【正文】 different prospects. Economists call this case of differing beliefs “heterogeneous expectations.” In such cases investors on each side of a financial position see themselves as speculating rather than gambling.Notice that a risky investment with a risk premium of zero, sometimes called aChapter 5constructing an investor portfolio can be viewed as a sequence of two steps: (1) selecting the position of one39。pRisk Aversion and Utility ValuesThe history of rates of return on various asset classes presented inA2A portfolio has an expected rate of return of 20% and standard deviation of 30%. Tbills offer a safe rate of return of 7%. Would an investor with riskaversion parameterAdominatesP,= 4, presented int easy to quantify.Many experts warn, however, that the questionnaires should be used simply as a first step to assessing risk tolerance. “They are not precise,” says Ron Meier, a certified public accountant.s a cheap investment, too2.t changed. After you finish gloating, what do you do?a.Definitely notb.If you scoredAfter the sale, the proportions of each asset in the risky portfolio are in fact unchanged:Given this simplification, we can now turn to the desirability of reducing risk by changing the risky/riskfree asset mix, that is, reducing risk by decreasing the proportionBy:The weights of each asset class in the plete portfolio are as follows:The risky portfolio makes up 70% of the plete portfolio.p. 169s overall portfolio prises two mutual funds, one invested in stocks and the other invested in longterm bonds. For now, we take the position of the risky portfolio as given and focus only on the allocation between it and riskfree securities. In the next chapter, we turn to asset allocation and security selection across risky assets.YOUR SCORE$2,000 in cashb.Sellb.Sell to avoid further worry and try something elseb.s impossible for someone to assess their risk tolerance alone,” says Mr. Bernstein. “I may say I don39。to take.P,depends on the exact nature of the investor39。This is the meanstandard deviation, or equivalently,s tradeoff between risk and return by plotting the characteristics of potential investment portfolios that the individual would view as equally attractive on a graph with axes measuring the expected value and standard deviation of portfolio the characteristics of one portfolio denoted= 0) judge risky prospects solely by their expected rates of return. The level of risk is irrelevant to the riskneutral investor, meaning that there is no penalty for risk. For this investor a portfolio39。= 2, while the lowrisk portfolio,is an index of the investor39。Both Paul and Mary 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. 162CONCEPTCHECKAn expected return in excess of that on riskfree securities. The premium provides pensation for the risk of an investment.(theWhile the task of constructing an optimal risky portfolio is technically plex, it can be delegated to a professional because it largely entails welldefined optimization techniques. In contrast, the decision of how much to invest in that portfolio depends on an investor39。expectedexcess return) and the standard deviation of the rate of return, which we use as the measure of portfolio risk. We demonstrated these concepts with a scenario analysis of a specific risky portfolio (Spreadsheet ). To emphasize that bearing risk typically must be acpanied by a reward in the form of a risk premium, we first distinguish between speculation and gambling.Risk, Speculation, and GamblingOne definition ofIntuitively, 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?s risk aversion. The factor of 189。Evaluating Investments by Using Utility ScoresConsider three investors with different degrees of risk aversion:L,would be passed over even by the most riskaverse of our three investors. All three portfolios beat the riskfree alternative for the investors with levels of risk aversion given in the table.Now we can say that a portfolio is desirable only if its certainty equivalent return exceeds that of the riskfree alternative. A sufficiently riskaverse investor may assign any risky portfolio, even one with a positive risk premium, a certainty equivalent rate of return that is below the riskfree rate, which will cause the investor to reject the risky portfolio. At the same time, a less riskaverse investor may assign the same portfolio a certainty equivalent rate that exceeds the riskfree rate and thus will prefer the portfolio to the riskfree alternative. If the risk premium is zero or negative to begin with, any downward adjustment to utility only makes the portfolio look worse. Its certainty equivalent rate will be below that of the riskfree alternative for all riskaverse investors.p.