Question

Your client has his retirement portfolio allocated with 80% in an index fund designed to replicate S&P500 returns and 20% in an index fund replicating Nasdaq market returns. S&P500 returns have an annual standard deviation of 24%, Nasdaq returns have standard deviation of 32%, and the correlation between the two market returns has historically been 0.85. Given this information, what is the expected standard deviation of your client's portfolio?

Answer 1

Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.8^2*0.24^2+0.2^2*0.32^2+2*0.8*0.2*0.24*0.32*0.85
Variance	0.06185
Standard deviation=	(variance)^0.5
Standard deviation=	24.87%