Question:

(a) You are given the following information on two risky assets A and B.

E(X) = 25% E(Y) = 30%
Var (X) = 16% Var (Y) = 49%

The correlation matrix is ( 1 0.5)
( 1 )

Required:

(i) Find the expected return and standard deviation of returns of the minimum variance portfolio.

(ii) If the two assets X and Y are perfectly correlated, what is the expected return and standard deviation of returns for an equally weighted portfolio? State your assumptions.

(b) An individual has the following utility function u(w) = ln (w). Her initial wealth is Rs 15,000. She has the possibility of participating in the following gamble at a cost of Rs 500, with a 30% chance of winning Rs 6,000, a 50 % chance of winning Rs 1000 and a 20% chance of losing Rs2,000.

(i) If she accepts the gamble, what is her expected utility of wealth?
(ii) What is her certainty equivalent wealth?
(iii) What is her risk premium?
(iv) What is the Savage-Friedman hypothesis about?
(v) If she lost in the first round, what is her expected utility in the second round?
(c) If car insurance was not compulsory by law, would economic agents still buy insurance? Explain.