In this thesis three aspects of the CAPM model are investigated.
The first aspect is the theoreticalbackground of the model. Here, mean-variance
analysis (MVA) is thoroughly examined. We first present mathematical arguments
from utility theory that can motivate the implementation of MVA. Then, we
examine efficient portfolios in a mean-standard deviation space assuming there
is no risk-free asset. We show the incentive to diversify ones portfolio and
derive the efficient frontierconsisting of the portfolios with the maximum
expected return for a given variance. Using mathematical and economic
arguments, we find out that the market portfolio consisting of all risky assets
is mean-variance efficient. We then include a riskless asset in the analysis
and get the Capital Asset Market Line (CML) in a mean-standard deviation space.
We argue that this is the efficient frontier when a risk-free rate exists. We also
present the separation theorem which implies that all investors will maximize
utility in some combination between the risk-free asset and the
market portfolio. Based on the CML, we derive the Capital Asset Pricing Model
(CAPM) in three differentways. The first two represent the original approaches
from the architects behind the model. The last approach extends the formal
derivation of the efficient frontier when only risky assets exist to include
the risk-free rate. We find that the CAPM relates the expected return on any
asset to its beta.
We argue that when investors only care about expected return and
variance, beta makes sense as arisk measure. As beta is based on the covariance
of returns between an asset and the market portfolio, it follows that CAPM only
rewards investors for their portfolios responsiveness to swings in the overall
economic activity. We find that this makes sense, as rational investors can
diversify away all but the systematic risk of their portfolios. In the second
part of the thesis, the econometric methods for testing the CAPM are developed.
First, the traditional model is rewritten in order to work with excess returns.
We then focus on testing the mean-variance efficiency of the market portfolio.
We impose the assumption that returns are independent and identically
distributed and jointly multivariate normal. Based on this assumption, we
derive the joint probability density function (pdf) of excess returns
conditional on the market risk premium. Using this pdf we first derive maximum likelihood
estimators of the market model parameters. We then show that they are, in fact,
equivalent to the ordinary least squares estimators.
A number of different test statistics are derived based on these
estimators. The first is an asymptoticWald type test. We then transform this
test into an exact F-test. Moreover, we develop anasymptotic likelihood ratio
test including a corrected version with better finite-sample properties.
Also, noting that the above distributional assumptions are rather
strict, we use the Generalized Method of Moments (GMM) framework to develop a
test robust to heteroskedasticity, temporal dependence and non-normality.
Finally, we present some cross-sectional tests of other implications of the
CAPM. Specifically, we develop statistics to check whether the empirical market
risk premium is significant and positive and whether other risk measures than
beta have explanatory power regarding expected excess returns. The third part
of the thesis is an empirical study. It starts out by discussing a number of
relevant topics regarding the implementation of the statistical tests. In
specific, we discuss the choice of proxies, the sample period length and
frequency, and the construction of the dependant variable.
Then, the tests are carried out on a 30 year sample of American
stocks. For the overall period, we cannot reject the mean-variance efficiency of
the proxy for the market portfolio. However, for the sub-periods of 5 years, the
results are not so clear-cut. We also find that the empirical risk premium is
not significant. The last point clearly contradicts the CAPM framework.
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