【正文】 or 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.Table . 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?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 returnis the utility value and is just a scaling convention. To useEquation s degree of risk aversion. More riskaverse investors (who have the larger values ofA1A3implies that all three investors would assign a utility score of .05 to the riskfree alternative.would be chosen only by the investor with the lowest degree of risk aversion,We can interpret the utility score ofof 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.= 4 prefer to invest in Tbills or the risky portfolio? What ifinvestors (with(for whomupwardThe tradeoff between risk and return of a potential investment portfolio,P,P39。It can be stated as follows: portfolioifandand at least one inequality is strict (rules out the equality).Figure , the preferred direction is northwest, because in this direction we simultaneously increase the expected returnP. it must be pensated for by an increase in expected return. Thus pointis equally desirable to this investor aswhich connects all portfolio points with the same utility value (Figure ).Figure To determine some of the points that appear on the indifference curve, examine the utility values of several possible portfolios for an investor withFigure ?b.Time for Investing39。No, not those. RISK.to take but also how much risk you can“Most people can stand to lose a heck of a lot temporarily,” says Mr. Schatsky, a financial adviser in New York. The real acid test, he says, is how much of your portfolio39。As it turns out, most people rank as middleoftheroad risktakers, say several advisers. “Only about 10% to 15% of my clients are aggressive,” says Mr. Roge.WHAT’S YOUR RISK TOLERANCE?Circle the letter that corresponds to your answer1.Buy more. It was a good investment before。s part of a portfolio being used to meet investment goals with three different time horizons.2A..Buy morep. 1672B..Buy more2C..Buy more3.Stay put and hope for more gainc.re investing for retirement, which is 15 years away. Which would you rather do?a.You just won a big prize! But which one? It39。A 20% chance to win $15,0006.Yes7.Two months39。Reprinted with permission from Company. All Rights Reserved Worldwide. implied risk aversion coefficients.The most fundamental decision of investing is the allocation of your assets: How much should you own in stock? How much should you own in bonds? How much should you own in cash reserves? … That decision [has been shown to account] for an astonishing 94% of the differences in total returns achieved by institutionally managed pension funds. … There is no reason to believe that the same relationship does not also hold true for individual We will denote the investor39。F.For example, assume that the total market value of an initial portfolio is $300,000, of which $90,000 is invested in the Ready Asset money market fund, a riskfree asset for practical purposes. The remaining $210,000 is invested in risky securities—$113,400 in equities (E) and $96,600 in longterm bonds (B). The equities and long bond holdings prise “the” risky portfolio, 54% inP,andExample Evaluating Investments by Using Utility ScoresSuppose that the owner of this portfolio wishes to decrease risk by reducing the allocation to the risky portfolio from= .56. The risky portfolio would then total only .56 $300,000 = $168,000, requiring the sale of $42,000 of the original $210,000 of risky holdings, with the proceeds used to purchase more shares in Ready Asset (the money market fund). Total holdings in the riskfree asset will increase to $300,000 (1 ? .56) = $132,000, the original holdings plus the new contribution to the money market fund:$90,000 + $42,000 = $132,000EEEAs long as we do not alter the weights of each security within the risky portfolio, the probability distribution of the rate of return on the risky portfolio remain