1. Are the following statements True or False? If the statement is correct, write down T. Otherwise write down F.

1. The diversification benefit from constructing a risky portfolio of two risky assets will be maximized when the correlation between returns of two risky assets is equal to zero.
2. The Dow Jones Industrial Average is calculated using price-weighted average which gives higher-priced shares less weight in determining performance of the index.
3. When the distribution of an asset return is negatively skewed and fat-tailed, then the standard deviation of the asset return overestimates its risk.
4. The actual sale price that a buyer pays for the bond includes accrued interest if the bond is purchased between coupon payments.

2. Assume that you manage a risky portfolio with an expected rate of return of 18% and a standard deviation of 28%. The T-bill rate (risk-free rate) is 8%. Your client chooses to invest 70% in the risky portfolio in your fund and 30% in a T-bill money market fund. We assume that investors use mean-variance utility: U = E(r) 0.5A 2, where E(r) is the expected return, A is the risk aversion coefficient and 2 is the variance of returns.

a) What is the expected value and standard deviation of the rate of return on your clients portfolio?

b) Your clients degree of risk aversion is A = 3.5.

(i) What proportion, y, of the total investment should be invested in your risky fund?

(ii) What is the expected value and standard deviation of the rate of return on your clients optimized portfolio?

c) Prove that the optimal proportion of the risky asset in the complete portfolio is given by the equation y = E(rp)rf A2 p , where rf is the risk-free rate, E(rp) is the expected return of the risky portfolio, 2 p is variance of returns, and A is the risk aversion coefficient. For each of the variables on the right side of the equation, discuss the impact of the variables effect on y and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse.