Question

A stock fund has a standard deviation of 20% and a bond fund has a standard deviation of 8%. The correlation of the two funds is 0.11

#1)  What is the weight of the stock fund in the minimum variance portfolio?

#2) What is the standard deviation of this minimum variance portfolio?

		#1. weight of stock fund = 1.25%
		#1. weight of stock fund = 10.82%
		#1. weight of stock fund = 24.21%
		#2. standard deviation of minimum-variance portfolio = 7.68%
		#2. standard deviation of minimum-variance portfolio = 11.25%
		#2. standard deviation of minimum-variance portfolio = 6.00%

Answer 1

Given about two funds,

Standard deviation of stock fund SD(S) = 20%

Standard deviation of bond fund SD(B) = 8%

Correlation between two funds Corr(S,B) = 0.11

1). For a minimum variance portfolio, weight of stock can be calculated as follow:

Weight of stock fund Ws = (SD(B)2 - SD(S)*SD(B)*Corr(S,B))/(SD(S)2 + SD(B)2 - 2*SD(S)*SD(B)*Corr(S,B))

So, Ws = (82 - 20*8*0.11)/(202 + 82 - 2*20*8*0.11) = 10.82%

So, option B is correct.

2) Weight of Bond is the portfolio is 1 - Ws

So, Wb = 1 - 0.1082 = 89.18%

Standard deviation of the portfolio is

SD(P) = SQRT((Ws*SD(S))2 + (Wb*SD(B))2 - 2*Ws*Wb*SD(S)*SD(B)*Corr(S,B))

SD(P) = SQRT((0.1082*20)2 + (0.8918*8)2 - 2*0.1082*0.8918*20*8*0.11) = 7.68%

So, option A is correct.