Question

#5. Suppose that the stock of the new microbrewer, Geoff deBrugge, Inc. (GBI), has been forecast to have a return distribution with a standard deviation 10% and a correlation with the market portfolio of +0.9. If the standard deviation of the return on the market portfolio is 8%, determine the relative holdings of the market portfolio and GBI stock needed to form a portfolio with a beta of+1.5. Shorting the portfolio or the stock may be necessary to obtain the desired beta. Can you report the equilibrium expected return on the portfolio with a beta of +1.5?

Answer 1

Beta of GBI=correlation with market*standard deviation of GBI/standard deviation of market=0.9*10%/8%=1.125

Let weight of GBI be w and weight of market portfolio be 1-w

Hence,
w*1.125+(1-w)*1=1.5
=>w=(1.5-1)/(1.125-1)
=>w=4

Hence, short three times market and long 4 times GBI

We need to know returns to calculate returns for beta of 1.5