Question

a. Compute the correlation between assets A and B if you know that the standard deviation of B is 50% of the standard deviation of A and the covariance between the two assets is 0.5 times the variance of asset A.

Correlation is 1

b. What is the risk (measured as the variance) of the portfolio created by investing 50% in asset A and 50% in asset B in the previous point? Assume that the variance of the asset A is 4/9.

Show working out (formulas used)

Answer 1

1.
0.5*variance of A=correlation*standard deviation of A*standard deviation of B

=>correlation=0.5*variance of A/(standard deviation of A*standard deviation of B)

=>correlation=0.5*variance of A/(standard deviation of A*0.5*standard deviation of A)

=>correlation=1

2.
=sqrt((0.5)^2*(4/9)+(0.5)^2*(0.25*4/9)+2*0.5*0.5*1*sqrt(4/9*0.25*4/9))=0.5