|
Assumptions of the CAPM
Table 9.1 enumerates the list of assumptions underlying the CAPM. In our discussion so
far, we have cited explicitly only these three assumptions:
1.a. Investors are rational, mean-variance optimizers.
1.c. Investors use identical input lists, referred to as homogeneous expectations .
2.a. All assets are publicly traded (short positions are allowed) and investors can
borrow or lend at a common risk-free rate.
The first assumption is far-reaching. Its “visible” part is that investors are not concerned
with higher moments (skew and kurtosis) that may “fatten” the left tail of the return distri-
bution. We can ascertain the validity of this assumption from statistical tests of the normal-
ity of return distributions as we did in Chapter 5.
Less visible is that, by assuming that only the mean and variance of wealth matter to
investors, Assumption 1(a) rules out concern with the correlation of asset returns with
either inflation or prices of important consumption items such as housing or energy. The
extra demand for assets that can be used to hedge these “extra market” risks would increase
their prices and reduce their risk premiums relative to the prediction of the CAPM.
11
To illustrate the meanings of significance and power, consider a test of the efficacy of a new drug. The agency
testing the drug may make two possible errors. The drug may be useless (or even harmful), but the agency may
conclude that it is useful. This is called a “Type I” error. The significance level of a test is the probability of a Type
I error. Typical practice is to fix the level of significance at some low level, for example, 5%. In the case of drug
testing, for example, the first goal is to avoid introducing ineffective or harmful treatments. The other possible
error is that the drug is actually useful, but the testing procedure concludes it is not. This mistake, called “Type
II” error, would lead us to discard a useful treatment. The power of the test is the probability of avoiding Type II
error (i.e., one minus the probability of making such an error), that is, the probability of accepting the drug if it
is indeed useful. We want tests that, at a given level of significance, have the most power, so we will admit effec-
tive drugs with high probability. In social sciences in particular, available tests often have low power, in which
case they are susceptible to Type II error and will reject a correct model (a “useful drug”) with high frequency.
“The drug is useful” is analogous in the CAPM to alphas being zero. When the test data reject the hypothesis that
observed alphas are zero at the desired level of significance, the CAPM fails. However, if the test has low power,
the probability that we accept the model when not true is too high.
bod61671_ch09_291-323.indd 303
bod61671_ch09_291-323.indd 303
6/21/13 3:39 PM
6/21/13 3:39 PM
Final PDF to printer
304
P A R T I I I
Equilibrium in Capital Markets
Similar extra-market risk factors would arise in a multiperiod model, which requires
the addition of Assumption 1(b), limiting investors to a common single-period horizon.
Consider a possible decline in future interest rates. Investors would be unhappy about this
event to the extent that it would reduce the expected income their investments could throw
off in the future. Assets whose returns are negatively correlated with interest rates (e.g.,
long-term bonds) would hedge this risk and thus command higher prices and lower risk
premiums. Because of such hedging demands, correlation with any parameter describing
future investment opportunities can result in violations of the CAPM mean-beta equation
(and therefore with the efficiency of the market portfolio). A single-period investor horizon
eliminates these possibilities.
Interestingly, Assumption 1(c) (investors optimize with the same input list), appears
ominously restrictive, but it actually is not all that problematic. With the addition of
Assumption 2(b) (all information is public), investors generally will be close to agreement.
Moreover, trades of investors who derive different input lists will offset and prices will
reflect consensus expectations. We will later allow for the likelihood that some investors
expend resources to obtain private information and exploit prices that don’t reflect the
insights derived from this information. But regardless of their success, it is reasonable to
assert that, absent private information, investors should assume alpha values are zero.
The assumption that all assets are tradable (2a) is essential for identical input lists.
It allows us to ignore federal and state assets and liabilities. More importantly, privately
held but nontraded assets such as human capital and private business can create large dif-
ferences in investor portfolios. Consider owners of a family business. Prudence dictates
that they avoid assets that are highly correlated with their businesses. Similarly, investors
should avoid stock returns that are positively correlated with their personal income; for
example, Boeing employees should avoid investing in the airline and related businesses.
Differential demands arising from this consideration can lead to violation of the mean-beta
equation and derail the mean-variance efficiency of the index portfolio.
Restrictions on borrowing (or significantly higher rates on borrowed funds), which vio-
lates Assumption 2(a), also can create problems for the CAPM, because borrowers and lend-
ers will arrive at different tangency portfolios and thus different optimal risky portfolios.
Taxes create conditions in which two investors can realize different after-tax returns
from the same stock. Such distortions could, in principle, lead to different after-tax opti-
mal risky portfolios to different investors; hence Assumption 2(c) (no taxes). Despite an
extension to the CAPM that incorporates personal taxes on dividends and capital gains,
12
Do'stlaringiz bilan baham: | 
