Question

The following information is available for three mutual funds:

Mutual			r
Fund	E(r)	s	A	B	C
A	9.20%	29.00%	1	0.61	0.64
B	7.00%	27.00%		1	0.56
C	11.00%	40.00%			1

(a) Calculate the weights of a portfolio of mutual funds B and C that has the same expected return

as mutual fund A.

(b) Does the portfolio of B and C dominate mutual fund A? Perform the necessary calculations to

answer the question.

Answer 1

(a) We need to calculate the weights of mutual fund B and C in a portfolio that has the same expected return as A.

Weight of Mutual fund B in the portfolio = W_B

Weight of Mutual fund C in the portfolio = W_C = 1- W_B

Expected return of portfolio = E[R_p] = W_B*E(R_B) + W_C* E(R_C)

W_B*E(R_B) + W_C* E(R_C) = E[R_A]

W_B*7% + (1- W_B)* 11% = 9.20%

11%-4%* W_B = 9.20%

W_B = (11%-9.2%)/4% = 0.45

Therefore, W_C = 1-0.45 = 0.55

W_B = 45%, W_C = 55%

(b) σ_B = 27%, σ_C = 40%, r(B,C) = 0.56 [r is the correlation between B and C]

Variance of the portfolio is calculated using the below formula:

σ²_p = W_B²* σ²_B + W_C²* σ²_C + 2 W_B*W_C *r* σ_{B *} σ_C

σ²_p = 0.45²* (27%)² + 0.55²* (40%)² + 2*0.45*0.55*0.56* (27%) _* (40%)

σ²_p = 0.01476225+ 0.0484+ 0.0299376 = 0.09309985

Therefore, Standard deviation of the portfolio of B and C = σ_p = (0.09309985)^1/2 = 0.305122680245176 = 30.512%

Standard deviation of mutual fund A = σ_A = 29%

σ_p > σ_A, Hence, we can say that the portfolio of B and C does not dominate mutual fund A.