Chapter 06_Hand-out 5

Chapter 06_Hand-out 5 - CHAPTER 6 RISK AVERSION AND CAPITAL...

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CHAPTER 6 RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETS 6.1 RISK AND RISK AVERSION Now, we must ask how much of an expected reward is offered to compensate for the risk involved in investing money in stocks. We measure the “reward”` as the difference between the expected HPR on the index stock fund and the risk-free rate , that is, the rate you can earn by leaving money in risk-free assets such as T- bills, money market funds, or the bank. We call this difference the risk premium on common stocks. Therefore, to study the risk premium available on risky assets we compute a series of excess returns , that is, returns in excess of the T-bill rate in each period. To emphasize that bearing risk typically mush be accompanied by a reward in the form of risk premium, we first distinguish between speculation and gambling. 1. Risk, Speculation, and Gambling One definition of speculation is “the assumption of considerable investment risk in obtaining 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 insufficient 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 say that the central 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 risk-return trade-off. To turn a gamble into 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 . 2. Risk Aversion and Utility Values Notice that a risky investment with a risk premium of zero, sometimes called a fair game, amounts to a gamble. Investors who are risk averse reject investment portfolios that are fair games or worse. Risk-averse investors are willing to consider only risk-free or speculative prospects with positive risk premiums. Loosely speaking, a risk-averse investor “penalizes” the expected rate of return of 1
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a risky portfolio by a certain percentage to account for the risk involved. The greater the risk, the larger the penalty. We can formalize the notion of a risk-penalty system. To do so, we will assume that each investor can assign a welfare, or utility, score to competing investment portfolios based on the expected return and risk of those portfolios. The utility score may be viewed as a means of ranking portfolios. Higher utility values are assigned to portfolios with more attractive risk-return profiles. AIMR (Association of Investment Management and Research) assigns a portfolio with
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This note was uploaded on 09/25/2011 for the course FINA 4320 taught by Professor John during the Spring '11 term at Houston Baptist.

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Chapter 06_Hand-out 5 - CHAPTER 6 RISK AVERSION AND CAPITAL...

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