(a) Write down an expression for the variance of the return on an N-stock portfolio. Assuming that the stocks in the portfolio have equal weights, show that the variance of the return on an N-stock portfolio tends to average covariance risk as N approaches infinity. Give the intuition for this result.

(b) Consider the payoffs in three states, I, II and III, of two independent investments, A and B, in the following table.

investment A Investment B

State payoff. probability payoff. probability

1 2 .25 3 0.4

2 3 .25 4 0.5

3 8 .5 6 0.1

Which investment is preferred on the basis of state-by-state dominance? Explain your answer. Which investment is preferred on the basis of mean-variance dominance? Explain your answer. Which investment is preferred on the basis of expected utility theory assuming the investor has a log utility function.? Explain your answer.