higher than the risk-free rate, leading her to accept the prospect.     CONCEPT C H E C K ☞ QUESTION 3 A portfolio has an expected rate of return of 20% and standard deviation of 20%. Bills offer a sure rate of return of 7%. Which investment alternative will be chosen by an investor whose A 4? What if A 8?     Because we can compare utility values to the rate offered on risk-free investments when choosing between a risky portfolio and a safe one, we may interpret a portfolios utility value as its "certainty equivalent" rate of return to an investor. That is, the certainty equiv- alent rate of a portfolio is the rate that risk-free investments would need to offer with cer- tainty to be considered equally attractive as the risky portfolio. Now we can say that a portfolio is desirable only if its certainty equivalent return ex- ceeds that of the risk-free alternative. A sufficiently risk-averse investor may assign any risky portfolio, even one with a positive risk premium, a certainty equivalent rate of return that is below the risk-free rate, which will cause the investor to reject the portfolio. At the same time, a less risk-averse (more risk-tolerant) investor may assign the same portfolio a certainty equivalent rate that exceeds the risk-free rate and thus will prefer the portfolio to the risk-free alternative. If the risk premium is zero or negative to begin with, any down- ward adjustment to utility only makes the portfolio look worse. Its certainty equivalent rate will be below that of the risk-free alternative for all risk-averse investors. In contrast to risk-averse investors, risk-neutral investors judge risky prospects solely by their expected rates of return. The level of risk is irrelevant to the risk-neutral investor, meaning that there is no penalization for risk. For this investor a portfolios certainty equiv- alent rate is simply its expected rate of return. A risk lover is willing to engage in fair games and gambles; this investor adjusts the ex- pected return upward to take into account the "fun" of confronting the prospects risk. Risk lovers will always take a fair game because their upward adjustment of utility for risk gives the fair game a certainty equivalent that exceeds the alternative of the risk-free investment. We can depict the individuals trade-off between risk and return by plotting the charac- teristics of potential investment portfolios that the individual would view as equally     Figure 6.1 The trade-off between risk and return of a potential investment portfolio.