CHAPTER 13: EMPIRICAL EVIDENCE ON SECURITY RETURNS
PROBLEM SETS
1.
Even if the singlefactor CCAPM (with a consumptiontracking 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
booktomarket ratio) factors of the FamaFrench threefactor model.
Therefore, it
is expected that the FamaFrench 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 consumptionbased 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 consumptionbased 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 consumptionbeta 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.
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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 twofactor 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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 Three '11
 3213
 Standard Error, Capital Asset Pricing Model, Modern portfolio theory

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