Question

You must allocate your wealth between two securities. Security 1 offers an expected return of 10% and has a standard deviation of 30%. Security 2 offers an expected return of 15% and has a standard deviation of 50%. The correlation between the returns on these two securities is 0.25.

a. Calculate the expected return and standard deviation for each of the following portfolios, and plot them on a graph:

% Security 1	% Security 2	E(R)	Standard Deviation
100	0
80	20
60	40
40	60
20	80
0	100

b. Based on your calculations in part (a), which portfolios are efficient and which are inefficient?

c. Suppose that a risk-free investment is available that offers a 4% return. If you must divide your wealth between the risk-free asset and one of the risky portfolios in the preceding table, which risky portfolio would you choose? Why?

d. Repeat your answer to part (c) assuming that the risk-free return is 8% rather than 4%. Can you provide an intuitive explanation for why the optimal risky portfolio changes?

Answer 1

E(R) of a portfolio = w₁R₁ + w₂R₂ + ...+ w_nR_n

R₁ = 10% , R₁ = 15%

Standard Deviation of a Portfolio =

Cov₁₂ = ?₁?₂Corr₁₂ = 0.30 * 0.50 * 0.25 = 0.375

When w₁ = 100% & w₂ = 0%

E(R) of a portfolio = w₁R₁ + w₂R₂ + ...+ w_nR_n

= (1*0.1) + (0*0.15) = 10%

= ? (1)²(0.3)² + (0)²(0.5)² + 2(1)(0)(0.375)

= ? 0.09 + 0+ 0

= 30%

Likewise, doing the same method for all the options of portfolios :

% Security 1	% Security 2	%E(R)	%Standard Deviation
100	0	10	30
80	20	11	68.38
60	40	12	50.24
40	60	13	53.33
20	80	14	53.25
0	100	15	50