of variation captures the effects of both risk and return, it is a better measure for eval-
uating risk in situations where investments have substantially different expected
returns.
Risk Aversion and Required Returns
Suppose you have worked hard and saved $1 million, which you now plan to invest.
You can buy a 5 percent U.S. Treasury security, and at the end of one year you will
have a sure $1.05 million, which is your original investment plus $50,000 in interest.
Alternatively, you can buy stock in R&D Enterprises. If R&D’s research programs are
successful, your stock will increase in value to $2.1 million. However, if the research is
a failure, the value of your stock will go to zero, and you will be penniless. You regard
R&D’s chances of success or failure as being 50-50, so the expected value of the stock
investment is 0.5($0) 0.5($2,100,000) $1,050,000. Subtracting the $1 million cost
of the stock leaves an expected profit of $50,000, or an expected (but risky) 5 percent
rate of return:
Thus, you have a choice between a sure $50,000 profit (representing a 5 percent
rate of return) on the Treasury security and a risky expected $50,000 profit (also rep-
resenting a 5 percent expected rate of return) on the R&D Enterprises stock. Which
one would you choose? If you choose the less risky investment, you are risk averse. Most in-
vestors are indeed risk averse, and certainly the average investor is risk averse with regard to
his or her “serious money.” Because this is a well-documented fact, we shall assume risk aver-
sionthroughout the remainder of the book.
What are the implications of risk aversion for security prices and rates of return?
The answer is that, other things held constant, the higher a security’s risk, the lower its
price and the higher its required return. To see how risk aversion affects security prices,
look back at Figure 3-2 and consider again U.S. Water and Martin Products stocks.
Suppose each stock sold for $100 per share and each had an expected rate of return of 15
percent. Investors are averse to risk, so under these conditions there would be a general
preference for U.S. Water. People with money to invest would bid for U.S. Water
rather than Martin stock, and Martin’s stockholders would start selling their stock and
using the money to buy U.S. Water. Buying pressure would drive up U.S. Water’s stock,
and selling pressure would simultaneously cause Martin’s price to decline.
These price changes, in turn, would cause changes in the expected rates of return
on the two securities. Suppose, for example, that U.S. Water’s stock price was bid up
from $100 to $150, whereas Martin’s stock price declined from $100 to $75. This
would cause U.S. Water’s expected return to fall to 10 percent, while Martin’s ex-
pected return would rise to 20 percent. The difference in returns, 20% 10%
10%, is a risk premium, RP,which represents the additional compensation investors
require for assuming the additional risk of Martin stock.
This example demonstrates a very important principle: In a market dominated by
risk-averse investors, riskier securities must have higher expected returns, as estimated by the
marginal investor, than less risky securities. If this situation does not exist, buying and selling
in the market will force it to occur.We will consider the question of how much higher the
returns on risky securities must be later in the chapter, after we see how diversification
$50,000
$1,000,000
5%.
$1,050,000$1,000,000
$1,000,000
Expected rate of return
Expected ending valueCost
Cost
112 CHAPTER 3 Risk and Return
110 Risk and Return
