第一章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? 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 1 页，共 10 页E(w) = .4 * .5 + .6 * 10 = 6.2 U(P) = .4e0.50 + .6e10 = 13,216.54 b. Construct a graph of this utility function. 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 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 2 页，共 10 页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. It has been shown by Daniel Ka hneman 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. 第二章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. 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 3 页，共 10 页b. Beta and standard deviation Beta is the CAPMs measure of risk. It takes into account an assets 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, p =(.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. 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. 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 4 页，共 10 页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 worlds billionaires , Forbes). Does this invalidate the EMH? Warren Buffetts 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 Buffetts 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? p2 = (.6)2(.28)2 + (.4)2(.48)2+ 2*.5(.6)(.4)(.28)(.48) = 9.7%, p = 31.2%第三章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 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 5 页，共 10 页Integration occurs when positions are lumped together, while segregation occurs when situations are viewed one at a time. c. Risk aversion and loss aversion 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.5when w 0 = -2(-w) .5when w 0 a. Is this individual loss-averse? Explain. 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 6 页，共 10 页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)= 9.55V(P3) = .5(44.72)+.5(-2)(31.62)= 9.265Therefore prospect P1 is preferred. 4. Now consider a person with the following value function under prospect theory: v(z) = z.8when z 0= -3(-z).8when z 0 This individual has the following weighting function: where we set =.65. a. Which of the following prospects would he choose? PA(.001, -5000) PB(-5) Compare the value of each prospect: V(PA) = .983(0) + (-3)(910.28)(.011) = -30.15 (note use of weights) V(PB) = 3 * 1 * -3.62 = -10.87 Therefore you would prefer B. b. Repeat the calculation but using probabilities instead of weights. What does this illustrate? 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 7 页，共 10 页V(PA) = .999 * 0 + 3 * .001 * -910.28 = -2.73 (note use of probability) V(PB) = 3 * 1 * -3.62 = -10.87 Therefore you would prefer A. The reason for the switch is that risk seeking is maintained in the domain of losses (implying rejection of losses) if probabilities are used instead of weights. 5. Why might some prefer a prix fixe (fixed price) dinner costing about the same as an a la carteone (where you pay individually for each item)? (Assume the food is identical.) Payment decoupling is encouraged with prix fixe. You only face the loss of money once rather than multiple times (occurring if you have to face the cost of each item individually using an la carte scheme). 第五章1. Differentiate the following terms/concepts: a.Primacy and recency effects A primacy effect is the tendency to rely on information that comes first when making an assessment, whereas a recency effect is the tendency to rely on the most recent information when making an assessment. b.Salience and availability The salience of an event refers to how much it stands out relative to other events, whereas the availability refers to how easily the event is recalled from memory. c.Fast-and-frugal heuristics and bias-generating heuristics Fast and frugal heuristics require a minimum of time, knowledge and computation in order to make choices. Often they lead to very good choices. Sometimes however heuristics go astray and generate behavioral bias. d.Autonomic and cognitive heuristics Autonomic heuristics are reflexive, autonomic, non-cognitive, and require low effort levels. Cognitive heuristics require more deliberation. Autonomic heuristics are appropriate when a very quick decision must be made or when the stakes are low, whereas cognitive heuristics are appropriate when the stakes are higher. 2. Which description of Mary has higher probability? 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 8 页，共 10 页a. Mary loves to play tennis. b. Mary loves to play tennis and, during the summer, averages at least a game a week. Explain your answer. Define the conjunction fallacy. How does it apply here? Assume for the purpose of illustration that the probability that someone loves to play tennis is .2; the probability that someone plays tennis once or more a week during the summer is .1; and the probability of one or the other of these things is .22. Pr(loves tennis) = .2 Pr(loves tennis AND averages 1+) = Pr(loves tennis) + Pr(averages 1+) - Pr(loves tennis OR averages 1+) = .2 + .1 - .22 = .08 The second probability has to be less because it has one more requirement (not only do you have to love tennis but you also have to play regularly, but some tennis lovers might just be too busy to do this). When people commit the conjunction fallacy (the belief that the joint probability is more likely than one of its components), they will think the second (joint) event is more likely because it sounds logical that someone who loves tennis will also play regularly. 3. Rex is a smart fellow. He gets an A in a course 80% of the time. Still he likes his leisure, only studying for the final exam in half of the courses he takes. Nevertheless when he does study, he is almost sure (95% likely) to get an A. Assuming he got an A, how likely is it he studied? If someone estimates the above to be 75%, what error are they committing? Explain.P(studied|A) = P(A|studied) * P(studied)/P(A) = .95 * (.5 / .8) = .59375 The “ sample” is that he got an A. Without knowing this you would have said the probability that he studied was .5. You rightfully shifted the probability upwards based on the sample, but you moved it too much. You should have stayed closer to the base rate, so you have committed base weight underweighting. Another example of this is, when watching sports and noticing that someone is playing better than they normally do, believing that they have permanently improved. 4. Why are two people who witnessed the same event last month likely to describe it differently today? Memory is very imprecise. The common view that past experiences have somehow been written 精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 9 页，共 10 页to the brain s hard-drive and are then retrieved, even if at considerable effort, is not the way our brain works. In fact, memory is reconstructive. Therefore people in remembering some event will reconstruct it in different ways. 5. How do gambling fallacy and clustering illusion relate to representativeness? Provide examples from sports. In what way are they different? Representativeness exists when one thinks that A should look like B. A can be the sample and B the distribution, or vice-versa. A belief in a hot hand is thinking the conditional distribution should look like the sample. But sometimes it seems that people think the reverse, namely that the sample, however small, should look like the distribution, in the sense that essential features should be shared. A hot hand often comes into play in sports when people don t know for certainthe skill level of an athlete, and the extent to which it may change. Gambler s fallacy is likely to exist when the underlying distribution (e.g., cards or dice) is well-known.精选学习资料 - - - - - - - - - 名师归纳总结 - - - - - - -第 10 页，共 10 页