a prior definition or knowledge of the average driving skills. Taylor and Brown (1998) show that individuals

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feel they are better than others and this by taking into account the knowledge and the positive attributes of personality. In fact, the self serving bias2 makes people assign more responsibility for success and less for failure to themselves, while others are not given the same credit. - Illusion of control and unrealistic optimism: Langer (1975) defines the illusion of control as an expectancy of a personal success probability inappropriately higher than the objective probability would warrant. In fact, the existence of illusion of control in purely chance driven tasks has repeatedly been proven experimentally, with the participants convinced that their skill or past experience can influence the outcome of predicting the result of the task (Langer and Roth, 1975).Weinstein (1980) notes that this phenomenon is similar to the phenomenon of unrealistic optimism. According to this latter, people are particularly optimistic about future events to which they are personally in favor. Most people’s beliefs are biased in the direction of optimism (Kahneman and Riepe, 1998). In fact, Optimists underestimate the likelihood of bad outcomes over which they have no control. Several statistical studies have shown that individuals tend to overestimate the relevance of their knowledge (Alpert and Raiffa, 1982; Fischhoff, Slovic and Lichtenstein, 1977). Moreover, according to Griffin and Tversky (1992), 'experts' are more overconfident than inexperienced individuals. Odean (1998b) assumes that traders, insiders and market makers may unconsciously overestimate the precision of their information and rely on it more than is warranted, while traders display a better than average effect, evaluating their information as better than average than that of their peers. Such overconfidence of market participants may cause an increase in the trading volume. Daniel, Hirshleifer and Subrahmanyam (1998) show theoretically that investors are overconfident only towards private (and not public) signals. They propose a model of overconfidence and biased self-attribution of investors, i.e. people overestimate the degree to which they are responsible for their own success), where security market under and overreactions respectively follow public and private signals. This paper implies that volume should increase following positive returns when such returns build confidence. Moreover, researchers tend increasingly to study overconfidence using questionnaires or experimental studies. De Bondt (1998), for example, studied different measures of overconfidence (better than average effect, illusion of control and unrealistic optimism) using a large questionnaire. The author shows that investors are overly optimistic about the performance of shares that they themselves own but not about the level of the stock index in general. Maciejovsky and Kirchler (2002) note from an experimental study a greater overconfidence at the end of the experiment, when participants gain more experience and start to rely more heavily on their overestimated knowledge. Glaser, Langer and Weber (2010) show, from experimental studies related to the field of finance, that overconfidence of financial experts (professional traders and bankers) is higher than that of lay men (students). Bias et al. (2005) constructed an experimental asset market with varying private information and find that miscalibrated (overconfident) agents perform worse than their better calibrated counterparts. In addition, despite the fact that miscalibration itself is

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See Alicke et al. (2005) et Skala (2008) for further details about this bias.

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approximately the same for both men and women; it reduces trading performance in the experimental market, only for men who turn out to be more active traders than women. Glaser and Weber (2009), using data on 215 online investors who responded to a survey, find that “the better than average effect” is related to trading frequency. According to the authors, at the individual level, overconfident investors will trade more aggressively: the higher the degree of overconfidence of an investor, the higher his or her trading volume. Odean (1998b) calls this finding “the most robust effect of overconfidence”. Using experimental data, Deaves et al. (2008) observe that miscalibration-based overconfidence is positively related to trading activity, while Bias et al. (2002) find that miscalibrationbased overconfidence reduces trading performance. Blavatskyy (2008), using an experimental study, shows that the subjects exhibit average confidence in their own knowledge. In addition, confidence does not depend on their attitudes towards risk or ambiguity. By contrast, Benoit et al. (2009) use a test as part of an experimental study to test the better than average effect. Their results do not reject the hypothesis that the data is provided by perfectly rational and confident agents. Using two analytic methods, Parker and Stone (2010) examine the implication of two common measures – labelled overconfidence and unjustified confidence- showing how and where they can lead to different conclusions when they are used to prediction. Ifcher and Zarghamee (2011) conduct a laboratory experiment to identify the effect of positive affect on overconfidence. They find that overconfidence may explain the effect of positive affect on trading volume and the persistence of speculative bubbles.

3 Hypothesis

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In order to examine the existence of the overconfidence bias on the Tunisian stock exchange, we will test the following hypothesis:

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3.1 Hypothesis 1: Overconfident Investors have Confidence in their Intuition

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"The trust in intuition" was confirmed by the work of Griffin and Tversky (1992), Daniel, Hirshleifer and Subrahmanyam (1998) and Odean (1998). Indeed, the personal implications have an influence on achieving favorable but random events (Langer and Roth, 1975). This can also be explained by the optimism bias. Indeed, subjects are optimistic about their fates (Bernartzi, Kahneman and Tversky, 1999). Kahneman and Riepe (1998) summarize the motivation of overconfidence as a combination of overconfidence and optimism that makes people overestimate their knowledge, underestimate risks and exaggerate in their ability to control the events.

3.2 Hypothesis 2: Overconfident Investors Trade more on the Stock Market Overconfident investors tend to trade more than rational investors. According to De Bondt and Thaler (1995), "The key behavioral factor needed to understand the trading puzzle is overconfidence." Odean (1998) and Gervais and Odean (2001) consider changes in trading volume as the first testable hypothesis of the theory of overconfidence. Gervais and Odean (2001) assume that overconfident traders achieve, on average, lower gains as they increase both trading and volatility which, in turn, negatively affects their

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trading results. They show that greater overconfidence leads to a higher trading volume and that this suggests that trading volume will be greater after market gains and lower after market losses. Moreover, Barber and Odean (2002) analyze trading volume and performance of a group of 1,600 investors who switched from phone based to online trading during the sample period. They find that those who switch to online trading perform well prior to going online and beat the market. Furthermore, they find that trading volume increases and performance decreases after going online. Other studies (Statman, Thorley and Vorkink, 2006; Chuang and Lee, 2006; Glaser and Weber, 2007, 2009)), find that trading volume increases after a series of high returns, since the success of investors increases their degree of overconfidence. These authors conclude that a high level of overconfidence leads to a significant trading volume. Using experimental studies, Biais et al. (2005) and Deaves et al. (2008) confirm that overconfidence is positively related to trading volume.

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3.3 Hypothesis 3: Overconfident Investors make little use of Available Information

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The amount of information and the strength of that information influences people’s confidence in their decisions (Koriat, Lichtenstein and Fischhoff, 1980). Peterson and Pitz (1986) theorized that when one piece of information is given, judgments become extreme and confident, whereas when several pieces of useful information are given they conflict with each other and the resulting prediction is close to the average but with low confidence, which reduces overconfidence. Overconfident investors tend to use a minimum of information sources when they select their assets. In fact, overconfidence often leads to the non-use of available information (Fishhoff, 1982; Wickens and Holland, 2000). Griffin and Tversky (1992) suggest that the less informed investors suffer from overconfidence. This result is confirmed by Bloomfield, Libby and Nelson (1996).

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3.4 Hypothesis 4: Overconfident Investors consider themselves Lucky

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According to Camerer and Lovello (1999), subjects entering the game (or the market) tend to overestimate their chances of success. Moreover, Weinstein (1980) and Taylor and Brown (1988) show that most people consider themselves better than average. They have excessive confidence in their own abilities and are optimistic about their future. According to Cooper, Woo and Dunkelberg (1988), entrepreneurs systematically overestimate their chances of success. Indeed, they showed that 33% of entrepreneurs had total confidence in their project and in their chance of success.

4 Empirical Studies 4.1 Objective The aim of our empirical studies is to test the existence of the overconfidence bias on a sample of individual investors on the Tunisian stock market, to study if they are victims of this bias in making their decisions. For that, we conducted a questionnaire survey. Indeed, the psychology, which can be defined as "the science of behavior�, must be taken into account by a method of investigation which can well describe the characteristics of

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the investor. The questionnaire appears to be a useful tool in determining how individual errors affect aggregate behavior. We will particularly understand how the decisions of many individual investors are incorporated into prices on financial markets.

4.2 Data

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The subjects are targeted on the individual private stock investors in Tunis 3. We addressed our questionnaire to 150 Tunisian investors4. We used two methods of data collection (face to face interviews and mail survey). We got a response rate of 83% and a final sample of 125 investors. The survey was conducted in July 2008. The face-to-face interviews5 allowed us to respond directly to questions that respondents were asked about the issue itself. It also allowed us to better control the representativeness of the sample. Furthermore, we avoided expressing any opinion or any form of approval or disapproval, to avoid influencing the respondent.

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4.3 Profile of Respondents

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Table 1 reports summary statistics for our sample of investors grouped by gender, age, education and business position. 73.6% of the subjects who responded to the questionnaire were men. This is easily understood since the number of men is higher than the number of women investing in the Tunisian stock market 6. A greater number of subjects (35.2%) were aged around 35~49 while 30.4% were aged between 25 and 34 years. 44% of the subjects have a bachelor degree while 44.8% have a master degree and above. We remark according to our sample, that the higher the degree of education, the more we invest in the stock market. Moreover, the proportion of executives is very high. In fact, they represent almost half of our sample (48%). Finally, most of the respondents belonged to the middle-income class with a monthly income between 600 and 2000 dinars7.

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We note that commercial agents working at the front offices in stock market intermediary houses help as to contact the investors. 4 Several questionnaires were omitted since too many questions had been left unanswered. 5 Face to face interviews represent 70% of total interviews. We chose to perform our investigation on the big Tunis (Tunis, Ben Arous, Ariana), because the population of the big Tunis is heterogeneous and diversified and therefore, it gives us a greater depth of information. 6 See Dellagi et al. (2005, p. 5). 7 100 Tunisian Dinars = 66.7074US Dollars as of 26/01/2012.

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Table 1: Profile of respondents Variables Gender

Response (in %) Female 26.4 25-34 35-49 30.4 35.2 Middle High 44.0 44.8 Middle High 58.4 18.4 Executive, Higher Middle intellectual management profession 48.0 20.8

Male 73.6 <25 12.8 low 11.2 Low 23.3 Merchant, Artisan, Entrepreneur 6.4

Age Education* Income** Business position

50-60 12.8

>60 8.8

Employee

Student

Retired

8.0

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*The education of low: high school or lower; middle: bachelor; high: master and above. **The income of low: < 600 dinars; middle: [600 dinars à 2000 dinars]; high: > 2000 dinars.

4.4 Methodology

Table 2 : Coding Variable

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Why do you manage your portfolio by yourself?

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Reason

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For our study, we used the “Sphinx” software (trial version, V5). This allowed us to design the questionnaire, to register the responses, and especially to process and analyze the data. We did not take missing data into consideration. Indeed, the terms "no answers" do not appear in the results: It could be either a deliberate refusal to answer certain questions or accidental omissions. The overconfidence bias is studied through the following four questions. For each question, one response modality is considered symptomatic of the psychological bias. If we accumulate three typical responses, we confirm the presence of the latter. We create a code for each question (variable) and each modality. This involves defining a label, that is to say an abstract in a smaller number of characters. Each theme is associated with a number. For example, the first question is associated with the code "Reason1. The coding variable is given in Table 2.

How many months on average do you keep a line?

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How many sources of information do you use to select your stocks?

Chance

Would you say that every day, you are

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Reason1 : it’s more amusing Reason2 : you trust your intuitions Reason3 : other Duration1 : less than 3 months Duration2 : from 3 to 6 Duration3 : from 6 to 9 Duration4 : from 9 to 12 Duration5 : 12 and above Information1 : only one, we shouldn’t disperse Information2 : some of them, this is not fixed Information3 : many, because we can never be too informed Chance1 : lucky Chance2 : unlucky Chance3 : no opinion

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After this coding, the data were entered on the Sphinx software. Finally, we presented the results of the analysis.

5 Results First, we will focus on the univariate analysis. Then, we will present the bivariate analysis. Finally, a multiple correspondence analysis will permit us to deepen our study and to represent, on the same graph, both active and status variables.

5.1 Univariate Analysis

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Table 4 : « Duration » Duration Number of (in months) observations Duration1 35 Duration2 25 Duration3 19 Duration4 2 Duration5 27 108 Total

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Reason1 Reason2 Reason3 Total

Table 3 : « Reason » Number of % observations 26 21.3% 81 66.4% 15 12.3% 122 100%

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Tables 3, 4, 5 and 6 report the results of the univariate analysis of the various variables of the overconfidence bias. The symptomatic modality of the bias is set in gray.

Table 6 : « Chance » Chance Number of observations Chance1 40 Chance2 18 Chance3 53 111 Total

32.4% 23.1% 17.6% 1.9% 25.0% 100

% 36.0% 16.2% 47.7% 100%

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Table 5 : « Information » Information Number of % observations Information1 9 7.2% Information2 47 37.6% Information3 69 55.2% 125 100% Total

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We observe from Table 3 that 66.4% of the respondents have confidence in their intuition against 21.3% who find amusement in managing their portfolios by themselves (Hypothesis 1 is thus confirmed). This was confirmed by the work of Langer and Roth (1975) and Daniel, Hirshleifer and Subrahmanyam (1998). Table 4 shows that 32.4% of the subjects retained, on average, their securities within 3 months (16.6% of them retain their stocks only one month). This is consistent with the studies of Odean (1998), Barber and Odean (2001), Gervais and Odean (2001), Chuang and Lee (2006) and Statman et al. (2006) (Hypothesis 2 is thus confirmed). Table 5 shows that 7.2% of the respondents use a single source of information to choose their securities against 55.2% that use several sources of information in the selection of their securities. This can be explained by the large number of graduates (Master and above represent 44.8%) and senior intellectuals executives (48%) in our sample. In addition, apart from the advice of his broker, the investor can use more and more Internet and newspapers to decide on the choice of his securities. (Hypothesis 3 is rejected).

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However, intensive use of information can also lead to overconfidence. Oskamp (1965) find that more information increases overconfidence via increasing confidence and not increasing accuracy. According to Slovic et al. (1977), from a certain level of information, the accuracy of predictions decreases but confidence continues to grow. Guiso and Jappelli (2005) show that overconfident investors collect a lot of information and base their decisions on it. Confidence seems to increase with the magnitude of the available information. This result was confirmed by Tsai et al. (2008), who conclude from three experimental studies that the confidence level increases with the amount of the available information. We note from Table 6 that 36% of the respondents consider themselves lucky against 16.2% who consider themselves unlucky (Hypothesis 4 is confirmed). Thus, we can conclude that Tunisian individual investors suffer from the overconfidence bias. A further study using bivariate and multivariate analysis seems to be interesting. It will allow us to confirm the obtained results.

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5.2 Bivariate Analysis

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We note from the histogram (Figure 1), crossing variables "reason" and "gender", that men tend to be more overconfident than women. Indeed, 76.5% of men have confidence in their intuitions against only 23.5% of women. This result confirms those of Beyer (1999), Biais et al. (2005) and Barber and Odean (2001). In addition, confidence seems more important for those having higher intellectual professions (55.6%) and those having a master's level and above (45.7%). RAISON x Sexe

76,5%

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Reason x Gender

69,2% 23,5% 0 30,8% C' est plus It’s more amusant

amusing G

Féminin Female

60,0% 40,0%

Vous avez You trust confiance dans vos your intuitions intuitions Masculin Male

Autre

Other

Figure 1: A cross between « Reason » and « Gender » variables

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5.3 Multivariate Analysis The histogram of the eigenvalues is presented in Table 7. These represent the inertia (or variance) for each axis.

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Cumuative % 18.170 35.135 50.770 64.748 76.856 88.516 98.154 99.730 100.000

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Number 1 2 3 4 5 6 7 8 9

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Table 7 : Histogram of eigenvalues Eigenvalues % Explained 0.334 18.170 0.311 16.965 0.287 15.635 0.257 13.978 0.222 12.107 0.214 11.660 0.177 9.638 0.029 1.576 0.005 0.270

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We can work with the first two axes as they render the maximum of the initial information (35.13%). Two sets of parameters are used to interpret the results, complementing the information given by the coordinates of the elements on the factorial axes: - The contributions (or absolute contributions) that describe the importance of the modality for the interpretation of the axis. - The square cosine (or relative contributions) that describe the importance of the axis for the interpretation of the modality. These settings are found in Table 8.

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Table 8: Main parameters of the correspondence analysis

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Coordinates axis2 axis3 -0.751 -0.093 -0.149 0.344 -0.637 0.788 0.063 1.139 0.060 -0.308 0.059 0.063 0.087 -0.764 -0.362 -0.610 0.059 0.803 -1.191 0.081 0.433 -0.037

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Reason1 Reason2 Reason3 Information1 Information2 Information3 Chance1 Chance2 Chance3 Sex F Sex M

axis1 1.174 -0.110 -1.322 0.072 0.072 0.082 -0.500 1.759 -0.198 -0.540 0.195

Contributions (%) axis1 axis2 axis3 22.239 9.743 0.163 41.208 1.114 6.379 16.279 4.047 6.716 0.332 1.498 7.242 1.756 7.007 2.773 3.361 10.179 0.169 6.197 0.200 16.853 34.556 1.564 4.830 1.288 0.124 24.644 5.977 31.123 0.156 2.166 11.476 0.089

Squared Cosine (%) axis1 axis2 axis3 0.366 0.150 0.002 0.022 0.040 0.212 0.242 0.056 0.086 0.000 0.000 0.100 0.003 0.002 0.056 0.008 0.004 0.005 0.122 0.004 0.286 0.530 0.022 0.064 0.030 0.003 0.499 0.104 0.505 0.002 0.101 0.501 0.004

Moreover, an interpretation of the first two factorial axes is possible by analyzing the positive and negative contributions of each axis (Table 9).

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Table 9: Contributions Table for the first two axes Axis1 Axis 2 (+19.14%) (+17.79%) Chance2 +35.97% Female +27.45% Positive Contributions Reason1 +25.64% Information1 +15.35% Information1 +8.99% Reason3 +14.67% Male +1.05% Reason1 +6.14% Information2 +4.46% Raison3 -14.28% Male -10.23% Negative Contributions Chance1 -6.72% Information3 -10.07% Female -2.90% Raison2 -10.06% Reason2 -1.64% Chance1 -0.79% Chance3 -1.43% Chance2 -0.04% Reason1 : It’s more amusing- Reason2 : You trust your intuitions - Reason3 : Other Information1 : Only one, we shouldn’t disperse - Information2 : Some of them, this is not fixed - Information3 : Many, because we can never be well informed – Chance1 : Lucky Chance2 : Unlucky - Chance3 : No opinion.

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- Interpretation of axis 1 It can be seen from Exhibit 9 that the first factorial axis (comprising 19.14% of inertia, that is to say, of the total information in the analysis), is the most important axis of the analysis, regrouping on one side (negative side) lucky investors and on the other side (positive side) the unlucky ones. The lucky ones seem to trust their intuition. - Interpretation of axis 2 Exhibit 9 informs as about the second factorial axis (comprising 17.79% of inertia). This area gathers on one side (the negative side) the confidents. These are men who have confidence in their intuitions, use multiple information and consider themselves lucky. On the other side (the positive side), this area includes the non-confidents that are women and use a single piece of information. Thus, this axis contrasts well the confidents with the non-confidents. - Interpretation of the factorial design The correspondence analysis allows us to represent graphically groupings of modalities involved in the analysis. Thus, we can have a graphic illustration of the individual investors (Figure 2). The modalities of the status variables are positioned closer to the modalities of opinion that resemble them the most, that is to say which are the most chosen by the same individuals.

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Axe 2 (17.79%)

Axis 2 (17.79%)

I1

R3

S1

R1 I2 C3 C2

C1

Axe 1 (19.14%)

Axis1 (19.14%)

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R2 I3 S2

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Figure 2: Factorial design -Axis1-Axis2The map shows the position of 11 modalities and coordinates of 108 observations. 39.93% of the variance is explained by two axes. The non-answers are ignored. R1 : It’s more amusing- R2 : You trust your intuitions - R3 : Other - I1 Only one, we shouldn’t disperse - I2 : Some of them, , it’s not fixed - I3 : Many, we can never be well informed- C1 : Lucky - C2 : Unlucky - C3 : No opinion - S1 : female - S2 : male.

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The factorial design formed by the first two axes shows interesting combinations between the modalities of the analysis. These are close if the individuals who take one or other of these modalities are not distinguishable for other variables: they form a group, and the distance involved in the distinction between these two modalities, do not disturb the cohesion of the group. We can see, from Figure 2, the formation of a homogeneous group (factorial cloud). This group consists of overconfident investors. Indeed, by projecting on this chart the four variables related to the overconfidence bias and the status variable (gender), we find that from the side of investors who trust their intuition, are placed in their majority, men that are lucky and use multiple information sources.

6 Conclusion Human decision making does not seem to conform to rationality and market efficiency, but exhibits certain behavioral biases that are clearly counter-productive from the financial perspective.

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In this paper, we tested the presence of the overconfidence bias on the Tunisian stock market. For that, we administered a questionnaire to a group of individual investors, to consider whether they are victims of this bias in their decision making. The results indicate that individual investors on the Tunisian stock exchange suffer from the overconfidence bias. In fact, they trust their intuition; they consider themselves lucky and trade their securities in an aggressive manner. Moreover, they use multiple information sources to select their stocks. Thus, these investors tend to overestimate the quality of information they have and their ability to interpret it. These features give them an illusion of control over the evolution of markets and distort their perception of risk. Besides, another interesting study could be made from the same research framework; it is to test the presence of other psychological biases such as herding, loss aversion, mental accounting and anchoring. Further research should further investigate overconfidence in the context of an experimental approach focusing on individual investment (Dittrich et al., 2001). Also, further research on the relation between overconfidence and personal traits, such as attribution styles or positive affects, is needed to learn how certain characteristics trigger overconfidence (Ifcher and Zarghamee, 2010).

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References

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[33] D. Kahneman, and M. Riepe, Aspects of Investor Psychology, Journal of Portfolio Management, 24, 1998, 52-65. [34] E. Kirchler, and B. Maciejovsky, Simultaneous over and underconfidence : Evidence from experimental asset markets, Journal of Risk and Uncertainty, 25(1), 2002, 65-85. [35] Koriat, A., Lichtenstein, S. and Fischhoff, B., Reasons for confidence, Journal of Experimental Psychology: Human Learning and Memory, 6, 1980, 107-18. [36] E.J. Langer, The illusion of control, Journal of Personality and Social Psychology, 32, 1975, 311-328. [37] E.J. Langer,. and J. Roth, Heads i win, tail itâ&#x20AC;&#x2122;s chance: The illusion of control as a function of the sequence of outcomes in a purely chance task, Journal of Personality and Social Psychology, 32, 1975, 951-955. [38] S. Lichtenstein, B. Fischhoff, and L.D. Philips, Calibration of probabilities: The state of the art to 1980, in Daniel, Kahneman, Paul Slovic, and Amos Tversky, ed.: Judgement under uncertainty: heuristics and biases, p. 306-334 (Cambridge University Press), 1982. [39] B. Maciejovsky, and E. Kirchler, Simultaneous over and underconfidence : Evidence from experimental asset markets, Journal of Risk and Uncertainty, 25(1), 2002, 65-85. [40] T. Odean, Are investors reluctant to realize their losses?, Journal of Finance, 53 (5), 1998a, 1775-1798. [41] T. Odean, Volume, Volatility, Price, and Profit When All Traders Are above Average, Journal of Finance, LIII, 1998b, 1887â&#x20AC;&#x201C;1934. [42] S. Oskamp, Overconfidence in case-study judgments, The Journal of Consulting Psychology, 29, 1965, 261-265. [43] A.M. Parker and E.R. Stone, Identifying the effects of unjustified confidence versus overconfidence: lessons learned from two analytic methods, SSRN Working Paper, (2010). [44] D.K. Peterson and G.F. Pitz, Effects of amount of information on predictions of uncertain quantities, Acta Psychologica, 61, 1986, 229-241. [45] D. Skala, Overconfidence in psychology and finance: an interdisciplinary literature review, Financial Markets and Institutions, 4, 2008, 33-50. [46] M. Statman, S. Thorley, and K. Vorkink, Investor overconfidence and trading volume, Review of Financial Studies, 19(4), 2006, 1531-1565. [47] O. Svenson, Are we all less risky and more skilful than our fellow drivers?, Acta Psychologica, 47, 1981, 143-148. [48] S. Taylor, and J.D Brown, Illusion and well being: A social psychology perspective and mental health, Psychological Bulletin, 103, 1988, 193-210. [49] C.I. Tsai, J. Klayman, and R. Hastie, Effects of amount of information on judgment accuracy and confidence, Organisational Behaviour and Human Decision Processes, 107, 2008, 97-105. [50] N.D.Weinstein, Unrealistic optimism about future life events, Journal of Personality and Social Psychology, 39(5), 1980, 806-820. [51] C.D. Wickens, and J.G. Holland, , Engineering psychology and human performance, (3rd edition). Upper Saddle River, NJ. Prentice Hall, (2000).

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The Effect of Foreign Aid on Real Exchange Rate in Ghana

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Peter Arhenful 1

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This paper assesses the effect of foreign aid inflows on real exchange rate in Ghana in order to test the hypothesis that large foreign aid inflows might lead to the appreciation of the real exchange rate of the recipient country and thus, impact negatively on its trade position, a case known as “The Dutch Disease” effect. Using the ordinary least squares method of estimation, the paper finds that although foreign aid inflows to Ghana are quite high, foreign aid inflows have positive impact on the real exchange rate. In other words, foreign aid inflows lead to the depreciation of the cedi, implying that “The Dutch Disease” hypothesis of large foreign aid inflows is rejected in the case of Ghana. In terms of policy recommendation, the results suggest that Ghana can still receive aid without fear of harming its exports competitiveness.

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JEL classification numbers: F310 Keywords: Foreign aid, Real Exchange Rate and Dutch Disease Effect.

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1 Introduction

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Foreign aid, more commonly known as official development assistance (ODA) comprises medium and long term concessional and grants from bilateral (e.g. governments) and multilateral (e.g. International Monetary Fund, World Bank) sources (Moreira, 2002). Foreign aid has been transferred to developing countries in the form of project aid, commodity aid (including food aid), technical assistance, and programmed aid (balance of payments support and budget aid) (Cassen, 1994). A fundamental argument for aid, at least on economics, is that it contributes to economic growth in recipient countries. This has been the driving economic objective of aid for decades, formally established in the “two gap” model of Chenery and Strout (1966). In this approach investment is the cornerstone of growth and, at least initially, this requires imported capital goods. 1

Lecturer, Accra Polytechnic.

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1.1 Statement of the Problem

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However, low-income countries typically face fundamental constraints, or financing gaps. First domestic savings rates are insufficient to provide the resources to meet desired levels of investment. Second, export earnings are not adequate to finance the importation of capital goods. Consequently, such countries are constrained in their ability to achieve a target growth rates. In this approach, the contribution of aid is to finance investment, including imports and capital goods. Early empirical work on the impact of aid on growth was based on the “two-gap” model, often concentrating on the impact of aid on investment or savings rather than on growth per se. Recent studies of aid effectiveness have been based on some variant of neoclassical or endogenous growth models and assess the impact of aid on growth controlling for other variables, especially indicators of economic policy. One prominent view is that the correlation between aid and growth is, at best weak (Burnside and Dollar, 1997). Aid only appears to be effective in countries with appropriate economic policies, that is, “Aid works in a good environment” (World Bank, 1998). From this perspective, good policy is a necessary condition for aid effectiveness. During the 1980s, several African countries experienced negative economic growth despite a substantial increase of aid inflow to these countries (White, 1992). “A large number of countries became more aid-dependent in the 1990s than they were in the late 1970s” (Tsikata, 1998). This grim reality has raised many concerns over the effectiveness of aid. Questions such as “What is effective aid?”, “What is ineffective aid?”, and whether aid works or not have become a substantial source of debate among academic researchers and aid practitioners over the past few decades. These questions raised are directly applicable to Ghana.

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Concerns that large aid inflows will induce an appreciation of the real exchange rate and discourage the expansion of exports, particularly non-traditional exports, thereby damaging growth prospects in the recipient economy are rarely far the center of contemporary debates on the macroeconomics of aid to low-income countries. The Ghanaian economy, with support from the World Bank and International Monetary Fund (IMF), has since September 1980 witnessed the introduction of mechanisms to halt the downturn of the economy and to move on a path of sustained growth and development. This change elicited tremendous donor assistance in the form of grants, concessional loans and technical assistance. Net official development assistance (ODA), which constituted about 4% of GDP in 1980, rose to 10% in 1990 and has been in that neighborhood ever since. The overwhelming dependence on external aid inflows from developed countries for the supply of basic import commodities has made the Ghanaian economy vulnerable to policy conditionality that might accompany such assistance (Sackey, 2001). Depending on whether these aid inflows have been temporary or permanent, and whether they were spent on imports or domestically produced goods and services, they have had various repercussions. Throughout the economic adjustment agenda, exchange rate and trade reform occupied a core position. The real exchange rate, by virtue of its impact on the international competitiveness of an economy, assumed an overriding importance among the cohorts of policy variables. Surges in aid inflows are believed to be causing “Dutch disease” problems for the macroeconomic management of the economy. The management of aid has been

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characterized by a combination of foreign exchange accumulation (both building reserves and eliminating arrears), credit to the banking system, and increased public spending especially on development projects. Efforts to maintain the real exchange rate in an area of increased aid inflows have kept inflation high (Younger, 1992). Yet, arguably, in the absence of aid inflows Ghana’s growth and development efforts would have been stifled.

1.2 Objectives of the Study

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In broad terms, the study sought to determine whether foreign aid inflows have generated “Dutch Disease” effect in Ghana or not. In order to achieve this broad objective, the following specific objectives were set:  To find out whether foreign aid inflows have led to the depreciation or appreciation of the real exchange rate in Ghana.  To determine whether foreign aid inflows have positively or negatively affected exports in Ghana.  To make recommendations from the findings for macroeconomic management.

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1.3 Justification of the Study

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Both Ghanaians and donors should ask themselves, has the aid done any good? Thus, a study in this area is justified because it will:  Let the general public realize the effect of foreign aid on the Ghanaian economy.  Serve as an effective source to strengthen aid management measures to policy makers.  Assist both donors and recipient governments to address the policy implications for making foreign aid more effective.  Serve as basis for further research.

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2 Review of Related Literature 2.1 Theoretical Review

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Theoretically, there are two principal definitions of real exchange. In internal terms, real exchange rate has been defined as the ratio of the domestic price of tradable (exportable and importable) goods to non-tradable (domestic) goods within a single economy. That is: RER = Price of tradable goods / price of non- tradable goods. Where tradable goods refer to goods which are traded across national boundaries and non-tradable refer to goods which are not traded across national boundaries (Van Wijnbergen, 1985 and 1986). In internal terms, Lansdsburg and Feinstone (1997) defined real exchange rate as the quantity of domestic goods required to buy one foreign good. This is expressed in terms of the price levels as: Real Exchange Rate (RER) = eP’ / P Where e = nominal exchange rate. P = the consumer price index of the domestic country. P’ = the consumer price index of a country. The term “Dutch Disease” refers to the deindustrialization of a nation’s economy that occurs when the discovery of a natural resource raises the value of that nation’s currency, making manufactured goods less competitive with other nations, increasing imports and decreasing exports. The term was devised to describe the adverse impact on Dutch manufacturing of the increase in income associated with the discovery of natural gas in

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the Netherlands in the 1960s, essentially through the appreciation of the Dutch real exchange rate (RER). The focal point of the theory on aid inflows and Dutch Disease has been the impact exerted by aid on the relative prices of non-tradable goods (Van Wijnbergen 1985 and 1986). This theory holds that part of foreign aid will be channeled to the non-tradable sector of the economy causing a possible increase in the demand for non-tradable goods, thereby raising their price. Given that the real exchange (RER) is defined as the relative price of tradable goods to that of non-tradable goods (i.e., RER = Price of tradable goods / price of non- tradable goods), a rise in the price of the latter would result in a decline in the real exchange rate.

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2.2 Empirical Review

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Analysis of countriesâ&#x20AC;&#x2122; experiences with sectoral booms has revealed varied results. The windfall gains from diamond exports in Botswana have not been associated with the Dutch disease (Harvey, 1992). Benjamin, Devarajan, and Weiner (1989) conduct a simulation with a computable general equilibrium (CGE) model of Cameroon and find that as an result of a boom in the oil sector, the agricultural sector is most likely to be hurt, whereas some components of the manufacturing sector will benefit. On balance, the nonoil tradable sector may not necessarily shrink. In their analysis of the macroeconomic impact of aid in Nicaragua, Vos and Johanasson (1994) find that aid is weakly but negatively correlated with export volumes. They indicate that the simple negative correlation, which they find to be stronger during years of small aid inflows (the 1970s) than during the period of large aid inflows (the 1980s and 1900s), does not seem to make the case of a typical aid-associated Dutch disease. Ogun (1995) also carried out a research on the relation between foreign aid and real exchange rate in Nigeria and found that aid inflows led to depreciation of the currency. Using the newly developed technique to cointegration, the autoregressive distributed lag approach, Outtara and Issah (2003), used time series data from Syria to test the hypothesis that foreign aid inflows generate â&#x20AC;&#x153;Dutch diseaseâ&#x20AC;? in the recipient country. They found that foreign aid inflows are associated with depreciation of real exchange rate. In a model of the RER for Tanzania during 1967-93, Nyoni (1998) finds that aid was associated with RER depreciation. He presents figures indicating that the RER depreciated more sharply over the period 1985-93 than in the earlier nine-year period, despite a significant increase in ODA flows. This contrasts with the predications of the Dutch disease model since RER appreciation, the main channel through which aid is conjectured to affect the tradable sector adversely, did not materialize. However, Falck (1997) also undertakes an assessment of aid-induced real exchange rate appreciation in Tanzania. The model for the determination of the real exchange rate specifies among other variables the real exchange rate lagged one period, rate of change of the nominal exchange rate, foreign aid, macroeconomic policy proxied by the growth of excess domestic credit, international terms of trade and investment. He computes twelve different real exchange rates indexes for Tanzania, applies a three-stage selection procedure to each one of them and estimates the model by the use of ordinary lest squares. Falck finds that foreign aid inflows cause the real exchange rate to appreciate which in sharp contrast to the findings of Nyoni (1998). Van Wijnbergen (1986) applies a single regression equation to estimate the aid-real exchange rate nexus model for Africa countries. He finds a significantly negative

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relationship between aid and the real exchange rate in four out of six African countries. He also demonstrates that the effect of the “aid boom” permanently lowers the total productivity in the export sector. Despite the real exchange rate being allowed to depreciate after the effect of the “aid boom”, productivity does not return to the level before the “aid boom”. Nevertheless, he argues that if capital markets were perfect, there should have been no problem after the effect of the “aid boom” as the private sector can re-borrow and re-invest after the economic recovery from this effect. Analyzing the link between aid and “Dutch disease”, Edwards (1989) estimate an empirical model specifying explanatory variable like international terms of trade, government consumption of non-tradable, measure of extent of controls over external aid inflows, index of severity of trade restrictions and exchange controls, measure of technological progress and ratio of investment to GDP. Ordinary least squares and instrumental variables techniques were used. He found that excessive aid inflows put pressure on the real exchange rate and causes it appreciate in the short run. Using the CGE model, Weisman (1990) investigates the impact of aid inflows to Papua New Guinea. He finds that aid inflows increased government spending, which in turn increased the prices of non-traded goods and services. Producers responded to the increase in prices of non-traded goods by increasing supply in this sector and shifting resource from the production of traded goods. Therefore, aid inflows brought about the “Dutch disease” effect that threatened the export earning of Papua New Guinea. Collier and Gunning (1992) also apply the CGE model to examine “Dutch disease” effects in African economies. They find that aid supported government spending that raised aggregate demand and exerted upward pressure on the prices of non-tradable sectors. As a result of the booming of non-tradable sectors, labour and capital were drawn away from the tradable sector. They illustrated that devaluation does reduces this inverse effect on tradable sectors. White (1992a) points out that aid will lead to real exchange rate appreciation so long as part of the aid inflows is spent on non-tradable goods. The upward pressure on the real exchange rate is greater, the higher is the marginal propensity to spend on traded goods, the lower is the responsiveness of supply of non-traded goods, and the higher is the responsiveness of demand to price changes. The impact of previous aid inflows is that the real exchange rate has to depreciate when aid flows cease (White, 1992c). On his part, Vos (1993) indicates that if the aid boom is temporary, there may be an inclination to consume the additional wealth or accumulate reserves to safeguard the economy against future losses. Where aid is of a permanent nature, the rational choice would seem to be to invest the “windfall gain” in order to maximize future consumption. Analyzing the macroeconomic aspects of the effectiveness of foreign aid, Van Wijbergen (1986) points out that temporary aid flows will lead to temporary appreciation of the real exchange rate and will lead to a decline in the production of traded goods as well as exports. Collier and Gunning (1992), on the other hand, writing on aid and exchange rate adjustment in African trade liberalization is export promotion. In a simple exchange rate model, a higher export price is the only effect of liberalization. Aid-only liberalizations, although technically feasible, produce perverse resource shifts and require massive rapid nominal wage flexibility to avoid unemployment. In an empirical analysis of the impact of aid on the RER in four CFA countries – Burkina Faso, Cote d’Ivoire, Senegal, and Togo during 1980 -1993, Adenauer and Vagassky (1998) find evidence of a direct relationship between aid flows and RER appreciation. They suggest that, during the period when the four countries received large aid flows,

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their government deficits increased through high wage bills and para-public spending and their trade balances widened. The developments appear to lead support to the idea of Dutch disease, Nevertheless, as economic performance in the four countries was affected by adverse developments in the world prices of their primary exports and the appreciation of the French franc against the dollar during the latter part of the 1980s, it would have been useful to ascertain the role played by the CFA frances per U.S. dollar or French francs per U.S dollar exchange rates in the development of RER. Also, real export figures could help ascertain whether the deteriorating trade balances were driven by declining world prices, declining trade volumes, or both. In an econometric model of RER behavior for Sri Lanka during 1974-88, White and Wignaraja (1992) find a direct relationship between total aid and remittances and RER appreciation. They suggest that increased aid flows, among other factors, played an important role in the failure of the RER to depreciate, despite depreciations of the nominal rate. Also, they associate the RER behavior with a disappointing performance of the manufacturing sector, lending support to the Dutch disease theory. In contrast, Bandara (1995) does not find support for the Dutch disease theory in an analysis of the impact. He indicates that despite the RER appreciation associated with foreign capital inflows, some tradable sectors may expand a result inline that of Benjamin, Devarajan, and Weiner (1989).

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2.3 Review of Studies on Ghana

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Assessing the impact of aid on macroeconomic management in Ghana, Younger (1992) finds that the increase in foreign aid to Ghana from an annual average of 3 percent of GDP during 1981-83 to 6 percent of GDP during 1984-87 gave rise to macroeconomic management problems that were associated with high inflation, an appreciating RER, and tight credit to the non-bank private sector. First, the increased availability of foreign exchange in the economy did not come from aid alone. The rise in aid flows was accompanied by a significant increase in private transfer and capital, consistent with the idea of pro-cyclicality between private capital, such a foreign direct investment (FDI) and foreign aid associated with policy reforms, while Younger suggests that the private sector was crowed out; the evidence to support such a claim is, best, very weak. He indicates that the Ghana governmentâ&#x20AC;&#x2122;s response to aid inflows was a combination of foreign exchange accumulation, provision of credit to the banking sector, and increased public spending, especially on development projects. At the same times although private investment remained low, as the author indicates, the figures the presents indicates that the private investment-to-GDP ratio doubled to 5 percent during 1984-89, compared with 2.5 percent during 1980-83. Third, not only did Ghanaâ&#x20AC;&#x2122;s overall economic performance improve as compared with the period preceding the aid increase, but it also compared favorably with the average for low income countries in the sub-Saharan African region on many indicators, including growth of total and sectoral GDP, exports, and goes domestic investment. Sackey (2001) a adopts a cointegration technique to examine the aid-real exchange rate relationship using annual time series data for the period 1962-1996 and found that although aid inflows are quite high, aid inflows have led to depreciations in the real exchange rate. He also estimated an export performance model for Ghana and found that aid inflows have also had a positive impact on export performance. He concluded his paper by emphasizing that for external aid to be an effective investment, policy

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management needs to focus on ensuring the prevalence of sound macroeconomic fundamentals, among others. The results of their estimations appear to be conflicting. Whilst some of the like Falck (1997) for Tanzania, White and Wignaraja (1992) for Sri Lanka and Younger (1992) for Ghana found that aid inflows caused the real exchange rate to appreciate, other such as Ogun (1995) for Nigeria, Nyoni (1998) for Tanzania and Sackey (2001) for Ghana found no evidence of “Dutch Disease”. Thus, this study attempts to contribute to the aid –real exchange rate nexus by using a more targeted approach. In the next chapter, we outline the detailed methodology for the study.

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3 Methodology

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3.1 Model Specification

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In order to estimate the effect of foreign aid inflows on the real exchange rate in Ghana, we establish a model in which real exchange rate is a function of foreign aid. However, since foreign aid is not the only determinant of real exchange rate, we include some other de like government consumption, GDP per capital, openness, terms of trade, growth of money supply as other explanatory variables. Thus, based on the works of Ouatarra and Strobl (1989), the baseline regression equation is assumed to take the form:

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RERt = a0 +a1Aid t +a2Gt + a3GDPPCt +a4 Opent + a5TOTt+a6GMt+εt where: RER = Real exchange rate Aid = Official development assistant G = Real government consumption GDPPC = Real per capita income Open = Openness of the economy TOT = Terms of trade GM = Growth of money ε = Error term Real exchange rate is defined as the quantity of domestic goods required to buy one foreign good. This is expressed in terms of the price levels as: Real Exchange Rate (RER)=eP1 / P where e = nominal exchange rate. P = the consumer price index of a good in a foreign country. P = the consumer price index of a good in the domestic country. Foreign aid specifically refers to official development assistance (ODA) such as loans and grants. Ratios are computed using values in U.S. dollars converted at official exchange rates. Real government consumption includes all government current expenditures for purchases of goods and services (including compensation of employees). It also includes most expenditure on national defense and security, but exclude government military expenditure that are part of government capital formation. Real income per capita (Gross Domestic Product per capita) is gross domestic product divided by midyear population. GDP is the sum of gross value added by all resident producers in the economy plus any product taxes and minus any subsidies not included in

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the value of the products. It is calculated without making deductions for depreciation of fabricated assets or for depletion and degradation of natural resources. Data are in constant U.S. dollars. Openness of the economy is given by the sum of exports and imports of goods and services measured as a share of gross domestic product. The terms of trade refer to the ratio of the export price to the ratio of the import price. That is TOT = Px / Pm.

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The growth of money refers to the average annual growth rate in money and quasi money. Money and quasi money comprise the sum of currency outside banks, demand deposits other than those of the central government, and the time, savings, and foreign currency deposits of resident sectors other than the central government. This definition is frequently called M2; it corresponds to lines 34 and 35 in the International Monetary Fundâ&#x20AC;&#x2122;s (IMF) International Financial Statistics (IFS). The change in the money supply is measured as the difference in end-of-year totals relative to the level of M2 in the preceding year. The expected theoretical impacts of the respective variables included in our model are as follows: (-)

Tends to cause real appreciation by changing the composition of the demand for traded and non-traded goods, according to the â&#x20AC;&#x153;Dutch diseaseâ&#x20AC;? theory of foreign aid.

GDPPC

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The expected effect of this variable on RER is to be negative. This is because as development takes place, the productivity improvement in the tradable goods sector exceeds that of non-tradable goods sector. This implies that the decreased in the price of the former is relatively bigger than that in the later, thus, causes appreciation of the RER. The effect depends on the composition of government of consumption. Consumption of non-tradable tends to appreciate the RER, while that tradable leads to real depreciation. Openness of the economy would cause real depreciation (appreciation) if it reduces (increases) the demand for non tradables.

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The effect of the terms of trade on the real exchange rate depends on whether the substitution or the income effect dominates. If the income (substitution) effect dominates then a deterioration of the TOT tends to cause real depreciation (appreciation).

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GM

(-)

Changes in the money supply (expansionary monetary policies) would tend to raise the general price level and thus lead to an appreciation of the RER.

NB: Following our definition for the real exchange rate, a negative sign represents an appreciation of the real exchange rate whilst a positive sign represents a deprecation of the real exchange rate.

3.2 The Exports Equation

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In order to estimate the relationship between export performance and real exchange rate, a simple export performance model abstracted from Vos (1998) is used. In this model, growth of real exports (Exp) is assumed to be a function of real exchange rate (RER, foreign aid inflows (Aid) and price of exports. That is:

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EXP = β0 + β1 RER + β2Aid + β3Px+εt

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Exports of goods and services represent the value of all goods and other market services to the rest of the world. They include the value of merchandise, freight, insurance, transport, travel, royalties, license fees, and other services, such as communication, construction, financial, information, business, personal, and government, services. They exclude labor and property income (formerly called factor services) as well as transfer payments. Data are in constant 1995 U.S. Dollars. The price of exports is a weighted average of the prices in U.S. dollars of goods and services exported with their respective share in the total exports of goods service as weights. It can be recalled that real exchange rate and foreign aid have been defined already under section 3.2.1. The expected theoretical impacts are as follows:

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Increase in the real exchange rate are expected to result in exports expansion. A good policy environment (proxied by real net ODA toGhana) tends to elicit positive response from the export sector. Aid inflows, by providing some sort of assistance to the export sector tend to encourage export competitiveness and output enhancement. A rise in the price of exports, all other things being equal, will lead to an increase in the supply of exports.

3.3 Sources of Data The study employs annual time series data from Ghana over the period of 1970-2002. The data used to estimate the models are obtained from a number of the sources. The real exchange rates are obtained from the IMF International Financial Statistics Yearbook 1995. All the other variables were obtained from the World Bank World Development Indicators (WDI), 2004, CD Rom version except the series on price of exports that were extracted from the African Development Indicators, (2004).

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3.4 Estimation Techniques

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In order to estimate equations (1) and (2), we employ the ordinary least squares (OLS) methods of estimation. Thus, based on the classical assumptions, some relevant residual and specification tests are rigorously carried out. Since the presence of serial correlation in the residuals reduces the efficiency and forecasting powers of the estimators based on OLS estimates, the Durbin-Watson test for first order serial correlation in the residuals is conducted to ensure that there is no autocorrelation in the residuals. The variance inflation factors test for checking the extent of collinearity between the explanatory variables will also conducted to ensure that the extent of collinearity between the explanatory variable is not severe. For, if the inter correlation between the explanatory variables is high, the estimates are indeterminate and the standard errors of these estimates become infinitely large (Koutsoyiansnis, 1973). The Whiteâ&#x20AC;&#x2122;s test for heteroscedasticity will also be performed. This test is motivated by the observation that in many economic time series, the magnitude of the residuals appears to be related to the magnitude of the recent residuals. The presence of heteroscedasitcity itself does not invalidate standards least squares. However, ignoring it may result in loss of efficiency in the estimated parameters. The null hypothesis is that hetorscedasticity is not present. The Ramsey RESET test is a general test for model specification errors resulting from omitted variable, incorrect functional from and correlation between the independent variable and the residuals, which may be due to errors in measurements, simultaneity and serially correlated disturbances. Under such specification errors, least square estimates will be biased and inconsistent and for that matter conventional inference procedures will be invalidated. The model is correctly specified if the F-statistic is insignificant at the given error level (mostly 5%). The Jarque-Bera statistic is for testing whether the residuals are normally distributed. If the residuals normally distributed, the Jarque-Bera statistic, which has a chi-square distribution under the null hypothesis of normally distributed errors, should be insignificant.

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4 Ordinary Least Squares Estimation

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4.1 Results of the Real Exchange Rate Equation The result of the real exchange rate equation (equation 1) estimated with OLS are presented in Table 4.2. The results of all the diagnostic tests performed are very satisfactory. The results of the F-test show that the F-statistic (F (6,26) = 45.0279) is statistically significant at 1 present error level. This implies that we can reject the null hypothesis that all the parameters are zero at one percent error level this further implies that the overall regression is statistically significant. The R2 of 0.912212 (Adjusted R21 = 0.891953) shows that approximately, 91 percent of the variations in real exchange rate can be explained by foreign aid, real government consumption, real per capita income, the degree openness of the economy, terms of trade and growth of money. This high value of the R 2 shows that the overall model is statistically significant.

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The results also show that there is absence of autocorrelation in the residuals. The DurbinWatson statistic of 1.75 is closer to 2 (no autocorrelation) than to zero (perfect autocorrelation). Also, the first order autocorrelation coefficient which is 01131 is closer to zero (no autocorrelation) than 1 (perfect autocorrelation). This is therefore a confirmation that serial correlation between the error terms is not a serious problem in our model. The Ramsey RESET test for the regression specification revealed that the model is correctly specified. The null hypothesis HO: specification is adequate is tested against the alternative hypothesis H1: specification is not adequate. The F-statistic F (2, 24) = 3.02827 has a probability value of 0.067184. This implies that the null hypothesis cannot be rejected at 5 percent error level. This confirms that the model is correctly specified. The White test for hetorosecedasticity is employed to test the presence or otherwise of hetoeroscedasitctiy. The null hypothesis “Heteroscedasticity is not present” is tested against the alternaive hypothesis “Heteroscedasticity is present”. The Chi-square value of 30.913 is significant only at 27.5 percent error level. This means that we accept the null hypothesis of no heteroscedasticity implying that the model is free from heteroscedasticity. By employing the variance inflation factors (VIF) technique of determining the presence of or absence of multitcollinearity among the variables, we found that there is a less problem of collinearity between the variables in the model. The VIF (j) = 1 / (1-R (j)2), where R (j) is the multiple correlation coefficient between variable j and the other independent variables. Minimum posisbel value = 1.0 Values greater than 10.0 may indicates a collinearity problem. The results of the VIF test is shown in table 1

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Table 1: Results of the Variance Inflation Factors Test VIF 3.413 1.628 4.540 3.756 2.988 1.457

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Variable Aid G GDPPC Open TOT GM2

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From the table above, since all the values are far less than 10, it can categorically be concluded that multicollinearity is not a serious problem in the model. Thus, the model passes all assumption of the OLS estimates. Table 2 presents the results of the parameters. Table 2: Results of the Real Exchange Rate Equation Variable Constant Aid G GDPPC Open TOT GM2

Coefficient -1351.91 3172.91 -800.624 5.99041 1127.63 -704.172 521.944

Stand. Error 440.964 1694.43 2353.14 1.52254 251.699 191.271 265.745

T-statistic -3.0658 1.8726 -0.3402 3.9345 4.4801 -3.6815 1.9641

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P-value 0.005014 0.072418 0.736412 0.000554 0.000133 0.001067 0.060296

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R2 F-Statistic

= =

Adjusted R2 DW

0.912212 45.0279

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0.891953 1.74873

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The estimated coefficient of the aid variable is positive (3,172.91) and is statistically significant at 10 percent error level. This means that aid is statistically important determination of real exchange rate. The coefficient implies that an increase in aid by one million U.S. dollars will cause the real exchange rate (measured as cedis per dollar) to increase by 3172.91. In other words, an increase in aid causes the price of the dollar in terms of the cedis to rise; implying a deprecation of the cedi. This result is contrary to the “Dutch disease” theory of foreign aid which states that an increase in foreign aid tends to cause real appreciation of the local currency. Thus, as far as Ghana is concerned, surges in foreign aid inflows causes depreciation of the cedi instead of appreciation. However, this result confirms that of Isaa and Quattara (2004) who found that increases in aid to Syria causes depreciation of the local of Syeria. His result was also significant at 10 percent. This same result corroborates the findings by Ogun (1995) for Nigeria, Nyoni (1998) for Tanzania, Sackey (2001) for Ghana and Quattara and Strobol (2003) for panel of CFA franc counties. Therefore, the potential “Dutch disease” effect associated with foreign aid inflows is not supported by this study. That is; aid does not generate “Dutch disease” in Ghana. The coefficient of real government consumption is negative. This implies that increases in real government consumption cause the cedi to appreciate. The coefficient implies that an increase in government spending by one million US dollars causes the cedi to appreciate by 800.64 cedis all other things being equal. As argued earlier, this scenario could occur if government consumption is dominated by non-tradable goods. However, the coefficient is not statistically significant. In other words, the coefficient of real government of Ghana spends equally on tradable and non tradable goods. The coefficient of real per capita income is positive (5.99041) and is statistically significant at 1 percent error level. This implies that higher income levels tend to increase the real exchange rate and hence depreciate the cedi. This is contrary to the prediction made in chapter three that, higher levels of income causes an appreciation of real exchange rate in a sense that, increases in GDP per capita will lead to a productivity improvement in the tradable goods sector and hence cause the prices of the tradable goods to fall and thus appreciation of the currency. On the other hand, in a country where the marginal propensity is high, an increase in income will lead to an increase in imports and thus create demand for foreign currency. This will increase the supply of the domestic currency at the foreign exchange market. The combined effect will therefore be the depreciation of the currency. Hence, the contradictory result could be explained that the marginal propensity to import for most Ghanaian is directory related to level of income. The coefficient of degree of openness of the economy, measured as the sum of exports and imports as a ratio of GDP is positive (1127.63) and is significant at 1 percent error level. This result suggests that openness leads to a depreciation of the cedi in Ghana. This could mean that the degree of openness tend to reduce the demand for non tradable goods in Ghana and increase that of tradable goods. The positive relationship between the degrees of openness of the economy variable might have resulted from the lifting of tariffs and other barriers by the Ghanaian government and its trading partners to encourage trade with each other. The terms of trade variable is negative (-704.172) and is statistically significant at 1 percent level of significance. This means that terms of trade negatively affects real

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exchange rate. This may be due to the fact that the substitution effect associated with changes in the terms of trade appears to be greater than the income effect. Finally, the coefficient of growth of money variable is positive (521.944) and is significant at 10 percent error level. Implying that, increases money supply lead to the depreciation of the cedi. The direct relationship between money supply and the real exchange rate could still be explained by the fact that the marginal propensity to import in Ghana is very high. Therefore an increase in money supply without a corresponding increase in output causes people to import more and hence put pressure on the foreign currency leading to a depreciation of the local currency.

4.2 Results of the Export Equation

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The exports equation stated in chapter three was also estimated with OLS method and the results are presented in Table 4.3. The model passes all the diagnostic tests except autocorrelation. The results of the F-tests show that the F-statistic at (F (3,29) = 18.6658) is statistically significant at one percent error level. The Durbin Watson Statistic of 1.00881 and the first order autocorrelation coefficient of .494206 indicate that there is a serious problem of autocorrelation. The results are shown on the table below:

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Table 3: Results of the Exports Equation Coefficient Stand. Error T-statistic 974854 193241 5.0448 -2739.07 4624.37 -0.5923 1056.74 153.032 6.9053 -4.55664e+06 3.36467e+06 -1.3543

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P-value 0.000022*** 0.558232 <0.00001*** 0.186112

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Variable Const PX RER Aid

0.658813 0.62353518 18.6658 1.00881

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The estimated coefficient of real exchange rate is positive (1056.74) and is statistically significant at 10 percent error level. The coefficient implies that an increase in real exchange rate will lead to an increase in exports. This is consistent with the predication made earlier on in chapter three. The positive relationship between exports and real exchange rate is also a confirmation that the â&#x20AC;&#x153;Dutch diseaseâ&#x20AC;? hypothesis of aid is not validated in Ghana, owing to the fact increases in real exchange rate or depreciations of the cedi, positively affect export performance. The coefficient of aid is negative (-4.55664e+06). This implies that aid inflows are negatively related to exports performance. However, the estimated coefficient is not statically significant implying that there is no direct meaningful relationship between foreign aid and export performance in Ghana. Finally, the price of exports variable is negative implying that the price of exports is negatively related to the volume of exports. This is consistent with a prior theoretical expectation that a rise in the price of exports, all things being equal will lead to a reduction in the demand for exports. However, due to the problem of autocorrelation, the results are not good for analysis, inferences and forecasting. Thus, we change the estimation technique by using the

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Cochrane-Orcutt Interactive procedure in order to overcome the problem of autocorrelation to ensure efficiency in our predictions. The results of the Cochrane-Orcutt Interactive estimation are presented on the table 4: Table 4: Results of the Cochrane-Orcutt Iterative Estimation Variable Coefficient Stand. Error T-statistic Const 6.82969e+06 4.45864e+06 1.5318 PX -7001.07 3156.75 -2.2178 RER -64.1907 119.604 -0.5367 Aid 1.42396e+06 1.78517e+06 0.7977 0.919036 0.910361

F-statistic DW

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1.77315 1.42374

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R2 Adjusted R2

P-value 0.136796 0.034854 0.595719 0.431781

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It can be seen clearly from the table the Durban-Watson statistic and the R square have significantly improved. This is an indication of the null hypothesis of no autocorrelation in the residuals. All the other diagnostic tests with regard to heteroscedasticity, normality of residuals, parameter stability and correct functional form are all satisfiactory. The results from the Cochrane-Orcutt estimation are therefore very good and reliable for analysis, inferences and forecasting. The estimated coefficient of real exchange rate is negative (-64.1907). This implies that an appreciation or a full in the real exchange rate will lead to an increase in the volume of exports, and vice versa. The estimated coefficient of aid is now positive (1.42396e+06) implying the foreign aid has a direct relationship with exports. This supports our finding that foreign aid has caused the depreciation of the cedi rather than appreciation since in general, a depreciation of a currency leads to an increase in the volume of exports. Finally, the price of exports variable is negative implying that the price of exports is negatively related to the volume of exports. This is consistent with the prediction made in chapter three that a rise in the price of exports, all things being equal will lead to a reduction in the demand for exports.

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4.3 Two-Stage Least Square Estimation

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The estimation of these two equations, that is, equation (1) and (2), without any consideration of possible simultaneity bias can generate misleading results. Thus, estimation was performed by using the two-stage least square (2SLS) method to determine whether the results would be consistent with the OLS results or not. The twostage least squares (2SLS), like other simultaneous-equation techniques, aims at the elimination as far as possible of the simultaneous-equation bias (Koutsoyiannis, 1973). The two-stage least squares (2SLS) method of estimation boils down to the application of two-stage least squares (2SLS) method of estimation in two stages. In the first stage we apply OLS to the reduced-form equation in order to obtain an estimate of the exact and random components of the endogenous variables. In the second stage, we replace the endogenous variables appearing in the right-hand side of the equation with their estimated value, and we apply OLS to the transformed original equation to obtain estimates of the structural parameters. The formulae for the two-stage least squares (2SLS) method of estimation are the same as those of the ordinary least squares (OLS) method of estimation

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(Koutsoyiannis, 1973). Hence the assumptions underlying the two-stage least squares (2SLS) method of estimation are almost the same as those of the ordinary least squares (OLS) method of estimation. The results of both the real exchange rate equation (equation 1) and the exports equation (equation 2), estimated with 2SLS are presented in Table 4.5 and Table 4.6 respectively.

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Table 5: 2SLS Results of the Real Exchange Rate Equation Variable Coefficient Stand. Error T-statistic P-value Constant -1603.059 984.7429 -1.627896 0.1161 Aid 23770.560 3545.512 0.668609 0.5099 G -3950.057 4015.817 -0.983625 0.3347 GDPPC 8.022621 3.033296 2.644853 0.1039 Open 1019.871 458.2757 2.225453 0.0353 TOT -907.9635 303.7557 -2.989125 0.0062 GM2 952.4069 775.2282 1.228550 0.2307 2 R = 0.900344 F-statistic = 34.07998 Adjusted R2 = 0.876426 DW = 1.72

R2 Adjusted R2

0.521831 0.470599

F-statistic DW

= =

P-value 0.0303 0.0000 0.1024 0.7395 18.6658 1.23747

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Table 6: 2SLS Results of the Real Exchange Rate Equation Variable Coefficient Stand. Error T-statistic Const 724.4808 317.4628 2.282097 RER 1.483757 0.223991 6.624168 Aid -13339.64 7898.561 -1.688870 PX 3.683078 10.96604 0.335862

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The results obtained from the 2SLS method of estimation are almost the same as those of the OLS method of estimation. With regard to the signs, all the variables (parameters) as well as the constant term had the same signs in both estimations. Real Government Consumption (G) was not statistically significant in both cases whilst Real per capita income (GDPPC), Opennes (Open) and Terms of Trade (TOT) were all highly statistically significant in both cases. Perhaps, the only difference observed is that in the first estimation, both Aid and Growth of money (GM2) were significant only at 10 percent error level but in the second estimation, both variable were not significant at all, even at 10 percent error level; meaning that both Aid and Growth of money have no significant impact on real exchange rate in Ghana. In terms of the various diagnostic tests conducted, the R 2 for the OLS estimation 0.912212 whilst that of the 2SLS estimation was 0.9000344. Also, the Adjusted R 2 for the OLS estimation 0.891953 whilst that of a 2SLS estimation was 0.876426. The F-statistic obtained in the case of the OLS estimation was 45.0279 whilst that of the 2SLS estimation was 18.6658. It should be noted that both F-values are highly statistically significant. Again, the DW statistic obtained in the case of the OLS estimation was 1.74873 whilst that of the 2SLS estimation was 1.72. It can clearly be seen that the two

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values are almost the same and can be concluded that autocorrelation was absent in both approaches. With regard to the export equation, it was also observed that the results obtained from the 2SLS method of estimation are almost the same as the results obtained from the OLS same signs in both estimations. Just as it was in the first case, it was only the real exchange rate variable that was highly statistically significant in 2SLS estimations. From the above discussions, it can be seen that the results of the two estimations performed, that is, the OLS estimation and the 2SLS estimation are similar. We see that the coefficients differ only in terms of magnitudes but not in terms of signs. This implies that the OLS results obtained earlier are without simultaneity bias and can therefore be used for analysis, inferences and forecasting, as far as the Ghanaian economy is concerned.

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The study found that foreign aid inflows lead to real depreciation of the cedi rather than appreciation of the cedi. Hence, the hypothesis that foreign aid inflows generate “Dutch disease” is rejected in the context of Ghana. The coefficient of foreign aid was positive and statistically significant at 10 percent error level. The coefficient of real government consumption is negative implying that increase in real government consumption causes the exchange rate to fall. However, the coefficient is not statistically significant. That is government spending has no significant impact on real exchange rate in Ghana. The impact of real per capita income is positive and is statistically significant at 1 percent error level, thus implying that higher income levels tend to increase the real exchange rate and hence depreciate the cedi. The coefficient of degree of openness of the economy is positive and is highly significant at 1 percent error level. This result suggests that openness leads to a depreciation of the cedi in Ghana. The coefficient of the terms of trade variable in negative and is statistically significant at 1 percent error level. This means that terms of trade negatively affects real exchange rate in Ghana. Finally, the coefficient of growth of money variable is positive and is significant at 10 percent error level. This implies that increases in the growth of money causes the real exchange rate to increase. With regard to the export equation, using the Cochrane-Orcutt Iterative procedure; the following findings were made: The estimated coefficient of real exchange rate is negative implying that real exchange rate and exports are negatively related in Ghana. However, this variable was no found to be significant even at 10 percent error level. This means that the real exchange rate is not a major determinant of exports in Ghana. The study also found that foreign aid inflows are positively related to exports performance. However, the estimated coefficient is not statistically significant implying that there is no direct meaningful relationship between foreign aid and export performance in Ghana. In other words there are more relevant factors than these. Further researches can therefore these factors.

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5 Summary of Major Findings

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Finally, the price of exports variable is negative implying that the price of exports is negatively related to the volume of exports. This is consistent with the prediction made in chapter three that a rise in the price of exports, all things being equal will lead to a reduction in the demand for exports.

5.1 Recommendations

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The main policy recommendation to be drawn from this study is that because aid inflows are associated with the depreciation of the real exchange rate, the Ghana government can continue to receive aid without fear of harming its export competitiveness. Aid can be used to finance supply sides improvement which would sustain higher exporter values and quality too. Based on the results related to the openness of the economy, we suggest that the government of Ghana should reexamine the concept of over-liberalization of the economy. There is the need to check the volume of imposts so that it will not lead to over-depreciation of the cedi. Finally, the fact that government consumption appreciates the real exchange rate implies the public sector has to introduce some fiscal discipline by curtailing its consumption or composition of tradable goods.

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References

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[33] Nyoni, T.S. (1998) Foreign Aid and Economic Performance in Tanzania, World Development, 26. [34] OECD (1997), Geographical Distribution of Financial Flows to Developing Countries, Data on CD â&#x20AC;&#x201C;ROM, Organization for Economic Co-operation and Development, Paris. [35] Osei, R. Morrissey, O. and Tim L (2001), Aid, Exports and Growth in Ghana, CREDIT Research Paper, Nottinggham. [36] Ogun, O. (1995), Real Exchange Rate Movements and Export Growth: Nigeria, 1960-1990, African Economic Research Consortium Research Paper. [37] Ouattara, B. (2004), The Impact of Project Aid and Programme Aid on Domestic Savings: A Case Study of Cote dâ&#x20AC;&#x2122;Ivoire, Centre for the study of African Economics. [38] Ouattara, B. and Issah, H. (2003), Foreign Aid Inflows And Real Exchange Rate: Evidence From Syria, Manchester School Discussion Paper 00331. [39] Papanek, G. (1973), Aid, Foreign Private Investment, Saving and Growth in Less Developed Countries, Journal of Political Economy. [40] Sackey, H.A. (2001), External Aid Inflows and the Real Exchange Rate in Ghana. Nairobi, The Regal Press. [41] Stoneman, C. (1975), Foreign Capital and Economic Growth, Applied Economies, Vol. 25. [42] Tsikata, T. (1998), Aid Effectiveness: A Survey of The Recent Empirical Literature, Paper on Policy Analysis and Assessment, IMF, Washington, D.C. [43] Van Wijnbergen, S. (1986), Aid Export Promotion and The Real Exchange Rate: An African Dilemma, Macroeconomic division, Development Research Department, world Bank, and Centre for Economic Policy Research, London. [44] Voivodas, C. (1973), Exports, Foreign Capital Inflow and Economic Growth, Journal of International Economics, Vol. 3. [45] Vos, R. (1998), Aid Flows and Dutch Diseases in a General Equilibrium Framework for Pakistan, Journal of Policy Modeling, Vol. 20. [46] Vos R. and Johansson, S. (1994), Macroeconomic Impact of Aid in Nicaragua, Department of Economics Reprint Series No. 134 (Stockholm: Handelshogskoland I Stockholm). [47] Weisman, E. (1990), Aid as A Booming Sector: Evidence From a Computable General Equilibrium Model of Papua New Guinea, Islands Australia Working Paper No. 90/13, Canberra: National Centre for Development Studies, The Australian National University. [48] White, H. & Wignaraja, G. (1992), Exchange Rates, Trade Liberalization and Aid: The Sri Lankan Experience, World Development, 20. [49] White, H. (1992), The Macroeconomic Impact of Development Aid: A Critical Survey, Journal of Development Studies, Vol. 28. [50] World Bank (1998), Assessing Aid, Washington D.C.: Oxford University Press.Younger, S. (1992), Aid and the Dutch Diseases: Macroeconomic Management When Everybody Loves You. World Development, Vol. 20.

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Interbank Exposures and Risk of Contagion in Crises: Evidence from Finland in the 1990s and the 2000s

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Mervi Toivanen1

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By analysing the risk of interbank contagion during two distinctive crises, namely the Finnish banking crisis in the 1990s and the most recent financial crisis of the 2000s, this paper provides evidence on negative domino effects in a small open economy with a concentrated banking system. Simulations based on interbank exposures and maximum entropy estimations shed light on the magnitude of the contagion and the vulnerability to cross-border risks. The results show that just before the onset of the Finnish banking crisis the contagion would have affected almost half of the banking system, indicating that without the government bailout the implications for society would have been severe. In the 2000s the domestic contagion peaked after the collapse of Lehman Brothers and amid the sovereign debt crisis. The analysis suggests that the higher the concentration of the banking system, the more vulnerable it is to severe contagion. Moreover, strong interbank linkages with foreign banks increase the domestic risks.

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JEL classification numbers: G01, G21, N24 Keywords: Contagion, Interbank Exposures, Banking Crises, Finland, Maximum Entropy

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The history of financial crises extends to the early 20th century and beyond, including incidences such as the Wall Street Crash of 1929 and the sub-prime crisis. Frequently, the crises impact negatively on the financial stability of the banking sector and are extremely costly for an economy as a whole. From the historical perspective, relatively little emphasis has, nevertheless, been placed on analysing how the crises spread across institutions and borders, although the recent financial crisis highlights the importance of the interconnectedness of financial institutions. The interbank markets, in which banks borrow and lend funds, may act as transmission

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Senior Economist, Bank of Finland, PO Box 160, 00101 Helsinki, Finland

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channels for shocks during crises. These linkages are especially vulnerable since banks can relatively easily reduce interbank lending should their confidence in counterparties deteriorate. In the worst case scenario, the losses from interbank loans may lead to contagion (or so-called domino effect), i.e. one bank failure leads to failures of other banks even if the latter are not directly affected by the initial shock or do not hold open positions with the first failing bank [1].2 This paper examines the possibility of contagion via banks’ interbank exposures in a small open economy with a concentrated banking sector during two distinctive crises. Academic literature is enriched, firstly, from the focus on significant crises periods, namely the Finnish banking crisis in the 1990s, which is one of the “Big 5” banking crises [5], and on the recent financial crisis of the 2000s. Insights into similarities and differences in the two crises and into the patterns of contagion are provided for the estimation periods. The specific case of a small open economy such as Finland is interesting because of the vulnerability to cross-border risks, given the dependence on foreign trade: exports of almost 40% of GDP in 2010. Moreover, Finland’s GDP decreased by 8% in 2009 and by 10% in 1991–1993, causing a severe stress to the banking system. Secondly, the role of contagion in the Finnish banking crisis has not been discussed in previous literature. The systematic nature of the crisis in the 1990s forced authorities to bail out banks in order to save the rest of the banking system by limiting the effects of contagion. The contagion simulations shed light on the magnitude of problems that society would have faced if banks had been allowed to fail. Thirdly, there is relatively little public information on network effects of the banking system, and during the last decade risk assessments have mainly concentrated on individual institutions. A deeper understanding of interbank linkages and transmission channels is therefore desirable to increase our knowledge of contagion and to help lessen the danger of "moral hazard", i.e. excessive risk-taking. Finally, cross-border vulnerabilities of the Finnish banking system from 2005 onwards are identified. The Finnish banking sector is highly concentrated and nowadays dominated by foreign banking groups, making Finland a prominent example for other similar banking systems. Banks’ bilateral interbank lending is estimated by using the maximum entropy method and data on banks’ balance sheets, interbank assets and liabilities. On the basis of these estimates, the effects of a bank failure in the Finnish interbank market are subsequently simulated. The results suggest that during the banking crisis in the 1990s three banks were able to trigger contagion, while indicating five large and middle-sized banks as sources of contagion in 2005–2011. During the 1990s the contagion would have affected almost half of the banking system (assuming 100% loss ratio) and thus the implications for society would have been severe without the authorities’ rescue measures. In 2005–2011, the negative shock caused by a failure of a foreign bank (with a 100% loss-given-default) affects 77% of the total assets of the Finnish banking sector, while contagion from a Finnish bank impacts 66% of the total assets of the sector. In addition, the estimations show that the higher the concentration of the banking system, the greater the system’s vulnerability to contagion. This is worrying in terms of a country that has large

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Other contagion channels include information, sale of illiquid assets or joint macroeconomic shocks but they are beyond the scope of this paper. (See [2], [3] and [4])

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cross-border exposures with foreign banks. In terms of average contagion, the fragility of the banking system increases before the crisis irrespective of the original source (domestic/international) of the crisis. Although the interbank market exhibits higher risk levels in the current crisis than in the 1990s, a bad outcome has not materialized owing to the absence of a trigger. The macroeconomic shock was milder and more transitory in the 2000s than in the 1990s, banks’ capital buffers are currently large, interest rates are lower than in the early 1990s and many borrowers and lenders have learned from the experience of the 1990s, and so acknowledge the dangers of over-borrowing. The rest of the paper is organised as follows. The previous literature is reviewed in section 2, and section 3 describes the Finnish banking sector and the crisis periods. Section 4 presents the data and method of estimating bilateral exposures and simulating contagious effects. This section also briefly discusses the simulation parameters. The results are introduced in section 5 and section 6 concludes.

2 Previous Research

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The Finnish banking crisis is dealt with in several papers, describing the boom and subsequent bust of the Finnish banks and economy in the early 1990s (see, for instance, [6], [7], [8] and [9]). No single, individual cause for the negative outcome can be identified, as several factors such as financial deregulation, abundant refinancing opportunities for banks, over-borrowing of firms and households, excessive risk taking, lack of adequate risk management, policy and supervisory measures, and negative macroeconomic shocks all played a role. Although the Finnish crisis shares common features with other financial crisis in general and with Nordic banking crises in particular (see [6], [7], [10], [11], [12], [13]), it is one of the worst banking crises (so-called “Big 5” crises) of the post-WW II era, as listed in [5]. Despite the extensive coverage, the role of contagion in the Finnish banking crisis has not yet been discussed. Theoretical evidence on the consequences of the banking sector’s structure for contagion is twofold. If all banks are connected with each other (i.e. the interbank market is complete), the initial impact of a financial crisis may be attenuated [14]. But if each bank is connected with a small number of other banks (incomplete interbank markets), the crisis may be felt strongly in neighbouring institutions. However, some papers provide evidence that an incomplete structure renders the banking system less vulnerable to contagion. [15], [16] Empirical research finds potential for significant contagion effects but regards as unlikely a substantial weakening of the whole banking sector ([17], [18], [19], [20], [21], [22], [23], [24]). Other empirical studies have estimated contagion by considering a wider variety of risks and factors (see e.g. [3], [25], [26]). These studies support the above findings and also indicate significant cross-border contagion. Regarding cross-border contagion, [27] shows that the contagion is more widespread between countries geographically close to each other. Furthermore, they suggest that the risk of cross-border contagion has increased over the years.

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3 The Finnish Banking Sector and the Crises 3.1 Banking Sector in Finland

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In the 1990s the majority of Finnish banking market was dominated by KOP, SYP, savings banks, cooperative banking group, Post office bank and Skopbank. Of these institutions, KOP and SYP were the largest ones and were fierce rivals. The third largest banking group was the savings bank group, which comprised about 250 savings banks and Skopbank, which served as the group’s central financial institution. OKO Bank financed the cooperative banks that belonged to the cooperative banking group, and Post office bank was a government-owned commercial bank. The Finnish banking market was already then highly concentrated, as the remaining banks were relatively small. ([6], [8]) According to the balance sheets, the main banking groups in Finland are currently: Nordea Bank Finland, OP-Pohjola Group, Sampo Bank, savings banks (incl. Aktia) and local cooperative banks. Nordea and Sampo banks are foreign-owned, and the Finnish banking sector is highly concentrated, as the three main players account for approximately 75% of total lending. All together, there are about 360 individual credit institutions in Finland, several of which belong to a larger consolidated banking group.

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The deregulation of the Finnish financial market in the mid-1980s planted the first seeds of the Finnish banking crisis, as it expanded banks’ choice set of assets and liabilities (for more details, see [7]). The interbank market was established in 1986, providing a new funding source for Finnish banks. Banks were no longer bound to traditional deposit funding but could finance the growing lending stock with market funding. At the same time, the private sector started to accumulate debt, as low real interest rates, a growing real economy and general optimism unleashed the demand that had been suppressed during the regulation era. Moreover, banks competed fiercely over market shares in private sector lending. During the second half of the 1980s, Skopbank's and savings banks' lending increased aggressively, but other banks too were quick to react to the competition. Foreign currency loans were especially easy to sell owing to interest rate differentials and a pegged exchange rate regime. When the overall economic situation weakened, banks' traditional loan losses started to accumulate and their situation worsened. Finally, the banking crisis was trigged by steeply rising interest rates, devaluation of the Finnish currency, and the collapse of the real estate bubble and exports to the Soviet Union. A severe depression followed, and GDP decreased by 10% in 1991–1993. The Finnish experience with financial liberalization, lending boom and systemic banking crisis resembles in many ways the crises that took place in Sweden and Norway in the 1990s although some differences remain. [6] Turning to individual banks, Skopbank's strategy had been highly dependent on the availability of market funding and, as Skopbank’s loan losses soared, the markets became sceptical as to Skopbank’s ability to meet its obligations. The lack of confidence prevailing in money markets increased and finally Skopbank’s liquidity collapsed in September 1991 when other banks refused to buy Skopbank’s certificates of deposit. To prevent the whole banking system from collapsing, the central bank took over Skopbank.

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In the first half of 1992, the savings banks that were on the brink of collapse merged to form the Savings Bank of Finland (SBF), but its financial standing deteriorated during the year as loan losses doubled and the costs of market funding increased. Ultimately, SBF was not able to follow its special recovery plan and the bank was split up between four competitors in October 1993. The recent global financial crisis started in 2007 when the sub-prime mortgage market collapsed in the US and the value of mortgage backed securities plummeted, causing large losses for financial institutions that had invested in these instruments. As the crisis deepened, panic spread in financial markets and equity values declined. Lehman Brothers failed in September 2008, after which the financial crisis intensified. Several US and European banks were either bailed out by governments or merged with other companies. Iceland’s banking sector was hit especially hard, while Swedish banks booked large loan losses on lending to Baltic States, and many small banks in Denmark faced difficulties. [13], [28] The over-indebtedness of several European countries, along with a downturn in the global economy, bursting property bubbles, as well as investment and loan losses in the European banking sector, contributed to an unfolding of the European sovereign debt crisis. The crisis began at the start of 2010 when the magnitude of Greece’s fiscal deficit was revealed. Amid fears of crisis escalation and downgrading of Greek sovereign debt, the situation in the international financial markets deteriorated in early May 2010. Since then, Ireland and Portugal have also received rescue packages. Throughout the sovereign debt crisis the international money markets have remained extremely volatile, although several policy measures have been undertaken. The situation has remained fragile, and financial markets have been repeatedly hit by renewed worries related to the debt crisis. The financial markets continue to be divided into weak banks dependent on public support and strong banks still able to access markets on their own. With limited exposures to ailing governments’ bonds and low traditional loan losses, the Finnish banks have been relatively well-placed compared to their European and Scandinavian peers in recent years.

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Contagion analyses of the Finnish interbank market in 1988–1996 and 2005–2011 include the Finnish deposit banks. 3 The analysis for 2005–2011 is based on balance sheet, counterparty exposure and liquidity risk data, whereas data were not collected on counterparty exposures and liquidity risk in the 1990s, so that only balance sheet data are used for the earlier crisis period. Balance sheet information is based on data collected from banks’ annual reports for the

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KOP, OKO Bank, SYP, Merita Bank, savings banks, Postbank, Skopbank, STS Bank and Bank of Åland in 1988–96 and Nordea Bank Finland, Sampo Bank, Pohjola (former OKO), Aktia Savings Bank, Bank of Åland, Evli, eQ Bank, Tapiola Bank, S-Bank, local co-operative banks and local savings banks in 2005–2011. Local co-operative banks and local savings banks are each combined into a separate banking group.

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1990s and on data collected by the Finnish Financial Supervisory Authority (FSA) for the 2000s. Yearly data on aggregated interbank loans and receivables vis-à-vis financial institutions are available for the 1990s; for the 2000s we have quarterly data on interbank loans and receivables as well as on banks’ bonds and certificates of deposit.4 Table 1 shows the total assets of Finnish banks as well as interbank liabilities relative to banks' total assets in 1988 and 2006. At a maximum, interbank liabilities were approximately one fifth of total assets in 2006 although there are differences between institutions. The share of interbank liabilities has diminished over the years, as there are currently fewer institutions with exposures exceeding 10% of total assets.

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Table 1: Finnish deposit banks’ total assets and share of interbank liabilities in 1988 and 2006 1988 2006 Total assets, Interbank Total assets, Interbank EUR million liabilities EUR million liabilities over Total over Total assets, % assets, % KOP 24,322 1.2 % OKO (Pohjola) Bank 7,375 16.2 % 24,196 4.5 % Postbank 12,582 0.7 % Skopbank 10,681 11.5 % STS Bank 1,832 10.2 % SYP (Unitas) 22,305 0.5 % Savings Banks 16,643 14.5 % 5,648 1.0 % Bank of Åland 462 11.1 % 2,189 2.8 % Nordea Bank Finland 130,985 22.3 % Sampo Bank 26,627 1.8 % Aktia plc 5,492 16.2 % Evli Bank 698 10.7 % eQ Bank 627 0.0 % Tapiola Bank 546 0.0 % Local co-operative banks 3,467 0.2 % Source: banks’ annual reports Counterparty exposure data give accurate quarterly snapshots of interbank business and provide information on unsecured and secured loans at the group level. However, the FSA’s data set covers only the 10 largest domestic and foreign counterparties of each reporting bank and does not shed light on all exposures. In order to fill in this gap, FSA’s quarterly liquidity risk data are used to clarify the

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bilateral interbank relationship among small Finnish local banks and their central financial institutions5. Cross-border contagion is assessed by using counterparty data on Finnish banks’ interbank lending to foreign banks. According to the counterparty exposure data most of the banks’ exposures are unsecured. In 2005–2011 the unsecured receivables from both domestic and foreign financial counterparties fluctuated between EUR 12.0 billion and EUR 19.2 billion, constituting 73–113 per cent of the banks’ total capital. In September 2008, amidst the international financial crisis, the main counterparties of Finnish banks were domestic ones. Since then the share of Finnish counterparties have gradually decreased, while the share of foreign banks has increased. Based on the available data the Finnish interbank sector does not form a complete structure in the sense of [14]. All banks are nevertheless connected to each other via common counterparties. The three largest banks, in the heart of the interbank market, have room to manoeuvre in either the domestic or international money markets. The ability to access international capital markets reduces their dependence on the national interbank market, although they interact with each other and with other Finnish banks. Middle-sized institutions are also able to raise funding from international markets but also acquire funding from the largest Finnish banks. Finally, small, local banks use other Finnish banks as their central financing institutions and thus form ‘satellites’ around these banks. For example, local savings banks and local co-operative banks use Aktia as their central financial institution. In a similar fashion, Pohjola finances local co-operative banks that belong to the OP-Pohjola Group.

4.2 Estimating Bilateral Matrices

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As balance sheets and large exposure data do not give complete information on individual banks' actual counterparty exposures, the method of entropy maximization has been used to fill the gaps in the data sets. Following [17] and [19], this paper assesses domestic and foreign contagion in the Finnish interbank market. The problem of estimating the matrix for banks’ bilateral exposures is posed as: "Given a matrix C, determine a matrix X that is close to matrix C and satisfies a given set of linear conditions on its entries" (see [29] and Appendix). Matrix C contains all available statistical information on the bilateral unsecured exposures among Finnish banks as well as between foreign and Finnish banks, while balance sheet data on total interbank assets and liabilities provide the set of linear conditions for the estimation problem. The overall distribution of interbank loans and deposits (i.e. matrix X) is subsequently estimated by using the entropy maximization. This problem is easily solved using the RAS algorithm by [30]. The data permit us to compute two matrices of bilateral exposures. These sub-matrices are formed for loans and receivables as well as for bonds and certificates of deposit. After having estimated a bank-to-bank matrix for the sub-categories, these matrices are combined into the total domestic exposure matrix. This composite matrix is then been used to test the possibility of contagion.

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The data set includes information on interbank deposits and loans between Aktia, on one side, and local co-operative banks and savings banks, on the other side. Similar data exist for Pohjola Bank and co-operative banks in the OP-Pohjola Group.

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4.3 Simulating Contagion Once the matrix of interbank linkages is in place, the scope of contagion is simulated by letting banks go bankrupt one at a time and by computing the overall effect on the banking sector due to direct or indirect exposures to the first failing bank. The simulations follow a sequential (or round-by-round) algorithm ([2], [31]). At the start, there are several banks b, b = 1,â&#x20AC;Ś,N, in the Finnish banking sector. All these banks have capital cb as well as an exposure xbb towards another domestic bank. Contagion simulation involves the following steps:

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1. By assumption, bank i fails at t0. 2. A lender defaults if the amount of losses from lending to the failed bank exceeds the lender's own capital. So, a bank j fails if its exposure towards bank i, x ji, multiplied by an exogenously given parameter for the loss-given-default (LGD), exceeds the bank j's capital cj. So, bank j fails if LGD * xji > cj at t1. 3. Contagion need not be confined to such first-round effects, but a failure of the first bank can trigger a chain of failures (domino effect). A second round of contagion occurs for any bank k for which LGD * (xki + xkj) > ck at t2. Contagion stops if no additional banks go bankrupt. Otherwise, a third round of contagion takes place.

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The impact of the failure of a foreign bank is successively studied by letting each of the M foreign banks go bankrupt one at a time and simulating the contagion within the domestic interbank market with a given LGD. In the simulations, bank institutions stand alone. In reality this may not always be the case, since several Finnish banks are members of a larger group. Thus, when facing difficulties, a parent corporation may provide funding to its banking subsidiary. This funding can extend the bank's ability to sustain market turbulence and restrain contagion. However, the recent financial crisis has shown that banks may not have time to react in a crisis. A sudden drying up of interbank markets and short-term funding or a lack of other forms of safety nets on which banks could rely in a case of problems may quickly squeeze the bank out of the interbank markets. Should the analysis take into account all ramifications of a bank failure such as adjustments by depositors the impact is likely to be even more devastating.6 Simulations focus on gross exposures and do not take into account netting. As the focus is on maximum exposure and contagion is assumed to proceed without delays, netting is not an option. Moreover, in Finland banks cannot net interbank claims that can be used as collateral for central bank funding. What happens after all contagion rounds and the bankruptcy of a bank is beyond the scope of this paper.

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4.4 The Choice of Parameters

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The key parameters in determining the existence of contagion are the loss-given-default (LGD) ratio and the solvency ratio. The LGD refers to the share of assets that cannot be recovered in the event of a bankruptcy. The choice of LGD is by no means obvious, as it can vary significantly. Historical evidence on the failures of international banks such as Continental Illinois, BCCI and Herstatt indicates that the loss ratio may range between 5–90% depending on the time period when losses are expected to materialize. ([2], [17]) The uncertainty about eventual recoveries suggests that it may not be the actual losses borne by the creditor banks but rather the expected losses at the moment of a failure that matter. The loss ratio also depends on the availability of collateral for interbank claims vis-à-vis creditors. According to the Finnish counterparty exposure data, collateralized lending by Finnish banks is almost non-existent. Since the purpose of the study is to find the maximum negative shock that could hit the market, it is assumed that most of the interbank loans reported in the balance sheet are indeed unsecured. Given the difficulties in determining the appropriate loss rate, the possibility of contagion is tested using a broad range of values for LGD, 25%, 50%, 75% and 100%, which remain constant across banks. The solvency ratio forms a requirement for a bank’s equity. The current minimum Tier 2 capital ratio is set at 8% by regulatory authorities. In reality, banks seldom go bankrupt out of the blue; there are at least some rumours about the difficulties beforehand. If the institution is too big or too systematic to fail, regulators are likely to take action to address the issue by closing the bank, by moving doubtful assets to a special financing vehicle or by providing liquidity for the bank. This kind of policy response was evident during the Nordic banking crises and during the latest financial crises when authorities bailed out the majority of significant banks, for instance, in Ireland and the UK. Nevertheless, as the focus here is on the maximal negative effect and the short-term contagion effects, it is assumed that regulators do not have time to react.

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5 Estimating the Danger of Contagion on the Finnish Interbank Market 5.1 The Banking Crisis in the 1990s In 1988–1990 contagion was triggered by savings banks, Skopbank and OKO Bank. The magnitude of contagion in each case increased steadily. (Figure 1) If savings banks had failed in 1988, contagion7 would have affected 26% of banking sector assets (assuming a 100% loss ratio) and the negative impact would have been somewhat smaller with lower LGDs. Two years later, just before the onset of the actual crisis, savings banks’ failure would have affected 38% of the total assets of the banking sector. The case of Skopbank is interesting, as it was actually taken over by the central bank in

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1991. Simulations show that the bank’s failure in 1988–1990 would have had a more profound impact on the markets than the failure of the savings banks. In 1988 and in 1989 the negative effect would have caused 31% and 48% of the banking sector to collapse, respectively. A year before the failure of the bank, contagion would have affected almost half of the banking system, indicating that without the bailout of the bank the implications for the society would have been severe. The contagion is somewhat milder with the lower loss-given-default (LGD) ratios. Note: The y-axis represents the proportion of Finnish banking sector (measured by percentage of failing banks’ assets in banking sector's total assets) that will run into problems as a result of a default of Savings banks, Skopbank or OKO bank, after all banks in the system have been exposed to the contagion. The extent of the effect is assessed for four different loss-given-default (LGD) rates. The assets of the first failing Finnish bank are excluded. A missing bar means that the failing bank does not trigger a domino effect. 75 %

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Figure 1: Contagion in Finnish banking system in 1998–1990, grouped by LGD The fact that the analysis identifies OKO Bank as the most severe source of contagion during 1988–1990 is a new finding. The cooperative banking group did have problems during the crisis, but it is generally acknowledged that the Group was able to survive due to their more conservative strategy and the Group's joint responsibility in dealing with loan losses. The results are likely driven to some extent by the fact that OKO Bank acts as a central financial institution for the co-operative banking group, acquiring refinancing from the markets and passing on the funds to cooperative banks. And, market funding constituted an increasing share of OKO's balance sheet. Another interesting result is that commercial banks KOP and SYP do not show up as possible sources of contagion, though they were the largest banks. Although they were active in the interbank markets their interbank lending relative to their total assets was not

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as large as in other banking groups (see Table 1). If certificates of deposit, which were widely used instruments in the Finnish interbank market in the 1980s, are also included in interbank assets and liabilities, the results indicate that all banks' exposures to short-term money markets were such that no bank would have survived a sudden drying up of external funding. The contagion analysis is replicated with data on the most severe recession year 1992, followed by the recovery years 1994 and 1996. However, these data points are somewhat problematic since by that time banks had received substantial subsidies from the government. Assuming a 100% loss ratio, the contagion would have impacted 14%, 33% and 53% of the banking sector’s assets in 1992, 1994 and 1996, respectively. Owing to restructuring of the banking sector, the risk of contagion declined in 1992 but started to increase after that. During these years saving banks, OKO Bank, Merita Bank and Post office bank were possible contagion sources. The savings banks were still contagious in 1992, affecting 21% of the banking sector (with 100% LGD), but after the final resolution the group did not cause contagion in 1994 and 1996. OKO Bank's exposure is due to its position as a central monetary institution, while Merita Bank was formed in a merger of two large banks in 1996, and thus constituted a large share of the banking system. It should be noted that the Post office bank's position was not, in reality, worrisome since it was owned by the state. In light of the historical knowledge, the estimations seem to be able to identify banks that were the most troublesome during the banking crisis. The evidence also indicates that banks with a significant share of interbank assets are more prominent sources of contagion than the others.8

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According to simulations for 2005–2011, five out of the ten banks could trigger contagion in Finland. In addition to the large commercial banks, there are also middle-sized banks that are capable of producing negative spillover effects. The five banks that are identified as a starting point for contagion remain the same for whole estimation period. On average9 and assuming 100% loss rate, 66% of banking sector assets would have been affected in 2005–2011 (Figure 2). Although the case of the 100% loss-given-default (LGD) is harsh, it is interesting as a “worst case scenario”, portraying the outcome if everything goes badly. The result is at the upper end of earlier estimates, which vary from 4% for Belgium to 96% for the Netherlands. While the worst case scenario might be only a theoretical possibility, the quite plausible 75% and 50% loss ratios in the short-run seem to have already significant effects on the banking market. Over the estimation period, the average negative impact on total assets is 39% and 19%, respectively.

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This supports [2] arguing that direct contagion happens only if interbank exposures are large compared to the capital. 9 A simple average for the banking sector over the estimation period for stated LGD.

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25 %

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Assuming 25 % loss-given-default, the average contagion affects 11% of banking sector assets.10 The LGD ratio has an obvious effect on the speed of contagion and the outcome. This is intuitively appealing, since higher values of the ratio have the potential to increase pressure in the system. At some point, a critical mass of losses is reached and the interbank market collapses. For instance, the larger the LGD, the quicker the pace of contagion and the more severe the negative impact on the banking system. Note: The y-axis represents the proportion of the Finnish banking sector (measured by percentage of failing banksâ&#x20AC;&#x2122; assets in banking sector's total assets) that will run into problems as a result of a default of a domestic bank, after all banks in the system have been exposed to the contagion. The extent of the effect is assessed for four different loss-given-default (LGD) rates. Results for each loss rate and each quarter are based on a simple average for the individual banks. The assets of the first failing Finnish bank are excluded.

Figure 2: Contagion in Finnish banking system in 2005â&#x20AC;&#x201C;2011, grouped by LGD The volume of contagion also depends on the bank that fails first. Only one bank is extremely contagious in the Finnish banking system, being able to cause mayhem in the market already with the smallest loss ratio. With 25% LGD, around one half of the

10

The effect of contagion is also estimated by letting local co-operative banks and local savings banks enter the simulations as individual banks instead of combining them into two representative banking groups. In this set-up, there are 42 local co-operative banks, 39 local savings banks and 8 commercial banks. The effect on the results is nevertheless negligible and the contagion is 0.1%â&#x20AC;&#x201C;2.6% lower depending on the loss rate. However, in reality this difference may prove important for local communities and individual banks, as local co-operative banks and local savings banks are not liable for each others' debts.

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Finnish banking system would collapse due to the problems of this bank. If the loss ratio is larger, this bank is a source of contagion that affects the whole banking system and ultimately causes the system to collapse. Of the other four banks identified as a source of the contagion, two banks are systematically important from June of 2008 onwards and with higher loss ratios. The contagion from the last two banks is usually limited in nature albeit some noticeable exceptions remain. Nevertheless, the negative effects imposed by these banks are almost non-existent if the loss rate is less than 100%. The limited number of contagious banks portrays the high concentration of the banking sector. Turning to developments over the years, the aggregated11 domestic contagion intensified at the beginning of the domestic and international crisis in both the 1990s and the 2000s (Figure 3). The magnitude of the contagion was relatively mild up to 2007, remaining under the levels of 1988–1990. For instance, in December 2006 the first failing bank would have caused around 11 % of Finnish banking sector to collapse. In the run-up to the banking crisis in 1990s as well as before the collapse of Lehman Brothers, the severity of contagion increased in Finland. The contagion risk peaked at the end of 2008 after the collapse of Lehman Brothers, when a first failing bank would have caused, on average, almost 50% of the banking system to collapse. After the initial culmination of the crises, the magnitude of contagion decreased. Nevertheless, the positive development was reversed and the risk of contagion rose towards the end of 2009. The actual magnitude of Greece’s fiscal deficit was revealed at the turn of the year 2010, triggering the sovereign debt crisis and raising the contagion risk in Finnish interbank market above the 50% impact level in June 2010. After this peak the contagion risk declined until mid-2010 but started to increase again towards the end of the estimation period, possibly reflecting renewed worries related to the debt crisis and the changing pattern of interbank linkages. The freezing of money markets may have negatively impacted cross-border interbank lending, which has been – at least partially – replaced by lending between domestic institutions. Growing importance of domestic counterparties naturally increases the magnitude of domestic contagion.

11

Aggregation is based on a simple average over the individual banks and the loss-given-default ratios for each individual year.

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Note: The y-axis represents the proportion of the Finnish banking sector (measured by percentage of failing banks’ assets in the banking sector's total assets) that will run into problems as a result of a default of a bank, after all banks in the system have been exposed to the contagion. Aggregation for each time period is based on a simple average for the individual banks and the loss-given-default ratios. The assets of the first failing Finnish bank are excluded. 60

%

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Figure 3: Aggregated contagion in 1988–1996 and 2005–2011

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The results concerning banking sector structure and contagion suggest that an incomplete interbank market with highly concentrated banking sector correlates positively with contagion. In Finland, the concentration measured by the Herfindahl index 12 and contagion grew, respectively, from 2,730 and 17% in 2005 to 3,700 and 49% in 2011. The simple correlation between these two time series was 66% in 2005–2011, suggesting that there is a positive link between higher contagion and increasing concentration of incomplete markets. This vulnerability to severe contagion gets support from previous studies, indicating that banking sectors dominated by a few large banks (such as the Dutch and Finnish banking sectors) exhibit high contagion risk. At the same time, contagion seems to have a somewhat milder effect in countries with two-tier systems and low concentration (such as Germany and Italy). ([17], [20], [23]) Furthermore, [19] finds that the change from complete structure towards a more decentralised structure reduces the risk and impact of contagion.

12

Data for the index from Statistical data warehouse (SDW) of the ECB (www.http://sdw.ecb.europa.eu/).

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5.3 Cross-border Contagion

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The analysis of this section concentrates on whether a failing foreign bank can trigger a default of a Finnish bank and whether there is a subsequent domino effect within the domestic banking sector. As no information on bilateral financial linkages between foreign banks is available, simulations cannot take into account the overall cross-border contagion, which hinders the analysis of second-round effects abroad and potential indirect impacts on Finnish banks after the initial failure of a foreign bank. This limitation affects all the literature on financial contagion. Only [27] investigates overall contagion across countries but the paper is limited to aggregate country level data, as it lacks data on individual banks. Overall, the default of a foreign bank can trigger contagion in the domestic interbank market, leading in general to the immediate failure of a few (from zero to four) Finnish banks. On average13, the instant first-round impact of the failure of a foreign bank amounts to 8% of the total assets of the Finnish banking sector in 2005–2011. The magnitude of the effect varies over time, peaking at 17% in June 2007 and amounting to about 8.5% at the end of the estimation period (Figure 4). Note: Line shows the share of Finnish banks’ assets that initially go bankrupt in the first-round due to the failure of a foreign bank. Columns represent the aggregated percentage of failing Finnish banks’ assets in the banking sector's total assets, after all banks in the Finnish banking sector have been exposed to the subsequent domestic contagion rounds after the initial impact. Aggregation for each quarter is based on a simple average over the individual banks and loss-given-default ratios. contagion within Finland

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Figure 4: Contagion triggered by a foreign bank in 2005–2011

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A simple average over the individual banks, LGDs and quarters.

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The failure of a foreign bank impacts large, medium-sized and small banks alike. In addition to French, British and American banks, the contagion is often triggered by Swedish and Danish banks. The result thus supports the findings of [27] which showed that a default of a Scandinavian bank affects the neighbouring banking systems. Nordic banks are the main international counterparties for Finnish banks and thus they form potential channels through which international contagion or market disturbances may spread to Finland. Within the Finnish banking sector, foreign contagion follows similar patterns as domestic contagion although the high risk of domestic contagion is not reflected in the negative spillover effects of a foreign bank’s default in 2009–2010. All in all, contagion caused by a failure of a foreign bank is slightly more severe than contagion triggered by a Finnish bank during the estimation period. After all contagion rounds, the contagion from a foreign bank affects 77% of the total assets of the Finnish banking sector in 2005–2011 and with a 100% LGD, while contagion from a Finnish bank impacts 66% of the total assets of the sector. Nevertheless, the impact depends on the loss-given-default, as with lower LGDs the impact from a Finnish bank is more pronounced. The findings are in line with those of [19] and [23], indicating that the more concentrated the banking system, the more vulnerable it is for foreign contagion.

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5.4 The Crisis in Comparison

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The operational environment of banks in the 1990s and in 2005–2011 bears several similarities. During both periods, the Finnish banking sector was highly concentrated and there were only a few large players in the market. The Finnish banks started to finance their growing lending by acquiring short-term funding from money markets at the end of 1980s. Similarly, interbank markets grew in significance in the 2000s, as liquidity was abundant in the international financial markets, which constrained the cost of financing and enabled banks to easily refinance themselves. As a consequence, some foreign banks became dependent on external (short-term) market financing and the growth of interbank assets increased the risk of contagion. However, there are also notable differences between the periods. In 2005–2011 the interest rate level was nowhere near that of the early 1990s, the corporate sector was not as badly indebted as before and banks’ capital buffers are currently larger. In addition, many borrowers and lenders are currently more aware of the dangers of over-indebtedness. In Finland, the macroeconomic shock was also somewhat milder and more transitory in the 2000s than in the 1990s. Therefore, several negative triggers and factors such as the banking system’s structural weaknesses and hazardous incentive structures that were present in the 1990s were missing in the 2000s, and thus removed the initial knock-out effect. All in all, the current crisis has not eroded Finnish banks’ solvency ratios, so that banks are now more resilient to domestic contagion, and bank default is a low probability event.

6

Conclusion

This paper investigates the possibility of financial contagion using data on the Finnish interbank market and the maximum entropy methodology. First, we compare the pattern and development of contagion before and during two distinctive crisis periods. These

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contagion simulations shed light on the magnitude of the problems that society would face if banks fail. Secondly, as the importance of network effects is recently highlighted, the analysis provides more information on the importance of interbank linkages and transmission channels. Thirdly, the paper provides evidence on the domestic and foreign-based contagion in a concentrated banking system that is dominated by foreign banking groups and thus vulnerable to cross-border shocks. The analysis suggests that the contagion increased both in 1988–1990 and in 2005–2011, irrespective of the original source (domestic/international) of the crisis. The method identifies five large and middle-sized Finnish banks that are able to cause contagion in 2005–2011, while suggesting that three banks were contagious during the banking crisis in the 1990s. Before the onset of the crisis in 1990 the contagion would have affected almost half of the banking system (assuming 100% loss ratio), indicating that without the bank bailouts the implications for society would have been severe. In 2005–2011, the negative impact caused by a failure of a foreign bank (with a 100% loss-given-default) affects 77% of the total assets of the Finnish banking sector, while contagion from a Finnish bank impacts 66% of the total assets. There are also indications that the more concentrated the banking system, the more vulnerable it is to severe contagion. Moreover, strong interbank linkages with foreign banks increase the risk for domestic contagion.

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ACKNOWLEDGEMENTS: I would like to thank Panu Kalmi, Hannu Piekkola, Jouko Vilmunen and Glenn Harma for their helpful comments and suggestions; and Christian Upper for providing the code for the RAS algorithm. The financial support from Yrjö Jahnsson Foundation is gratefully acknowledged. All remaining errors and omissions are the sole responsibility of the author. The views expressed in this paper are those of the author and do not necessarily reflect those of the Bank of Finland.

[3] [4] [5] [6]

[7] [8]

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M.Pericoli and M. Sbracia, A Primer on financial contagion, Journal of Economic Surveys, 17(4), (2003), 571 – 608. C. Upper, Simulation methods to assess the danger of contagion in interbank markets, Journal of Financial Stability, 7(3), (2011), 111 – 125. J. Müller, Interbank credit lines as a channel of contagion, Journal of Financial Services Research, 29(1), (2006), 37 – 60. A. Pais and P.A. Stork, Contagion risk in the Australian banking and property sectors, Journal of Banking and Finance, 35(3), (2011), 681 – 697. C. Reinhart and K. Rogoff, Banking Crises: An equal opportunity menace, CEPR Discussion Paper Series 7131, (2009). L. Jonung, J. Kiander and P. Vartia (eds), The Great financial crisis in Finland and Sweden – The Nordic experience of financial liberalization, Edward Elgar Publishing, Cheltenham, (2009). P. Nyberg and V. Vihriälä, The Finnish banking crisis and its handling (an update of developments through 1993), Bank of Finland Discussion Papers 7, (1994). V. Vihriälä, Banks and the Finnish credit cycle 1986–1995, Bank of Finland Economic Studies E:7, Oy Trio-Offset, Helsinki, (1997).

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64

Mervi Toivanen

Appendix The Method of Maximizing Entropy The concept of entropy maximization originates in information theory, in which entropy is a measure of the average information content of a random variable. The greater the entropy of the message, the greater information content of the message. Maximizing entropy means setting up probability distributions on the basis of partial knowledge and thus denotes the most likely outcome given the a priori knowledge about the event xi. (For more details see [33], [34], [35].) When the probability of the outcome is maximized, the uncertainty diminishes and the estimates of parameters xi are close to real values of xi.

 x11    X   xi1     xN 1 

 x1N w1N 1  w1M         x1N           xNN wNN 1  wNM 

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 x1 j    xij

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Figure A: Matrix of interbank loans and deposits Sources: [17] and [19].

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Suppose now that there are N Finnish banks that may lend to each other. In this case, the interbank lending relationships can be presented in an N*N matrix (see left-hand side of the matrix X in Figure A). [2] As there is usually no knowledge on individual interbank loans and deposits, individual xij:s are generally unknown. However, a priori data on actual individual interbank relationships and their magnitudes is gathered into an a priori matrix C that resembles matrix X. The diagonal of the matrix C is usually set at zero, since it is assumed that no bank lends to itself. Balancing the matrix yields a unique estimate of matrix X. Matrix is defined to be balanced if it satisfies the given set of linear restrictions of the problem. These restrictions consist of the row sums (ai), i.e. bank i's total claims on other banks, and column sums (lj), i.e. bank j's liabilities in the interbank market. These sums are obtained from balance sheet data. More formally, the problem is as follows: n

Min  xij

i 1

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s.t. n

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Interbank Exposures and Risk of Contagion in Crises Evidence from Finland n

x j 1

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 ai

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65

(3)

xij  0

(4)

In the case of foreign contagion, the same methodology applies, but now X becomes an (N × (N+M)) matrix (Figure A). This matrix of bilateral exposures presents the interbank exposures of Finnish banks toward the other (N-1) Finnish banks and the M foreign banks. The initial estimation problem and linear restrictions remain the same except for restriction (3), which becomes:

w j 1

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in which wij represents the gross exposure of Finnish bank i to foreign bank j and fa i stands for interbank assets of bank i. [19]

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Further Evidence of Deficiencies in Classical Finance Erhard Reschenhofer1 and Kevin Windisch2

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Reviewing the basics of meanâ&#x20AC;&#x201C;variance portfolio optimization and the capital asset pricing model, this paper discusses the plausibility of some of the underlying assumptions. It is pointed out that a positive in-sample relationship between the expected return of an asset and its covariance with the market portfolio can be a statistical artifact because it can be explained without using any economic arguments. In an empirical analysis of two sets of assets consisting of individual stocks and indices, respectively, no indication of any out-of-sample relationship is found. In the absence of such a relationship or any other additional information about the expected returns, simple averages of past returns must be used as input for portfolio-optimization procedures. Empirical evidence is presented which suggests that portfolio optimization is of little practical value in this case and, in addition, that the use of robust estimators can hardly make any difference.

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JEL classification numbers: C58, G11, G17 Keywords: Portfolio optimization, Risk-return relationship, Robust estimation

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Modeling the returns of a set of assets as random variables with different means and variances, classical portfolio optimization tries to find a mixture of these assets which either minimizes the variance for a given expected return or maximizes the expected return for a given variance. In general, it is much easier to reduce the variance than to increase the expected return. While the variance of a mixture of assets will practically always be smaller than the minimum of the individual variances, the mean of the mixture can never exceed the maximum of the individual means (see Figure 1). A large variance reduction can already be achieved by using equal weights for all assets. Any further reduction requires knowledge of the covariances between the individual returns. Although the covariances are not only unknown but are also changing over time, they can be

1 2

University of Vienna. University of Vienna.

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forecasted with some accuracy. But this means only that variance minimization is a worthwhile exercise, it does not mean that the theoretical concept of a risk-return trade-off is of any practical use. The problem is that the prediction of future returns is much harder than that of future risks. However, additional economic assumptions, which include the unrealistic possibility of unrestricted borrowing and lending at a riskfree rate [12, 15] or, alternatively, the equally unrealistic possibility of unrestricted shortselling [3], imply a linear relationship between the expected value of the return of an asset and the covariance between this return and the market return. If this hypothetical relationship was true, it could be used to obtain forecasts of expected returns from forecasts of covariances. This paper confronts the fundamental principles of classical finance with data. The bar is not set very high. Nobody expects a perfect agreement between theory and empirical results. Previous empirical studies have already revealed striking discrepancies (for an overview, see [8]). The only remaining question is whether the theory can at least be used to improve the trading performance in a statistically significant and economically relevant manner. If the answer is no, we should first try slight modifications before we abandon classical finance and turn to more complex asset pricing models such as the multi-factor CAPM [6, 7] and the downside-beta CAPM [2, 4, 9, 10] or to a completely different approach such as behavioral finance (for a survey, see [1]). At least, the use of conventional methods for the estimation of the variances and covariances should be questioned. Robust estimators are possibly more appropriate because of the apparent deviations from normality (for a survey of robust portfolio strategies, see [5]). Although the use of robust estimators has the positive side effect that the portfolio turnover is reduced, further stabilization measures might be necessary, e.g., smoothing of the portfolio weights. The results of empirical studies [11, 16, 17] suggest that the use of robust methods may improve portfolio performance. However, the significance of these results is difficult to evaluate because the performance is usually reported only for the whole observation period and, occasionally, also for two subperiods. There is no continuous assessment. Moreover, the observation periods are often very short (typically about ten years or less). In view of the vast amount of available financial data, it seems to be always possible to find certain assets and certain time periods which support or challenge a given hypothesis or model. To avoid this obvious danger of a data-snooping bias, the sole criterion for the selection of our data was the availability of a long history of daily prices at Yahoo!Finance. Both indices and individual stocks are used. No efforts are made to reduce the variance by searching for sets of most dissimilar assets or to increase the precision of estimates of model parameters such as the betas by replacing real assets by synthetic ones which are just collections of similar assets. Section 2 gives a short review of the basics of meanâ&#x20AC;&#x201C;variance portfolio optimization, which is based on the work of Markowitz [13, 14], and the capital asset pricing model (CAPM), which is based on the work of Sharpe [15] and Lintner [12]. In this section, it is also pointed out that some unrealistic assumptions are dispensable. Section 3 presents the empirical results. The focus is on the comparison of classical methods and robust methods. Also of particular interest is the in-sample relationship between the expected return of an asset and its covariance with the market portfolio. Section 4 concludes.

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Figure 1: Comparison of cumulative returns (a) and cumulative squared returns (b) of nine components of the DJIA with the cumulative average returns (a) and cumulative squared average returns (b) from 02-01-1962 to 31-05-2013. Data: AA (red), BA (pink), CAT (orange), DD (gold), DIS (brown), GE (green), HPQ (blue), IBM (gray), KO (black), Average (magenta)

2 Review of the Basics of Classical Finance 2.1 Portfolio Optimization Suppose we are given K assets with stochastic returns R1,...,RK. The return of a portfolio which is a mixture of these assets is determined by the portfolio weights w1,...,wK, i.e., K

Rw   wk Rk  ( w1,..., wK ) ( R1,..., RK )T  wT R

(1)

k 1

The mean and the variance of Rw are given by K

 w  E ( Rw )   wk E ( Rk )  ( w1,..., wK ) ( 1,...,  K )T  wT   k 1

(2)

k

and

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 w2  Var( Rw ) 

K

  11  12   22 T   21 w j wk Cov ( R j , Rk )  w        k 1   ij   K1  K 2

  1K     2K  w  w T w ,       KK 

K

 j 1

(3)

respectively. The method of Lagrange multipliers can be used to solve the Markowitz [13] problem of finding weights w1,...,wK that minimize the portfolio variance (or, equivalently, half the portfolio variance) for a desired expected return

wT   0

(4)

subject to the constraint K

 wk  wT 1  1 .

(5)

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k 1

Setting the partial derivatives of the Lagrange function

L( w, 1, 2 )  12 wT w  1( 0  wT  )  2 (1  wT 1)

Fi

to zero, we obtain

of

w  1  21  0 ,

ew

0  wT   0 , 1  wT 1  0 ,

Re

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which is a system of K+2 linear equations in the K+2 unknowns w1,...,wK,1,2. The first K equations yield

w  1 1  2 11

an

and the last two

A

 0  1  q  r  0         2  1  pq  r   r p  1 

N or

and

1

th

 1   p r        2   r q 

m

er ic

 0  wT    1 T  1  21T  1    T  1 1T  1  1   p r  1             T    T 1 T 1   T 1 T 1     r q    1  1  1  1    1 1 1 1   w      2    1 2  2     Thus,

q0  r  1   d   r  p  0  

 w2  wT w  (1 T 1  21T 1)  (11  211)   1

2 T

1

1 2T 1 1  121T  1  22 1T  11

( 1 T 1 2 T1 1 ) 1 T T  1 w   2 w 1

T 1 T 1  2(  1   2 1  )1

  10  2

) 0  d1 ( p r0 ) . d1 (q0  r Rewriting the equation

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2

d w2  q 20  2r0  p  q( 0  qr ) 2  p  rq  d /q

as

 w2 1 q

( 0  qr )2 d q2

 1,

(6)

na nc e

we see that it defines a hyperbola with center (0,r/q) and vertices (  1 / q , r / q) . A portfolio implying a point above the vertex on the right branch of the hyperbola is called an efficient frontier portfolio because no other portfolio with the same expected return can have a smaller variance (see Figure 1). The minimum variance portfolio is that efficient frontier portfolio with the smallest variance (see Figure 1). The tangency portfolio is that efficient frontier portfolio which minimizes the Sharpe [15] ratio

Fi

w  rf , w

(7)

N or

th

A

m

er ic

an

Re

vi

ew

of

where rf is the (deterministic) return of the (hypothetical) risk-free asset (see Figure 1). If short selling is not allowed, the nonnegativity constraints (8) w1, , wK  0 must be imposed. Under these constraints, portfolio optimization is more difficult and requires the use of numerical methods.

Figure 2: Markowitz hyperbola (6) in the  plane with efficient frontier (green line), tangency portfolio (green point), and minimum variance portfolio (blue point). The red line is the tangent to the hyperbola from the red point which has -coordinate 0 and -coordinate rf.

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2.2 The Capital Market Line We consider portfolios that are mixtures of a market-portfolio with stochastic return Rm and a risk-free asset with interest rate rf. The return of a portfolio with weights  and 1- is given by (9) R  Rm  (1   )rf and its mean and variance by

   E ( R  )  E ( Rm )  (1   )r f   m  (1   )r f

(10)

and

 2  2Var( Rm )  2 m2 ,

(11)

respectively. It follows from

   rf 

m  r f    g (  ) m

Fi

that

na nc e

 m

(12)

of



Re

2.3 The Capital Asset Pricing Model

vi

ew

The slope of the capital market line g is the Sharpe ratio of the market-portfolio and its intercept is the risk-free interest rate.

m

er ic

an

The derivation of the CAPM relies on the critical assumption that for any given risk  the highest possible expected return is g(). We consider portfolios that are mixtures of a risky asset with stochastic return Rk and a market portfolio with stochastic return Rm. The mean and the variance of the return R of a portfolio with weights  and 1- are given by   E ( Rk )  (1   ) E ( Rm )  m   ( k  m ) (13) and

A

 2  2Var( Rk )  2 (1   )Cov( Rk , Rm )  (1   )2Var( Rm )

N or

th

  2 k2   2 (1 )km  (1  ) 2 m2  2 ( k2  2 k m   m2 )  2 ( k m   m2 )   m2 .    Ak

(14)

Bk

The capital market line g intersects the function

 Bk  Bk2  Ak ( m2   2 ) Bk2 2   f1 ( )   m  ( k  m ) ,    m  Ak Ak    1 ( )

at the point ( m ,  m ) if Bk  0 and the function

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(15)


  f 2 ( )   m 

 Bk  Bk2  Ak ( m2   2 ) B2 (  k   m ) ,    m2  k A Ak  k  

(16)

2 ( )

if Bk  0 . The capital asset line g can only be a tangent to fj at the point (m,m) if the respective function is increasing. The function f1 is increasing if  k   m and f2 is increasing if  k   m (see Figure 3). Thus, the critical assumption of the optimality of

na nc e

the capital market line already implies a positive relationship between B k and  k   m , i.e., Bk  0   k   m  0 , Bk  0   k   m  0 or, equivalently,

 km  1  k  m  0 ,  k  1  k  m  0 .  m2 Equating the slopes of g and f1 or f2 at the point (m,m) shows that this relationship is

Fi

k 

of

linear. It follows from

2  2 Ak  j ( ) j  ( )  2 Bk  j  ( ) ,

vi

and

ew

 2  Ak 2j ( )  2Bk  j ( )   m2 ,

Re

2 m  2 Ak  j ( m ) j  ( m )  2Bk  j  ( m )  2( k m   m2 ) j  ( m )   

an

0

that

m

er ic

m  r f m ( k  m )  f j  ( m )   j  ( m )( k  m )  m  k m   m2  km   m2 ( m  r f )  k  m .  m2

A

and

th

(  k  1)( m  r f ) 

N or

The CAPM is obtained by rewriting the last equation as  k ( m  r f )  k  r f .

(17)

2.4 The "Broken" CAPM Modifications of the CAPM which avoid the unrealistic assumption of borrowing at the risk-free rate have already been proposed in the early 1970s [3]. In contrast, Subsection 2.3 has implicitly assumed that borrowing at the risk-free rate is possible and shorting does not entail additional costs. Both assumptions can be avoided by using only proper weights, i.e., 0    1 . If   1 , the CAPM can still be obtained by equating the slope of g to the derivative of f2 from the left (see Figure 3.c). If   1 , the derivative of f1 from the right must be used and the borrowing rate rb must be used instead of the risk-free rate rf in the definition of the capital market line (see Figure 3.a). Of course, the concept

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of a broken capital market line with different rates for lending and borrowing does not automatically compromise its optimality property because the expected returns must in the case of negative weights also be adjusted when the costs of shorting are taken into account. In practice, the "broken" CAPM

 k  r f   k ( m  r f ) if  k  1  k  rb   k ( m  rb ) if  k  1

k  

(18)

N or

th

A

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an

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vi

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of

Fi

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will not make a big difference because the discrepancy between rb and rf is usually small compared to the size of m.

Figure 3: (a) The capital asset line g is a tangent to f1 at (m,m) if Bk  0 and  k   m . (b) The capital asset line g cannot be a tangent to f1  f 2 at (m,m) if Bk  0 . (c) The capital asset line g is a tangent to f2 if Bk  0 and  k   m .

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3 Empirical Results

na nc e

Two sets of assets are used. The first set consists of those nine components of the Dow Jones Industrial Average the prices of which are available at Yahoo!Finance since January 2, 1962. The selected components are Alcoa (AA), Boeing (BA), Caterpillar (CAT), Du Pont (DD), Walt Disney (DIS), General Electric (GE), Hewlett-Packard (HPQ), IBM (IBM), and Coca-Cola (KO). The second set consists of nine major US indices the prices of which are available at Yahoo!Finance since June 4, 1996. The selected indices are Nasdaq Bank (^IXBK), Nasdaq Biotechnology (^NBI), Nasdaq Insurance (^IXIS), Nasdaq Telecommunications (^IXUT), Nasdaq Transportation (^IXTR), AMEX Gold Bugs (^HUI), AMEX Oil (^XOI), AMEX Pharmaceutical (^DRG), and PHLX Semiconductor (^SOX). For both sets, the sample period ends on May 31, 2013.

3.1 Empirical Evidence on the CAPM

s 1

=

 Rk ( s )Ra ( s )  Ra2 ( s )

s 1

Fi

t

t

 Bˆ k ( s )

of

Figure 4.a shows a plot of

N or

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A

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an

Re

vi

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against time t  1,..., n , where Rk(s) is the return of the kth stock at time s and Ra(s) is the return of the equally weighted portfolio at time s. The average of the K=9 DJIA components is used instead of a broad market index in order to avoid a survival bias. This will not be necessary when the set of indices is analyzed. In the latter case, it makes more sense to use the S&P 500 as a proxy for the market. Overall, there seems to be no obvious relationship between the return Rk (Figure 1.a) and the parameter Bk (Figure 4.a). However, using the sign of Bˆ k ( s ) to switch between Rk(s) and Ra(s) is an apparently successful strategy. For each k, the switching strategy outperforms both the average (Figure 4.b) and the respective stock (Figure 4.c). Additional strong evidence in favor of such a relationship is obtained when all stocks are used simultaneously. The strategy which always switches to the stock with the kth largest value has just the kth best performance (Figure 6.a). Because of the relative stability of Bˆ k , it might be expected that past values are also related to present and future returns. Figure 5 and Figures 6.b-c show that this is definitely not the case. The out-of-sample performance of switching strategies based on sums of past returns is extremely poor. The explanation for this apparent paradox is purely statistical. Suppose that Rk and Ra are positively correlated random variables with practically identical means but different variances. If positive returns occur more frequently than negative returns, the conditional means of Rk and Ra given RkRa<0 will be smaller than the unconditional means and probably be negative. It is then safer to choose the asset with the smaller variance. Figure 7 shows that the conditional mean of Rk given RkRa<0 is indeed negative for each k. Clearly, this relationship holds only for a fixed pair of random variables and is therefore of no use for the prediction of subsequent returns. Because of its technical nature it has absolutely no economic relevance and must be interpreted with great caution.

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However, the use of the more robust statistics:

 Bk (t )  Rk (t ) signRk (t )Ra (t )  Ra (t )

or

~ Bk (t )  Rk (t )  Ra (t ) instead of Bˆ k (t ) brings a spark of hope. Overall, strategies which invest in stocks with

N or

th

A

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er ic

an

Re

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of

Fi

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larger estimates appear to outperform the equally weighted portfolio out-of-sample (Figure 8). However, the evidence is not very strong and is practically non-existent in extended subperiods. Moreover, an analogous analysis of the second data set yields a disappointing result (Figure 14). In general, the evidence obtained from the indices is less conclusive (Figures 9-14) than that obtained from the stocks (Figures 1, 4-8). This may be due to the smaller sample size as well as to the presence of indices with divergent behavior (Figure 9.a). A further important difference is that the S&P500 is used as a proxy for the market instead of the average of the indices.

Figure 4: In-sample dependence of Rk on Bˆ k (a) Cumulative sums of Bˆ k (b) Performance of switching between Rk and Ra based on the sign of Bˆ k (c) Performance of switching between Rk and Ra relative to Rk Data: AA (red), BA (pink), CAT (orange), DD (gold), DIS (brown), GE (green), HPQ (blue), IBM (gray), KO (black), Average (magenta)

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na nc e Fi of ew vi Re an er ic m A th

N or

Figure 5: Out-of-sample performance relative to that of average (equally weighted portfolio) (a) Switching between Rk and Ra based on sign of Bˆ k (t  1)

(b) Switching between Rk and Ra based on sign of Bˆ k (t  5)  ...  Bˆ k (t  1)

(c) Switching between Rk and Ra based on sign of Bˆ k (t  250)  ...  Bˆ k (t  1) Data: AA (red), BA (pink), CAT (orange), DD (gold), DIS (brown), GE (green), HPQ (blue), IBM (gray), KO (black)

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na nc e Fi of ew vi Re an er ic m A th

N or

Figure 6: In-sample (a) and out-of-sample (b-c) performance relative to that of average (a) Switching to Rk if Bˆ k is largest (darkgreen), 2nd largest (green), 3rd (lightgreen), 4th (yellowgreen), 5th (yellow), 6th (orange), 7th (pink), 8th (red), 9th (darkred) ... (b) Switching to Rk if Bˆ k (t  1) is largest (darkgreen), ... (c) Switching to Rk if

Bˆ k (t  5)  ...  Bˆ k (t  1) is largest (darkgreen),…

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na nc e Fi of ew vi Re an er ic m A th N or

Figure 7: Conditional mean of Rk given that Rk Ra  0 (red), Rk Ra  0  Rk  Ra (green), Rk Ra  0  Rk  Ra (lightblue), conditional mean of Ra given that

Rk Ra  0 (orange), Rk Ra  0  Rk  Ra (yellowgreen), Rk Ra  0  Rk  Ra (purple) Data: AA (a), BA (b), CAT (c), DD (d), DIS (e), GE (f), HPQ (g), IBM (h), KO (i)

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na nc e Fi of ew vi Re an er ic m

N or

th

A

Figure 8: Relative out-of-sample performance of robust switching between DJIA   components: (a) Switching to Rk if Bk (t  5)  ...  Bk (t  1) is largest (darkgreen), 2nd largest (green), 3rd (lightgreen), 4th (yellowgreen), 5th (yellow), 6th (orange), 7th   (pink), 8th (red), 9th (darkred) (b) Switching to Rk if Bk (t  250)  ...  Bk (t  1) is

~

~

largest (darkgreen), ... (c) Switching to Rk if Bk (t  5)  ...  Bk (t  1) is largest

~

~

(darkgreen), ... (d) Switching to Rk if Bk (t  250)  ...  Bk (t  1) is largest (darkgreen), ...

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na nc e Fi of ew vi Re an er ic m A th N or Figure 9: Comparison of cumulative returns (a) and cumulative squared returns (b) of nine major US indices with the cumulative S&P500 returns (a) and cumulative squared S&P500 returns (b) from 04-06-1996 to 31-05-2013. Data: ^IXBK (red), ^NBI (pink), ^IXIS (orange), ^IXUT (gold), ^IXTR (brown), ^HUI (green), ^XOI (blue), ^DRG (gray), ^SOX (black), S&P500 (magenta)

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na nc e Fi of ew vi Re an er ic m A th N or

Figure 10: In-sample dependence of Rk on Bˆ k (a) Cumulative sums of Bˆ k

(b) Performance of switching between Rk and Rm based on the sign of Bˆ k (c) Performance of switching between Rk and Rm relative to Rk Data: ^IXBK (red), ^NBI (pink), ^IXIS (orange), ^IXUT (gold), ^IXTR (brown), ^HUI (green), ^XOI (blue), ^DRG (gray), ^SOX (black), S&P500 (magenta)

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na nc e Fi of ew vi Re an er ic m A th N or

Figure 11: Out-of-sample performance relative to that of S&P500 (a) Switching between Rk and Rm based on sign of Bˆ k (t  1)

(b) Switching between Rk and Rm based on sign of Bˆ k (t  5)  ...  Bˆ k (t  1) (c) Switching between Rk and Rm based on sign of Bˆ k (t  250)  ...  Bˆ k (t  1) Data: ^IXBK (red), ^NBI (pink), ^IXIS (orange), ^IXUT (gold), ^IXTR (brown), ^HUI (green), ^XOI (blue), ^DRG (gray), ^SOX (black)

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na nc e Fi of ew vi Re an er ic m A th N or

Figure 12: In-sample (a) and out-of-sample (b-c) performance relative to that of S&P500 (a) Switching to Rk if Bˆ k is largest (darkgreen), second largest (green), 3rd (lightgreen), 4th (yellowgreen), 5th (yellow), 6th (orange), 7th (pink), 8th (red), 9th (darkred) (b) Switching to Rk if Bˆ k (t  1) is largest (darkgreen), ... (c) Switching to Rk if

Bˆ k (t  5)  ...  Bˆ k (t  1) is largest (darkgreen), ...

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na nc e Fi of ew vi Re an er ic m A th

N or

Figure 13: Conditional mean of Rk given that Rk Ra  0 (red), Rk Ra  0  Rk  Ra (green), Rk Ra  0  Rk  Ra (lightblue), conditional mean of Ra given that

Rk Ra  0 (orange), Rk Ra  0  Rk  Ra (yellowgreen), Rk Ra  0  Rk  Ra (purple) Data: ^IXBK (a), ^NBI (b), ^IXIS (c), ^IXUT (d), ^IXTR (e), ^HUI (f), ^XOI (g), ^DRG (h), ^SOX (i)

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na nc e Fi of ew vi Re an er ic

A

m

Figure 14: Relative out-of-sample performance of robust switching between US indices   (a) Switching to Rk if Bk (t  5)  ...  Bk (t  1) is largest (darkgreen), 2nd largest (green), 3rd (lightgreen), 4th (yellowgreen), 5th (yellow), 6th (orange), 7th (pink), 8th   (red), 9th (darkred) (b) Switching to Rk if Bk (t  250)  ...  Bk (t  1) is largest

~

~

th

(darkgreen), ... (c) Switching to Rk if Bk (t  5)  ...  Bk (t  1) is largest

~

~

N or

(darkgreen), ... (d) Switching to Rk if Bk (t  250)  ...  Bk (t  1) is largest (darkgreen), ...

3.2 Empirical Evidence on the Performance of Portfolio Optimization Procedures Because of the failure of the CAPM to provide suitable forecasts of future returns, simple historical means are used instead. In a rolling analysis, the returns of the last 200 trading days are used as input for the R/Rmetrics "fPortfolio" package [18] to find the optimal portfolio weights (long only) for the next trading day. The risk-free rate is either set to zero (rf=0) or obtained from the 13-week treasury bill rate (rf=r13). Figure 15.a shows the relative performance of the minimum variance portfolio as well as the tangency portfolios with risk-free rates rf=0 and rf=r13, respectively. Only the latter tangency

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N or

th

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portfolio can outperform the equally weighted portfolio over an extended period of time. However, its miserable performance in the last decades wrecks all hopes. In another try to corroborate the theoretical results, the portfolio variance is minimized for different return targets (first, second and third quartile of historical 200-day means). Contrary to expectations, the lowest target return yields the highest return and the highest target return yields the lowest return (Figure 15.b). Finally, in a last attempt, the portfolio-optimization procedure is robustified by using alternative covariance estimators. Unfortunately, the results do not get any better. They are still the wrong way round (Figure 15.c). The fact that the observed performance differences are possibly not even significant is only small comfort. Similarly, there is also no indication that the performance depends on the specification of the target return in the case of the second data set (Figures 16.b-c).

Figure 15: Relative out-of-sample performance of optimized portfolios of DJIA components (a) Minimum variance portfolio (red), tangency portfolios with rf=0 (blue) and rf=r13 (green) (b) Minimum variance for given low (red), medium (blue) and high (green) target return (c) Minimum variance for given low (red), medium (blue) and high (green) target return based on Spearman's rank estimator

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Figure 16: Relative out-of-sample performance of optimized portfolios of major US indices (a) Minimum variance portfolio (red), tangency portfolios with rf=0 (blue) and rf=r13 (green) (b) Minimum variance for given low (red), medium (blue) and high (green) target return (c) Minimum variance for given low (red), medium (blue) and high (green) target return based on Spearman's rank estimator

th

4 Conclusion

N or

Meanâ&#x20AC;&#x201C;variance portfolio optimization and the CAPM are the pillars of classical finance. Both focus on the first and second moments of the returns of financial assets. Despite the usually large sample sizes in financial applications, it is practically impossible to obtain precise estimates of these quantities because they change over time. Naturally, the non-normality of the returns seriously complicates the estimation of the variances and covariances. In the case of the means, it is their smallness (compared to the size of the variances) that makes the estimation so difficult. While the former problem can possibly be overcome by using robust estimation methods, additional information is required for the latter one. Thus, the validity of the CAPM which claims that there is a linear relationship between the expected return of an asset and its covariance with the market portfolio is not only important for its own sake but is also of vital importance for the practical implementation of portfolio-optimization procedures. On the one hand, the discussion in 2.4 shows that some unrealistic assumptions usually required for the derivation of the CAPM can be relaxed and, on the other hand, it is argued in 3.1 that a relationship of the CAPM-type can as well be explained by statistical

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effects alone. The empirical results obtained from two sets of assets consisting of individual stocks and indices, respectively, suggest that the CAPM is either wrong or of no practical value (not even when robust methods are used and transaction costs are disregarded), and, in addition, that portfolio optimization is of little use for managing the trade-off between risk and return. Only the trivial task of reducing the risk appears to be doable. Of course, nicer results could easily be obtained by fiddling around with different assets, time periods, estimation methods, parameters (such as risk-free rates and return targets) and - most conveniently - sampling frequencies (anything can be "proven" with monthly data). However, the evidence obtained in this way would not be of any significance.

[6] [7]

[10]

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[16] T. Tsagaris, A. Jasra and N. Adams, Robust and adaptive algorithms for online portfolio selection, Quantitative Finance, 12, (2012), 1651-1662. [17] R.E. Welsch and X. Zhou, Application of robust statistics to asset allocation models, REVSTAT – Statistical Journal, 5, (2007), 97–114. [18] D. Würtz, Y. Chalabi, W. Chen and A. Ellis, Portfolio Optimization with R/Rmetrics, Rmetrics eBook, Rmetrics Association and Finance Online, Zurich, 2009.

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