Question

You are considering the following investing in a US stock index fund and a US bond index fund. These represent the only 2 investments available to you at this time. You have the following additional information:

	US Stocks	US Bonds
Expected Return	25%	15%
Standard Deviation	27%	20%
Variance	0.0729	0.0400
PS,B	0.70
Covariance (S,B)	0.0378

Calculate the weights for stocks and bonds for the minimum variance portfolio. Show your work (if you are using Excel, include a screenshot of your Solver setup).

Suppose you have a target expected return of 17% for your portfolio.

i.      Calculate the weights of the Stock/Bond portfolio that satisfies this requirement.

   ii.      Calculate the standard deviation of your target portfolio Show your work.

Answer 1

i)	Optimum Weights of Minimum Portpolio Risk
	Weights (B)	(s.d.(S)^2 - Covariance(S,B)) / (s.d.(B) ^2) + (S.d.(S)^2) - 2Coveraince (S,B)
	=	(0.27*0.27)-0.0378 / ((0.2*0.2) + (0.27*0.27)-(2*0.0378))
	=	0.941019
	=	94.10%
	Weights (S)	1-0.941
	=	5.90%
ii)	Weights when Target Return =17%
	R(portpoilo)=(R(stocks)* W(Stocks) )+(R(Bonds)* W(Bonds) )
	17%=(25%*X)+15% (1-X)			Let W(Stocks)=X
	X=20%
	W(Stocks)=20%
	W(Bonds)=80%
iii)	S.D. of target potpolio
	P(S,B)	0.7
	=	((s.d.(S)*w(S))^2 + (s.d.(B)*w(B))^ 2 + (2 *s.d.(S)*w(S)*s.d.(B)*w(B)*p(S,B))) ^1/2
	=	(((0.27*0.2)^ 2)+((0.2*0.8) ^2 ) + 2 *(0.27*0.2)*(0.2*0.8)*0.7)^1/2
	=	0.020306
	S.D. of target potpolio	0.2