David has an endowment of $10,000 that he wants to invest in the stockmarket, which consist of two firms, A and B. Each firm's stock is worth $100 today, and will be worth $140 in one year with probability1/2 (fraction) or will stay at $100 with probability1/2 ( fraction). Assume that the evolution of both stocks is independent: that is, the probability that stock A rises in value does not vary or depend on what has happened to stock B, and vice-versa. Finally, assume that David's utility function isU(w)= w sqrt, and interest rate is zero.

E1)What is David's utility of not investing? (In this and the following questions, include the wealth endowment in your calcuations.)

Un=

2.Calculate the expected value and David's expected utility of investing solely in stock A.

EVa=

Ua=

What about investing only in stock B?

EVb=

Ub=

E2) Does David prefer investing to not investing? In which company?

a)David prefers investing in stock B

b)David is indifferent between investing and not investing

c)David prefers investing, but is indifferent between stock A and stock B

d)David prefers not investing

e)David prefers investing in stock A

E3)Now suppose that David wants to diversify and invests half his money in stock A and the other half in stock B.

What are the payoffs of this strategy and their respective probabilities?

a)1/3$14000,1/3$12000,1/3$10000

b)1/8$14000,3/4$12000,1/8$10000

c)None of the above

d)1/3$28000,1/3$24000,1/3$20000

e)1.$12000

f)1/2$14000,1/2$10000

E4)What is the expected value of the strategy in PS9.3.2, and David's expected utility?

EVab=?

Uab=?

E5)Is David better off from diversifying his investments? What is the effect at work here?

a)David prefers diversifying, because he is risk averse

b)David is indifferent about diversifying, because he is risk neutral

c)David prefers not diversifying, because he is risk loving

d)David prefers not diversifying, because he is risk averse

e)David prefers diversifying, because he is risk loving