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Unformatted text preview: PHALL82241 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 0501.EPS PHALL82241 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 0502.EPS PHALL82241 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 0503.EPS PHALL82241 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 0504.EPS 40 PHALL82241 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 0505.EPS PHALL82241 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 assetsTreasury bills, which are risk
free, and stocks. The budget line describes the tradeoff 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 upwardsloping because a riskaverse investor will require a higher
expected return if she is to bear a greater amount of risk. The utilitymaximizing investment
portfolio is at the point where indifference curve U2 is tangent to the budget line. Fig 0506.EPS PHALL82241 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 riskfree
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 0507.EPS PHALL82241 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 margini.e., by borrowing from
a brokerage firm to help finance her investment. Fig 0508.EPS PHALL82241 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 earningspershare) rose from 1980 to 2002 and then dropped. Fig 0509.EPS 0
2008 Dividend yield (percent) 5 35 ...
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 Spring '11
 Prof.Eco

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