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1、Chapter6: Risk Aversion and Capital Allocation to Risky AssetsChapter OpenerPART IIp. 160THE PROCESS OF constructing an investor portfolio can be viewed as a sequence of two steps: (1) selecting the composition of ones portfolio of risky assets such as stocks and long-term bonds, and (2) deciding ho
2、w much to invest in that risky portfolio versus in a safe asset such as short-term Treasury bills. Obviously, an investor cannot decide how to allocate investment funds between the risk-free asset and that risky portfolio without knowing its expected return and degree of risk, so a fundamental part
3、of the asset allocation problem is to characterize the riskreturn trade-off for this portfolio.While the task of constructing an optimal risky portfolio is technically complex, it can be delegated to a professional because it largely entails well-defined optimization techniques. In contrast, the dec
4、ision of how much to invest in that portfolio depends on an investorspersonal preferences 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 journe
5、y into portfolio theory by establishing a framework to explore this fundamental decision, namely, capital allocation between the risk-free and the risky portfolio.We begin by introducing two themes in portfolio theory that are centered on risk. The first is the tenet that investors will avoid risk u
6、nless they can anticipate a reward for engaging in risky investments. The second theme allows us to quantify investors personal trade-offs between portfolio risk and expected return. To do this we introduce a personal utility function, which allows each investor to assign welfare or “utility” scores
7、 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.Armed with the utility model, we can resolve the investment decision that is m
8、ost 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 co
9、nstruct 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 risk-free asset.6
10、.1 Risk and Risk Aversionp. 161In Chapter 5 we introduced the concepts of the holding-period return (HPR) and the excess return over the risk-free rate. We also discussed estimation of the risk premium An expected return in excess of that on risk-free securities. The premium provides compensation fo
11、r the risk of an investment.(the 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 5.1). To emphasize that bearing risk typically m
12、ust be accompanied by a reward in the form of a risk premium, we first distinguish between speculation and gambling.Risk, Speculation, and GamblingOne definition of speculation is “the assumption of considerable investment risk to obtain commensurate gain.” Although this definition is fine linguisti
13、cally, it is useless without first specifying what is meant by “considerable risk” and “commensurate gain.”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 insuff
14、icient to make up for the risk involved. By “commensurate gain” we mean a positive risk premium, that is, an expected profit greater than the risk-free alternative.To gamble is “to bet or wager on an uncertain outcome.” If you compare this definition to that of speculation, you will see that the cen
15、tral difference is the lack of “commensurate gain.” Economically speaking, a gamble is the assumption of risk for no purpose but enjoyment of the risk itself, whereas speculation is undertaken in spite of the risk involved because one perceives a favorable riskreturn trade-off. To turn a gamble into
16、 a speculative prospect requires an adequate risk premium to compensate risk-averse investors for the risks they bear. Hence, risk aversion and speculation are not inconsistent. Notice that a risky investment with a risk premium of zero, sometimes called a fair gameAn investment prospect that has a zero risk premium., amounts to a gamble. A risk-averse investor will reject it.In some cases a gamble may appear to the participants as speculation. Suppose two investors disagree sharply
