(8th edition) (the pearson series in economics) robert pindyck, daniel rubinfeld microecon 206

CHAPTER 5 • Uncertainty and Consumer Behavior 181

Expected
return, Rp

U3
U2
U1

Rm
Budget Line

R*

Rf

0

σ*

σm

Standard
deviation of
return, σp

F IGURE 5.6

CHOOSING BETWEEN RISK AND RETURN
An investor is dividing her funds between two assets—Treasury bills, which are risk free,
and stocks. The budget line describes the trade-off between the expected return and

its riskiness, as measured by the standard deviation of the return. The slope of the budget line is (Rm− R f )/␴m, which is the price of risk. Three indifference curves are drawn,
each showing combinations of risk and return that leave an investor equally satisfied.
The curves are upward-sloping because a risk-averse investor will require a higher expected return if she is to bear a greater amount of risk. The utility-maximizing investment portfolio is at the point where indifference curve U2 is tangent to the budget line.

Of the three indifference curves, the investor would prefer to be on U3. This
position, however, is not feasible, because U3 does not touch the budget line.
Curve U1 is feasible, but the investor can do better. Like the consumer choosing
quantities of food and clothing, our investor does best by choosing a combination of risk and return at the point where an indifference curve (in this case U2)
is tangent to the budget line. At that point, the investor’s return has an expected
value R* and a standard deviation ␴*.
Naturally, people differ in their attitudes toward risk. This fact is illustrated
in Figure 5.7, which shows how two different investors choose their portfolios.
Investor A is quite risk averse. Because his indifference curve UA is tangent to
the budget line at a point of low risk, he will invest almost all of his funds in
Treasury bills and earn an expected return RA just slightly larger than the riskfree return Rf. Investor B is less risk averse. She will invest most of her funds in
stocks, and while the return on her portfolio will have a higher expected value
RB, it will also have a higher standard deviation ␴B.
If Investor B has a sufficiently low level of risk aversion, she might buy stocks
on margin: that is, she would borrow money from a brokerage firm in order