Question

Consider a portfolio that consist of 2 assets A and B;

Asset	Expected Return	Standard Deviation	Correlation
A	20%	10%
B	40%	20%
A&B			-1

Compute the asset weights (WA and WB) so that an investor obtains a zero risk portfolio. Show all your workings and calculations.

Answer 1

Standard deviation of zero risk portfolio = 0

Correlation = -1

Standard deviation of portfolio = ( (Wa*Standard Deviation of A)^2 + (Wb*Standard Deviation of B)^2 + 2*Wa*Wb* Standard Deviation of A*Standard Deviation of B * (-1))^0.5

0 = ((Wa*Standard Deviation of A - Wb * Standard Deviation of B)^2)^0.5

Wa*Standard Deviation of A = Wb * Standard Deviation of B

Wa + Wb =1

Wa*Standard Deviation of A = (1-Wa) * Standard Deviation of B

Wa = Standard Deviation of B / (Standard Deviation of A+Standard Deviation of B)

Wa = 20 / ( 20 +10) = 0.67

Wb = 1 - 0.67 = 0.33