Question

Suppose that the correlation coefficient between the rates of return on Knowlode Mutual Fund and the market portfolio is 0.7. The standard deviations of the rates of return are 0.20 for Knowlode and 0.15 for the market portfolio. How would you combine the Knowlode Fund and the riskless asset to obtain a portfolio with a beta of 1.5?

Answer 1

X = KNOWLODE MUTUAL FUND

Y = MARKET PORTFOLIO

CORRELATION = COVARIANCE(X,Y) /(SD_X)(SD_Y)

THEREFORE COVARIANCE(X,Y) =CORRELATION*(SD_X)*(SD_Y) = 0.7 X20 X 15 = 210

SO BETA OF X = COVARIANCE(X,Y) /(SD_X) = 210/ (15)² = 0.9333

NOW WE WANT TO BUILD A PORTFOLIO WITH BETA 1.5

1.5 = (Z) * (BETA OF X ) + (1-Z)*(BETA OF T BILL)

1.5 = (Z) * (0.9333 ) + (1-Z)*(0) [T BILL IS RISK FREE ASSET, SO BETA =0]

Z = 1.607

1-Z = -0.607

SO WEIGHT OF X = 1.607 & THAT OF T BILLS = -0.607

SO IN SHORT, WE HAVE TO BORROW AND INVEST IN X, THAT IS KNOWLODE MUTUAL FUND

GO THROUGH IT. ANY DOUBTS, FEEL FREE TO ASK. GIVE POSITIVE FEEDBACK