Question

The Bank of Tinytown has two $50,000 loans that have the following characteristics: Loan A has an expected return of 12 percent and a standard deviation of returns of 15 percent. The expected return and standard deviation of returns for loan B are 8 percent and 12 percent, respectively.

a) If the correlation coefficient between loans A and B is 0.10, what are the expected return and standard deviation of this portfolio?

b) What is the standard deviation of the portfolio if the correlation is -0.35?

Answer 1

1.
Expected returns=0.5*12%+0.5*8%=10.00%

Standard deviation=sqrt((0.5*15%)^2+(0.5*12%)^2+2*0.5*15%*0.5*12%*0.10)=10.06%

2.
Expected returns=0.5*12%+0.5*8%=10.00%

Standard deviation=sqrt((0.5*15%)^2+(0.5*12%)^2+2*0.5*15%*0.5*12%*(-0.35))=7.79%