【正文】 l. 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. 162CONCEPTCHECKpWhat is more likely, however, is that the bet results from differences in the probabilities that Paul and Mary assign to the oute. Mary assigns itprisk aversion and speculation are not inconsistent.An expected return in excess of that on riskfree securities. The premium provides pensation for the risk of an investment.(theArmed with the utility model, we can resolve the investment decision that is most consequential to investors, that is, how much of their wealth to put at risk for the greater expected return that can thus be achieved. We assume that the construction of the risky portfolio from the universe of available risky assets has already taken place and defer the discussion of how to construct that risky portfolio to the next chapter. At this point the investor can assess the expected return and risk of the overall portfolio. Using the expected return and risk parameters in the utility model yields the optimal allocation of capital between the risky portfolio and riskfree asset. Risk and Risk Aversionp. 161Inutility function,Chapter6: Risk Aversion and Capital Allocation to Risky AssetsChapter OpenerPARTconstructing an investor portfolio can be viewed as a sequence of two steps: (1) selecting the position of one39。While 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。which allows each investor to assign welfare or “utility” scores to alternative portfolios on the basis of expected return and risk and choose the portfolio with the highest score. We elaborate on the historical and empirical basis for the utility model in the appendix to this chapter.Chapter 5expectedexcess 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 ofTo gamble is “to bet or wager on an uncertain oute.” If you pare this definition to that of speculation, you will see that the central difference is the lack of “mensurate gain.” Economically speaking, a gamble is the assumption of risk for no purpose but enjoyment of the risk itself, whereas speculation is undertakenNotice that a risky investment with a risk premium of zero, sometimes called a= .5 to each oute. In that case the expected profit to both is zero and each has entered one side of a gambling prospect.p .5. They perceive, subjectively, two 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.Chapter 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.risk averseTo 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 inIntuitively, 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?utilityThe measure of the welfare or satisfaction of an investor.,Us risk aversion. The factor of 189。the investor39。Example Evaluating Investments by Using Utility ScoresConsider three investors with different degrees of risk aversion:= , andEquation H,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.certainty equivalent rateThe certain return providing the same utility as a risky portfolio.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. 164CONCEPTCHECKAriskneutralSee riskaverse.s certainty equivalent rate is simply its expected rate of return.risk loverSee riskaverse. this investor adjusts the expected returnP.Figure PortfolioPbecause its expected return is equal to or greater thans.p. 165meanvariance (MV) criterionThe selection of portfolios based on the means and variances of their returns. The choic of