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.
第二章
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, σp =(.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.
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?
σp2 = (.6)2(.28)2 + (.4)2(.48)2 + 2*.5(.6)(.4)(.28)(.48) = 9.7%, σp = 31.2% 第三章
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 ≥ 0 = -3(-z).8 when z < 0
This individual has the following weighting function:
错误！未找到引用源。
where we set ?=.65.
a. Which of the following prospects would he choose?
PA(.001, -5000) PB(-5)