riskaversionandcapitalallocationtoriskyassets(编辑修改稿)

riskaversionandcapitalallocationtoriskyassets(编辑修改稿)内容摘要：

while the lowrisk portfolio,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.We can interpret the utility score ofriskyportfolios as acertainty equivalent rateThe certain return providing the same utility as a risky portfolio.of return. The certainty equivalent rate is the rate that riskfree investments would need to offer to provide the same utility score as the risky portfolio. In other words, it is the rate that, if earned with certainty, would provide a utility score equivalent to that of the portfolio in question. The certainty equivalent rate of return is a natural way to pare the utility values of peting portfolios.Table Utility scores of alternative portfolios for investors with varying degrees of risk aversionNow 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. 164CONCEPTCHECK2A 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 parameterA= 4 prefer to invest in Tbills or the risky portfolio? What ifA= 2?In contrast to riskaverse investors,riskneutralSee riskaverse.investors (withA= 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。 s certainty equivalent rate is simply its expected rate of return.Arisk loverSee riskaverse.(for whomA 0) is happy to engage in fair games and gambles。 this investor adjusts the expected returnupwardto take into account the “fun” of confronting the prospect39。 s 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 riskfree investment.We can depict the individual39。 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 denotedP.Figure The tradeoff between risk and return of a potential investment portfolio,PortfolioP,which has expected returnE(rP) and standard deviation σP, is preferred by riskaverse investors to any portfolio in quadrant IV because it has an expected return equal to or greater than any portfolio in that quadrant and a standard deviation equal to or smaller than any portfolio in that quadrant. Conversely, any portfolio in quadrant I is preferable to portfolioPbecause its expected return is equal to or greater thanP39。 s and its standard deviation is equal to or smaller thanP39。 s.p. 165This is the meanstandard deviation, or equivalently,meanvariance (MV) criterionThe selection of portfolios based on the means and variances of their returns. The choic of the higher expected return portfolio for a given level of variance or the lower variance portfolio for a given expected return..It can be stated as follows: portfolioAdominatesBifandand at least one inequality is strict (rules out the equality).In the expected return–standard deviation plane inFigure , the preferred direction is northwest, because in this direction we simultaneously increase the expected returnanddecrease the variance of the rate of return. This means that any portfolio that lies northwest ofPis superior to it.What can be said about portfolios in quadrants II and III? Their desirability, pared withP,depends on the exact nature of the investor39。 s risk aversion. Suppose an investor identifies all portfolios that are equally attractive as portfolioP.Starting atP,an increase in standard deviation lowers utility。 it must be pensated for by an increase in expected return. Thus pointQinFigure is equally desirable to this investor asP.Investors will be equally attracted to portfolios with high risk and high expected returns pared with other portfolios with lower risk but lower expected returns. These equally preferred portfolios will lie in the mean–standard deviation plane on a curve called theindifference curveA curve connecting all portfolios with the same utility according to their means and standard deviations.,which connects all portfolio points with the same utility value (Figure ).Figure The indifference curveTo determine some of the points that appear on the indifference curve, examine the utility values of several possible portfolios for an investor withA= 4, presented inTable . Note that each portfolio offers identical utility, because the portfolios with higher expected return also have higher risk (standard deviation).Estimating Risk AversionHow might we go about estimating the levels of risk aversion we might expect to observe in practice? A number of methods may be used. The questionnaire in the nearby box is of the simplest variety and, indeed, can distinguish。