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2011ÄêÉ½¶«¸ß¿¼µÂÓïÊÔÌâ¼°´ð°¸ CHAPTER 1: Discussion Questions and Problems 1. Differentiate the following terms/concepts:

a. Prospect and probability distribution

A prospect is a lottery or series of wealth outcomes, each of which is associated with a probability, whereas a probability distribution defines the likelihood of possible outcomes.

b. Risk and uncertainty

Risk is measurable using probability, but uncertainty is not. Uncertainty is when probabilities can¡¯t be assigned or the possible outcomes are unclear.

c. Utility function and expected utility

A utility function, denoted as u(?), assigns numbers to possible outcomes so that preferred choices receive higher numbers. Utility can be thought of as the satisfaction received from a particular outcome.

d. Risk aversion, risk seeking, and risk neutrality

Risk aversion describes someone who prefers the expected value of a lottery to the lottery itself. Risk seeking describes someone who prefers a lottery to the expected value of a lottery. And risk neutrality describes someone whose utility of the expected value of a lottery is equal to the expected utility of the lottery.

2. When eating out, Rory prefers spaghetti over a hamburger. Last night she had a choice of spaghetti and macaroni and cheese and decided on the spaghetti again. The night before, Rory had a choice between spaghetti, pizza, and a hamburger and this time she had pizza. Then, today she chose macaroni and cheese over a hamburger. Does her selection today indicate that Rory¡¯s choices are consistent with economic rationality? Why or why not?

Rory¡¯s preferences are consistent with rationality. They are complete and transitive. We see that her preference ordering is:

Pizza ? spaghetti ?macaroni and cheese ?hamburger

3. Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has a 40% chance of wealth of $50,000 and a 60% chance of wealth of $1,000,000 as summarized by P(0.40, $50,000, $1,000,000).

a. What is the expected value of wealth?

E(w) = .4 * .5 + .6 * 10 = 6.2 U(P) = .4e0.50 + .6e10 = 13,216.54

b. Construct a graph of this utility function.

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The function is convex.

c. Is this person risk averse, risk neutral, or a risk seeker?

Risk seeker because graph is convex.

d. What is this person¡¯s certainty equivalent for the prospect?

ew = 13,216.54 gives w = 9.4892244 or $948,922.44

4. An individual has the following utility function: u(w) = w.5 where w = wealth.

a. Using expected utility, order the following prospects in terms of preference, from the most to the least preferred:

P1(.8, 1,000, 600) P2(.7, 1,200, 600) P3(.5, 2,000, 300)

Ranking: P2, P3, P1 with expected utilities 31.5972, 31.0209, and 30.1972 for prospects 2, 3, and 1, respectively

b. What is the certainty equivalent for prospect P2?

998.3830

c. Without doing any calculations, would the certainty equivalent for prospect P1 be larger or smaller? Why?

The certainty equivalent for P1 would be smaller because P2 is ranked higher than P1.

5. Consider two prospects: Problem 1: Choose between Prospect A: $2,500 with probability .33, $2,400 with probability .66, Zero with probability .01. And Prospect B: $2,400 with certainty. Problem 2: Choose between Prospect C: $2,500 with probability .33, Zero with probability .67. And Prospect D: $2,400 with probability .34, Zero with probability .66.

?2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly available website, in whole or in part.

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It has been shown by Daniel Kahneman and Amos Tversky (1979, ¡°Prospect theory: An analysis of decision under risk,¡± Econometrica 47(2), 263-291) that more people choose B when presented with problem 1 and when presented with problem 2, most people choose C. These choices violate expected utility theory. Why?

This is an example of the Allais paradox. The first choice suggests that u(2,400) > .33u(2,500) + .66u(2,400) or .34u(2,400) > .33 u(2,500) while the second choice suggests just the opposite inequality. Chapter 2: Discussion Questions and Problems 1. Differentiate the following terms/concepts:

a. Systematic and nonsystematic risk

Nondiversifiable or systematic risk is risk that is common to all risky assets in the system and cannot be diversified. Diversifiable or unsystematic risk is specific to the asset in question and can be diversified.

b. Beta and standard deviation

Beta is the CAPM¡¯s measure of risk. It takes into account an asset¡¯s sensitivity to the market and only measures systematic, nondiversifiable risk. The standard deviation is a measure of dispersion that includes both diversifiable and nondiversifiable risks.

c. Direct and indirect agency costs

Agency costs arise when managers¡¯ incentives are not consistent with maximizing the value of the firm. Direct costs include expenditures that benefit the manager but not the firm, such as purchasing a luxury jet for travel. Other direct costs result from the need to monitor managers, including the cost of hiring outside auditors. Indirect costs are more difficult to measure and result from lost opportunities.

d. Weak, semi-strong, and strong form market efficiency

With weak form market efficiency prices reflect all the information contained in historical returns. With semi-strong form market efficiency prices reflect all publicly available information. With strong form market efficiency prices reflect information that is not publicly available, such as insiders¡¯ information.

2. A stock has a beta of 1.2 and the standard deviation of its returns is 25%. The market risk premium is 5% and the risk-free rate is 4%.

a. What is the expected return for the stock?

E(R) = .04 + 1.2(.05) = .10

b. What are the expected return and standard deviation for a portfolio that is equally invested in the stock and the risk-free asset?

E(Rp) = .5(.10) +.5(.04) = .07, ¦Òp =(.5)(.25) = .125

c. A financial analyst forecasts a return of 12% for the stock. Would you buy it? Why or why not?

If you believe the source is very credible, buy it as it is expected to generate a positive abnormal (or excess) return.

?2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly available website, in whole or in part.

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3. What is the joint hypothesis problem? Why is it important?

If when testing one hypothesis another must be assumed to hold, a joint-hypothesis problem arises. For us, this is of particular interest when we are testing market efficiency because of the need to utilize a particular risk-adjustment model to produce required returns, that is, to risk-adjust. This would not be a problem if we knew with certainty what the correct risk adjustment model is, but unfortunately we do not. If a test rejects the EMH, is it because the EMH does not hold, or because we did not properly measure abnormal returns? We simply do not know for certain the answer to this question.

4. Warren Buffett has been a very successful investor. In 2008 Luisa Kroll reported that Buffett topped Forbes Magazine¡¯s list of the world¡¯s richest people with a fortune estimated to be worth $62 billion (March 5, 2008, The world's billionaires,Forbes). Does this invalidate the EMH?

Warren Buffett¡¯s experience does not necessarily invalidate the EMH. There is the possibility that he is just lucky: given that there are numerous money managers, some are bound to perform well just by luck. Still many would question this here because Buffett¡¯s track record has been consistently strong.

5. You are considering whether to invest in two stocks, Stock A and Stock B. Stock A has a beta of 1.15 and the standard deviation of its returns has been estimated to be 0.28. For Stock B, the beta is 0.84 and standard deviation is 0.48.

a. Which stock is riskier?

Stock A is riskier, though stock B has greater total risk.

b. If the risk-free rate is 4% and the market risk premium is 8%, what is the

expected return for a portfolio that is composed of 60% A and 40% B?

Rp = .6(.132) + .4 (.1072) = .12208

c. If the correlation between the returns of A and B is 0.50, what is the standard

deviation for the portfolio that includes 60% A and 40% B?

22

¦Òp = (.6)(.28)2 + (.4)2(.48)2 + 2*.5(.6)(.4)(.28)(.48) = 9.7%, ¦Òp = 31.2%

Chapter 3: Discussion Questions and Problems 1. Differentiate the following terms/concepts:

a. Lottery and insurance

A lottery is a prospect with a low probability of a high payoff. Many people buy lottery tickets, even with negative expected values. These same people buy insurance to protect themselves from risk. Normally, insurance is a hedge against a low-probability large loss. These choices are inconsistent with traditional expected utility framework but can be explained by prospect theory.

b. Segregation and integration

Integration occurs when positions are lumped together, while segregation occurs when situations are viewed one at a time.

c. Risk aversion and loss aversion

?2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly available website, in whole or in part.

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A person who is risk averse prefers the expected value of a prospect to the prospect itself, whereas for a person who is loss averse, losses loom larger than gains.

d. Weighting function and event probability

Event probability is simply the subjective view on how likely an event is. The weighting function is associated with the probability of an outcome, but is not strictly the same as the probability as in expected utility theory.

2. According to prospect theory, which is preferred?

a. Prospect A or B?

Decision (i). Choose between: A(0.80, $50, $0)and B(0.40, $100, $0)

Prospect A is preferred due to risk aversion for gains. While both have the same expected change in wealth, A has less risk.

b. Prospect C or D?

Decision (ii). Choose between: C(0.00002, $500,000, $0) and D(0.00001, $1,000,000, $0) Prospect D, with more risk, is preferred due to the risk seeking that occurs when there are very low probabilities of positive payoffs.

c. Are these choices consistent with expected utility theory? Why or why not?

Violation of EU theory because preferences are inconsistent. The same sort of Allais paradox proof from chapter 1 can be used. It is also necessary to make the assumption of preference homogeneity, which means that if D is preferred to C, it will also be true that D* is preferred to C* where these are:

C*:(0.00002, $50, $0) and D*: (0.00001, $100, $0)

3. Consider a person with the following value function under prospect theory v(w) = w.5 when w > 0 = -2(-w) .5 when w < 0

a. Is this individual loss-averse? Explain.

This person is loss averse. Losses are felt twice as much as gains of equal magnitude.

b. Assume that this individual weights values by probabilities, instead of using a

prospect theory weighting function. Which of the following prospects would be preferred?

P1(.8, 1000, -800) P2(.7, 1200, -600) P3(.5, 2000, -1000)

We calculate the value of each prospect: V(P1) = .8(31.62)+.2(-2)(28.27)= 13.982 V(P2) = .7(34.64)+.3(-2)(24.49)= 9.55 V(P3) = .5(44.72)+.5(-2)(31.62)= 9.265 Therefore prospect P1 is preferred.

4. Now consider a person with the following value function under prospect theory: v(z) = z.8 when z ¡Ý 0 = -3(-z).8 when z < 0

This individual has the following weighting function:

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