BUSF_A01.qxd

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

7.8 Tests of CAPM

In developing CAPM several assumptions need to be made. These are as follows:

1 Investors are risk-averse, and maximise expected utility of wealth.

2 The capital market is not dominated by any individual investors.

3 Investors are interested in only two features of a security, its expected returns and

its variance (or standard deviation).

4 There exists a risk-free rate at which all investors may borrow or lend without limit

at the same rate.

5 There is an absence of dealing charges, taxes, and other imperfections.

6 All investors have identical perceptions of each security.

A glance at these assumptions indicates that some are likely to be valid in the real

world, whereas others clearly are not. For example, Assumption 1 seems to be true;

certainly most people seem to prefer more wealth to less (all things being equal) and most

of us are risk-averse. Assumption 5, on the other hand, is clearly invalid in reality.

Whether or not the invalidity of certain of these assumptions seriously weakens the

model is probably discernible only by looking at how well CAPM works in practice.

7.8 Tests of CAPM

For most of us, certainly for most financial managers, the only important feature of a

theoretical derivation like CAPM is how well it explains, and more particularly how

well it predicts, real events.

then:

bAce==1.56

Thus Ace plc equity has a fairly high beta.

The explanation of the calculation of the market factors shown in the first table above is

as follows:

l pmtis the value for the index used as a surrogate for the market, and is shown in col-

umn 2.

l rmtis the return for the year on the market. It is calculated as the gain during the year, that

is, the end-of-year value (pmt)less the start-of-year value (pmt− 1 )divided by the start-of-year

value (pmt− 1 ). For example, the return during 1999 was the increase in the index from 1998

to 1999 (12) divided by the value at the start of 1999 (218).

l Smis the mean of the annual returns, that is, the sum of them divided by the number of

returns (10).

l Column 4 is deduced by deducting the mean annual return (0.056) from each year’s return

(column 3).

l Column 5 is column 4 squared.

The figures in the table relating to Ace plc are similarly derived.

0.0036

0.0023