The trouble with the standard NPV is …
Investment Decision under Uncertainty (Brief Review from ECO358!)
There is a lot of uncertainty – we don’t know the future payments for sure. => must use expected values F the For th same expected t d value, l individuals i di id l normally prefer the less risky one. Must find a way to determine “required rates of return” for uncertain payoffs. The CAPM or the APT provide the benchmark!
Computing NPV
Basic story
• This set of slides is a review of the NPV computations covered in ECO358. • If you need to review this material in more detail, please consult Ross Chapters 44-6. • I will ill expectt th thatt you know k the th following f ll i 4 basic NPV rules. • C denotes the annual cash flows, r -- the discount (“interest”) rate, g – the annual growth rate, and T – the number of periods for an annuity.
Investors require to be compensated for risk. By holding portfolios consisting of many assets, one can reduce exposure of risk stemming from individual assets => > principle of diversification General message: Idiosyncratic risk can be diversified away, for required returns only the “joint” risk matters. => even if payoffs are highly volatile, only the part that correlates with the rest is priced. 1
Basic NPV Rules From ECO358 you know the following formulae:
Portfolio Risk as a Function of the Number of Stocks in the Portfolio
In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not.
Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk Portfolio risk Nondiversifiable risk; Systematic Risk; Market Risk n Thus diversification can eliminate some, but not all of the risk of individual securities.
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Definition of Risk When Investors Hold the Market Portfolio
Expected return E
Relationship Between Risk & Expected Return
Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta () of the security. Beta measures the responsiveness of a security to movements in the market portfolio.
i
1.0
Cov( Ri , RM )
2 ( RM )
Stock C-MAC Industries Nortel Networks Bank of Nova Scotia Bombardier Investors Group. Maple Leaf Foods Rogers Communications Canadian Utilities TransCanada Pipeline
To summarize
Beta 1.85 1.61 0.83 0.71 1.22 0.83 1.26 0.50 0.24
The CAPM gives us a nice benchmark for the returns that investors require on an uncertain future payoff. The formula applies to both bonds and stocks (although for the same corporation, the required rates differ as bond/stock payoffs differ!)
R
F
β i (R
Beta of the Risk+ × = security free rate
M
R
Market risk premium
• Assume i = 0, then the expected return is RF. • Assume i = 1, then R i R M
F
Multi--factor Models and Rates of Return Multi The CAPM says that all systematic return variations are explained by the market rate of return.
This formula is called the Capital Asset Pricing Model (CAPM) i
R i RF β i ( R M RF )
Expected Return on an Individual Security
R
RM
RF
Estimates of for Selected Stocks
Expected return on a security
R i RF β i ( R M RF )
)
New research shows that other variables may y do a better job, or at least, that there are other factors that influence returns Which factors?
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Multifactor Models
Required rates
While there are no general rules, these factors should, on some level, have a relation to security returns. Thus the average growth in the rainfall in growth of Timbuktu is a nonsensical variable --- g industrial production is a little better. One should make sure that the variables have the same units: Returns are measured in %, thus the factors should be measured in %. Example: Changes in GDP does not work, GDP growth does.
Required rates with the FamaFama-French factors are then
Ri RF βi ( R M RF ) isizesize - factor ib 2m book - to - market - factor
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Multifactor models cont’d The two major papers on factor analysis are: Chen, Roll and Ross (1986). They use growth of industrial production, changes in expected inflation, unexpected inflation, unexpected changes in inflation, unexpected changes in the difference between returns on corporate and government bonds, unexpected changes in the difference between returns on long and short--term government bonds. short Fama and French 1992, 1996, 1993. They use Market returns (on a very broad market index), the “size” factor, and the “book“book-to to-market” factor.
Fama and French factors To get the two factors, size and B2M, FF do the following (here for B2M)
For each year, they sort all assets according to their book to market ratios. They take the bottom 10% and the top 10% and compute wellwell-diversified portfolios. They compute the returns for these two portfolios and then compute the difference in returns. This difference is the factor for a given year.
Please not that the B2MB2M- or size size--factor are not asset-specific --- these are macro assetmacro--variables! They have nothing to do (directly) with a firms market capitalization or its bookbook-to to--market ratio!
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