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# CHAPTER 05 - PHALL-82241 PINDYCK CHAPTER 05 page 6 of 14...

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Unformatted text preview: PHALL-82241 PINDYCK CHAPTER 05 page 6 of 14 FIGURE 5.1 Outcome Probabilities for Two Jobs Probability 0.2 Job 2 0.1 Job 1 \$1000 \$1500 \$2000 Income The distribution of payoffs associated with Job 1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2. Both distributions are flat because all outcomes are equally likely. Fig 05-01.EPS PHALL-82241 PINDYCK CHAPTER 05 page 7 of 14 FIGURE 5.2 Unequal Probability Outcomes Probability 0.3 0.2 Job 2 0.1 Job 1 \$1000 \$1500 \$2000 Income The distribution of payoffs associated with Job 1 has a greater spread and a greater standard deviation than the distribution of payoffs associated with Job 2. Both distributions are peaked because the extreme payoffs are less likely than those near the middle of the distribution. Fig 05-02.EPS PHALL-82241 PINDYCK CHAPTER 05 page 8 of 14 FIGURE 5.3 Risk Averse, Risk Loving, and Risk Neutral Utility E 18 D 16 C 14 13.5 A F B 10 0 10 15 16 20 (a) Utility 30 Income (\$1000) Utility E 18 E 18 C 12 C 8 6 3 0 A A 10 20 (b) 30 Income (\$1000) 0 10 20 (c) 30 Income (\$1000) People differ in their preferences toward risk. In (a), a consumer’s marginal utility diminishes as income increases. The consumer is risk averse because she would prefer a certain income of \$20,000 (with a utility of 16) to a gamble with a .5 probability of \$10,000 and a .5 probability of \$30,000 (and expected utility of 14). In (b), the consumer is risk loving: She would prefer the same gamble (with expected utility of 10.5) to the certain income (with a utility of 8). Finally, the consumer in (c) is risk neutral and indifferent between certain and uncertain events with the same expected income. Fig 05-03.EPS PHALL-82241 PINDYCK CHAPTER 05 page 9 of 14 FIGURE 5.4 Risk Premium Utility G 20 18 E C 14 10 F Risk Premium A 10 16 20 Income (\$1000) 30 The risk premium, CF, measures the amount of income that an individual would give up to leave her indifferent between a risky choice and a certain one. Here, the risk premium is \$4000 because a certain income of \$16,000 (at point C) gives her the same expected utility (14) as the uncertain income (a .5 probability of being at point A and a .5 probability of being at point E) that has an expected value of \$20,000. Fig 05-04.EPS 40 PHALL-82241 PINDYCK CHAPTER 05 page 10 of 14 FIGURE 5.5 Risk Aversion and Indifference Curves Expected income U3 U2 Expected income U1 U3 U2 U1 Standard deviation of income (a) Standard deviation of income (b) Part (a) applies to a person who is highly risk averse: An increase in this individual’s standard deviation of income requires a large increase in expected income if he or she is to remain equally well off. Part (b) applies to a person who is only slightly risk averse: An increase in the standard deviation of income requires only a small increase in expected income if he or she is to remain equally well off. Fig 05-05.EPS PHALL-82241 PINDYCK CHAPTER 05 page 11 of 14 FIGURE 5.6 Choosing Between Risk and Return Expected return, Rp U3 U2 U1 Rm Budget Line R* Rf 0 s* sm Standard deviation of return, sp An investor is dividing her funds between two assets-Treasury bills, which are risk free, and stocks. The budget line describes the trade-off between the expected return and its riskiness, as measured by the standard deviation of the return. The slope of the budget line is (Rm? Rf )/⌠m, which is the price of risk. Three indifference curves are drawn, each showing combinations of risk and return that leave an investor equally satisfied. The curves are upward-sloping because a risk-averse investor will require a higher expected return if she is to bear a greater amount of risk. The utility-maximizing investment portfolio is at the point where indifference curve U2 is tangent to the budget line. Fig 05-06.EPS PHALL-82241 PINDYCK CHAPTER 05 page 12 of 14 FIGURE 5.7 The Choices of Two Different Investors Expected return, Rp UA UB Rm Budget Line RB RA Rf 0 sA sB sm Standard deviation of return, sp Investor A is highly risk averse. Because his portfolio will consist mostly of the riskfree asset, his expected return RA will be only slightly greater than the risk-free return. His risk ⌠A, however, will be small. Investor B is less risk averse. She will invest a large fraction of her funds in stocks. Although the expected return on her portfolio RB will be larger, it will also be riskier. Fig 05-07.EPS PHALL-82241 PINDYCK CHAPTER 05 page 13 of 14 FIGURE 5.8 Buying Stocks on Margin UB UA RB Budget Line Rm RA Rf 0 sA sm sB Because Investor A is risk averse, his portfolio contains a mixture of stocks and riskfree Treasury bills. Investor B, however, has a very low degree of risk aversion. Her indifference curve, UB, is tangent to the budget line at a point where the expected return and standard deviation for her portfolio exceed those for the stock market overall. This implies that she would like to invest more than 100 percent of her wealth in the stock market. She does so by buying stocks on margin-i.e., by borrowing from a brokerage firm to help finance her investment. Fig 05-08.EPS PHALL-82241 PINDYCK CHAPTER 05 page 14 of 14 FIGURE 5.9 Dividend Yield and P/E Ratio for S&P 500 50 7 45 6 Dividend Yield 40 P/E ratio 30 4 25 3 20 15 2 10 P/E Ratio 1 5 0 1980 1984 1988 1992 1996 2000 2004 The dividend yield for the S&P 500 (the annual dividend divided by the stock price) has fallen dramatically, while the price/earnings ratio (the stock price divided by the annual earnings-per-share) rose from 1980 to 2002 and then dropped. Fig 05-09.EPS 0 2008 Dividend yield (percent) 5 35 ...
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