The Mathematics of Financial Modelingand Investment Management

17-Capital Asset Pricing Model Page 513 Wednesday, February 4, 2004 1:10 PM

Capital Asset Pricing Model 513

investors make investment decisions based on two parameters, the

expected return and the variance of returns. Assumption 1 indicates that

in the CAPM the same two parameters are used by investors. Assump-

tion 2 indicates that in order to accept greater risk, investors must be

compensated by the opportunity of realizing a higher return.

The CAPM assumes (Assumption 3) that the risk-averse investor

will ascribe to Markowitz’s methodology of reducing portfolio risk by

combining assets with counterbalancing covariances or correlations. By

Assumption 4, all investors are assumed to make investment decisions

over some single-period investment horizon. How long that period is

(i.e., six months, one year, two years, etc.) is not specified. In reality, the

investment decision process is more complex than that, with many

investors having more than one investment horizon. Nonetheless, the

assumption of a one-period investment horizon is necessary to simplify

the mathematics of the theory.

To obtain the Markowitz efficient frontier which we will be used in

developing the CAPM, it will be assumed that investors have the same

expectations with respect to the inputs that are used to derive the efficient

portfolios: asset returns, variances, and covariances. This is Assumption 5

and is referred to as the “homogeneous expectations assumption.”

It is assumed that there is a risk-free asset. An investor in this asset

earns a risk-free rate. Moreover, it is assumed that investors cannot

only earn a risk-free rate, but if they want to borrow, they can do so at

the risk-free rate (Assumption 6).

Finally, it is assumed that the capital market is perfectly competitive

(Assumption 7). In general, this means the number of buyers and sellers

is sufficiently large, and all investors are small enough relative to the

market so that no individual investor can influence an asset’s price. Con-

sequently, all investors are price takers, and the market price is deter-

mined where there is equality of supply and demand. In addition,

according to Assumption 7, there are no transaction costs or impedi-

ments that interfere with the supply of and demand for an asset.

SYSTEMATIC AND NONSYSTEMATIC RISK

A risk-averse investor who makes decisions based on expected return and

variance should construct an efficient portfolio using a combination of the

market portfolio and the risk-free rate. The combinations are identified by

the CML. Based on this result, Sharpe derived an asset pricing model that

shows how a risky asset should be priced. In the process of doing so, we

can fine-tune our thinking about the risk associated with an asset. Specifi-