CHAPTER • Uncertainty and Consumer Behavior 181 Expected return, Rp U3 U2 U1 Rm Budget Line R* Rf 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 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