Economics

[Wesley]

1. Consider a portfolio comprising two securities (A and B) with the following characteristics:

Security E(R_i) s(R_i)

A 0.04 0.10
B 0.08 0.25

E(R_i) denotes the expected return for security i, and s(R_i) denotes the standard deviation of the returns on security i.

(a) Assuming the correlation between the returns on securities A and B, denoted r(R_A,R_B), is zero, calculate:

(i) the expected portfolio return, E(R_P), and
(ii) the standard deviation of the portfolio return, s(R_P)

for the following sets of portfolio weights:
(x_A, x_B) = (1.5, –0.5), (1 0), (0.5, 0.5), (0, 1), (–0.5, 1.5)

(b) Using an analytical method, calculate the portfolio weights that are associated with the minimum variance portfolio. What is the minimum attainable variance?

[HINT:
- write down an equation for var(R_P) in terms of x_A and x_B;
- replace x_B with (1–x_A), to obtain an equation for var(R_P) in terms of x_A only;
- differentiate the resulting expression with respect to x_A, and set the derivative to zero;
- solve the resulting equation for x_A.]

(c) Repeat parts (a) and (b), assuming r(R_A,R_B)=0.5.

(d) Using your results from parts (a) to (c), sketch the combination lines for the two cases of r(R_A,R_B)=0 and r(R_A,R_B)=0.5.

(e) With reference to the results of parts (a) to (d), explain briefly how the correlation between the returns on individual securities affects the gain (in terms of reduction in risk) available to an investor who is willing to construct a diversified portfolio.



Ok, I have this question to answer for homework and haven't a clue where to begin. Anyone help?