【正文】 EEvaluating Investments by Using Utility ScoresSuppose that the owner of this portfolio wishes to decrease risk by reducing the allocation to the risky portfolio fromandFor 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% inF.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 Reprinted with permission fromYes7.You just won a big prize! But which one? It39。Stay put and hope for more gainc.Buy more2C..s part of a portfolio being used to meet investment goals with three different time horizons.2A..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.to take but also how much risk you canTime for Investing39。which connects all portfolio points with the same utility value (Figure ).Figure it must be pensated for by an increase in expected return. Thus pointifandand at least one inequality is strict (rules out the equality).P,(for whominvestors (with= 4 prefer to invest in Tbills or the risky portfolio? What ifWe can interpret the utility score ofwould be chosen only by the investor with the lowest degree of risk aversion,A3Equation is the utility value andTable . 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?fair gameAn investment prospect that has a zero risk premium.,By “considerable risk” we mean that the risk is sufficient to affect the decision. An individual might reject an investment that has a positive risk premium because the potential gain is insufficient to make up for the risk involved. By “mensurate gain” we mean a positive risk premium, that is, an expected profit greater than the riskfree alternative.we introduced the concepts of the holdingperiod return (HPR) and the excess return over the riskfree rate. We also discussed estimation of theWe begin by introducing two themes in portfolio theory that are centered on risk. The first is the tenet that investors will avoid risk unless they can anticipate a reward for engaging in risky investments. The second theme allows us to quantify investors39。s portfolio of risky assets such as stocks and longterm bonds, and (2) deciding how much to invest in that risky portfolio versus in a safe asset such as shortterm Treasury bills. Obviously, an investor cannot decide how to allocate investment funds between the riskfree asset and that risky portfolio without knowing its expected return and degree of risk, so a fundamental part of the asset allocation problem is to characterize the risk–return tradeoff for this portfolio.IIp. 160THE PROCESS OFpreferences about risk versus expected return, and therefore it cannot easily be delegated. As we will see in the chapter on behavioral finance, many investors stumble over this cardinal step. We therefore begin our journey into portfolio theory by establishing a framework to explore this fundamental decision, namely, capital allocation between the riskfree and the risky portfolio.is “the assumption of considerable investment risk to obtain mensurate gain.” Although this definition is fine linguistically, it is useless without first specifying what is meant by “considerable risk” and “mensurate gain.”of the risk involved because one perceives a favorable risk–return tradeoff. To turn a gamble into a speculative prospect requires an adequate risk premium to pensate riskaverse investors for the risks they bear. Hence,1 exceeds $ one year from now, whereas Mary will pay Paul if the pound is worth less than $. There are only two relevant outes: (1) the pound will exceed $, or (2) it will fall below $. If both Paul and Mary agree on the probabilities of the two possible outes, and if neither party anticipates a loss, it must be that they assigns assessment isAssume 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?Table Available risky portfolios (Riskfree rate = 5%)E(r) and variance of returns σ2Equation , rates of return must be expressed as decimals rather than percentages.A) 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.= 2,Table 2to take into account the “fun” of confronting the prospect39。s and its standard dev