6: The Trade-Off Between Risk and ReturnIf diversification is easy, and if it eliminates unsystematic risk, then what reward should investors
expect if they choose not to diversify and to bear systematic risk? Simple intuition predicts that bearing
unsystematic risk offers no incremental reward. The reason is that investors can easily eliminate
unsystematic risk by diversifying. In other words, investors do not have to bear this kind of risk, nor do they
have to pay a lot to get rid of it. Therefore, the market will reward investors only for bearing systematic risk.
In Figure 6.6, we observed an almost linear relation between standard deviation and average return
for three asset classes: shares, bonds and bills. In Figure 6.9, the relationship between standard deviation
and return is not as clear. The difference between the figures is that in one case (Figure 6.6), we are
looking at portfolios of assets, and in the other case (Figure 6.9), we are looking at individual assets.
A well-diversified portfolio contains very little unsystematic risk. This is why the standard deviation of
a portfolio of securities is typically so much lower than the standard deviation of a single security. For a
portfolio, the standard deviation of returns consists almost entirely of systematic risk. For an individual
asset, the standard deviation contains both types of risk. Therefore, if the market rewards systematic
risk only, then in Figure 6.6, we see a nice linear relationship between portfolio standard deviation
(systematic risk) and average returns, but in Figure 6.9, standard deviation (systematic + unsystematic
risk) seems almost unrelated to average returns.
To conclude this chapter, let us take a step back and think about our original objective. The
fundamental goal of finance is to value things. Usually, valuation involves projecting an asset’s future
cash flows, choosing a discount rate that is appropriate, given the asset’s risk, then calculating the present
value of the asset’s future cash flows. In this chapter, we have made some progress in understanding the
second step of the valuation process. We know that what really matters is an investment’s total return,
and we want to know how that return relates to risk. But not all risks are equal, so we need to focus
on an asset’s systematic risk, because that is what should drive the asset’s return. Diversified portfolios
contain very little unsystematic risk; thus, a measure like the standard deviation of the portfolio’s return
provides a good measure of the portfolio’s systematic risk. As expected, a portfolio’s standard deviation
and its return are closely linked.
But complications arise for individual assets, because their fluctuations reflect both systematic and
unsystematic factors. Therefore, the standard deviation of returns for a single share does not focus
exclusively on the share’s systematic risk. As a result, when we compare standard deviations and average
returns across many different shares, we do not see a reliable pattern between those two variables.
This is an important problem because both managers and investors have to assess the risk of individual
investments, not just portfolios. They need a way to measure the systematic risk, and only the systematic
risk, of each and every asset. If it is possible to quantify an individual asset’s systematic risk, then we should
expect that measure of risk to be reliably related to returns. This is precisely our focus in Chapter 7.
CONCEPT REVIEW QUESTIONS 6-4
9 Why is the standard deviation of a portfolio usually smaller than the standard deviations of the
assets that comprise the portfolio?10 In Figure 6.8, why does the line decline steeply at first and then flatten out?11 Explain why the dots in Figure 6.9 appear to be almost randomly scattered.