NARF 2013 1.0. by Editor NAAJ

North American Review of Finance Volume 13 (1)

North American Review of Finance Volume 12, Number 4

North American Review of Finance Volume 13, Number 1

Articles Testing the Profitability of a Volume-Augmented Momentum Strategy in the Philippines Equity Market Lim Kai Jie Shawn, Darius Lim Dawei, Mak Weijie, Poh Zi En Benjamin………………………………………………………………….…….……..….…… 1 - 12 Portfolio Theory Forward Testing Marcus Davidsson …................................................................................13 –33 Return and Risk-Return Ratio Based Momentum Strategies: A Fresh Perspective Chia Rui Ming Daryl, Lim Kai Jie Shawn and Chan Ho Yan Sabrina…………………………………………………………………….…….……….…… 34 - 46 Currency Exposure, Second-Moment Exchange Rate Exposure and Asymmetric Volatility of Stock Returns: The Effects of Financial Crises on Taiwanese Firms René Ferenc (Franck) Varga……………………………………………………..…... 47 –69

Testing the Profitability of a Volume-Augmented Momentum Strategy in the Philippines Equity Market Lim Kai Jie Shawn1, Darius Lim Dawei2, Mak Weijie3, Poh Zi En Benjamin4

Abstract

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This study contributes new empirical evidence on the profitability of a momentum strategy in the Philippines equity market. The study was conducted over the time period January 2000 to June 2012. We evaluated a momentum strategy based only on past return information as well as a strategy that incorporates information on volume for 16 different time combinations with varying formation and holding periods. For the strategy based only on past return information, we find little evidence in support of the profitability of a momentum strategy with the results suggesting the presence of mean-reverting prices. When volume information is incorporated, the strategies that select stocks based on volume and return information from the past 3 months show positive average monthly returns. However, after adjusting for the risk of these strategies using a single factor model and a model with market-dependent betas we find that such a strategy does not outperform the benchmark. Hence, we conclude that there is little evidence to support the profitability of a volume-augmented momentum strategy in the Philippines equity market.

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JEL classification numbers: C15, G01, G11, G17 Keywords: Momentum, Philippines Equity Market, Volume-Augmented Strategies, Trading Strategies, Market Efficiency

Department of Economics, University College London. e-mail: kai.lim.11@ucl.ac.uk 2 Department of Economics, Univeristy of Nottingham. e-mail: leyddl@nottingham.ac.uk 3 Department of Economics, University of Nottingham. e-mail: leywm@nottingham.ac.uk 4 Department of Economics, College Universitaire, Sciences Po Paris Article Info: Received : October 2, 2012. Revised : October 30, 2012. Published online : January 15, 2013

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1 Introduction

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The ability of momentum strategies to continue to remain profitable in equity markets is an issue that has confounded academics for an extended period of time. Early writers such as DeBondt & Thaler [1] attributed the persistence of profitable medium term momentum strategies to the tendency for markets to overreact in the short term and since then a range of other behavioral explanations have been suggested [2]. The ability and continued persistence of price continuation in financial time series has also led to its inclusion as a factor in some asset pricing models, such as that in [3], which lends weight to its importance as a potential explanatory variable of stock market returns. Jegadeesh and Titman [4 and 5] proved in 2 separate papers the presence of momentum in the time series of US stock markets using a zero-cost arbitrage strategy of buying past winners and selling past losers and since then their methodology has become the standard approach adopted in tests on the profitability of momentum strategies. In line with the approach of present literature we employ an adaptation of that methodology in this paper. The profitability of momentum strategies has also been documented internationally in a number of markets. Rouwenhorst conducted studies on emerging market stocks and the European equity markets and found evidence for the profitability of a momentum strategy, [6]. Similar results have been reported in the Asian markets by Chui, Titman and Wei [7], in the Australian market by Aharoni, Ho and Zheng [8] and a wide range of countries around the world by Hu and Chen [9]. Beyond the profitability of a pure momentum strategy, a range of other papers have explored the ability to improve the profitability of a momentum strategy using other sources of information. Studies ranking stocks in the formation period using a reward-risk stock selection criterion, found that they result in portfolios with a lower total return but a superior risk-adjusted performance,[10, 11]. Lee and Swaminathan incorporate the use of volume information in the portfolio formation step and find that it can be useful in improving the performance of a momentum strategy, [12]. They argue that volume can serves as a proxy for investor misperception of future earnings. The importance of volume in predicting the direction and likely persistence of a trend is also a key concept within the field of technical analysis (Edwards, Maggee & Bassetti [13] ). Since then, a range of papers have tested the ability of a volume-augmented momentum strategy to deliver superior returns. Hameed & Kusnadi test the strategy for 6 Asian markets, Glaser & Weber test the strategy for the German market and Agyei-Ampomah tests the strategy for the UK market, (see [14], [15] and [16]). The results from these tests are mixed, with limited evidence found in the 6 countries that were tested in the Asian markets but significant evidence in the German and UK markets. This suggests that the profitability of a strategy enhanced with volume information is likely to be highly dependent on the market in which it is implemented. We believe that this paper contributes to the existing literature on momentum studies by extending them in 2 different ways. Firstly, while momentum is a subject that has been debated in the academic community for a substantial period of time, most of that research work has been focused on the developed markets with limited research in some regions such as South East Asia. In this paper we test the profitability of trading strategies in the Philippines equity market that, to the best of our knowledge, has not been tested over a recent time period in any paper for both a pure momentum strategy and a volume-augmented momentum strategy. This paper thus adds to present studies by presenting new empirical results for the Philippines equity market. We conduct this study

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over a fairly recent time period that spans January 2000 to June 2012. Next, we extend the basic methodology from Jegadeesh and Titman [4, 5] by studying the impact of including volume as an additional ranking factor on the profitability of a momentum strategy in line with the approach detailed in Lee & Swaminathan [12]. This inclusion of an alternative source of information in the form of volume allows us to provide additional insights into the factors that may influence the profitability and persistence of momentum strategies in the Philippines equity market. The rest of the paper is arranged into 3 areas. Section 2 describes the data we employ in this test and outlines the methodology used for this paper. Section 3 presents the results from our study and discusses their implications on the profitability of momentum strategies. Finally, section 4 presents an overview of our findings and concludes the paper.

2 Data and Research Methodology

2.1 Data

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We use the daily stock price data for the components of the Philippines All-Share Index over the period of January 2000 to June 2012. The data was extracted from Bloomberg and was adjusted for non-trading days and to incorporate the impact of dividends on returns. In order to achieve a sample consisting only of stocks that are sufficiently liquid, stocks with an average price of less than $1.00 were removed from the sample. The return for each period was calculated using the following equation:

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where : Return of a stock for period t, where t represents quarters : Stock price at the end of the period : Stock price at the start of the period

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We define volume as the average daily turnover in percentage terms during the portfolio formation period, where daily turnover is the ratio of the number of shares traded each day to the number of shares outstanding at the end of the day. To calculate this figure, the number of shares traded each day was also collected for each stock along with the number of shares outstanding. The volume was then calculated on a quarterly basis and normalized by dividing the number of shares traded in each quarter by the average number of shares outstanding over that quarter. Where there were missing data points for the number of shares traded, we calculated the average normalized daily volume for each stock and converted it to a figure for that period. Although this process of averaging may result in the loss of some data accuracy in the actual volume for each quarter, we believe that the impact of this loss in precision on our conclusions is not significant as we utilize the normalized volume primarily for ordinal rankings to aid the construction of portfolios which is likely to be preserved during the averaging process. The normalized volume is calculated using the following equation:

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2.2 Testing the Profitability of a Momentum Strategy

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where : Normalized volume for period t : Number of trading days in period t : Number of days with volume data in period t : Number of shares outstanding on day i : Volume traded on day i, where i = 1, â&#x20AC;Ś, . For days where volume data was not available, =0

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In order to examine the profitability of a momentum strategy, we employ the approach described in Jagadeesh and Titman, [4, 5]. First, we sort all the stocks with data for the entire formation (J) and subsequent holding (K) period based on their return over the past J time periods, where J = 3, 6, 9, 12. We then construct winner (W) and loser (L) portfolios which are held for a subsequent K periods, where K = 3, 6, 9, 12. This yields a total of 16 portfolio combinations based on different combinations of formation and holding periods. The W portfolios are constructed by selecting the top 10% of securities by return in the formation period and holding these securities for the holding period. The L portfolios are constructed by selecting the bottom 10% of securities by return in the formation period and holding these securities for the holding period. The portfolios are then formed on an equally weighted basis for the both the W and L portfolio. In order to avoid some of the bid-ask spread, price pressure and lagged reaction effects we skip a month between the end of the portfolio formation period and the start of the portfolio holding period. In accordance with Jagadeesh and Titman [4, 5], we construct the portfolios on an overlapping holding period basis and employ a series of portfolios that are rebalanced monthly to maintain equal weights instead of a series of buy and hold portfolios. What this means is that at any one point in time, the portfolio will consist of securities selected based on k different formation periods and at the end of each month the trading strategy of the portfolio and carry forward the rest from the will revise the weights of previous month. For example, a strategy with J = 3 and K = 3 that starts in January, i.e. a strategy that selects portfolios based on returns in the past 3 months and holds the portfolio for 3months after, will have a third of the portfolio calculated based on the ranking in December, a third of the portfolio calculated based on the ranking in November and a third of the portfolio calculated based on the ranking in October. Thus, for this strategy, a third of the stocks will change each month, with the remainder carried forward from the last month. We calculate the annualized return from this strategy for 3 portfolios, the W portfolio, the L portfolio and a zero-cost â&#x20AC;&#x153;Winner minus Loserâ&#x20AC;? (W-L) portfolio. The W-L portfolio represents a portfolio in which the L portfolio is sold short and the proceeds are used to purchase the W portfolio. The return from these 3 strategies for all 16 possible portfolio combinations are reported in Table 1 along with the associated t-statistics.

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2.3 Testing the Profitability of a Volume-Augmented Momentum Strategy

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Having evaluated the results of a momentum strategy based on price, we proceed to investigate whether incorporating volume information can enhance the returns of a pure momentum strategy. We adapt the approach set out by Lee and Swaminthan [12] for this section of the study. We obtain W and L portfolios in a similar manner to section 3.2, but for each W and L portfolio we further divide the stocks into 3 volume portfolios (V1, V2, V3) by sorting the firms into 3 categories according to their volume over the period, with V1 representing the lowest trading volume portfolio and V3 representing the highest trading volume portfolio. These portfolios are calculated for the same 16 possible time combinations as in section 2.2. The results from these tests are reported in tables 2, 3 and 4.

2.4 Calculating Risk-Adjusted Returns

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To evaluate how robust our results are, we conduct further analysis for a representative strategy that selects portfolios for both a pure and volume-augmented momentum strategy using a 6 month formation period and a subsequent 6 month holding period, in line with the common reference periods used in momentum studies. First, we calculate risk-adjusted excess returns using the Sharpe-Linter Capital Asset Pricing Model.The excess monthly returns of L, W and L-W portfolios over the risk-free rate are regressed against the excess returns of the market portfolio (all the stocks included in the ranking) over the risk free rate using the following equation:

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The results from this regression are presented in table 5 and table 6. Finally, we calculate market risk-adjusted returns to allow for market-dependent betas. This is done to decompose the returns to a momentum strategy for periods where the market as a whole is trending upwards and for periods where the market as a whole is trending downwards. We conduct this analysis by regressing the monthly returns of L, W and L-W in excess of the risk-free rate against all the market return using the following equation:

where : Return of the strategy for at time t : Risk-free rate at time t : Return of the market at time t, where the market includes all stocks that had sufficient data for inclusion in the ranking process : Dummy variable that takes a value of one if the market return is positive in month t and a value of zero if the market return is negative in month t.

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The results from this regression are presented in table 7 and table 8.

3 Main Results 3.1 Profitability of a Momentum Strategy

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Formation 3

Table 1: Portfolio Rankings Based on Price Panel A Holding Period Portfolio 3 6 9 12 Winner 1.0036 1.0027 0.9993 0.9947 Loser 1.0071 1.0008 0.9969 0.9954 Winner â&#x20AC;&#x201C;Loser -0.0036 0.0019 0.0024 -0.0006 (t-stat) (-0.5035) (0.2880) (0.4228) (-0.1223) Loser - Winner 0.0036 -0.0019 -0.0024 0.0006 (t-stat) (0.5035) (-0.2880) (-0.4228) (0.1223) Winner 1.0104 1.0072 1.0030 1.0007 Loser 1.0202 1.0131 1.0116 1.0087 Winner -Loser -0.0098 -0.0059 -0.0086 -0.0080 (t-stat) (-0.9526) (-0.6390) (-1.0835) (-1.1531) Loser - Winner 0.0098 0.0059 0.0086 0.0080 (t-stat) (0.9526) (0.6390) (1.0835) (1.1531) Winner 1.0095 1.0054 1.0046 1.0057 Loser 1.0210 1.0168 1.0154 1.0142 Winner -Loser -0.0115 -0.0114 -0.0109 -0.0085 (t-stat) (-1.0579) (-1.1400) (-1.1945) (-1.0852) Loser - Winner 0.0115 0.0114 0.0109 0.0085 (t-stat) (1.0579) (1.1400) (1.1945) (1.0852) Winner 1.0053 1.0036 1.0059 1.0059 Loser 1.0293 1.0254 1.0225 1.0213 Winner -Loser -0.0240 -0.0218 -0.0166 -0.0154 (t-stat) (-1.9589) (-2.0221) (-1.8180) (-1.8439) Loser - Winner 0.0240 0.0218 0.0166 0.0154 (t-stat) (1.9589)* (2.0221)* (1.8180)* (1.8439)* *95% Confidence level, **99% Confidence level

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Table 1 shows the results from the simulated portfolios based on a normal momentum strategy that buys past winners and sells past losers. From the results, we see that the strategy was largely not profitable with most of the different combinations of formation and holding periods for the zero-cost W-L portfolio resulting in a negative average monthly return. A few combinations exhibit a weakly positive return, but these results did not prove to be statistically significant when the t-test was applied. In addition, many of the other combinations with a negative average return did not prove to be statistically significant, with only all the combinations based on a 12 month formation period showing negative and statistically significant results. The negative average return for our zero-cost strategy suggests that a contrarian strategy, which would involve purchasing the loser and selling the winner would have been profitable for this particular market. This is consistent with mean-reverting prices and suggests that a momentum strategy would not have been profitable for the Philippines Equity Market.

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3.2 Profitability of a Volume-Augmented Momentum Strategy Table 2: Portfolio Rankings Based on Volume (Top third for Volume, W1, L1)

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Portfolio Winner Loser Winner –Loser (t-stat) Loser – Winner (t-stat) Winner Loser Winner –Loser (t-stat) Loser – Winner (t-stat) Winner Loser Winner –Loser (t-stat) Loser – Winner (t-stat) Winner Loser Winner –Loser (t-stat) Loser – Winner (t-stat)

Ranking Period 3

Panel A Holding Period 3 6 9 12 1.0042 0.9953 0.9896 0.9818 0.9980 0.9855 0.9787 0.9788 0.0062 0.0098 0.0109 0.0029 (0.5554) (1.1061) (1.4860) (0.4478) -0.0062 -0.0098 -0.0109 -0.0029 (-0.5554) (-1.1061) (-1.4860) (-0.4478) 1.0000 0.9960 0.9914 0.9873 1.0114 1.0037 1.0005 0.9975 -0.0114 -0.0076 -0.0091 -0.0102 (-1.0041) (-0.7448) (-1.0656) (-1.3105) 0.0114 0.0076 0.0091 0.0102 (1.0041) (0.7448) (1.0656) (1.3105) 1.0077 1.0054 1.0057 1.0066 1.0138 1.0049 1.0039 1.0019 -0.0061 0.0005 0.0018 0.0046 (-0.4844) (0.0508) (0.1900) (0.5389) 0.0061 -0.0005 -0.0018 -0.0046 (0.4844) (-0.0508) (-0.1900) (-0.5389) 1.0036 1.0047 1.0096 1.0071 1.0182 1.0162 1.0150 1.0139 -0.0146 -0.0115 -0.0053 -0.0068 (-1.2153) (-1.1549) (-0.5829) (-0.7635) 0.0146 0.0115 0.0053 0.0068 (1.2153) (1.1549) (0.5829) (0.7635) *95% Confidence level, **99% Confidence level

Ranking 3

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Table 3: Portfolio Rankings Based on Volume (Middle third for Volume, W2, L2)

Portfolio Winner Loser Winner -Loser (t-stat) Loser- Winner (t-stat) Winner Loser Winner -Loser (t-stat) Loser – Winner (t-stat)

3 0.9975 1.0064 -0.0088 (-0.9991) 0.0088 (0.9991) 1.0053 1.0221 -0.0168 (-1.2434) 0.0168 (1.2434)

Panel A Holding Period 6 9 0.9991 0.9941 1.0051 1.0048 -0.0060 -0.0106 (-0.7911) (-1.4356) 0.0060 0.0106 (0.7911) (1.4356) 1.0077 1.0074 1.0161 1.0124 -0.0083 -0.0050 (-0.7590) (-0.5454) 0.0083 0.0050 (0.7590) (0.5454)

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12 0.9910 1.0006 -0.0097 (-1.5236) 0.0097 (1.5236) 1.0072 1.0098 -0.0026 (-0.3455) 0.0026 (0.3455)

Winner Loser Winner -Loser (t-stat) Loser-Winner (t-stat) Winner Loser Winner -Loser (t-stat) Loser-Winner (t-stat)

1.0093 1.0077 1.0082 1.0149 1.0147 1.0152 -0.0056 -0.0069 -0.0070 (-0.5171) (-0.7250) (-0.9549) 0.0056 0.0069 0.0070 (0.5171) (0.7250) (0.9549) 1.0024 1.0039 1.0078 1.0251 1.0250 1.0246 -0.0277 -0.0211 -0.0168 (-1.9336) (-2.1772) (-1.9341) 0.0277 0.0211 0.0168 (1.9336)* (2.1772)* (1.9341)* *95% Confidence level, **99% Confidence level

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1.0102 1.0179 -0.0077 (-0.6330) 0.0077 (0.6330) 1.0045 1.0307 -0.0263 (-1.9183) 0.0263 (1.9183)*

Table 4: Portfolio Rankings Based on Volume (Bottom third for Volume, W3, L3)

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3 1.0122 1.0154 -0.0032 (-0.2314) 0.0032 (0.2314) 1.0235 1.0275 -0.0040 (-0.2451) 0.0040 (0.2451) 1.0095 1.0306 -0.0212 (-1.3431) 0.0212 (1.3431) 1.0078 1.0377 -0.0299 (-1.6084) 0.0299 (1.6084)

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Portfolio Winner Loser Winner -Loser (t-stat) Loser – Winner (t-stat) Winner Loser Winner -Loser (t-stat) Loser – Winner (t-stat) Winner Loser Winner -Loser (t-stat) Loser – Winner (t-stat) Winner Loser Winner -Loser (t-stat) Loser – Winner (t-stat)

Ranking 3

Panel A Holding Period 6 9 12 1.0139 1.0140 1.0114 1.0097 1.0051 1.0065 0.0042 0.0089 0.0049 (-0.3620) (0.9998) (0.5680) -0.0042 -0.0089 -0.0049 (0.3620) (-0.9998) (-0.5680) 1.0161 1.0081 1.0064 1.0196 1.0219 1.0196 -0.0034 -0.0138 -0.0132 (-0.2548) (-1.1239) (-1.1436) 0.0034 0.0138 0.0132 (0.2548) (1.1239) (1.1436) 1.0036 1.0030 1.0040 1.0306 1.0274 1.0250 -0.0270 -0.0244 -0.0209 (-1.8166) (-1.8275) (-1.7105) 0.0270 0.0244 0.0209 (1.8166)* (1.8274)* (1.7105)* 1.0041 1.0045 1.0022 1.0340 1.0259 1.0234 -0.0299 -0.0215 -0.0212 (-1.7748) (-1.4332) (-1.5979) 0.0299 0.0215 0.0212 (1.7748)* (1.4332) (1.5979) *95% Confidence level, **99% Confidence level

When the strategy is augmented through the use of volume information (Tables 2,3,4), we see that W-L portfolios based on 3 month formation periods exhibit positive returns for

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the highest volume (V1) and lowest volume (V3) combinations. The remaining time combinations show a negative average monthly return, consistent with the results from the normal momentum strategy. This suggests that the inclusion of volume information has some value in augmenting the performance of a momentum strategy, particularly for portfolios formed based on recent information. However, it should also be noted that transaction costs have not been incorporated in the evaluation of returns and the performance of these volume-augmented momentum strategies are likely to be greatly diminished once that has been explicitly modeled.

3.3 Analysis of Risk-Adjusted Returns

t(α)

t(β)

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Table 5: Risk-Adjusted Returns (Normal) α

Portfolio

P(α)

-0.0062

-0.7119

0.8938

8.9540

Winner

-0.0120

-2.5497

0.8888

16.4328

Winner - Loser

-0.0100

-1.0549

-0.0046

-0.0420

Loser - Winner

0.0016

0.1747

0.0055

0.0508

0.4779

<0.0001

0.4025

0.0121

<0.0001

0.6941

0.2936

0.9666

<0.0001

0.8616

0.9596

<0.0001

Loser

P(β)

–

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– – – – – – – –

t(β)

0.7424 0.8286 0.0867 1.0342 0.9657 -0.0680 0.8781 0.8410 -0.0366 -0.2052 -0.0490 0.2238 0.0881 0.0991 -0.1928 0.0500

7.7494 10.9075 0.7171 9.3663 14.1083 -0.5267 6.0067 10.0069 -0.2298 -1.5836 -0.2900 2.0690 0.5726 0.8356 -1.4463 0.2961

-0.0130 -0.0221 -0.0133 -0.0056 -0.0128 -0.0113 0.0005 -0.0023 -0.0070 -0.0207 -0.0268 -0.0039 -0.0175 0.0066 -0.0008 0.0185

t(α) -1.5671 -3.3561 -1.2632 -0.5843 -2.1482 -1.0095 0.0419 -0.3129 -0.5038 -1.8391 -1.8270 -0.4140 -1.3065 0.6407 -0.0724 1.2632

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Table 6: Risk-Adjusted Returns (Volume) Portfolio Loser V1 Winner V1 Winner V1 Loser V2 Winner V2 Winner V2 Loser V3 Winner V3 Winner V3 Winner V1 Winner V1 Winner V2 Winner V2 Winner V3 Winner V3 Loser V3

P(α) 0.1197 0.0011 0.2090 0.5601 0.0337 0.3148 0.9667 0.7549 0.6153 0.0684 0.0702 0.6796 0.1939 0.5230 0.9424 0.2090

P(β) <0.0001 <0.0001 0.4747 <0.0001 <0.0001 0.5994 <0.0001 <0.0001 0.8187 0.1160 0.7723 0.0407 0.5680 0.4050 0.1507 0.7677

R2 0.3354 0.5000 0.0043 0.4244 0.6258 0.0023 0.2327 0.4570 0.0004 0.0206 0.0007 0.0347 0.0027 0.0058 0.0173 0.0007

Table 7: Market Dependent Risk-Adjusted Returns (Normal) Portfolio Loser

t(α) 0.0159

1.3099

Winner

-0.0009

-0.1312

Winner – Loser

-0.0207

-1.5269

β+ 1.4709

t(β+)

β-

t(β-)

P(α)

P(β+)

P(β-)

5.9419

0.6508

4.7574

0.1928

2.9220E-08

5.6030E-06

0.4334

1.1790

8.7571

0.7666

10.3041

0.8958

<0.0001

0.7077

-0.2839

-1.0304

0.1131

0.7428

0.1295

0.3049

0.4591

0.0102

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Portfolio

Table 8: Market Dependent Risk-Adjusted Returns (Volume) β+

t(α)

β-

t(β+)

t(β-)

P(α)

P(β+)

P(β-)

1.3961

1.4981

6.4602

0.4240

3.3090

0.1653

<0.0001

0.0012

0.3994

Winner V1

-0.0055

-0.5962

1.2627

6.6994

0.6457

6.1992

0.5522

<0.0001

0.5252

Winner V1 – Loser V1 Loser V2

-0.0253

-1.6817

-0.2273

-0.7425

0.2189

1.2940

0.0953

0.4593

0.1982

0.0147

0.0150

1.1038

1.5712

5.6932

0.8080

5.2982

0.2719

<0.0001

0.4454

Winner V2

-0.0146

-1.7047

0.9183

5.2705

0.9856

10.2370

0.0909

<0.0001

0.6261

Winner V2 – Loser V2 Loser V3

-0.0334

-2.1013

-0.6448

-1.9915

0.1749

0.9776

0.0377

0.0487

0.3303

0.0331

0.0178

0.9807

1.3289

3.5964

0.6882

3.3704

0.0174

1.7091

1.3559

6.5282

0.6241

5.4377

-0.0042

-0.2123

0.0351

0.0864

-0.0668

-0.0243

-1.5032

-0.3004

-0.9110

-0.0272

-1.2854

-0.0581

-0.0344

-2.6529

-0.0363

-1.8988

-0.0023

-0.1578

-0.0014

-0.0836

0.0010

0.2440

0.0901

<0.0001

0.4885

0.8323

0.9313

0.7662

0.0008

-0.9057

0.1355

0.3642

0.3670

0.0215

-0.0452

-0.1901

0.2012

0.8930

0.8496

0.0007

-2.1683

0.5589

3.8358

0.0091

0.0321

0.0002

0.1155

-1.0354

0.2948

1.3722

0.0600

0.3026

0.1726

0.0184

-0.1342

-0.4457

0.1973

1.1863

0.8749

0.6566

0.2379

0.0118

-0.2073

-0.6107

-0.1866

-0.9952

0.9335

0.5425

0.3217

0.0173

-0.4025

-0.2980

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an -0.1349

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-0.5717

0.0005

Winner V3 – Loser V3 Winner V1 – Loser V2 Winner V1 – Loser V3 Winner V2 – Loser V1 Winner V2 – Loser V3 Winner V3 – Loser V1 Winner V3 – Loser V2

0.3288

Winner V3

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0.0159

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Loser V1

We analyse the risk-adjusted performance of the various portfolios using the single factor Capital Asset Pricing Model. Tables 5,6,7,8 report the results from this analysis and show that the W-L portfolios for the price-based momentum strategy tend to underperform their benchmark with negative alphas for most of the portfolios. When the strategy is augmented with volume information, all the reported alpha values are negative as well even for the strategies that reported positive average monthly returns. This suggests that while the addition of volume information can improve the profitability of momentum strategies in this market on an absolute basis, the strategy still underperforms the benchmark on a risk-adjusted basis.

North American Review of Finance, vol.13, no.1

Besides the single factor model, we also conducted the analysis using market-dependent betas. The results from this regression reveal some insights into the poor performance of momentum strategies. We see that the Loser portfolios tend to have a higher beta than the Winner portfolios when market returns are positive and a lower beta when market returns are negative, consistent with the result of negative alphas for the zero-cost portfolio.

4 Conclusion

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The profitability of a momentum strategy is highly dependent upon the characteristics of a market. In this paper, we tested the profitability of a price-based momentum strategy and a volume-augmented momentum strategy for the Philippines Equity Market. For the strategy based only on past return information, we find little evidence in support of the profitability of a momentum strategy with the results suggesting the presence of mean-reverting prices. The Philippines Equity Market is a thinly traded market and hence the reasons for large moves that lead to returns falling into the top or bottom deciles in the ranking period could be due to large volumes being traded during that period that push prices in a particular direction and might not contain information on the likely future direction of the stock. This could be a possible reason that past winners tend to perform badly and past losers tend to do well for this particular market. When volume information is incorporated, the strategies that select stocks based on volume and return information from the past 3 months show positive average monthly returns. However, the returns are often not statistically significant and after the effect of transaction costs from the rebalancing of the portfolio are accounted for the positive average monthly returns quickly disappear. In addition, after adjusting for the risk of these strategies using a single factor model and a model with market-dependent betas we find that such a strategy does not outperform the benchmark. Hence, we conclude that while the use of volume information improves the performance of a momentum strategy, such a volume-augmented strategy still does not appear to be particularly profitable within this market and the evidence seems to suggest that a contrarian strategy may prove profitable instead.

References

Wer ner F. M. de Bondt and Richard H. Thaler, Further Evidence on Investor Overreaction and Stock Market Seasonality, The Journal of Finance, 42(3), (1986), 557 - 581. [2] N. Barberis and A. Shleifer, Style Investing, The Journal of Financial Economics, 68, (2003), 161-199. [3] Mark M. Cahart, On Persistence in Mutual Fund Performance, The Journal of Finance, 52(1), (1997), 57-82. [4] N. Jegadeesh and S. Titman, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, The Journal of Finance, 48(1), (1993), 65-91. [5] N. Jegadeesh and S. Titman, Profitability of Momentum Strategies: An Evaluation of Alternate Explantations, The Journal of Finance, 56(2), (2001), 699-720.

[1]

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[14] [15] [16]

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[12]

[11]

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[10]

[9]

[8]

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[7]

K. Geert Rouwenhorst, ‘International momentum Strategies’, The Journal of Finance, 53(1), (1998), 267-284. Andy C.W. Chui, S. Titman and K.C. John Wei, ‘Individualism and Momentum around the World’, The Journal of Finance, 65(1), (2010), 361-392. G. Aharoni and Tuan Q. Ho and Q. Zheng, ‘Testing the growtwh option theory: the profitability of enhanced momentum strategies in Australia’, Accounting and Finance Journal, 52, (2012), 267-290. John W.S. Hu and Y.C Chen, ‘The Performance of Momentum Investment Strategies: An International Examination of Stock Markets’, International Journal Of Management, 28(4), (2011), 165-176. A. Biglova, S. Rachev, T. Jasic and Frank J. Fabozzi, ‘Profitability of momentum strategies: application of novel risk/return ratio stock selection criteria’, Investment Management and Financial Innovations, 4, (2004), 48-62. ] S. Rachev and T. Jasic and S. Stoyanov and Frank J. Fabozzi, ‘Momentum strategies based on reward-risk stock selection criteria’, Journal of Banking & Finance, 31, (2007), 2325-2346. Charles M.C. Lee and B. Swaminathan, ‘Price Momentum and Trading Volume’, The Journal of Finance, 55(5), (2000), 2017-2069. Edwards, R. D., Magee, J., & Bassetti, W. H. C, (2007). Technical analysis of stock trends. 9th ed. A. Hameed and Y. Kusnadi, ‘Momentum Strategies: Evidence from Pacific Basin Stock Markets’, The Journal of Finance Research, 25(3), (2002), 197-383. M. Glasser and M. Webber, ‘Momentum and Turnover: Evidence from the German Stock Market’, Schmalenbach Business Review, 55, (2003), 108-135. Sam A.Ampomah, ‘On the Profitability of Volume-Augmented Momentum Trading Strategies: Evidence from the UK’, Investment Management and Financial Innovations, 3(3), (2006), 91-106.

[6]

North American Review of Finance, vol.13, no.1

Portfolio Theory Forward Testing Marcus Davidsson1

Abstract

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Portfolio Theory has during many decades been considered as the holy grail of investment despite the fact that very few empirical studies in the public domain have shown that portfolio theory outperforms a random equal weighted portfolio. We will in this paper empirically investigate how successful portfolio theory is when it comes to generating large positive returns with low return volatility. The dataset that is used consists of approximately 4000 US stocks. We find weak support that portfolio theory by itself would have generated any returns different than a random portfolio allocation. In general optimized historical cumulative returns are not the same as forward cumulative returns.

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JEL classification numbers: G00, G1, Keywords: Portfolio theory, investment, finance

1 Introduction and Theory

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Risk is something that can be quantified by using statistics. Uncertainty however is something that cannot be quantifiable (Knight, 1921). Uncertainty in information theory in the form of entropy has a little bit different meaning since it is directly related to risk (Shannon, 1951). Uncertainty, in the form of unpredictable outcomes, can also be found in deterministic (non stochastic) chaotic systems due to the so called Butterfly effect (Lorenz, 1963). Uncertainty in finance can be found both in the estimation of the expected return and in the estimation of the standard deviation of return i.e. both can change over time. It is also important to note that gambling and speculation are defined differently. Taleb (2007) explains that gambling takes place in a closed laboratory environment where the return distribution is known and where uncertainty is nonexistent. The expected return for a gambler is zero and remains constant over time. Risk and uncertainty in such a world is essentially parameterised. Speculation (Babusiaux et al, 2011) on the other hand takes place in an open environment where the future return distribution is not known and where 1

55316 Jรถnkรถping, SWEDEN e-mail: davidsson_marcus@hotmail.com

Article Info: Received : January 21, 2013. Revised : February 12, 2013. Published online : May 1, 2013

North American Academic Journals, 2013

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uncertainty is plentiful. The expected return for a speculator is undefined and it does not remain constant over time. The speculator is forced to use historical data to try to make inference about the shape of the return distribution in the future. Due to the large amount of uncertainty, the confidence interval that surrounds the speculator’s decision making will become much larger than suggested by traditional statistics. Portfolio theory was introduced to the world in six steps: Markowitz (1959), Sharpe (1964), Ross (1976), Black and Litterman (1992), Fama & French (1993) and Carhart (1997). The main objective for portfolio diversification is to minimize portfolio variance. Portfolio variance is a function of the return volatility for each security in the portfolio and the cross correlation of returns. Since cross correlation can be negative return variance can be cancelled out. However, the same idea can also be applied to highly positive correlated stock return portfolio by artificially creating negative cross correlation in return by short selling. Portfolio variance is the amount of return noise around the portfolio’s expected return. Diversification can to a large extend eliminate such return noise. Markowitz (1959) mainly looks at diversification from an asset class perspective where an investor that spreads his risk between different asset classes will achieve a greater “diversification”. Brinson et al (1986) found that asset class allocation (compared to market timing and stock picking) can explain on average 93.6 per cent of the variation in total return. It is also interesting to note that the bond returns in general tend to be the only return that will not become negative during a market crash (Longin and Solnik 1995). This means that bonds provides a good source of diversification due to return stability especially when markets has become more positive cross correlated during the last thirty years and even though the return on “risk free” government bonds has steadily been declining for the last 40 years. The Capital Asset Pricing Model (CAPM) which was introduced by Sharpe (1964) points out that market risk also plays an important role for the smoothness of the equity curve. Aportfolio with a large beta (i.e. highly sensitive to changes in market returns) will have more risk than a portfolio with a zero beta. An investor can reduce such market risk by balancing long and short positions. Market risk plays an important role when it comes to investing in financial markets because market returns accounts for a large fraction of stock returns (Fama and French, 1992). Ross (1976) introduced the so called Arbitrage Pricing Theory which illustrates that asset returns can be modelled as linear functions of various factor indices. Black and Litterman (1992) introduced the so called Black- Litterman model which starts by assuming that the benchmark index is meanvariance efficient and from such assumption derive the expected return of the benchmark portfolio. Fama & French (1993) introduced the three factor models which includes beta, book-to- market-ratio and stocks size which they claim will reduced return noise even further. Finally Carhart (1997) extend such a three-factor model to a four-factor model which also includes a momentum component which explains even more of the return variance. Conditional expected return also known as greed and conditional return volatility also known as fear are heavily used in portfolio theory i.e. the Sharpe ratio. Conrad & Kaul (1988) and Jegadeesh & Titman (1993) have found that conditional expected return is positive serial correlated and Mandelbrot (1963) and Engle (1982) have found that conditional return volatility is positive serial correlated. Serial correlation in returns tends to be insignificant (Runde & Kramer, 1991). Positive serial correlation in expected return and volatility is a contributing factor why we see price trends in financial markets. Even though we have positive serial correlation in the mean and volatility this is where most of the portfolio risk comes in. Portfolio rebalancing hence becomes the primary tool to North American Review of Finance, vol.13, no.1

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minimize such risk (Karoglou, 2010) and (Powers, 2010). Previous studies such as Mandelbrot (1963) and Fama (1965) have also shown that finacial makrets tend to have fatter tails and a larger amount of kurtosis than the normal distribution. Portfolio theory can also be understood by looking at the random walk model S(t)=a+b*S(t-1)+R where R is an independent and identically distributed (i.i.d) random variable drawn from a normal distribution with mean μ and standard deviation σ, b takes a value of 1 and a is the drift coefficient i.e. expected return which can be either positive, negative or zero. The return for such a random walk model is given by S(t)-S(t1)=a+R(t) which means that the return for a random walk has two components; expected return a and random return noise R(t). The random return noise R(t) represents the fluctuations around the expected return a. The objective for most investors is to eliminate such random return noise R(t) element through diversification. For a highly diversified portfolio the random return noise R(t) is canceled out hence return becomes expected return a.

2 Empirics

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In this section we will apply portfolio theory to empirical data. When we have a large global universe of stocks the easiest way to apply portfolio theory is to use least-squares. Such an approach is fast and can handle many 1000’s of securities. We start by specifying the linear system. The linear system is given by ER=R.W where ER is a column vector containing the investor specified portfolio expected return for each time period which we

min ||R.W – ER|| 22 .

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is assume is 2%, R is the return matrix and W is a weight vector. An error vector introduced hence the linear system can be written as r=R.W - ER. The objective becomes to minimize the sum of all the elements in r. Since we are only interested in the absolute error we minimize the sum of the square of which means that our objective function can be written as:

or th

The dataset consist of approximately 4000 US stocks. The dataset is split into three groups; S&P-SUPERCOMP (1115 stocks), NASDAQ (1415 stocks) and NYSE (1440 stocks). Each group is then split into back-testing and forward-testing data. Such a separation makes sure that we minimize curve fitting. We then apply statistical analysis on the back-tested and forward-tested sample. We test the hypothesis that the mean and standard deviation is the same for the two groups. In a perfect world the mean and standard deviation of the back-testing sample should be the same as the men and standard deviation of the forward-testing sample. However, as seen in table 1, 2, 3 and 4 there is quite a large difference. When you run the back-testing the equity curve is super smooth and upward sloping with an expected return equal to 2% and portfolio return variance close to zero. The forward-testing introduces a lot of volatility into the equity curve. In figure 1-4 we can see the expected return and portfolio variance of the forward-tested allocations. Table 5 to 7 contain the forward testing return correlation matrices. Table 8 contains the normality test and table 9 contains the simulated total return and the forward tested return.

North American Academic Journals, 2013

Table 1: Statistical Analysis of S&P-SUPERCOMP (1115 stocks)

2.000

0.207

-3.829

0.002

Rejected

2.000

-2.745

-1.159

0.270

Accepted

2.000

5.389

0.529

0.6

Accepted

2.000

-0.594

-3.000

0.012

Rejected

2.000

-1.558

-3.697

2.000

-2.591

-1.473

2.000

1.057

-0.823

2.000

1.447

-0.192

2.000

-0.893

2.000

12.539

2.000

0.168

Rejected

0.168

Accepted

0.427

Accepted

0.003

Accepted

0.142

Accepted

1.192

0.257

Accepted

-0.532

0.605

Accepted

0.850

-1.578

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Standard T-Test on One Sample (Unknown Variance) Null Hypothesis: Sample drawn from population with mean 2 Alt. Hypothesis: Sample drawn from population with mean not equal to 2 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXX S&P-SUPERCOMP Backtest Mean Forward Test Mean StudentT P-Value Outcome

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Chi-Square Test on One Sample Null Hypothesis: Sample drawn from population with standard deviation equal to 0.01 Alt. Hypothesis: Sample drawn from population with standard deviation not equal to 0.01 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXX S&P-SUPERCOMP Backtest StDev ForwardTest Stdev ChiSquare P-Value Outcome BT 2000 FT=2001 4.41*10^-15 1.620 289028.000 0.000 Rejected BT 2000-2001 FT=2002 7.01*10^-15 14.182 2.21*10^7 0.000 Rejected BT 2000-2002 FT=2003 7.80*10^-15 22.187 5.41*10^7 0.000 Rejected BT 2000-2003 1.19*10^-14 2.995 986733 0.000 Rejected FT=2004 BT 2000-2004 1.18*10^-14 3.333 1.22*10^6 0.000 Rejected FT=2005 BT 2000-2005 7.99*10^-15 10.791 1.28*10^7 0.000 Rejected FT=2006 BT 2000-2006 FT=2007 1.26*10^-14 3.966 1.73*10^6 0.000 Rejected BT 2000-2007 FT=2008 1.49*10^-14 9.943 1.08*10^7 0.000 Rejected BT 2000-2008 FT=2009 1.21*10^-14 6.350 4.43*10^6 0.000 Rejected BT 2000-2009 1.64*10^-14 30.572 1.02*10^8 0.000 Rejected FT=2010 BT 2000-2010 1.78*10^-14 11.922 1.56*10^7 0.000 Rejected FT=2011

North American Review of Finance, vol.13, no.1

Table 2 : Statistical Analysis of NASDAQ (1415 stocks)

FT=2001 2000-2001

2.000

-0.524

-5.161

0.000

Rejected

2.000

0.046

-2.961

0.012

Rejected

2.000

-2.532

-1.729

0.111

Accepted

2.000

-214.417

-0.989

0.347

Accepted

2.000

-0.561

-3.040

2.000

1.547

-0.474

2.000

-0.025

-1.354

2.000

1.269

-0.167

0.869

Accepted

2.000

9.721

0.111

Accepted

2.000

8.947

0.908

0.382

Accepted

2.000

14.903

0.289

0.777

Accepted

2000-2002 2000-2003

2000-2005

2000-2007

2000-2009 2000-2010

1.728

2000-2008

0.011

Rejected

0.644

Accepted

0.202

Accepted

2000-2006

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2000-2004

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BT 2000 BT FT=2002 BT FT=2003 BT FT=2004 BT FT=2005 BT FT=2006 BT FT=2007 BT FT=2008 BT FT=2009 BT FT=2010 BT FT=2011

Standard T-Test on One Sample (Unknown Variance) Null Hypothesis: Sample drawn from population with mean 2 Alt. Hypothesis: Sample drawn from population with mean not equal to 2 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXX NASDAQ Backtest Mean ForwardTest Mean StudentT P-Value Outcome

2000-2002

2.67*10^-15

315822.000

0.000

Rejected

4.69*10^-13

2.285

574458.000

0.000

Rejected

9.077

9.064*10^6

0.000

Rejected

4.27*10^-13

764.681

6.432*10^6

0.000

Rejected

6.34*10^-14

2.918

936924

0.000

Rejected

1.52*10^-14

3.308

1.204*10^6

0.000

Rejected

3.78*10^-14

5.180

2.95*10^6

0.000

Rejected

2.84*10^-14

15.077

2.50*10^7

0.000

Rejected

1.43*10^-13

15.477

2.63*10^7

0.000

Rejected

1.10*10^-13

26.485

7.71*10^7

0.000

Rejected

1.08*10^-13

154.187

2.61*10^9

0.000

Rejected

1.694

FT=2001 2000-2001

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4.80*10^-13 2000-2003 2000-2004

BT 2000 BT FT=2002 BT FT=2003 BT FT=2004 BT FT=2005 BT FT=2006 BT FT=2007 BT FT=2008 BT FT=2009 BT FT=2010 BT FT=2011

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2000-2005 2000-2006 2000-2007 2000-2008 2000-2009 2000-2010

North American Academic Journals, 2013

Table 3 : Statistical Analysis of NYSE (1440 stocks) Standard T-Test on One Sample (Unknown Variance) Null Hypothesis: Sample drawn from population with mean 2 Alt. Hypothesis: Sample drawn from population with mean not equal to 2 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXX NYSE Backtest Mean ForwardTest Mean StudentT P-Value Outcome FT=2001 2000-2001

2.000

0.532

-2.251

0.045

Rejected

2.000

-0.796

-5.262

0.000

Rejected

2.000

-3.041

-3.747

0.000

Rejected

2.000

-1.334

-3.825

0.002

Rejected

2.000

-2.148

-2.469

2.000

1.214

-0.337

2.000

-2.975

-0.808

2.000

3.810

0.397

2.000

-5.972

2.000

0.285

2.000

-1.418

2000-2002 2000-2003

2000-2005

2000-2007

2000-2009 2000-2010

Rejected

0.742

Accepted

0.435

Accepted Accepted

0.199

Accepted

-1.077

0.304

Accepted

-0.882

0.396

Accepted

0.698

-1.365

2000-2008

0.03

2000-2006

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BT 2000 BT FT=2002 BT FT=2003 BT FT=2004 BT FT=2005 BT FT=2006 BT FT=2007 BT FT=2008 BT FT=2009 BT FT=2010 BT FT=2011

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Chi-Square Test on One Sample Null Hypothesis: Sample drawn from population with standard deviation equal to 0.01 Alt. Hypothesis: Sample drawn from population with standard deviation not equal to 0.01 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXX NYSE Backtest StDev ForwardTest Stdev ChiSquare P-Value Outcome BT 2000 FT=2001 2.65*10^-15 2.251 557574.000 0.000 Rejected BT 2000-2001 FT=2002 5.29*10^-15 1.840 372815.000 0.000 Rejected BT 2000-2002 FT=2003 6.51*10^-13 4.660 2.38*10^6 0.000 Rejected BT 2000-2003 1.81*10^-13 3.019 1.00*10^6 0.000 Rejected FT=2004 BT 2000-2004 5.00*10^-13 5.818 3.72*10^6 0.000 Rejected FT=2005 BT 2000-2005 9.18*10^-15 8.064 7.15*10^6 0.000 Rejected FT=2006 BT 2000-2006 FT=2007 1.52*10^-14 21.317 4.99*10^6 0.000 Rejected BT 2000-2007 FT=2008 1.92*10^-13 15.766 2.73*10^7 0.000 Rejected BT 2000-2008 FT=2009 2.58*10^-14 20.231 4.50*10^7 0.000 Rejected BT 2000-2009 1.91*10^-13 5.512 3.34*10^6 0.000 Rejected FT=2010 BT 2000-2010 6.63*10^-14 13.424 1.98*10^6 0.000 Rejected FT=2011

North American Review of Finance, vol.13, no.1

Table 4 : Statistical Analysis of All Data (approx 4000 stocks) Standard Z-Test on One Sample (Known Variance) Null Hypothesis: Sample drawn from population with mean 2 and known standard deviation 1 (the backtested standard deviation is close to zero so a standard deviation of 1 is generous) Alt. Hypothesis: Sample drawn from population with mean not equal to 2 and known standard deviation 1 XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXXXXXXX Backtest Mean

ForwardTest Mean

Statistics

P-Value

Outcome

2.000

0.207

-6.207

5.3*10^-10

Rejected

2.000

-2.745

-16.440

9.8*10^-61

Rejected

2.000

5.389

11.742

7.6*10^-32

Rejected

2.000

-0.594

-8.986

2.5*10^-19

Rejected

2.000

-1.558

-12.325

6.5*10^-35

Rejected

2.000

-2.591

-15.905

2.000

1.057

2.000

1.447

2.000 2.000

2.000

0.0010

Rejected

-1.913

0.055

Accepted

-0.893

-10.021

1.2*10^-23

Rejected

12.539

36.511

7.4*10^-89

Rejected

0.168 ForwardTest Mean

-6.343 Statistics

2.2*10^-10 P-Value

Rejected Outcome

-0.524

-8.746

2.1*10^-18

Rejected

2.000

0.046

-6.768

1.3*10^-11

Rejected

-2.532

-15.701

1.4*10^-55

Rejected

2.000

-214.417

-749.691

Rejected

2.000

-0.561

-8.874

7.0*10^-19

Rejected

2.000

1.547

-1.568

0.116

Accepted

2.000

-0.025

-7.016

2.2*10^-12

Rejected

2.000

1.269

-2.530

0.011

Rejected

2.000

9.721

26.747

1.3*10^-9

Rejected

2.000

8.947

24.068

5.4*10^-98

Rejected

2.000 Backtest Mean

14.903 ForwardTest Mean

44.700 Statistics

0 P-Value

Rejected Outcome

5.8*10^-57

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2.000 Backtest Mean

2.000

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NYSE

North American Academic Journals, 2013

0.532

-5.084

3.6*10^-7

Rejected

2.000

-0.796

-9.688

3.3*10^-22

Rejected

2.000

-3.041

-17.463

2.7*10^-68

Rejected

2.000

-1.334

-11.552

7.1*10^-31

Rejected

2.000

-2.148

-14.370

7.9*10^-47

Rejected

2.000

1.214

-2.722

0.006

Rejected

2.000

-2.975

-17.236

1.4*10^-66

Rejected

2.000

3.810

6.271

2.000

-5.972

-27.616

2.000

0.285

-5.938

2.8*10^-9

Rejected

2.000

-1.418

-11.841

2.3*10^-32

Rejected

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2.000

Rejected

7.0*10^-94

Rejected

2.5*10^-10

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Figure 1: Expected Value and Standard Deviation Forward Testing

North American Review of Finance, vol.13, no.1

S&P SUPERCOMP

-20

-50

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- 100

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NASDAQ

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100

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NYSE

-60

-40

-20

Figure 2: Forward Return Distributions

North American Academic Journals, 2013

-0.15

-0.21

0.34

0.21

0.07

-0.07

0.38

-0.18

-0.54

0.13

0.37

-0.08

0.19

-0.06

-0.14

0.10

0.18

0.15

0.33

1.00

0.07

-0.08

-0.17

0.96

-0.18

0.33

0.61

0.05

-0.06

0.18

0.10

-0.19

-0.06

-0.16

-0.28

0.33

0.04

-0.13

0.14

0.08

0.13

0.07

1.00

-0.37

0.53

0.18

-0.01

0.15

-0.08

-0.15

0.29

0.05

0.41

0.23

0.04

-0.62

-0.47

0.59

-0.13

0.95

-0.01

-0.15

-0.08

-0.37

1.00

-0.15

-0.06

0.36

0.10

0.33

0.74

-0.09

0.20

-0.36

0.54

-0.16

0.63

0.18

-0.11

0.28

-0.43

0.19

-0.21

-0.17

0.53

-0.15

1.00

-0.22

-0.34

-0.31

-0.34

-0.03

-0.34

-0.45

0.45

-0.15

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-0.27

-0.47

-0.32

0.14

-0.05

-0.01

-0.50

0.50

-0.12

0.34

0.96

0.18

-0.06

-0.22

1.00

-0.05

0.52

0.61

0.15

0.06

0.29

0.00

-0.14

0.06

-0.20

0.49

0.27

-0.10

0.26

0.07

0.21

-0.18

-0.01

0.36

-0.34

-0.05

1.00

0.31

-0.12

0.00

0.14

0.38

-0.37

Fi n

-0.41

0.35

0.09

0.53

0.03

0.17

0.39

0.51

0.04

0.37

0.21

0.33

0.15

0.10

-0.31

0.52

0.31

1.00

0.43

0.39

0.23

0.21

-0.34

0.21

0.18

-0.15

-0.10

0.69

0.67

-0.21

0.16

0.02

0.07

0.61

-0.08

0.33

-0.34

0.61

-0.12

0.43

1.00

0.52

0.27

0.54

0.11

0.13

0.18

-0.05

-0.28

0.31

0.12

-0.05

0.25

-0.07

0.05

-0.15

0.74

-0.03

0.15

0.00

0.39

0.52

1.00

0.20

-0.38

0.33

0.20

0.21

-0.06

0.01

-0.14

-0.15

-0.10

0.38

-0.06

0.29

-0.09

-0.34

0.06

0.14

0.23

0.27

0.20

1.00

0.52

-0.12

0.27

0.90

-0.35

-0.49

0.10

0.16

0.33

0.31

0.26

-0.18

0.18

0.05

0.20

-0.45

0.29

0.38

0.21

0.54

0.20

0.52

1.00

0.25

0.03

0.48

0.10

-0.70

0.32

0.35

0.54

0.16

0.40

-0.54

0.10

0.41

-0.36

0.45

0.00

-0.37

-0.34

0.11

-0.38

-0.12

0.25

1.00

-0.27

-0.29

-0.42

-0.37

0.25

0.16

-0.04

0.39

0.20

0.13

-0.19

0.23

0.54

-0.15

-0.14

0.35

0.21

0.13

0.33

0.27

0.03

-0.27

1.00

0.00

0.16

0.02

0.12

0.24

0.29

-0.01

0.07

0.37

-0.06

0.04

-0.16

-0.47

0.06

0.09

0.18

0.20

0.90

0.48

-0.29

0.00

1.00

-0.20

-0.47

-0.03

0.00

0.24

0.14

0.04

-0.08

-0.16

-0.62

0.63

-0.32

-0.20

0.53

-0.15

-0.05

0.21

-0.35

0.10

-0.42

0.16

-0.20

1.00

0.34

-0.37

-0.32

0.23

-0.59

-0.11

0.19

-0.28

-0.47

0.18

0.14

-0.41

0.03

-0.10

-0.28

-0.06

-0.49

-0.70

-0.37

0.02

-0.47

0.34

1.00

-0.46

-0.43

-0.23

-0.53

0.00

-0.06

0.33

0.59

-0.27

-0.05

0.49

0.17

0.69

0.31

-0.06

0.10

0.32

0.25

0.12

-0.03

-0.37

-0.46

1.00

0.90

-0.12

0.58

-0.05

-0.14

0.04

0.59

-0.11

-0.01

0.27

0.39

0.67

0.12

0.01

0.16

0.35

0.16

0.24

0.00

-0.32

-0.43

0.90

1.00

0.06

0.58

0.13

0.10

-0.13

0.28

-0.50

-0.10

0.51

-0.21

0.12

-0.14

0.33

0.54

-0.04

0.29

0.24

0.23

-0.23

-0.12

0.06

1.00

-0.11

0.67

0.18

0.14

0.95

-0.43

0.50

0.26

0.04

0.16

-0.05

-0.15

0.31

0.16

0.39

-0.01

0.14

-0.59

-0.53

0.58

-0.11

1.00

0.04

0.15

0.08

-0.01

0.19

-0.12

0.07

0.37

0.02

0.25

-0.10

0.26

0.40

0.20

0.07

0.04

-0.11

0.00

-0.05

0.13

0.67

0.04

1.00

North American Review of Finance, vol.13, no.1

0.13

0.33

1.00

or th

Table 5 : Correlation Matrix Forward Return S&P and NASDAQ

Portfolio Theory Forward Testing

235

0.25

0.03

0.48

0.10

-0.70

0.32

0.35

0.54

0.16

0.40

-0.12

-0.46

-0.20

0.10

-0.27

0.06

0.03

-0.15

-0.12

0.74

-0.26

0.25

1.00

-0.27

-0.29

-0.42

-0.37

0.25

0.16

-0.04

0.39

0.20

-0.36

-0.39

-0.45

0.22

-0.57

-0.51

-0.40

-0.15

-0.29

0.45

0.09

0.03

-0.27

1.00

0.00

0.16

0.02

0.12

0.24

0.29

-0.01

0.07

-0.26

0.22

-0.22

0.29

-0.01

0.02

0.17

-0.01

-0.11

-0.36

0.48

-0.29

0.00

1.00

-0.20

-0.47

-0.03

0.00

0.24

0.14

0.04

-0.10

-0.09

0.06

0.20

-0.32

-0.04

0.03

0.21

-0.13

0.18

-0.06

0.10

-0.42

0.16

-0.20

1.00

0.34

-0.37

-0.32

0.23

-0.59

-0.11

0.10

-0.30

0.31

-0.32

0.53

0.17

0.31

0.16

0.24

0.21

0.19

-0.70

-0.37

0.02

-0.47

0.34

1.00

-0.46

-0.43

-0.23

-0.53

0.00

0.43

0.20

0.35

-0.38

0.37

0.04

-0.01

0.20

0.17

-0.52

0.25

0.32

0.25

0.12

-0.03

-0.37

-0.46

1.00

0.90

-0.12

0.58

-0.05

0.25

0.36

-0.67

0.11

-0.25

0.54

0.12

-0.38

0.03

0.29

-0.76

0.35

0.16

0.24

0.00

-0.32

-0.43

0.90

1.00

0.06

0.58

0.13

0.20

0.45

-0.64

0.10

-0.12

0.57

0.17

-0.15

0.02

0.25

-0.90

0.54

-0.04

0.29

0.24

0.23

-0.23

-0.12

0.06

1.00

-0.11

0.67

-0.01

-0.21

0.23

0.16

0.33

0.17

0.35

0.31

0.32

0.13

0.02

0.16

0.39

-0.01

0.14

-0.59

-0.53

0.58

-0.11

1.00

0.04

-0.18

0.15

-0.77

0.72

-0.37

0.04

0.20

-0.08

0.21

-0.02

-0.27

0.40

0.20

0.07

0.04

-0.11

0.00

-0.05

0.13

0.67

0.04

1.00

-0.09

0.04

0.08

0.07

-0.04

-0.06

-0.08

0.09

-0.08

-0.03

-0.12

-0.36

-0.26

-0.10

0.10

0.43

0.25

0.20

-0.01

-0.18

-0.46

-0.39

0.22

-0.09

-0.30

0.20

0.36

0.45

-0.21

0.15

-0.20

-0.45

-0.22

0.06

0.31

0.35

-0.67

-0.64

0.23

0.10

0.22

0.29

0.20

-0.32

-0.38

0.11

0.10

0.16

-0.27

-0.57

-0.01

-0.32

0.53

0.37

-0.25

-0.12

0.06

-0.51

0.23

-0.04

0.17

0.04

0.54

0.57

0.03

-0.40

0.02

0.03

0.31

-0.01

0.12

-0.15

0.17

0.21

0.16

0.20

-0.38

-0.12

-0.29

-0.01

-0.13

0.24

0.17

0.03

0.74

0.45

-0.11

0.18

0.21

-0.52

0.29

-0.26

0.09

-0.36

-0.06

0.19

-0.76

an c

Fi n

0.24

1.00

0.50

0.09

-0.50

0.42

0.53

0.20

-0.24

0.26

-0.27

-0.24

-0.09

0.50

1.00

-0.22

0.26

0.42

0.01

-0.01

-0.03

-0.53

-0.54

0.23

0.04

0.09

-0.22

1.00

-0.40

0.52

0.04

0.13

0.10

0.14

-0.25

0.45

0.72

0.08

-0.50

-0.22

-0.40

1.00

-0.25

-0.09

0.33

0.10

0.42

-0.18

0.18

0.33

-0.37

0.07

0.42

0.26

0.52

-0.25

1.00

0.53

0.64

0.10

0.62

-0.44

0.11

0.17

0.04

-0.04

0.53

0.42

0.04

-0.09

0.53

1.00

0.68

-0.10

0.56

-0.12

-0.59

0.17

0.35

0.20

-0.06

0.20

0.01

0.13

0.33

0.64

0.68

1.00

0.25

0.93

-0.18

-0.01

-0.15

0.31

-0.08

-0.24

-0.01

0.10

-0.10

0.25

1.00

0.14

0.03

0.07

0.02

0.32

0.21

0.09

0.26

-0.03

0.14

0.42

0.62

0.56

0.93

0.14

1.00

-0.38

0.20

0.25

0.13

-0.02

-0.08

-0.27

-0.53

-0.25

-0.18

-0.44

-0.12

-0.18

0.03

-0.38

1.00

-0.25

-0.90

0.02

-0.27

-0.03

-0.24

-0.54

0.45

0.18

0.11

-0.59

-0.01

0.07

0.20

-0.25

1.00

-0.77

or th

0.25

0.24

1.00

Table 6 : Correlation Matrix Forward Return NASDAQ and NYSE

North American Academic Journals, 2013

0.13

-0.15

-0.21

0.34

0.21

0.07

-0.07

0.38

0.43

0.32

0.03

0.34

0.22

0.24

0.35

-0.09

0.48

-0.65

0.20

0.33

1.00

0.07

-0.08

-0.17

0.96

-0.18

0.33

0.61

0.05

-0.06

0.27

-0.02

-0.05

0.06

0.01

0.12

-0.05

-0.91

0.07

-0.11

0.12

0.13

0.07

1.00

-0.37

0.53

0.18

-0.01

0.15

-0.08

-0.15

0.29

-0.28

0.26

-0.82

0.73

-0.43

0.00

-0.04

0.09

-0.07

-0.33

-0.08

-0.37

1.00

-0.15

-0.06

0.36

0.10

0.33

0.74

-0.09

-0.20

-0.28

0.29

-0.07

0.29

0.18

0.08

-0.08

0.04

0.07

-0.07

-0.21

-0.17

0.53

-0.15

1.00

-0.22

-0.34

-0.31

-0.34

-0.03

-0.34

-0.38

-0.06

-0.39

an c

0.07

-0.15

0.43

-0.25

-0.11

0.03

-0.24

0.18

0.34

0.96

0.18

-0.06

-0.22

1.00

-0.05

0.52

0.61

0.15

0.06

0.30

0.10

Fi n

-0.38

-0.14

0.08

0.02

0.30

0.06

-0.89

0.10

-0.06

-0.12

0.21

-0.18

-0.01

0.36

-0.34

-0.05

1.00

0.31

-0.12

0.00

0.14

0.38

0.22

-0.24

-0.07

0.40

0.44

0.40

0.20

0.28

0.12

-0.40

0.21

0.33

0.15

0.10

-0.31

0.52

0.31

1.00

0.43

0.39

0.23

0.52

0.51

-0.29

-0.22

-0.08

0.63

-0.01

-0.48

-0.11

0.02

-0.79

0.07

0.61

-0.08

0.33

-0.34

0.61

-0.12

0.43

1.00

0.52

0.27

0.04

-0.40

0.06

0.09

-0.29

0.20

-0.10

-0.64

-0.04

0.29

-0.11

-0.07

0.05

-0.15

0.74

-0.03

0.15

0.00

0.39

0.52

1.00

0.20

-0.28

-0.25

0.20

0.08

-0.08

0.20

0.00

-0.26

-0.10

0.08

-0.20

0.38

-0.06

0.29

-0.09

-0.34

0.06

0.14

0.23

0.27

0.20

1.00

-0.18

-0.05

-0.19

0.40

-0.49

-0.09

0.17

-0.18

0.14

-0.18

0.43

0.27

-0.28

-0.20

-0.38

0.30

0.38

0.52

0.04

-0.28

-0.18

1.00

0.50

0.09

-0.50

0.42

0.53

0.20

-0.24

0.26

-0.27

-0.24

0.32

-0.02

0.26

-0.28

-0.06

0.10

0.22

0.51

-0.40

-0.25

-0.05

0.50

1.00

-0.22

0.26

0.42

0.01

-0.01

-0.03

-0.53

-0.54

0.03

-0.05

-0.82

0.29

-0.39

-0.14

-0.24

-0.29

0.06

0.20

-0.19

0.09

-0.22

1.00

-0.40

0.52

0.04

0.13

0.10

0.14

-0.25

0.45

0.34

0.06

0.73

-0.07

0.43

0.08

-0.07

-0.22

0.09

0.40

-0.50

-0.22

-0.40

1.00

-0.25

-0.09

0.33

0.10

0.42

-0.18

0.18

0.22

0.01

-0.43

0.29

-0.25

0.02

0.40

-0.08

-0.49

0.42

0.26

0.52

-0.25

1.00

0.53

0.64

0.10

0.62

-0.44

0.11

0.24

0.12

0.00

0.18

-0.38

0.30

0.44

0.63

0.20

-0.09

0.53

0.42

0.04

-0.09

0.53

1.00

0.68

-0.10

0.56

-0.12

-0.59

0.35

-0.05

0.07

0.08

-0.11

0.06

0.40

-0.01

-0.10

0.00

-0.09

0.20

0.01

0.13

0.33

0.64

0.68

1.00

0.25

0.93

-0.18

-0.01

-0.09

-0.91

-0.04

-0.08

0.03

-0.89

0.20

-0.48

-0.64

-0.26

0.17

-0.24

-0.01

0.10

-0.10

0.25

1.00

0.14

0.03

0.07

0.48

0.07

0.09

0.04

0.03

0.10

0.28

-0.11

-0.04

-0.10

-0.18

0.26

-0.03

0.14

0.42

0.62

0.56

0.93

0.14

1.00

-0.38

0.20

-0.65

-0.11

-0.07

0.07

-0.24

-0.06

0.12

0.02

0.29

0.08

0.14

-0.27

-0.53

-0.25

-0.18

-0.44

-0.12

-0.18

0.03

-0.38

1.00

-0.25

0.20

0.12

-0.33

-0.07

0.18

-0.12

-0.40

-0.79

-0.11

-0.20

-0.18

-0.24

-0.54

0.45

0.18

0.11

-0.59

-0.01

0.07

0.20

-0.25

1.00

er -0.29

or th

0.08

North American Review of Finance, vol.13, no.1

0.33

1.00

Table 7: Correlation Matrix Forward Return S&P and NYSE

na nc e Fi of ew Re vi an er ic m A or th N Figure 3: Back Testing and Forward Return Equity Curve

North American Academic Journals, 2013

Table 8: Total Return, Risk Adjusted Return and Normality Test Forward Return Shapiro and Wilk's W-Test for Normality Null Hypothesis: Sample drawn from a population that follows a normal distribution Alt. Hypothesis: Sample drawn from population that does not follow a normal distribution XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXXXXXX NYSE Total Return Risk Adj.Return Statistics P-Value Outcome 0.128 -0.193 0.242 -0.198 -0.467 -0.240 0.266 0.145 -0.140 0.410 0.014 Risk Adj.Return

0.895 0.458 0.536 0.945 0.965 0.615 0.933 0.819 0.976 0.693 0.717 Statistics

BT 2000 FT=2001 BT 2000-2001 FT=2002 BT 2000-2002 FT=2003 BT 2000-2003 FT=2004 BT 2000-2004 FT=2005 BT 2000-2005 FT=2006 BT 2000-2006 FT=2007 BT 2000-2007 FT=2008 BT 2000-2008 FT=2009 BT 2000-2009 FT=2010 BT 2000-2010 FT=2011 NYSE BT 2000 FT=2001 BT 2000-2001 FT=2002 BT 2000-2002 FT=2003 BT 2000-2003 FT=2004 BT 2000-2004 FT=2005 BT 2000-2005 FT=2006 BT 2000-2006 FT=2007 BT 2000-2007 FT=2008 BT 2000-2008 FT=2009 BT 2000-2009 FT=2010 BT 2000-2010 FT=2011

-6.299 0.552 -30.392 -2573.006 -6.742 18.565 -0.306 15.233 116.654 107.374 178.845 Total Return 6.387 -9.562 -36.495 -16.018 -25.780 14.570 -35.710 45.724 -71.666 3.428 17.021

-0.309 0.020 -0.279 -0.280 -0.192 0.467 -0.004 0.084 0.628 0.337 0.096 Risk Adj.Return 0.236 -0.432 -0.652 -0.442 -0.369 0.150 -0.139 0.241 -0.295 0.051 -0.105

0.950 0.925 0.665 0.333 0.943 0.919 0.869 0.763 0.801 0.467 0.586 Statistics 0.937 0.957 0.863 0.941 0.887 0.852 0.572 0.631 0.686 0.942 0.669

Re vi

er ic

or th

0.130 1.6*10^-6 9.3*10^-6 0.525 0.797 6.0*10^-5 0.389 0.013 0.926 0.000 0.000 P-Value

Accepted Rejected Rejected Accepted Accepted Rejected Accepted Rejected Accepted Rejected Rejected Outcome

0.598 0.315 0.000 1.2*10^-7 0.508 0.269 0.061 0.002 0.008 2.0*10^-6 2.9*10^-5 P-Value 0.435 0.697 0.050 0.476 0.103 0.036 2.1*10^-5 8.9*10^-5 0.000 0.494 0.000

Accepted Accepted Rejected Rejected Accepted Accepted Accepted Rejected Rejected Rejected Rejected Outcome Accepted Accepted Accepted Accepted Accepted Rejected Rejected Rejected Rejected Accepted Rejected

na nc e

2.495 -32.951 64.678 -7.130 -18.697 -31.096 12.691 17.371 -10.717 150.477 2.026 Total Return

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na nc e Fi of ew Re vi an er ic m A or th N Figure 4: Cumulative Return Forward Testing

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Table 9: Random Portfolio Returns vs. Optimized Portfolio Returns Total Return Optimized Portfolio

Outcome

156

417

2.495

Random

-78

139

-32.951

Random

321

64.678

Random

-175

-4.3

-7.130

Random

-13

251

-18.697

Random

55.9

235

-31.096

Random

-5.3

196

12.691

Random

-6.5

199

17.371

Random

-89

661

-10.717

Random

31.3

257

150.477

Random

28.9

142

2.026

Random

Total Return Optimized Portfolio

Outcome

727

-6.299

Random

0.552

Random

167

-30.392

Random

196

-2573.006

Random

470

-6.742

Random

409

18.565

Random

444

-0.306

Random

116

15.233

Random

-117

1270

116.654

Random

879

2120

107.374

Random

-163

154

178.845

Not Random

Expected Total Return 10 Random Allocations

80th Percentile

Total Return Optimized Portfolio

Outcome

-191

192

6.387

Random

-18

190

-9.562

Random

106

504

-36.495

Random

199

-16.018

Random

317

-25.780

Random

188

14.570

Random

418

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-437

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-159 -9 -348

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BT 2000 FT=2001 BT 2000-2001 FT=2002 BT 2000-2002 FT=2003 BT 2000-2003 FT=2004 BT 2000-2004 FT=2005 BT 2000-2005 FT=2006

80 Percentile

Expected Total Return 15 Random Allocations

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80th Percentile

NASDAQ

Expected Total Return 15 Random Allocations

NYSE

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BT 2000-2006 FT=2007 BT 2000-2007 FT=2008 BT 2000-2008 FT=2009 BT 2000-2009 FT=2010 BT 2000-2010 FT=2011

226

-35.710

Random

528

45.724

Random

-169

100

-71.666

Random

248

3.428

Random

182

17.021

Random

3 Conclusion

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We have in this paper used empirical data to try to answer the question; how successful is portfolio theory when it comes to generating large and stable returns? The hypothesis that the expected return was equal to 2% for the forward testing sample was accepted by the standard t-test. However the chi-square test indicated that the return volatility was far from zero. The more powerful z-test rejected the notion that the backward and forward sample where drawn from the same distribution. We have also found empirical support for the fact that portfolio theoryâ&#x20AC;&#x2122;s total returns was on par or worse than the total return generated by a random portfolio allocation. This can also be seen in the cumulative returns in figure-3. It now becomes interesting to discuss why such phenomena w e r e observed. The fact is that the majority of stocks do not have stable price trends that continue for decades at a time. This author speculate that a very large global universe i.e. >10 000 stocks might be required to find these very rare diamonds in the bush i.e. stable price trends. Portfolio theory is based upon very scientific principles and in theory portfolio theory works outstanding. However, in this case the empirical evidence was simply not there. It is also worth pointing out that optimization per se is a somewhat romanticized science. Usually when someone uses the term optimized it implies that the outcome of such optimization will outperform i.e. if it would not outperform there would be no point in running the optimization. Such outperformance comes from the stable scientific foundation optimization rest on. However, sometimes stable scientific foundations are demolished by a simple fact that the expected return might be changing over time or even worse the expected return is not even positive to begin with. The historical cumulative return curve can be optimized to perfection i.e. an upward sloping straight line however when you take such an allocation and carry it into the future the same performance is not seen anymore. Two possible explanations; i) The future is truly uncertain which is something optimization never can capture. The optimization process is too perfect i.e. you need to introduce more randomness. ii) Our sample size was too small.

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References

[10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]

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[8]

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Babusiaux, D, Pierru, A and Lasserre, F (2011) Examining the Role of Financial Investors and Speculation in Oil Markets, The Journal of Alternative Investments, vol. 14, no. 1,pp 1 Black F and Litterman R (1992), Global Portfolio Optimization, Financial Analysts Journal, vol 48, issue 5, pp. 28–43 Brinson, G, Hood, R and Beebower, G (1986) Determinants of Portfolio Performance, Financial Analysts Journal, vol. 42, no. 4, pp. 39-44 Carhart, M (1997) On Persistence in Mutual Fund Performance. Journal of Finance, vol 52, issue 1, pp 57-82. Conrad, J & Kaul, G (1988) Time-Variation in Expected Returns, Journal of Business, Vol. 61, No. 4, pp. 409-425. Engle, R (1982) ARCH with Estimates of Variance of United Kingdom Inflation, Econometrica, 50:987-1008 Fama, E (1965) The behavior of stock market prices, Journal of Business, vol 38, no 1, pp 34-105. Fama, E and French, K (1992) The Cross-Section of Expected Stock Returns, Journal of Finance, Volume 47, Issue 2, pp, 427-465 Fama, E & French, K (1993) Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics 33 (1): 3–56 Jegadeesh, N & Titman, S (1993), Returns to buying winners and selling losers, Journal of Finance vol 48, pp 65–91 Karoglou, M (2010) Breaking down the non-normality of stock returns, The European journal of finance, vol 16, issue 1, pp 79-95 Knight, F (1921) Risk, Uncertainty and Profit, Library of Economics and Liberty http://www.econlib.org/library/Knight/knRUPCover.html Longin, F and Solnik, B (1995) Is the correlation in international equity returns constant, 1960-1990?, Journal of International Money and Finance, vol 14, pp 3-26 Lorenz, E (1963) Deterministic Nonperiodic Flow, Journal of the Atmospheric Sciences, vol 20, issue 2, pp 130-141 Mandelbrot, B (1963) The variation of certain speculative prices, Journal of Business, XXXVI, pp. 392–417. Markowitz, H (1959) Portfolio Selection: Efficient Diversification of Investment, New York: John Wiley & Sons Powers, M (2010) Presbyter Takes Knight, Journal of Risk Finance, vol. 11, issue 1 Ross, S (1976) The arbitrage theory of capital asset pricing, Journal of Economic Theory vol 13, issue 3, pp 341–360. Runde, R & Kramer, W (1991) Testing for autocorrelation among common stock returns, Statistical Papers, Vol 32, No 1, pp 311-322 Shannon, C (1951) Prediction and entropy of printed English, The Bell System Technical Journal, vol 30 pp 50-64 Sharpe, W (1964) Capital Asset Prices - A Theory of Market Equilibrium under Conditions of Risk, Journal of Finance, vol 19, issue 3, pp 425-442 Taleb, N (2007) Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, Thomson Texere London

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North American Review of Finance, vol.13, no.1

Appendices Appendix 1: Sample Portfolio Allocations

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Return and Risk-Return Ratio Based Momentum Strategies: A Fresh Perspective Chia Rui Ming Daryl1, Lim Kai Jie Shawn2 and Chan Ho Yan Sabrina3

Abstract

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In this study, we contribute to existing literature on momentum strategies by assessing a modified version of risk-return ratio based security selection criterion in an untested market â&#x20AC;&#x201C; the KOSPI 200 over June 2006 to June 2012. Besides conventional risk-return ratios such as the Sharpe ratio, we also employ the use of risk-return ratio based ranking criterion first introduced in Biglova et al. (2004) when ranking securities to form portfolios for these strategies. These ratios take into account the non-normality and kurtosis that are ubiquitous in equity time series returns. In contrast to their approach however, we invert the ordinal ranking of negative risk-return ratios to be consistent with the interpretation of negative ratios presented in Sharpe (1994). Applying these methods, this study quantifies and compares the performance of returns based and risk-return ratio based momentum strategies while estimating the transaction costs involved in implementing such strategies. For return based momentum strategies, we show that most strategies involving a 3 or 6 month formation period exhibit statistically significant positive returns, while those with a 9 or 12 month formation period do not. In addition, all risk-return ratio based strategies failed to generate returns that are significantly greater than zero.

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JEL classification numbers: G11, G14 Keywords: momentum strategies, risk-return ratio based selection criteria, portfolio turnover

Department of Statistics, University of Warwick, Coventry, UK. e-mail: r.m.d.chia@warwick.ac.uk 2 Department of Economics, University College London, London, UK. e-mail: kai.lim.11@ucl.ac.uk 3 Department of Economics, University of Cambridge, Cambridge, UK. e-mail: hysc3@cam.ac.uk Article Info: Received : December 4, 2012. Revised : December 29, 2012. Published online : February 10, 2013

North American Review of Finance, vol.13, no.1

1 Introduction

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Momentum refers to the short-term continuation of return performance based on prior short term returns or risk-adjusted returns. Implicit in the examination of momentum strategies is the selection of outperforming and underperforming securities based on past returns and an investigation into the dynamics of their future returns. Having garnered much attention for its simplicity in execution and apparent profitability, the performance of momentum strategies is now well documented in academic literature. Present academic literature is largely in support of the presence of momentum returns. Early studies on momentum find their roots in Levy (1967), which showed that the relative-strength trading rule of purchasing stocks with higher than average prices over a prior 27 week period led to significant abnormal returns. In support of such a concept was the relative success of the mutual funds studied by Grinblatt and Titman (1989, 1991), who showed that the majority of mutual funds in their sample displayed a tendency to purchase stocks that returned positively over a previous quarter. Also congruent with such findings was evidence from Copeland and Mayers (1982) and Stickel (1985) on the predictive power of Value Line rankings, of which was primarily driven by a relative- strength methodology. Later on, Rouwenhorst (1998) proceeded to show that an internationally diversified portfolio of top performing securities outperformed the bottom performing portfolio by 1 per cent per month over 1980 to 1995. The author also proceeded to dissect the source of returns with the use of factor models, showing that momentum returns weigh traditional return drivers of firm size and market return negatively. Modern literature have then continued to consistently support the presence of significant momentum-strategy returns, in particular Jegadeesh and Titman (2001), Hu and Chen (2011) and Elsayeda (2012), while Biglova et al. (2004) and Bornholt and Malin (2011) have shown that augmenting stock selection criteria in momentum strategies with volatility and risk metrics have further improved momentum returns. Still, while the wealth of evidence in support of momentum strategies remains convincing, employing a momentum strategy brings with it several forewarnings. First and foremost, seasonality in returns could serve to skew results if momentum strategies were initiated in certain months. For instance, tax-loss harvesting has shown to manifest itself in the January Effect and November effect, both of which significantly alters the performance of momentum strategies initiated in those months. Debondt and Thaler (1985) first showed in their study of contrarian trading strategies â&#x20AC;&#x201C; through a largely similar methodology as present momentum strategies, save for its long term time horizons â&#x20AC;&#x201C; that bottom performing loser portfolios experience abnormally large January returns as far as five years after portfolio formation. Jegadeesh and Titman (1993) then showed in their relative strength momentum strategy how January returns differed significantly from those during the other months, and that January returns were inversely related to firm size. To add on to the conundrum, the author further showed that consistently large returns in April were evident and was possibly explained by corporations having to transfer money to their pension funds by 15 April in order for the latter to qualify for a tax deduction in the prior year. Support for the presence of the January effect then continues to show in modern literature, most notably in Chu, Liu and Rathinasamy (2004), Anderson, Gerlach and DiTraglia (2007) and Moller and Zilca (2008). Johnston and Paul (2005) then showed how similar tax loss selling manifests itself in the November effect, and Das and Rao (2011) display international empirical evidence with Loughran (1997), showing that the value premium in January is three to nine times that of other months, with results being 35

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robust to sample period and value-growth indicators used. From the perspective of momentum strategies, Grinblatt and Moskowitz (2004) then showed that a significant fraction of momentum profits arrive from short positions initiated in November. Such is evidence to show that seasonality plays a large part in the success of momentum strategies. Next, research on exploiting the performance persistence of securities that perform well on a risk-adjusted basis through momentum strategies is virtually non-existent. Long standing research and the present body of literature have largely been focused on central tendency measure of returns, oblivious to second and higher order moments despite there being widespread evidence of how security returns follow non-normal and leptokurtic distributions. In that respect, alternative measures of ranking securities that consider higher order moments have still hardly been studied. Only recently did Biglova et al. (2004) introduce the concept of incorporating the Sharpe Ratio from Sharpe (1994) and newly conceived quantile-based coherent risk measures, known as the STARR Ratio and Rachev Ratio and detailed in Martin, Rachev, and Siboulet (2003) and Biglova et al. (2004b), in the security ranking and selection process. The authors successfully showed that the application of the STARR Ratio and Rachev Ratio to daily data led to the best performing momentum strategies based on cumulative returns and independent performance measures that employ coherent risk measures. These measures outperformed the Sharpe Ratio and traditional return-based ranking methodologies. Later on, the authors expanded their study to the 517 stocks in the S&P 500 index over the period of 1996 to 2003 in Rachev et al. (2007), finding that although the traditional return-based ranking methodology returned an annualised 15.35% while the alternative Rachev Ratio gave an annualised 10.32% return, the latter measure provided considerably better risk-adjusted performance. Further, they concluded that the stable Paretian distribution hypothesis provides a better fit to momentum returns, and further conclude that implicit in momentum investing is the exposure to heavy tail distributions, making the application of coherent risk measures all the more important in momentum strategies.Lastly, transaction costs serve to significantly erode returns. This is especially so given the frequent rebalancing required and the significant weighting of momentum portfolios to small and illiquid securities. Lesmond et al. (2004) found that momentum strategies involved the trading of stocks with relatively high costs, while Grinblatt and Moskowitz (2004) found that the majority of momentum returns were derived from trading small and illiquid stocks, though after trading costs momentum strategies remained profitable. Li, Brooks and Miffre (2009) quantified such costs in their study covering the UK equity market by integrating bid-offer spread and broker commission costs into their momentum model. The authors found that based on effective spread estimates computed from the Lee and Ready (1991) model, a 6 month holding cum investment period momentum strategy returned 5.79% after fees, a full 19.95 percentage points less than the annual momentum profit gross of fees. Alas, we aim to quantify in this paper returns based momentum strategy cumulative returns in a previously untested market over a recent long-term horizon encompassing the global financial crisis. On top of that, we investigate how the use of risk-return ratio based (â&#x20AC;&#x2DC;risk basedâ&#x20AC;&#x2122;) selection criterion affect the results, while estimating the turnover required to execute such strategies. The rest of this paper is structured as follows: Section 2 touches upon the background of our study, Section 3 our data and methodology, while Section 4 presents the results of our study and an evaluation of the results. We then conclude in section 5 and provide references in section 6. North American Review of Finance, vol.13, no.1

2 Background

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This study aims to contribute to existing literature by examining the returns of a range of momentum strategies in a presently untested market over a recent span of time. We investigate how momentum strategies performed amongst the KOSPI 200 index securities in the period of June 2006 to June 2012 which aptly comprises both a low volatility and a high volatility regime that is the Global Financial Crisis, with the aim of showing how a range of momentum strategies perform throughout a period of contrasting economic and trading regimes. While doing so, this study is the first to combine the classical momentum study employed in early literature, a seasonality study, the novel risk based security selection methodology pioneered by Biglova et al. (2004), and finally, a presentation of portfolio turnover figures as well. The range of strategies considered first spans different combinations of portfolio formation and holding periods. We perform the classical momentum study applied since early literature to determine how a permutation of portfolio formation period J months (the length of time which each security is observed and their respective cumulative returns are ranked) and holding period K months (the length of time that each chosen portfolio is held for and contributes to the returns of the strategy) fares in terms of returns when the strongest past performing securities are bought and an equal dollar amount of the weakest past performing securities are sold short. Previous studies have shown that each combination had significantly varying profitability, and it is such profitability which we will compare and examine the statistical significance. Then, we incorporate risk based security ranking methodologies to surmount the limitations past studies faced with regards to non-normal return distributions. These risk based methodologies are in the form of the Sharpe Ratio and the recently developed STARR Ratio and Rachev Ratio, of which were employed to significant success in ground-breaking research by Biglova et al. (2004) and Rachev et al. (2007), and of which have not been adopted by studies performed since then. Unlike these two studies, however, we offer a significantly different interpretation and treatment of negative Sharpe Ratios and STARR ratios as per stated in Sharpe (1994) and discussed further in Sharpe (1998) with regards to the Sharpe Ratio. That is, with a long/short strategy akin to momentum strategies, the risk adjusted performance of an investment correlates positively with the magnitude of any negative Sharpe Ratio. Put in other words, a highly negative Sharpe Ratio should be viewed favourably vis-Ă -vis a less negative Sharpe Ratio. This interpretation is converse to that when assuming the borrowing-lending scenario in CAPM and is supported by Sharpe (1994) and Sharpe (1998) when used in the context of going long and short positive and negative Sharpe Ratio securities respectively. It is of note, however, that by design the Rachev Ratio is almost immune to such ambiguity of interpretation â&#x20AC;&#x201C; by design, both the numerator and denominator of the Rachev Ratio are positive in virtually all circumstances. Finally, we display turnover figures for the range of strategies considered and allow the reader to evaluate based on the readerâ&#x20AC;&#x2122;s own transaction cost function how attractive each strategy remains when transaction costs are taken into account. It is hence through an especially holistic examination of the performance of the classical and the most recent in momentum strategies to the KOPSI 200 in the economic regime- varying 2006 to 2012 period that this study aims to contribute to existing literature.

North American Academic Journals, 2013

3 Methodology 3.1 Data

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Daily closing price and market capitalization data for the period June 2005 to June 2012 were extracted from the Bloomberg Professional service for each of the KOSPI 200 index constituents. In order to best reflect the investable opportunity set throughout the entire period, index constituents were refreshed every 12 months. Also, congruent with performing the momentum simulations from an ex-ante investment perspective, we included in the data extraction process the price data of firms which have been removed from the KOSPI 200 index but have not been entirely delisted from the stock exchange. Such is necessary as a momentum investor, post having a stock he has invested in removed from the index, would still hold a stock as long as it was deemed a buy or sell during the formation period. The price data was adjusted for normal cash dividends (regular cash, interim, income, estimated, partnership distribution, final, interest on capital, distributed and prorated), abnormal cash dividends (special cash, liquidation, capital gains, memorial, return of capital, rights redemptions, return premium, preferred rights redemption, proceeds/rights, proceeds/shares, proceeds/warrants) and capital changes (spin-offs, stocks splits/consolidations, stock dividend/bonus, rights offerings/entitlement). Such would ensure maximum return representativeness, given that momentum strategies involving long and short positions in securities will be exposed to the relevant long or short holding yields and costs. Finally, the price data was checked for missing data points â&#x20AC;&#x201C; apart from those prior to stock listing and after delisting â&#x20AC;&#x201C; of which were highly uncommon but which would serve to bias volatility statistics in the later part of our study. While such a situation was highly uncommon, we performed such a check to ensure that stocks were not ranked and considered if there was one or more monthsâ&#x20AC;&#x2122; worth of data missing from the formation period. Apart from price data, the study also involved the use of the daily closing yield to maturity of the generic Korean 3 month government bill, which similarly was extracted from the Bloomberg Professional service.

3.2 Classical Momentum Study

The aim of this study is to investigate the empirical returns of the return based momentum strategy over the period of June 2006 to June 2012 in the KOSPI 200, given 16 distinct permutations of J and K, where J = 3, 6, 9 or 12 and K = 3, 6, 9 or 12, and a 1 month time lag between the end of the J-month portfolio formation period and the K-month portfolio holding period. The first step involves identifying the bottom decile performers and top decile performers in an ordinal ranking of cumulative returns over the J-month formation period for each month between June 2005 and June 2012. Only securities with a full set of data in the formation period are considered for ranking. These two distinct groups, which are updated each month, are referred to as the recommended Winner and Loser securities respectively. It is of note that in order to apply the 1 month lag between the formation period and holding period, the J-month formation period for any month comprises the J-month period starting (J + 1) months prior to the start of the holding period. For instance, the 3-month formation period for June 2007 comprises of February, March and April 2007. Such a lag, of which has become standard practice since Jegadeesh and Titman (1993), is applied in order to circumvent the bid-ask spread, price pressure and lagged reaction effects that were detailed in Jegadeesh (1990) and Lehmann North American Review of Finance, vol.13, no.1 38 (1990).The first step involves identifying the bottom decile performers and top decile

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performers in an ordinal ranking of cumulative returns over the J-month formation period for each month between June 2005 and June 2012. Only securities with a full set of data in the formation period are considered for ranking. These two distinct groups, which are updated each month, are referred to as the recommended Winner and Loser securities respectively. It is of note that in order to apply the 1 month lag between the formation period and holding period, the J-month formation period for any month comprises the J-month period starting (J + 1) months prior to the start of the holding period. For instance, the 3-month formation period for June 2007 comprises of February, March and April 2007. Such a lag, of which has become standard practice since Jegadeesh and Titman (1993), is applied in order to circumvent the bid-ask spread, price pressure and lagged reaction effects that were detailed in Jegadeesh (1990) and Lehmann (1990). Next, recommended Winner and Loser portfolios are formed on each holding month by having them hold the recommended Winner or Loser securities from the relevant J-month holding period. Due to the need for time-overlapping of portfolios, however, these recommended portfolios are not exactly the ones the strategy will hold (only the first portfolio held consists entirely of recommended securities, i.e. the June 2006 held portfolio). Instead, the held portfolios are formed according to the rule that in any given month, each portfolio held consists of an equally weighted basket of the current month’s and previous (K – 1) months’ held portfolios. These time-varying portfolios are rebalanced every month to reflect the held portfolios of the most recent K-months in equal weight. It is of note that time-overlapping periods have become the standard since Jegadeesh and Titman (1993), and is necessary in order to negate the bias created due to cyclicality or seasonality in monthly return patterns. Finally, the monthly returns of these portfolios over the June 2006 to June 2012 period under study are calculated. The monthly Winner portfolio returns are then subtracted by the monthly Loser portfolio returns to derive the Winner Minus Loser portfolio returns, which represents the strategy of going long past winners and shorting past losers, essentially forming a zero cost portfolio. The above process is then repeated for all 16 permutations of J and K. These are, in the form J/K, 3/3, 3/6, 3/9, 3/12, 6/3, 6/6, 6/9, 6/12,9/3, 9/6, 9/9, 9/12, 12/3, 12/6, 12/9, 12/12. One-tailed t-tests are then performed toinvestigate if each strategy’s Winner Minus Loser cumulative return, i.e. the momentumreturn, is statistically greater than zero.

3.3 Risk-Return Based Security Selection

In this section, we apply the risk based security ranking methodology introduced with much success in Biglova et al. (2004), as explained in Section 1, to the 6/6 portfolio. The portfolio selection process, the nature of overlapping time periods and the one month lag between formation and holding periods are similar to that described in Section 3.2, except for the ranking methodology. In Section 3.2 for the 6/6 case in particular, we ranked securities based on cumulative return performance during the 6-month formation period and derived the Winner and Loser’s portfolio performance over the 6-month holding period. Now, instead of cumulative returns, we will instead rank securities based on the following three risk based ratios: 1. Sharpe Ratio. Adopted from Sharpe (1994), a security’s Sharpe Ratio is the ratio of its mean excess return over the risk free rate to the standard deviation of the excess return: (1) where, in our study, 39

North American Academic Journals, 2013

Ri : Daily return on a security iRf : Daily risk free rate calculated from the yield to maturity of the 3 month South Korean government bill. What makes this study unique, however, is its significantly different interpretation and treatment of negative Sharpe Ratios as previously explained in Section 2 above. In line with that, we sort securities from high positive Sharpe Ratios to low positive Sharpe Ratios, followed by highly negative Sharpe Ratios to less negative Sharpe Ratios. The same is performed for the STARR Ratio. 2. STARR Ratio. Adopted from Martin, Rachev, and Siboulet (2003), a security’s STARR ratio is the ratio between the security’s mean excess return to its Conditional Value at Risk (CVaR) at the (1-α) confidence level. (2)

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The CVaR is also commonly known as the Expected Tail Loss (ETL) and in this study, the CVaR is calculated on a non-parametric basis and is equal to the mean of the lowest (100α)% of daily returns for each security. We calculate the STARR Ratio for α = 0.01, 0.05, 0.1, 0.25 and 0.5, similar to those used in Biglova et al. (2004) and Rachev et al. (2007). As mentioned in the description of the Sharpe Ratio above, the STARR ratio faces the same treatment of negative values when sorting as when Sharpe Ratios are used.

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3. Rachev Ratio (R-Ratio). Adopted from Martin, Rachev, and Siboulet (2003), a security’s R-Ratio is the ratio between the ETL of the negative of the excess return at the (1-γ1) confidence level to the ETL of the excess return at the (1-γ2) confidence level. (3)

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In the non-parametric case, as with this study, the R-Ratio is calculated as the ratio of the mean of the highest (100γ1)% of returns to the mean of the lowest (100γ2)% of daily returns for each security. We calculate the R-Ratio for (γ1, γ2) = (0.01, 0.01), (0.05, 0.05), (0.09, 0.09), (0.5, 0.01) and (0.5, 0.05), similar to those used in Biglova et al. (2004) and Rachev et al. (2007). The Rachev Ratio is sorted in increasing order, unlike the Sharpe and STARR Ratios. It is both by the design of the ratio and the near impossibility of the Rachev Ratio being negative given the number of sample points in the 6-month formation period that such a sorting methodology is utilised. As a side note, it could be said that the circumvention for the non-monotonic sorting methodologies required with the Sharpe and STARR Ratios makes the Rachev Ratio more intuitive and eases communication when in use among practitioners. Once the securities under study have been ranked each month according to the above three ratios, we continue to apply the formation and holding methodologies as set out in section 3.2 to derive momentum return statistics for each of the three ratios above with each of the abovementioned parameters.

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3.4 Portfolio Turnover Finally, we calculate turnover figures for the momentum strategies under examination in order to allow readers to evaluate the cost of implementing the said momentum strategies based on their own transaction cost function. Each month’s turnover is calculated as the percentage of stocks that are dissimilar between two portfolios – the equally weighted Winner Minus Loser portfolio of a particular month and the Winner Minus Loser portfolio of the subsequent month. The turnover for a particular strategy is then calculated as the average monthly turnover over the entire period under study, and is presented as a monthly figure, just like return figures are in this study.

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4 Results and Discussion

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The results from adopting the range of momentum strategies under study over the period June 2006 to June 2012 are displayed on the following page. Specifically, the returns of the returns based momentum strategy and risk based momentum strategy are displayed in tables 1 and 2, with highlighted cells corresponding to those of the Winner Minus Loser portfolio. The range and central tendency of portfolio turnover over all strategies are then stated in the subsequent discussion. It is clear from the results that some of the classical returns based strategies achieved statistically significant positive returns in the Winner Minus Loser portfolio over the study period at the 95% confidence level of a one-tailed T-test. Namely, these are the 3/6, 3/9, 3/12, 6/6, 6/9, 6/12 portfolios. Such figures contribute to the well-established body of research in support of returns based momentum strategies. Further supporting the often discovered result of mean reversion, i.e. the ‘reversal’ of momentum in the longer term, the 9 and 12 month formation period portfolios show returns that are statistically insignificant from zero across the board. Surprisingly, however, and in contradiction with the Biglova et al. (2004) study – the first and only paper applying the Sharpe ratio and newly developed Rachev and STARR ratios to momentum strategies – the 6/6 portfolios failed to display any statistically significant positive returns, even though the 6/6 return-based strategy did. Such a result holds for all ratios tested – the Sharpe Ratio and STARR ratio, of which negative values were treated differently from Biglova et al. (2004) but in a manner in which Sharpe (1994) and Sharpe (1998) espoused, and the Rachev ratio, of which values were sorted in increasing order, similar to the methodology in Biglova et al. (2004).

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Table 1: Momentum Strategy Returns â&#x20AC;&#x201C; Returns Based Security Selection

6 6 9

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T-Statistic

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Standard Deviation of Return 8.64% 8.95% 6.30% 8.45% 9.09% 6.62% 8.52% 9.08% 6.13% 8.41% 8.88% 5.23% 9.34% 10.26% 9.53% 9.07% 9.86% 9.06% 8.96% 9.68% 8.03% 8.87% 9.48% 7.21% 11.43% 9.83% 10.21% 11.42% 8.92% 9.63% 11.52% 8.44% 8.86% 11.39% 8.12% 7.72% 11.92% 10.13% 11.57% 12.01% 9.05% 10.33% 12.07% 8.56% 9.25% 11.82% 8.26% 8.17%

1.14

1.73

2.38

2.83

1.44

Winner (W) Loser (L) W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L

Mean Monthly Return 0.98% 0.14% 0.84% 0.95% -0.40% 1.34% 0.91% -0.80% 1.71% 0.69% -1.05% 1.73% 1.35% -0.26% 1.61% 1.36% -0.67% 2.03% 1.33% -1.09% 2.42% 1.08% -1.24% 2.31% -11.19% -9.48% -1.71% -11.19% -9.68% -1.51% -11.13% -9.89% -1.24% -10.90% -10.08% -0.82% -11.02% -9.81% -1.21% -10.77% -10.00% -0.77% -10.38% -10.32% -0.07% -10.05% -10.72% 0.67%

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K, Holding Period (Months)

J, Formation Period (Months)

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1.91

2.57

2.74

-1.43

-1.34

-1.20

-0.91

-0.89

-0.63

-0.06

0.70

Table 2: Momentum Strategy Returns - Risk Based Security Selection, 6/6 portfolios Mean Monthly Return

Winner (W) Loser (L) W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L W L W-L

0.78% 0.07% 0.71% 0.35% 0.82% -0.46% 0.82% -0.59% 1.41% 0.70% -0.35% 1.05% 0.65% 0.60% 0.06% 0.60% 0.51% 0.09% 0.74% 0.19% 0.54% 0.73% 0.20% 0.53% 0.76% 0.08% 0.68% 0.76% 0.11% 0.65% 0.71% -0.01% 0.72%

Rachev(0.05,0.05)

Rachev(0.01,0.01)

STARR(0.25)

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STARR(0.5)

STARR(0.1)

STARR(0.01)

T-Statistic

1.04

-0.85

1.68

1.43

Rachev(0.5,0.01)

Rachev(0.5,0.5)

Rachev(0.09,0.09)

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Sharpe Ratio

Standard Deviation of Return 8.89% 7.10% 5.85% 8.10% 8.26% 4.69% 8.85% 8.11% 7.19% 8.88% 7.66% 6.26% 7.90% 8.15% 4.10% 7.50% 7.55% 3.30% 8.77% 7.15% 5.61% 8.70% 7.11% 5.53% 8.81% 7.19% 5.81% 8.85% 7.15% 5.76% 8.71% 7.05% 5.68%

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Ratio

0.12

0.23

0.83

0.82

1.00

0.97

1.08

5 Conclusion In this study, we contributed to the present momentum strategy literature by testing newly introduced risk based security selection criterion in an untested market. While second and higher order moments of return distributions were not taken into account previously, the use of novel risk based ranking criterion used in this study takes into account the nonnormality and kurtosis in equity time series returns. Further to that, we modified the

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model by utilising an approach to treating negative Sharpe and STARR ratios that is novel to the risk based momentum model employed in this study. Applying these methods, this study quantified and juxtaposed momentum strategy cumulative returns with returns based and risk based ranking measures. In support of the long standing and well documented momentum returns, we demonstrated the profitability of the returns based momentum strategy with the 3/6, 3/9, 3/12, 6/6, 6/9, 6/12 period strategies, with momentum returns being eroded by the phenomena of mean reversion in the longer term, as evident from insignificant returns when the 9 and 12 month formation period is employed. Further to that, we discovered a contradiction to the results of Biglova et al. (2004) â&#x20AC;&#x201C; the first and only study on momentum returns using the novel risk ratios adopted in this study â&#x20AC;&#x201C; by demonstrating how risk based ranking criterion failed to generate statistically significant returns in the specific equity market and time period under study. Such lacklustre profitability is then further worsened by transaction costs that are congruent with an approximate 174% annual portfolio turnover necessary to maintain such a strategy, while the lack of momentum returns to be had is further supported by the 87% monthly turnover of the sixth of the 6/6 portfolio which is reconstituted each month. Alas, while we have demonstrated the lack of profitability of risk based-momentum strategies in a specific market and time period, we refrain from making general conclusions with respect to their profitability. Such is simply because the body of literature that examines the effectiveness of such risk based measures is small â&#x20AC;&#x201C; this makes only the second paper applying risk based criterion to momentum strategies, and is the only paper to have modified the model to be congruent with the treatment of negative Sharpe and STARR ratios espoused by Sharpe (1994) and Sharpe (1998). In that vein, further research should be made into risk based momentum strategies, so that this novel strategy may be tested in a wider range of markets, time periods and trading regimes.

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[2]

R. Levy, Relative strength as a criterion for investment selection, Journal of Finance 22, 1967, 595-610. M. Grinblatt and S. Titman, Mutual fund performance: An analysis of quarterly portfolio holdings, Journal of Business 62, 1989, 394-415. M. Grinblatt and S. Titman, Performance measurement without benchmarks: An examination of mutual fund returns, Working paper, University of California at Los Angeles, 1991. D. Mayers, T. Copeland, The Value Line Enigma (1965-1978): A Case Study Of Performance Evaluation Issues, Journal of Financial Economics, November 1982, pp. 299-321. S. Stickel, The effect of Value Line Investment Survey rank changes on common stock prices, Journal of Financial Economics; 14, 1985, 121-143. K. Rouwenhorst, International Momentum Strategies, The Journal of Finance, Vol. 53, No. 1, Feb., 1998, pp. 267-284. N. Jegadeesh and S. Titman, Jegadeesh, Narasimhan, and Sheridan Titman, Profitability of momentum strategies: An evaluation of alternative explanations, Journal of Finance 56, 2001, 699-720.

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6 References

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J. Hu and Y.C. Chen, The Performance of Momentum Investment Strategies: An International Examination of Stock Markets, International Journal of Management, Vol. 28 Dec 2011, No. 4 Part 1. I. Elsayeda, Do Momentum and Contrarian Profits Exist in the Egyptian Stock Market?, International Research Journal of Finance and Economics ISSN 1450-2887 Issue 87, 2012 A. Biglova, T. Jašic, S. Rachev and F.J. Fabozzi, Profitability of momentum strategies: Application of novel risk/return Ratio stock selection criteria, 2004. G. Bornholt and M. Malin, Using Volatility to Enhance Momentum Strategies, JASSA The Finsia Journal of Applied Finance, Issue 2, 2011. W. Debondt and R. Thaler, Does the Stock Market Overreact?, The Journal of Finance, Vol. 40, No. 3, Papers and Proceedings of the Forty-Third Annual Meeting American Finance Association, Dallas, Texas, Jul., 1985, pp. 793-805. J. Chu, T. Liu and R. Rathinasamy, Robust Test of the January Effect in Stock Markets Using Markov-Switching Model. Journal of Financial Management and Analysis 17 (1), 2004, 22-33. L. Anderson, J. Gerlach and F. DiTraglia, Yes, Wall Street, There is a January Effect: Evidence from Laboratory Auctions, Journal of Behavioral Finance, 2007, 8 (1), 2007, pp. 1–8. N. Moller and S. Zilca, The Evolution of the January Effect, Journal of Banking and Finance, Vol. 32, No. 3, 2008. K. Johnston and C. Paul, Further evidence of the November effect, Journal of Economics and Finance, 29, 2005, 280 – 288. P. Das and S. Rao, The Value Premium and the January Effect, ISSN: 0307-4358, 2011. T. Loughran, Book-to-market across firm size, exchange, and seasonality, Journal of Fi- nancial and Quantitative Analysis 32, 1997, 249–268. M. Grinblatt and T. Moskowitz, Predicting Stock Price Move-ments from Past Returns: The Role of Consistency and Tax-Loss Selling, Journal of Financial Economics, 71, no. 3, 2004, pp. 541–579. W. Sharpe, The Sharpe Ratio, Journal of Portfolio Management, vol. 21, no. 1 (Fall), 1994, 49–58. D. Martin, S. Rachev, and F. Siboulet, Phi-alpha optimal Portfolios and Extreme Risk Management, Wilmott Magazine of Finance, 2003, pp.70-83. A. Biglova, S. Ortobelli, S. T. Rachev and S. Stoyanov, Different approaches to risk estimation in portfolio theory, Journal of Portfolio Management 31, 2004, 103–112. S. Rachev, T. Jasˇic, S. Stoyanov, F. Fabozzi, Journal of Banking & Finance 31, 2007, 2325–2346 D. Lesmond, M. Schill and C. Zhou, The Illusory Nature of Momentum Profits. Journal of Financial Economics 71, 2004, 349–380. C. Brooks and J. Miffre, Low-cost Momentum Strategies, Journal of Asset Management, Vol. 9, 6, 2009, 366–379. C. Lee and M. Ready, Inferring Trade Direction from Intraday Data, Journal of Finance 46, 1991, 733–746. W. Sharpe, Morningstar’s Risk-Adjusted Ratings, Financial Analysts Journal, Vol. 54, http://www.edhecrisk.com/research_news/choice/RISKReview1098452123721247487, 1998.

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[28] W. Sharpe, Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk, Journal of Finance, September, 19, 1964, pp. 425â&#x20AC;&#x201C;42. [29] J. Lintner, The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets, The Review of Economics and Statistics, Vol. 47, No.1, 1965, pp.13-37. [30] E. Fama and K. French, Common Risk Factors in the Return on Stocks and Bonds, Journal of Financial Economics, vol. 33, 1993. [31] N. Jegadeesh, Evidence of Predictable Behavior of Security Returns. Journal of Finance 45, 1990, 881-899.

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Currency Exposure, Second-Moment Exchange Rate Exposure and Asymmetric Volatility of Stock Returns: The Effects of Financial Crises on Taiwanese Firms RenĂŠ Ferenc (Franck) Varga1

Abstract Over the last two decades, a number of financial disasters have occurred due to failure in risk management procedures. If some, as the Asian financial crisis, had a very much more muted global impact (even though they sent shock waves through global financial markets, the main damage were fairly contained), the global financial crisis we are witnessing since 2007 is in many respects unparalleled. Compared to many other countries, we could observe that Taiwan performed better. But it does not mean that structural changes did not affect individual firms. This study investigates (i) the impact of first- and second-moment exchange rate exposure on individual firm value and the stock return volatility underlying exchange rate fluctuation, (ii) the time-varying exchange rate exposure following the 1997 Asian financial turmoil and the global financial crisis which started in 2007. We find a high percentage of exposed firms before the two crises but if this percentage decreases dramatically after, the exposure level is much larger. The two crises affect also the asymmetric profile of the firms and volatilities. Finally, when we study the breakdown between systematic and diversifiable risks, we find that the market risk of the Taiwanese firms decreases after the 1997 crisis but is higher after the 2007 crisis increasing thus their equity financing cost. JEL Classification: C22, F31, G12, G15, G31 Keywords: Exchange Rate Exposure, Asymmetric Currency Exposure, Financial Crises, Asymmetric volatility, GJR GARCH-M

Department of Global Politics and Economics, Tamkang University, Taiwan email: 134378@mail.tku.edu.tw Article Info: Received : November 28, 2012. Revised : December 21, 2012. Published online : March 1, 2013

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1 Introduction Financial theory holds that exchange rate movements significantly affect firm value via their effects on the competitiveness of the firm’s products, the cost of its inputs, the value of its foreign assets, its sensitivity to short-term cash flows (i.e. the probability of financial distress) and its cost of capital (i.e. growth opportunity). But there is also much evidence from practitioners that exchange rate movements affect firms. Hung [41] estimates for example that due to a strong dollar during the 1980s American manufacturers lost annually about USD23 billion, representing 10% of their gross profits. Rosenberg [64] mentioned another survey which indicates that more than 45% of American companies are adversely affected by a strong dollar and later when the dollar weakened around 2002, various industries experienced higher exports and earnings. This indicates that exchange rate movements affect both small and large firms. Without any doubt, similar observations have been made all around the world. The foreign exchange rate is even becoming a political tool. Academics and practitioners, all agree that fluctuations in foreign exchange rate are a source of uncertainty for the firm, regardless its size and whether the firm is domestically or internationally oriented. Empirical studies already document significant impacts of these fluctuations on firm cash flows, sales and competitive positions in product markets (Hung [41], Williamson [69]). Similarly, theoretical models predict that firms should display a significant exchange rate exposure (see for example Bodnar, Dumas and Marston [14]). A firm’s exchange rate exposure refers to the sensitivity of its economic value (or stock price) to exchange rate changes (Heckman [39]) or as stated by Adler and Dumas [1], its economic exposure to exchange risk. If the volatility of exchange rates affect firm value (stock price), the question is to know how sensitive is the value of the firms to exchange rate movements. In another word, it means how the market prices the currency risk. However, empirical studies have tended to document weak relations between exchange rate changes and firms’ stock prices, if any at all. These studies include Jorion [44] and [45], Amihud [5], Bodnar and Gentry [15], Bartov and Bodnar [9], Griffin and Stuls [37] or Dominguez and Tesar [30], just to name some. In most of the studies, the percentage of firms displaying statistically significant exposures tends to be only about twice the chosen level of statistical significance, hence the term “exposure puzzle”. Bartram and Bodnar [11] argue that the puzzle is mostly the result of “overly optimistic prior assumptions of the part of the researcher about the extent of significant exposures within a population of firms”. They explain that low percentages of exposed firms are the result from “exposure reducing actions” which include both financial and operational hedging activities. Bartram, Brown and Minton [12] show empirically that firms pass through part of currency changes to customers, which combined with operational hedging, each reduce firms’ exposure by 10% to 15%; moreover, financial hedging with foreign debt decreases exposure by about 40%. Nevertheless, it seems that small and open economies may be a better laboratory to explore the exposure puzzle, see for example Moran [57]. Varga [68] studied the currency exposure of Taiwanese firms. Taiwan is clearly an open economy according Friberg and Nydahl [33] criteria. He found that almost 89% of his sample (107 firms using daily data) is exposed to exchange rate fluctuations. Moreover, all the concerned firms are negatively exposed: they benefit from an appreciation of the domestic currency (TWD).

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The purpose of this paper is to increase our understanding of the relationship between exchange rates changes and stock returns at the individual firm level. More specifically, we want to investigate if this relationship is time-varying by focusing on the potential impacts on it from the 1997 financial Asian and the 2007 global financial crises. In other words, the question we want to address is not if Taiwanese firms are or not exposed (they are, see Varga [68]), but to see how (if) financial crises affect exchange rate exposures, exchange rate volatility and individual stock returns. On July 2nd, 1997 the financial Asian crisis started to spread in a larger way than most of the previous crises. Asian stock markets were affected as well worldwide economic growth. The wide foreign exchange fluctuations which followed increased the currency risk for most of the firms in the world. The Asian crisis seems to be more caused by financial imbalances in the private sector than in the public sector. So even thoughTaiwan was less impacted than other Asian countries, we can reasonably believe that vulnerability of Taiwanese firms to currency risk has increased. Then, ten years later, we have to face a financial tsunami. The global financial crisis of 2007 (-?) is in many aspects unparalleled. Compared to this tsunami, previous crises such as the Asian crisis or the Russian bond default had a very much more muted global impact, with fairly contained damages. In the early summer of 2007, fixed income markets were under considerable stress and then in July, equity markets experienced high volatility while currency markets were not affected yet. But with this uncertain environment, a major unwinding of the carry trade occurred on August 16 and many currency actors suffered huge losses. It marked the beginning of the crisis in the foreign exchange markets. The one-day change of the AUD/JPY was this day -7.7% compared to the average 0.7% one day earlier. Even with periods of time calmer than others, we started to experience a much higher volatility in the exchange rates. As for the 1997 East Asian crisis, the 2007 crisis cannot be without any consequences on Taiwanese firms and their vulnerability to currency risk. Using a sample of 107 Taiwanese firms, we find a high percentage of exposed firms before the two crises but if this percentage decreases dramatically after (from 70% to about 20%) the exposure level is much higher. All the concerned firms are negatively exposed (they benefit from an appreciation of the domestic currency). The two crises affect also the asymmetric profile of the firms: sign asymmetries are more pronounced after than before the crises (and inversely for the magnitude asymmetries). Volatilities are also greater after than before the crises. Finally, when we study the breakdown between systematic and diversifiable risks, we find that the market risk of the Taiwanese firms decreases after the 1997 crisis (-13%) but increases after the 2007 crisis (+21%). The reminder of this paper is organized as follows. The next section presents related papers. Methodology and sample selection are respectively described in sections 3 and 4. Section 5 reports the main empirical findings and section 6 concludes the paper.

2 Exposure to Exchange Rate Risks: Related Papers An extensive literature followed the paper of Adler and Dumas [1] which introduced a simple model with the stock return as the dependant variable and the change in the exchange rate as the explanatory variable. The resulting coefficient is the sensitivity of the firm to exchange rate movements. In a seminal paper, Jorion [44] investigates it using a

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sample of 287 American multinational firms and an augmented market model (See Jorion [44] and Bodnar and Wong [17] for a discussion of why it is important to include the market return in equation (1)): (1) Ri,t = βo,i + β1,i Rmt + β2,i FX t + εi,t with Ri,t denoting the stock return, Rmt the return on the market index and FX t the change in the exchange rate. More specifically, Jorion [44] used an exchange rate index. The author finds that only 15 firms, i.e. 5.23% of the sample, display a significant exposure at the 5% level of significance, even though the firms have been selected due to their consequential international activities. Amihud [5] does not succeed too even after using as his sample, 32 companies listed in the Fortune magazine’s “50 Leading Exporters” list. Bodnar and Gentry [15], in a multi-country study, find that 21% to 25% of the firms in USA, Japan and Canada display an exposure to exchange rate changes, percentage significantly higher than the ones obtained by Choi and Prasad [23] who used an American dollar index for their US multinational firms: 14.9% at the firm level and 10% at the industry level. Considering the special situation of American companies and currency, authors start to extend their studies outside the USA but with very mixed results. For example, He and Ng [38] find that 26.3% of their Japanese sample is exposed to an exchange rate index while Bartram [10] obtains only 7.5% of his German sample. Nydahl [60] documents a higher level of exposure for his Swedish sample (17%). Dominguez and Tesar [29] analyze exposure in different open, mature and developing countries at the firms and industry level. According the country, they find that between 14% and 26% of the firms are exposed, but one could have expected different results: only 14% of the Chilean sample is exposed, compared to the 47% obtained by Moran [57]. Among authors who do not document exposure at all, Priestley and Odegaard [63] investigate without success seven industries in Norway and none was exposed to the USD or ECU. Several authors choose to study firms’ exposure across many countries as for example Bartram and Karolyi [13] who study the impact of the introduction of Euro and Doidge et al. [28] who use a large sample of firms around North America, Europe and Asia. Both find results in conformity with Griffin and Stulz [37]: the exposure to exchange rate movements is small, not only statistically, but also economically. Many studies use an exchange rate index rather than a bilateral exchange rate, which can explain some mixed results. An index is not representative for an individual firm and can imply a diversification effect across currencies. However, it does not seem that using a bilateral exchange rate improves notably the measure of exposures as showed by Bartram [10]. Another change in the methodology is the use of orthogonalized models. Again, the results were not very different as for example Choi and Prasad [23] and Choi et al. [22]. Nevertheless some authors using orthogonalized model succeed to obtain better results, as Glaum et al. [36] – 49% of the sample being exposed, Priestley and Odegaard [62] – 69% exposed to the JPY and 40% to the ECU, Kiymas [48] – 62% or Chen et al. [21] – 24%. Exposure is a complex concept to measure, especially if we take into account the time the firm needs to adjust its financial management to exchange rate fluctuations or the fact that company information is only disclosed at regular moments in the year hence the time also needed by the market to adjust its valuation process. These facts may lead to mispricing of currencies movements, and push some authors to introduce one more change in the methodology: the lag effect. So, beside contemporaneous exchange rate fluctuations, authors use lagged exchange rate too. Bartov and Bodnar [9] find some evidence at the one-month lag level, but with a very low adjusted R² (0.2%). Frazer and Pantzalis [32] North American Review of Finance, vol.13, no.1

obtain some mixed results, with only 9% of their American sample being exposed. Di Iorio and Faff [26] find non-significant lag effects. Another change in methodology has also been proposed to improve the measurement of firmsâ&#x20AC;&#x2122; exposure: time varying factors, by using sub-periods analysis. The problem is that it is not always easy to explain the time variation of the exposure which may have different economic sources or could even been caused by some estimation errors. There are studies that provide evidence that exposure is more generally time dependant. Brunner et al. [19] find that exposure coefficients are not stable over time for their German sample. Moreover, several studies assert that long-horizon regressions more readily detect significant exposure see for instance Chow et al. [24], [25] and Bodnar and Wong [18]. Muller and Verschoor [59] find considerable evidence of long-term exposure, the short-term seeming to be well hedged. As the horizon increases, the estimation of the exposure improves, especially if the horizon is at least between 3 to 5 years. Chow et al. [24], [25] assert that market participants may wrongly assess the exchange rate risk on the long run. Some authors try to explain the source of the time variation of the exchange rate exposure. Allayannis and Ihrig [3] identify industry markups, Williamson 69] concludes that exposure of his automotive sample changes with market share while pass-through is the main factor for Bodnar and Marston [16]. Patro et al. [61] find that exposure of their OECD sample, varies particularly with import and export. Ihrig and Prior [43] find that some multinationals companies display significant exposure only during crisis periods. Koutmos and Martin [51] find that the variability in the time-varying exposure is smaller (larger) for the largest (smallest) firms and for industrial (technology) firms. The size effect is also confirmed by Hunter [42]. Another explanation of mixed results in measuring exchange rate exposure is related to the fact that most studies only assess the linear component of the exposure, ignoring the nonlinear (asymmetric) exposure. Financial theory indicates that exposure should be at least for one part nonlinear, knowing that cash flows are a nonlinear function of the exchange rates. Several authors investigate asymmetric response to appreciations and depreciations, as Koutmos and Martin [50], Bartram [10], Carter et al. [20] and Tai [67]. If the measurement of the exposure is better when taking into account the nonlinear component, most of the studies display a low marginal improvement. Bartram [10] using a German sample, finds that 14.5% of the firms display a nonlinear exposure (more specifically, a convex exposure â&#x20AC;&#x201C; U form) compared to 8.3% for linear exposure. Results are also mixed for Di Iorio and Faff [26]. But most of the authors agree that using an exchange rate index obscures somehow the detection of exposure. Hsu et al. [40] find that asymmetric exposures are based on industry characteristics. Rossi [66] studies a Brazilian sample of 196 firms and finds that at the 10% level of significance, 38% of the firms display a nonlinear exposure, compared to 29% showing a linear exposure. According several authors such as Koutmos and Martin [50] or Muller and Verschoor [58], various reasons can generate a nonlinear relationship between the value of the firm and the exchange rate movements, mainly asymmetric hedging, incorrect pricing of assets, hysteresis for firms involved in international trade, magnitude of exchange rate fluctuations, pricing policies and market structures, and government interference. Other authors as for instance Kanas [46] and Giurda and Tzavalia [35] cite evidence for the existence of volatility asymmetry in stocks returns, related to currency changes.

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2.1 Asymmetric Hedging One of the main factors to cause nonlinearity in the exchange rate exposure is the risk management chosen by the firm, through the use of hedging or financial derivatives. Firms always try to exploit opportunities and avoid adverse effects from macroeconomic changes, behavior which is reflected in their hedging strategies. It can generate nonlinear payoffs caused by the exchange rate movements leading to a nonlinear fluctuation of the cash flow and consequently the value of the firm. Options allow the company to make asymmetric gains (for example an importer will hedge against the depreciation of the domestic currency while making eventually a “profit” if the local currency appreciates) and the firm’s exposure will also be influenced by the magnitude of the currency fluctuation, see Miller and Reuer [56], Allayannis and Ofek [4] or Rossi [65]. The use of real or financial options means that market-value exposures is larger to beneficial macroeconomic changes than to adverse ones since this kind of hedging allows to protect the firm against adverse changes and exploit beneficial fluctuations, see Andren [6] for more details.

2.2 Errors in Assets’ Pricing Actors of the market may find uneasy to measure the consequences of an exchange rate movement on the firm’s value especially in case of shocks. Indeed, it is difficult to identify if a shock is permanent of just temporary hence the problem to measure the real impact on the firm. Moreover, the way firms disclose their financial information (hedging policies…) is not always totally transparent thus creating the risk to mislead investors in their valuation process. Muller and Verschoor [58] argue that may push investors into a “safe behavior” by ignoring lower magnitude of exchange rate movements and reacting more strongly to greater magnitude especially in case of “bad news”, hence emphasizing the nonlinear component of the exposure.

2.3 Hysteretic and Magnitude of Exchange Rate Change Asymmetries Another important source of asymmetry is the hysteretic behavior. If the depreciation of domestic currency persists, a number of new exporters may enter the market to benefit from the exchange rate movement. Therefore, the profits of the existing exporters may not increase as more firms are sharing the market. If the depreciation of the domestic currency is followed by a period of appreciation it is not sure that companies are in position to just quit the market, given the sunk costs the new comers had to pay. They are more likely to stay in the market with a lower profit or even losses in such a period. In these cases, the exchange rate fluctuations have a negative impact on the firm’s value. This creates an asymmetry in exchange rate exposure. The decrease in profits during appreciations is larger than the increase in profits during depreciations. The phenomenon of hysteresis is logically supposed to occur after greater magnitude exchange rate movement, since small fluctuations will not influence companies in their entry or exit decisions. Therefore, magnitude of exchange rate changes is also a source of asymmetry in the firms’ exposure. The magnitude leading to a response from the firm may depend on the company size, its industry, its past experience or macroeconomic factors. Thus the different responses of the firms to small and large exchange rate fluctuations give birth to the magnitude asymmetry of exchange rate exposure. The question remains in knowing for which

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threshold firms will start to respond and how long is supposed to be the period to attract new comers. See Baldwin [8] and Dixit [27] who describe hysteresis models.

2.4 Pricing-to-market There are several studies describing pricing-to-market behavior of companies which is too, an important source of asymmetry of exchange rate exposure, see for example Froot and Klemperer [34], Marston [54] or Knetter [49] who study this particular behavior which may take either two forms: pricing-to-market in view to maintain or improve the market share and pricing-to market under volume constraints. As Knetter [49] states, the former form assumes that the firms’ goal is to maximize their market share. So if the local currency appreciates, the exporter will not pass on the impacts to buyers by increasing the foreign prices of their products, to avoid the risk of losing market share to competitors from other countries. They may even be prone to reduce their export prices. On the contrary, if the domestic currency depreciates, exporters will maintain their mark-up at the same level, letting the export prices unchanged. Thus, they will not pass the benefits of depreciation by reducing the foreign prices of their goods. Consequently, exporters’ profits may increase to a lesser degree during depreciation periods than decrease in appreciation periods. Pricing-to-market under volume constraints occurs because quota or wrong investment in marketing capacity (bottlenecks). On contrary to the previous behavior, the mechanism works in the other direction. In the case of a depreciation of the domestic currency exporters will not be able to increase their sales volume, because the volume constraints. Therefore, they may increase their foreign price to clear the market, being not interested in passing the benefit of depreciation to the buyers. In the opposite situation, if the domestic currency appreciates, exporters may let the foreign prices reflect the fluctuations and may not use the pricing-to-market: they will not reduce the foreign prices.

2.5 Asymmetries due to Government Interference Government interference in the foreign exchange market may also be a source of asymmetry by indirectly helping domestic firms. If the exchange rate exceeds a certain level, the government may intervene to reduce the currency volatility and hence the firms’ exposure. By limiting the appreciation of the domestic currency, it may help exporters and by controlling the depreciations of the local currency, it will help companies holding debts in foreign currencies. 2.6 Asymmetry in Volatility of Stock Returns Underlying Exchange Rate Exposure The main explanation of the asymmetry in volatility of stock returns is the leverage effect, common concept in finance, through the leverage ratio debt / equity. Resulting from bad news, the negative return shock increases the leverage ratio and the volatility while good news will generate a positive return shock and a lower leverage ratio and volatility. But if we analyze the volatility of stock returns underlying exchange rate exposure, the picture is not so clear. When a domestic currency appreciates or depreciates, we cannot state that we are facing good or bad news. It will depend on the situation of the market participants (exporter, importer etc…) as mentioned by Bodnar and Gentry [15]. But a firm can play more than one role like for instance exporter and internationally priced input user. As

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Maghrebi et al. [52] state, “whether depreciation of domestic currency should be viewed as good news or bad news is an open question”. Other authors cite evidence for the existence of volatility asymmetry in stock returns related to exchange rate fluctuations as for instance Kanas [46] and Giurda and Tzavalia [35] so it seems that this volatility asymmetry is one of the exposure components we need to take into account, even though its mechanism is unclear.

3 Methodology 3.1 Orthogonalized Model There is a drawback of the above mentioned augmented CAPM models (Eq. 1). We cannot estimate the total impact of the exchange rate changes on stock returns as a single coefficient with this specification. Since market returns and exchange rate fluctuations are correlated, the influence of the latter on the firm value can be divided into two components: the direct exposure effect contained in β 2,i and the indirect effect included in β1,i . Alone, β 2,i may under/overestimate the firm’s true exposure to currency fluctuations. Moreover, these two effects may reinforce or offset each other. Under (Eq. 1) if exposure is zero, it does not mean that the firm has no exposure but just that its exposure is the same as the market. To address this issue, various authors as for instance Entorf and Jamin [31] use an auxiliary regression between market returns and exchange rate changes in order to avoid a possible multicollinearity which is usually more frequent when one uses a bilateral exchange rate instead of a trade weighted exchange rate index. It may explain why some authors do not find that orthogonalizing the market portfolio has an effect on their results, see for example Allayannis [2]. The auxiliary regression is described as: Rm,t = δ0 + δ1FX t + δ m,t

(2)

with δ m,t , the orthogonalized market returns, representing the component of market returns that is uncorrelated with exchange rate changes. We replace Rmt in (1) by δ m,t . Substituting (Eq. 2) into (Eq. 1) and rearranging, we obtain the orthogonalized model: * +β δ * Ri,t = β0,i 1,i m,t + β2,i FX t + εi,t

(3)

* = β +β δ β0,i 0,i 1,i 0

(4)

where:

βo,i

* = β +β δ β2,i 2,i 1,i 1 and β1,i β 2,i

(5) are

from

the

unorthogonalized

model

Ri,t = βo,i + β1,i Rmt + β2,i FX t + εi,t * is supposed to show the total impact of exchange rate fluctuations on the Under (3), β2,i firm value. It contains the direct effect β 2,i as well as the indirect effect β1,iδ1 .

The indirect effect is also a firm-specific component of the exposure (as the direct effect)

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in the sense that β1,i varies across firms: each company may have a specific relationship with the market portfolio. This process is just an auxiliary step aiming to measure the component of market returns that is uncorrelated with exchange rate changes in view to obtain an orthogonalized model. So, it is related to the main model to be tested, but not to any sub period.

3.2 Multiple Asymmetries The model captures both, sign asymmetry (responses from the firms after depreciation or appreciation of the domestic currency) and magnitude asymmetry (firms’ reaction to small and large exchange rate fluctuations by distinguishing asymmetric and exposure coefficients. We use dummy variables to measure the effects of an appreciation of the domestic currency (sign asymmetry) and a change in the exchange rate greater (magnitude asymmetry) than a specified filter (threshold). In order to take into account specificities of financial time series as the time-varying volatility, we add a GARCH specification, more precisely a GJR GARCH-M (1,1) which is able to accommodate asymmetry in volatility of stock returns which is as mentioned above, a stylized facts related to the exposure mechanism. The GARCH in Mean specifications allow to analyze the impact of the exchange rate volatility on firm return. The model is described as: * +β δ Ri,t = β 0,i 1,i m,t * +β D + (β2,i 3,i sign,i,t + β 4,i Damp,i,t )st + β5,i hs,t + ε i,t

(6)

where: st = the unexpected change in the exchange rate Dsign,i,t = 1 if st < 0 and 0 otherwise Damp,i,t = 1 if st

> x and 0 otherwise

x = 0.5% hs,t = the time-varying exchange rate volatility ε i,t = error term which follows a GJR GARCH (1,1) process as: ε i,t = µi,t hε ,i,t

(7)

and hε ,i,t = ωε ,i + αε ,iε t2−1 + γ i Di,t −1ε t2−1 + βε ,i hε ,i,t −1 where Di,t −1 is equal to 1 if ε i,t is negative and 0 otherwise.

(8)

hε ,i,t denotes the conditional variance of the residuals and µi,t the white noise error

term. The usual constraints related to GARCH models apply. In this model, it is associated to good news when ε i,t > 0 and bad news when ε i,t < 0. Both outcomes have differential effects on the conditional variance: good news has an impact on αi , while the bad news has an impact on ( αi + γ i ). If γ i > 0, bad news

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increases volatility (we say there is a “leverage effect”). If γ i is statistically significant, it implies the existence of an asymmetric volatility of stock returns underlying exchange rate exposure even though the mechanism through which it comes into being still remains unresolved. Depreciation or appreciation of the domestic currency is not automatically a good or bad news. The last step is to define the exchange rate dynamics. Many previous studies as for example Meese and Singleton [55], find that exchange rates follow martingale processes, so the best forecast for time t+1 is the value at time t. Therefore, changes in FX t follow a martingale of the form: (9) FX t = θ + FX t −1 + st where st is the unexpected change in the exchange rate (innovation) used in equation (6). The conditional variance of st follows a GARCH (1,1) process defined as: st = ρi,t hs,t

(10)

and hs,t = ω s,i +α s,i st2−1 + βs,i hs,t −1

(11)

hs,t denotes the conditional variance of st and ρi,t the white noise error term.

The usual constraints related to GARCH models apply. The time-varying exchange rate volatility hs,t , is used as variable in equation (6). [We tested the residuals before this stage (not reported here). At 5% significance, the White test confirms the existence of heteroskedasticity.] The parameters concerning the firm return and the exchange rate changes are estimated using the nonlinear numerical optimization method of Berndt, Hall, Hall and Hausman (BHHH), assuming that ε i,t and st are normally distributed with zero means and conditional variances given respectively by equations (7) and (10). The model is estimated using a two-step procedure: st and hs,t are estimated via maximum likelihood and then their values are used as variables in the estimation of equation (6). Table 1 summarizes the possible exposure coefficients according the various sign and magnitude changes in the exchange rate. β *2,i and β3,i may be positive or negative according the position of the firm (exporter, importer, etc…) and we do not set constraints for the sign of β 4,i which means that an exchange rate exposure associated with large fluctuations may be greater or lower than that of small changes. Indeed, Taiwanese firms may be more accustomed to relatively limited changes in the domestic currency (compared for instance to the JPY) given the Taiwan central bank policies. * and The various combination of the exposure and sign coefficients β2,i (respectively β3,i ) mean different sources of asymmetry as mentioned above.

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Table 1: Impacts of various sign and magnitude fluctuations Changes in exchange rate Appreciation lower than the filter: st < 0 and st < x

Exposure coefficients * + β β 2,i 3,i

Appreciation greater than the filter: st < 0 and st > x

* + β β 2,i 3,i + β4,i

Depreciation lower than the filter: st > 0 and st < x

* β 2,i

Depreciation greater than the filter:

* + β β 2,i 4,i

st > 0 and st > x

x = 0.5% In view to address this issue, we adopt the classification of Koutmos and Martin [50] as described in the table 2. Table 2: Possible sources of sign asymmetry of exchange rate exposure β*2,i > 0

β3,i > 0

β3,i = 0

β3,i < 0

β *2,i = 0

β *2,i < 0

#Net Exporters

#Net Importers

#Pricing-to-Market With Market Share Objective

#Hysteresis

#Net Exporters

#Net Exporters or Importers

#Net Importers

#Symmetric Exposure

#No Exposure

#Symmetric Exposure

#Net Exporters

#Net Importers

#Pricing-to-Market Under Volume Constraints

#Asymmetric Hedging

In section 2, we describe possible sources of asymmetric behavior, mainly asymmetric hedging, hysteresis and pricing-to-market (with market share objective or volume constraints). In the above table 2, Koutmos and Martin [50] show how different combinations of sign asymmetry coefficient ( β3,i ) and currency exposure ( β *2,i ) relate to * and β symmetric or asymmetric exposure. For example, positive β2,i 3,i are usually

associated to exporters who are supposed to benefit from a depreciation of the TWD,

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which means an appreciation of the other currency. That will illustrate the price-to-market case with market share objective: the exporters may not pass on the impacts to buyers by increasing the foreign prices of their products, to avoid the risk of losing market share to * means that firms suffer from an other competitors. In another example, a positive Î˛2,i appreciation of the TWD, while they benefit from it when Î˛3,i is negative: that describes the case where firms are encouraged to use financial derivatives to cover their risks (asymmetric hedging). By using similar reasoning, we can complete the above Table 2.

4 Sample selection All data are obtained from Taiwan Economic Journal Data Bank (TEJ). We only focus on non-financial Taiwanese companies listed on the Taiwan Stock Exchange (TSE). Financial institutions are not included due to their different asset characteristics and objectives with regard to financial risks. This restriction makes also the sample comparable to the ones used in most of the previous studies. As a starting point, we use our previous research based on a sample of Taiwanese non-financial firms from June 6th 1990 to July 14th 2010, see Varga [68]. This sample is designed to investigate the exchange rate exposure on the longest possible period of time, starting from 1990 (financial liberalization began mid of 1987 so we disregard the last years of the 1980s to avoid a structural break). At the time of sampling, 741 companies are listed on the TSE (199 firms in 1990) but after eliminating companies with unavailable information and financial firms, the final sample consists of 107 firms with data starting on June 6 1990 and finishing on July 14 2010. This period of time covers almost 22 years. The sample selection may introduce a survivorship bias in the results. Since all these firms have survived during the sample period, they are likely to be the ones that have effectively managed various risk exposure. It means that the bias is against finding significant exposure coefficient. In view to investigate the impacts from the 1997 Asian financial turmoil and the global financial crisis which started in 2007, we define 4 sub-samples: The first panel analyzes the impact of the Asian financial crisis using two sub-samples (before and after): from June 6th 1990 to June 30th 1997 and from July 1st 1997 to July 31st 2001. The second panel studies the consequences of the global financial crisis using also two subsamples (beforethand after): from August 1st 2001 to July 31st 2007 and from August 1st 2007 to July 14 2010. To verify that time points are statistically significant, we used a structural test, more precisely a stability test based on the Chow Breakpoint Test (not reported here). The breakpoints are: 7/01/1997, 8/01/2001 and 8/01/2007. For 89% of our sample, we reject the null hypothesis (no break at specified breakpoints). Thus, we may consider that the choice of the 4 sub periods is statistically significant. This study is at the firm level and we use daily adjusted stock prices, supplied by TEJ. We decide to select the firm as the unit of analysis for several reasons. Firstly, firms within the same industry are not homogenous and hence may display different exposure coefficients. Thus, individual exposure effects may be averaged out at the industry level. Secondly, industry return indices are often value-weighted, advantaging large firms.

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As Dominguez and Tesar [29] say, if small firms are more exposed to exchange rate fluctuations, analysis at the industry level will misjudge the true level of exposure. Thirdly, asymmetry effects can best be captured at the firm level since an industry can include both exporters and importers. Finally, if this study provides interesting conclusions, they may have a more practical impact and be more useful in exchange rate and assets management at the firm level. As a proxy for the returns on the market portfolio, we use the TAIEX which is the main index in the Taiwan stock exchange. We choose to employ a bilateral exchange rate instead of an exchange rate index to avoid its aggregated effects issues. Moreover, an exchange rate index is not always relevant for a firm. Currency changes may be measured in nominal and real terms. We choose to use the nominal exchange rate firstly because it avoids the trouble to adjust the other variables of our regressions for consistency purposes (Khoo [47]) and secondly, Mark [53] finds that nominal and real changes are almost perfectly correlated for the seven countries used in his study. His conclusion is also shared by Atindehou and Gueyie [7]. The American dollar is the currency mostly used by Taiwanese firms so as the nominal bilateral exchange rate we employ the direct quote USD / TWD (amount of Taiwanese dollar for one unit of American dollar). If the exchange rate change is negative (positive), the domestic currency (TWD) is appreciating (depreciating). If the firm displays a negative exposure coefficient, it will benefit from an appreciation of the TWD and if the exposure coefficient is positive, the firm will benefit from a depreciation of the domestic currency. We have 5245 individual observations representing 561,215 daily data. Table 3 provides the repartition of the firms per industry and table 4 gives the list of companies constituting our sample. Table 3: Sample: industries represented Industry Code 1 Cement 2 Foods 3 Plastics 4 Textile 5 Elec. & Mach. 6 Elec. Appliance & Cable 7 Chemicals 8 Glass & Ceramics 9 Paper & Pulp 10 Steel & Iron 11 Rubber 12 Automobile 13 Electronics 14 Construction 15 Transportation 16 Tourism 17 Wholesale & Retail 19 Others TOTAL

Sample

5 8 11 17 4 8 11 1 5 6 4 1 5 5 3 4 7 2

4.67% 7.48% 10.28% 15.89% 3.74% 7.48% 10.28% 0.93% 4.67% 5.61% 3.74% 0.93% 4.67% 4.67% 2.80% 3.74% 6.54% 1.87%

107

100.00%

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Industry Code 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4

Firm Code 1101 1102 1103 1104 1108 1201 1210 1213 1215 1216 1217 1218 1229 1301 1303 1304 1305 1307 1308 1309 1310 1312 1313 1326 1402 1409 1410 1413 1416 1417

Industry Code 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7

Table 4: Sample list Firm Industry Code Code 1418 7 1419 7 1423 8 1434 9 1435 9 1441 9 1436 9 1437 9 1439 10 1440 10 1443 10 1503 10 1504 10 1506 10 1507 11 1605 11 1608 11 1609 11 1611 12 1603 13 1604 13 1701 13 1702 13 1704 13 1707 13 1708 13 1709 14 1710 14 1711 14 1712 14

Firm Code 1713 1718 1802 1903 1904 1905 1907 1909 2002 2006 2007 2008 2009 2010 2102 2103 2104 2105 2201 2303 2371 2302 2305 2308 2311 2312 2501 2504 2509 2506

Industry Code 14 15 15 15 16 16 16 16 17 17 17 17 17 17 17 19 19

Firm Code 2540 2601 2603 2605 2701 2702 2704 2705 2915 2913 2901 2903 2904 2905 2906 9904 9902

5 Empirical Results and Major Findings Tables 5-1 and 5-2 provide the main results for respectively the Asian Crisis and the 2007 Global Crisis. We find a high percentage of exposed firms ( β 2* ) before the two crises: 68.2% (1997) and 72% (2007). All concerned firms are negatively exposed (they benefit from an appreciation of the TWD). The main difference between the two crises remains in the level of exposure which is almost 13% lower before the 2007 crisis compared to before the 1997 crisis. In both cases, sign asymmetries ( β3 ) increase after the crises. They are mostly negative, increasing thus the exposure level. But if the sign coefficient is lower after the 1997 crisis, it is much higher after the 2007 crisis. So in both crises, Taiwanese firms tend to benefit more from their sign asymmetric profile, especially after the 2007 crisis if we consider the level of the sign coefficient. Norththe American of Finance, vol.13, no.1 ( β4 ) cases decreases 60 For the two crises, numberReview of magnitude asymmetries

sharply after. For the 1997 crisis, the coefficient’ sign is well distributed before, but it is mostly negative after, increasing thus the level of exposure. For the 2007 crisis, the sign is mostly positive (before and after), pushing down the level of exposure. It shows that Taiwanese firms suffer more from large currency changes during the 2007 crises than during the 1997 one. The number of cases of asymmetric volatility of stock returns underlying exchange rate exposure (γ) decreases after the 1997 crisis by almost 60%. We observe the same trend for the 2007 crisis, but the change is less than 30%. Still, there are much more cases of asymmetric volatility before and after the 2007 crisis than for the 1997 crisis. The sign is mostly negative for both crises: bad news ( ε i,t < 0) decrease the volatility of the stock returns. But taking into account the number of cases, the impact on the volatility is much more accentuated in the 2007 crisis. Moreover, the positive impact on the volatility from the bad news (average γ) is the largest after the 2007 crisis. Nevertheless, the mechanism through which the asymmetric volatility comes into being still remains unresolved. Depreciation or appreciation of the domestic currency is not automatically a good or bad news. The number of cases of exchange rate volatility impacting the stock returns increases after both crises. But for the 1997 crisis, the sign is mostly positive: Taiwanese firms benefit from the currency volatility. But given the fact that we excluded from our sampling financial firms, the explanation of the positive relation between exchange rate volatility and stock returns is not obvious. Normally, we may observe for financial firms that volatility implies greater hedging and thus, revenues from for example the sale of currency derivatives should increase and thereby, a positive impact on the stock returns should be observed. But our sample only contains non-financial firms. Before the 2007 crisis, the sign is mostly negative: firms suffer from the currency volatility. And it confirms our conclusions concerning the effect of the magnitude asymmetry. One possible reason for a negative relation between stock returns and exchange rate volatility is that the concerned firms are frequent users of expensive hedging tools (as for example currency derivatives) and then a greater volatility translates to greater costs of hedging. Thus, it is logical to think that cash flows and stock returns will be adversely affected. But after the 2007 crisis, the volatility signs are evenly distributed. If the number of positive cases is not very consequent, it is still too large to be ignored for both crises. Obviously, more tests should be conducted in view to explain the positive relation between exchange rate volatility and stock returns. For Tables 5-1 and 5-2: * +β δ Ri,t = β0,i 1,i m,t * +β D + (β2,i 3,i sign,i,t + β 4,i Damp,i,t )st + β5,i hs,t + ε i,t

where: st = the unexpected change in the exchange rate, Dsign,i,t = 1 if st < 0 and 0

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otherwise, Damp,i,t = 1 if st > x and 0 otherwise; x = 0.5%. hs,t = the time-varying exchange rate volatility [ st follows a GARCH (1,1)]; ε i,t = error term which follows a and GJRGARCH(1,1) process: ε i,t = µi,t hε ,i,t hε ,i,t = ωε ,i + αε ,iε t2−1 + γ i Di,t −1ε t2−1 + βε ,i hε ,i,t −1 : Di,t −1 is equal to 1 if ε i,t is negative and 0 otherwise. hε ,i,t denotes the conditional variance of the residuals and µi,t the

white noise error term. Table 5-1. Results for the financial Asian crisis Before 1997 Crisis Firms Exposed at

10%

Firms Exposed (10%)

β3 %

Qty

68.2%

2.8%

11.2%

10.3%

35.51%

100.00%

100.0%

-0.03213

(persistence)

50.0%

-0.03385 0.027354

50.0%

100.0%

-0.024 0.019768

31.58%

68.42%

0.055264 -0.05116

0.957884 0.84792

After 1997 Crisis

107

Sample Size

β*2,i

Firms Exposed at

10%

β5

Mean

βε ,i

β4

Qty

% of Exposed (10%)

Mean β1

107

Sample Size

β*2,i

β3

β4

β5

Qty

17.8%

9.3%

4.7%

19.6%

14.95% <0

Firms Exposed (10%)

% of Exposed (10%)

5.26%

94.74%

Mean

0.030092

Mean β1 (persistence)

βε ,i

40.0%

-0.03424 0.027335

60.0%

20.0%

80.0%

81.0%

19.0% 37.50%

62.50%

-0.02301 0.020724 -0.02562 0.084684 -0.09046 0.009184 -0.01992

0.830507 0.773692

Table 5-2. Results for the 2007 global financial crisis Before 2007 Crisis Firms Exposed at

10%

Firms Exposed (10%)

β4

β5

Qty

72.0%

6.5%

12.1%

6.5%

43.93%

92.3%

7.7%

2.13%

97.87%

100.00%

42.9%

57.1%

28.6%

71.4%

-0.02764 0.046218 -0.02208 0.021691 -0.02033 0.030258 -0.04359 0.001948 -0.02206

Mean

(persistence)

β3

Qty

% of Exposed (10%)

Mean β1

107

Sample Size

β*2,i

βε ,i

0.778536 0.841758

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After 2007 Crisis Firms Exposed at

10%

β3

Qty

21 >0

19.6%

% of Exposed (10%)

100.00%

Mean

(persistence)

βε ,i

β4

Qty

Firms Exposed (10%)

Mean β1

107

Sample Size

β*2,i

1 12.5%

Qty

7.5%

7 87.5%

4 80.0%

β5 Qty

4.7%

1 20.0%

8 50.0%

Qty

15.0%

30.84%

50.0% 21.21%

78.79%

-0.03863 0.037915 -0.03884 0.025023 -0.03198 0.085102 -0.09752 0.097217

-0.1082

0.940581 0.78018

Table 6-1 describes the possible sources of asymmetries, using the classification in Koutmos and Martin [50] for the 1997 crisis, table 6-2 describing the possible sources for the 2007 crisis with the same classification. Table 6-1. Possible sources of asymmetries, for the 1997 crisis

The classification confirms our results concerning the exposed firms before and after the

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1997 crisis. But if we have much more less exposed firms after the crisis, asymmetric profiles are more pronounced even if Taiwanese firms are mostly symmetrically exposed. Table 6-2. Possible sources of asymmetries, for the 2007 crisis

As shown in the table 6-2, the conclusions are very similar for the 2007 crisis. The number of firms exhibiting at least one form of asymmetry is lower after both crises (not reported here): 45% and 24% for 1997 and 61% and 38% for 2007. We can notice that asymmetric profiles are more pronounced before and after the 2007 crisis than for the Asian crisis. For a consequent part of our sample, we observe the existence of an asymmetric volatility of stock returns (for both crises). But a large part of our sample which does not have an exchange rate exposure is also associated with this volatility asymmetry: 11% and 13% respectively before and after 1997 crisis and 13% and 22% respectively before and after the 2007 crisis (not reported). This phenomenon is more pronounced for the 2007 crisis. Nevertheless, the mechanism through which the existence of an asymmetric volatility of stock returns comes into being still remains unresolved. Our study shows clearly that stock return volatilities are time dependant. Persistence, measured by Î˛Îľ ,i , is quite high with an average of 0.848 / 0.774 before / after the 1997 crisis and 0.842 / 0.780 before / after the 2007 crisis. It suggests that there is a long memory in the stock return volatility process. So obviously, the time variance is an

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important variable in the conditional variance. But numbers show that it is truer before than after the crisis, persistence being lower after the crises. Finally, the two crises have different impacts on the market risk of Taiwanese firms. Surprisingly, it is lower by 13% after the 1997 crisis, but (more logically) it is higher by 21% after the 2007 crisis. Thus, the two crises have different consequences on the required rate of equity return from investors, to keep holding the firmâ&#x20AC;&#x2122;s shares. If negative consequences from the 1997 crisis had a very more muted impact on Taiwanese firms, the 2007 global financial crisis increased their equity financing costs. We conducted a test regression (not reported here), by adding dummy variables to our main model, in view to observe possible individual influences according the period of time: D1: = 1 if the period is between 6/06/1990 and 6/30/1997 and 0 otherwise D2: = 1 if the period is between 7/01/1997 and 7/31/2001 and 0 otherwise D3: = 1 if the period is between 8/01/2001 and 7/31/2007 and 0 otherwise The period from 8/01/2007 to 7/14/2010 will be the base category to interpret the results. For 24% of our sample, we have statistically significant dummy variables (mostly at 5% level of significance). Respectively for D1, D2 and D3 we have 13, 18 and 13 cases. But what is interesting to note is that for almost 80% of the cases, the coefficient is negative. It means that on average (keeping other variables constant), the first three periods tend to lower the stock return, compare to the base category (the fourth period). It is consistent with our other findings: firms benefit from their asymmetric profile, especially after the 2007 crisis.

6 Concluding Remarks This paper investigates whether the Asian crisis and the 2007 global crisis impacted Taiwanese exposure, volatilities and systematic risk with respect to the Taiwan equity market portfolio. We found that for both crises, the number of exposed firms decreased sharply after the crises, compared to the situation before the crises. We may explain it by the fact that following the consequences of the crises, Taiwanese firms are more engaged in hedging activities. The main difference between the two crises remains in the level of exposure which is almost 13% lower before the 2007 crisis compared to before the 1997 crisis, but 13% higher after the 2007 crisis, compared to after the 1997 crisis. Whatever the period of time or the crisis, all Taiwanese firms are negatively exposed, benefiting from an appreciation of the TWD. For both crises, sign asymmetries increase after the crisis. Being mostly negative, firms benefit from their asymmetric profile, especially after the 2007 crisis. Conversely, magnitude asymmetries decreased sharply after both crises, but for the 2007 crisis, the sign is mostly positive (before and after), pushing down the level of exposure. It shows that Taiwanese firms suffer more from large currency changes during the 2007 crisis than during the 1997 one. The number of cases of asymmetric volatility of stock returns underlying exchange rate exposure is lower after both crises, but it is more pronounced for the 2007 crisis. The sign is mostly negative (bad news reduce the volatility of stock returns). But a large part of non-exposed firms is also associated to the volatility asymmetry, especially for the 2007 crisis (not reported here). Nevertheless, the mechanism through which the 65 North American Academic Journals, 2013 asymmetric volatility comes into being still remains unresolved. Depreciation or

appreciation of the domestic currency is not automatically a good or bad news. The number of cases of exchange rate volatility impacting the stock returns increases after both crises. The sign is mostly positive for the 1997 crisis (before and after). Before the 2007 crisis, signs are mostly negative, and evenly distributed after. If financial theory clearly explains that cash flows and stock returns are adversely affected by the currency volatility, a positive relationship between exchange rate volatility and stock returns is not obvious, especially knowing that our sample does not include financial firms. If Taiwanese firms are clearly symmetrically exposed, asymmetric profiles are more pronounced for the 2007 crisis. Our study shows clearly that stock return volatilities are time dependent, even though persistence tends to decrease after both crises. Finally, the two crises have different consequences on the market risk of Taiwanese firms. Surprisingly, it is lower after the 1997 crisis, but (more logically) is higher after the 2007 crisis. Thus, the two crises have different impacts on the required rate of equity return from investors, to keep holding the firmâ&#x20AC;&#x2122;s shares. If negative consequences from the 1997 crisis had a very more muted impact on Taiwanese firms, the 2007 global financial crisis increased their equity financing cost.

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