bkmsol-ch13-9e corrected 7.29.2010

bkmsol-ch13-9e corrected 7.29.2010 - CHAPTER 13: EMPIRICAL...

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CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS PROBLEM SETS 1. Even if the single-factor CCAPM (with a consumption-tracking portfolio used as the index) performs better than the CAPM, it is still quite possible that the consumption portfolio does not capture the size and growth characteristics captured by the SMB (i.e., small minus big capitalization) and HML (i.e., high minus low book-to-market ratio) factors of the Fama-French three-factor model. Therefore, it is expected that the Fama-French model with consumption provides a better explanation of returns than does the model with consumption alone. 2. Wealth and consumption should be positively correlated and, therefore, market volatility and consumption volatility should also be positively correlated. Periods of high market volatility might coincide with periods of high consumption volatility. The ‘conventional’ CAPM focuses on the covariance of security returns with returns for the market portfolio (which in turn tracks aggregate wealth) while the consumption-based CAPM focuses on the covariance of security returns with returns for a portfolio that tracks consumption growth. However, to the extent that wealth and consumption are correlated, both versions of the CAPM might represent patterns in actual returns reasonably well. To see this formally, suppose that the CAPM and the consumption-based model are approximately true. According to the conventional CAPM, the market price of risk equals expected excess market return divided by the variance of that excess return. According to the consumption-beta model, the price of risk equals expected excess market return divided by the covariance of R M with g, where g is the rate of consumption growth. This covariance equals the correlation of R M with g times the product of the standard deviations of the variables. Combining the two models, the correlation between R M and g equals the standard deviation of R M divided by the standard deviation of g. Accordingly, if the correlation between R M and g is relatively stable, then an increase in market volatility will be accompanied by an increase in the volatility of consumption growth. 13-1
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Note: For the following problems, the focus is on the estimation procedure . To keep the exercise feasible, the sample was limited to returns on nine stocks plus a market index and a second factor over a period of 12 years. The data were generated to conform to a two-factor CAPM so that actual rates of return equal CAPM expectations plus random noise, and the true intercept of the SCL is zero for all stocks. The exercise will provide a feel for the pitfalls of verifying social- science models. However, due to the small size of the sample, results are not always consistent with the findings of other studies as reported in the chapter.
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bkmsol-ch13-9e corrected 7.29.2010 - CHAPTER 13: EMPIRICAL...

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