【正文】 y should be asking, Why is the other willing to invest in the side of a risky prospect that I believe offers a negative expected profit? The ideal way to resolve heterogeneous beliefs is for Paul and Mary to “merge their information,” that is, for each party to verify that he or she possesses all relevant information and processes the information properly. Of course, the acquisition of information and the extensive munication that is required to eliminate all heterogeneity in expectations is costly, and thus up to a point heterogeneous expectations cannot be taken as irrational. If, however, Paul and Mary enter such contracts frequently, they would recognize the information problem in one of two ways: Either they will realize that they are creating gambles when each wins half of the bets, or the consistent loser will admit that he or she has been betting on the basis of inferior forecasts.p. 162CONCEPTCHECK1Assume that dollardenominated Tbills in the United States and pounddenominated bills in the United Kingdom offer equal yields to maturity. Both are shortterm assets, and both are free of default risk. Neither offers investors a risk premium. However, a . investor who holds . bills is subject to exchange rate risk, because the pounds earned on the . bills eventually will be exchanged for dollars at the future exchange rate. Is the . investor engaging in speculation or gambling?Risk Aversion and Utility ValuesThe history of rates of return on various asset classes presented inChapter 5, as well as numerous elaborate empirical studies, leave no doubt that risky assets mand a risk premium in the marketplace. This implies that most investors are risk averse.Investors who arerisk averseA riskaverse investor will consider risky portfolios only if they provide pensation for risk via a risk premium. A riskneutral investor finds the level of risk irrelevant and considers only the expected return of risk prospects. A risk lover is willing to accept lower expected returns on prospects with higher amounts of investment portfolios that are fair games or worse. Riskaverse investors are willing to consider only riskfree or speculative prospects with positive risk premiums. Loosely speaking, a riskaverse investor “penalizes” the expected rate of return of a risky portfolio by a certain percentage (or penalizes the expected profit by a dollar amount) to account for the risk involved. The greater the risk, the larger the penalty. One might wonder why we assume risk aversion as fundamental. We believe that most investors would accept this view from simple introspection, but we discuss the question more fully in Appendix A of this chapter.To illustrate the issues we confront when choosing among portfolios with varying degrees of risk, consider a specific example. Suppose the riskfree rate is 5% and that an investor considers three alternative risky portfolios with risk premiums, expected returns, and standard deviations as given inTable . The risk premiums and degrees of risk (standard deviation, SD) of the portfolios in the table are chosen to represent the properties of lowrisk bonds (L), highrisk bonds (M), and large stocks (H). Accordingly, these portfolios offer progressively higher risk premiums to pensate for greater risk. How might investors choose among them?Intuitively, one would rank each portfolio as more attractive when its expected return is higher, and lower when its risk is higher. But when risk increases along with return, the most attractive portfolio is not obvious. How can investors quantify the rate at which they are willing to trade off return against risk?Table Available risky portfolios (Riskfree rate = 5%)We will assume that each investor can assign a welfare, orutilityThe measure of the welfare or satisfaction of an investor.,score to peting investment portfolios on the basis of the expected return and risk of those portfolios. Higher utility values are assigned to portfolios with more attractive risk–return profiles. Portfolios receive higher utility scores for higher expected returns and lower scores for higher volatility. Many particular “scoring” systems are legitimate. One reasonable function that has been employed by both financial theorists and the CFA Institute assigns a portfolio with expected returnE(r) and variance of returns σ2the following utility score:p. 163whereUis the utility value andAis an index of the investor39。s risk aversion. The factor of 189。 is just a scaling convention. To useEquation , rates of return must be expressed as decimals rather than percentages.Equation is consistent with the notion that utility is enhanced by high expected returns and diminished by high risk. Notice that riskfree portfolios receive a utility score equal to their (known) rate of return, because they receive no penalty for risk. The extent to which the variance of risky portfolios lowers utility depends onA,the investor39。s degree of risk aversion. More riskaverse investors (who have the larger values ofA) penalize risky investments more severely. Investors choosing among peting investment portfolios will select the one providing the highest utility level. The nearby box discusses some techniques that financial advisers use to gauge the risk aversion of their clients.Example Evaluating Investments by Using Utility ScoresConsider three investors with different degrees of risk aversion:A1= 2,A2= , andA3= 5, all of whom are evaluating the three portfolios inTable . Because the riskfree rate is assumed to be 5%,Equation implies that all three investors would assign a utility score of .05 to the riskfree alternative.Table presents the utility scores that would be assigned by each investor to each portfolio. The portfolio with the highest utility score for each investor appears in bold. Notice that the highrisk portfolio,H,would be chosen only by the investor with the lowest degree of risk aversion,A1= 2,