BUSF_A01.qxd

Chapter 7 • Portfolio theory and its relevance to real investment decisions

9.3 Capital market efficiency

The line rfSin Figure 7.7 is known as the capital market line(CML). The CML defines

the relationship between risk and return for efficient portfolios of risky securities.

Note that this line will shift up and down, closer to or further from the horizontal, as

interest rates (and, therefore, the risk-free rate) change over time.

We can see from Figure 7.7 that the expected return available to an investor is:

rf+Risk premium

The amount of the risk premium is dependent on how much of the investment is in

the portfolio of risky securities.

7.5 Capital asset pricing model

The CML defines the risk/return trade-off for efficient portfolios. What is probably of

more interest and, theoretically, of value to us is the relationship between expected

return and risk for individual securities. In fact, this is:

E(ri) =rf+[E(rm) −rf]

where E(ri)is the expected return from i, a particular individual security, rfis the

risk-free borrowing/lending rate, E(rm)the expected return on the market portfolio,

Cov(i, M) the covarianceof returns of security iwith those of the market portfolio,

and σm^2 the variance (square of the standard deviation) of the market returns.

This statement, known as the capital asset pricing model(CAPM), can be derived

directly from what is known about the CML. (The appendix to this chapter gives the

Appendix: Derivation of CAPM

Note that, in using CAPM to discover the expected return for any particular

security i, we use only one factor that refers specifically to i. This is Cov(i,M). All of

the other factors [E(rm), rfand σ^2 m] are general to all securities. The only factor that

distinguishes the expected returns of one security from those of another is the extent

to which the expected returns from the particular security co-vary with the expected

returns from the market portfolio.

This ties in pretty well with what we have discovered so far about specific and

systematic risk. We know that specific risk can easily be avoided; it is not therefore

surprising to find that, in theory at least, the returns that we expect to get from a

particular security bear no relation to specific risk. Even though higher risk usually

engenders higher expectations of returns, it is entirely theoretically logical that some-

one who is needlessly exposed to specific risk should not expect higher return.

CAPM tells us that, in theory, expectations of returns will be enhanced by the extent

of the covariance of expected returns from the particular security with those of the

market portfolio. Again this ties in with what we already know in that systematic risk,

which the investor is forced to bear, relates to factors that tend to affect all securities.

The greater their effect on a particular security, the greater the systematic risk, and log-

ically, the greater the returns expected from that security. It is not surprising that

covariance with the generality of securities is a measure of systematic risk.

Cov (i, M)

σ^2 m

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