You believe that Rocky Mountain Gold, Inc. will announce earnings during the nex

Question

You believe that Rocky Mountain Gold, Inc. will announce earnings during the next month that will exceed the market's expectations. Rocky Mountain's stock has a beta of 0.8, and the standard deviation of the stock's monthly return is 15%. You have purchased $50,000 of the stock, but you wished to hedge against market moves by short selling the S&P; (the "market"). The monthly return on the S&P; has a standard deviation of 7%. How much (dollar amount) of the S&P; would you short in order to minimize the variance of the profit your hedge position? Consider an investor who does not possess your insights about Rocky Mountain Gold. This investor is armed only with his opinion that CAPM holds, the expected return on the market (S&P;) is 1.5% per month. What would this investor's expect profit on the overall hedged position constructed in part a?

Explanation / Answer

a) $ Amount of S&P you should short=.8*50,000=$40,000

b) Return on stcok according to CAPM=Rf+.8*(1.5%-Rf)

Profit on hedged position=(Rf+.8*(1.5%-Rf))*50,000-40,000*.015

Profit on hedged position=(Rf-.8Rf))*50,000

Profit on hedged position=.2Rf*50,000

Profit on hedged position=10,000* Rf where Rf is risk free rate per month.

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