Introduction to Corporate Finance

PART 2: VAlUATION, RISK AND RETURN

Figure 6.6 plots the relationship between average returns and standard deviation for shares, bonds and

bills. In the figure, we chose to plot nominal returns, but switching to real returns would make very little

difference. The figure also includes a trend line through the three data points. Notice that the relationship

shown in the figure is almost perfectly linear, meaning that the dots fall very close to the trend line.^10

This is not the last time that we will see evidence of a straight-line relationship between risk and

return. What are the implications of such a relationship? The most important implications are that: (1)

investors who want higher returns have to take more risk; and (2) the incremental reward from accepting

more risk is constant. In other words, if an investor wants to increase his return from 5% to 10%, the

additional risk that he has to accept is the same as the additional risk that another investor has to accept to

increase her returns from 10% to 15%. In economics, we frequently see evidence of diminishing returns.

This evidence shows up in graphs as a curve with a decreasing slope. For example, a factory can produce

more output if there are more workers present, but at some point the incremental output produced by an

additional worker – the marginal product– begins to fall as diminishing returns set in. With respect to risk

and return, Figure 6.6 shows no similar evidence of diminishing returns to risk taking.

Thus far, we have seen that a trade-off between risk and return exists for major asset classes including

equities, Treasury bonds and bills. Suppose we want to compare the investment performance of two

specific assets, such as a share of General Electric and a share of Intel. Does this same trade-off appear

when we examine individual securities? As we will see in the next section, the answer is, ‘It depends.’

10 The trend line here is estimated using linear regression. We will discuss regression lines again in Chapter 7, but you may recall from your

statistics class that a measure of ‘goodness of fit’ for a regression line is the R-square statistic. The R-square value ranges between 0% and

100%, with a higher number indicating a stronger relationship between the two variables. In Figure 6.6, the R-square value of our line is

almost 97%, indicating a very tight relationship between standard deviation and returns.

FIGURE 6.6 THE RELATIONSHIP BETWEEN AVERAGE (NOMINAL) RETURN AND STANDARD

DEVIATION FOR SHARES, TREASURY BONDS AND BILLS, 1900–2010

The figure indicates that a positive relationship exists between the average returns offered by an asset class and the

standard deviation of returns for that class.

Standard deviation (%)

Average return (%)

0

2

4

6

8

10

12

14

0 5 10 15 20 25

Shares

Bonds

Bills

Source: Elroy Dimson, Paul Marsh and Mike Staunton, ‘Triumph of the Optimists,’ in Global Investment Returns Yearbook 2010.

Published by ABN AMRO, London. Updates provided by Dimson et al. to 2009. Author’s calculations for 2010. Reprinted with permission.