BUSF_A01.qxd

7.3 Security investment and risk

The expected value/variance criterion (EVC) may be summarised as follows:

l where the expected value of Project A is equal to or greater than that of Project B, A

should be preferred to B if A has a lower variance; and

l where the variance of Project A is equal to or smaller than that of Project B, A

should be preferred to B if A has a higher expected value.

What the expected (or mean) value criterion does not tell us is how to choose

between two investments where both the expected value and the variance of Project A

are greater than those of Project B. We shall look at how this dilemma can theoretically

be addressed after we have looked at how diversification can reduce risk in practice.

7.3 Security investment and risk

If we were to select a number of marketable securities at random, form them into port-

folios of varying sizes, measure the expected returns and standard deviation of returns

from each of our various-sized portfolios, and then plot standard deviation against

size of portfolio, we should obtain a graph similar to that in Figure 7.1.

Before we go on to consider the implications of Figure 7.1, just a word of explana-

tion on its derivation. The expected returns, r, referred to are the monthly returns of a

security or a portfolio of securities. These are calculated as:

rt=

where Ptis the market value of the security or portfolio at the end of month t, Pt− 1 the

value at the start of the month, and dtthe dividend (if any) arising from the security or

portfolio during the month. The expected value of returns for a security or portfolio is

based on past experience, say of returns over the past 60 months. Thus the expected

value could be the average (mean) of the monthly returns for the past five years.

The various-sized portfolios are constructed randomly. Several portfolios of each

size are constructed, and the returns and standard deviations depicted in Figure 7.1

are the average of the returns and standard deviations of all of the portfolios for each

size (see Evans and Archer 1968).

As standard deviation of returns around the mean is a reasonable measure of risk,

Figure 7.1 suggests that a large reduction in risk can be achieved merely by randomly

combining securities in portfolios. This provides empirical support for the maxim ‘Do

not put all your eggs in one basket’, which is often applied to investment in securities.

Pt−Pt− 1 +dt

Pt− 1

A risk-averse investor is faced with two competing investment projects, dispersions of both

of whose possible outcomes are symmetrical about their expected values. Which should the

investor select?

Project A B

Expected net present value (£) 20,000 20,000

Variance (£^2 ) 10,000 12,000

Project A would be selected since this offers an equal expected net present value to Project

B but with less risk. By selecting Project A (and, therefore, rejecting project B), maximisation

of the utility of wealth of any risk-averse investor will be promoted.

Example 7.2