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3. Let r be the risk free rate. Assume that we have a U.S. stock portfolio with price Pt) and the portfolio excess return on the market over the risk free rate is Re(ie. Rp- e would like to hedge the risk of the portfolio wsing short position of P(e S&P 500 index futures. Let Rf be the return of S&P 500 index futures. Applying regression model, we obtain RP-ARF + E with β-1.25. The current portfolio price Pt) 1,000,000, current S&P 500 index price is S(t) 2,500. We know the contract size of the S&P 500 index futures is S250x(S&P 500 index price). How many share of shorts of the futures we need to do the perfect hedge?

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DAT PAG Ca Ca.tn 11250000

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