You work for a hedge fund and have created a portfolio worth $1,680,000 which you believe will deliver a positive abnormal return over the next month. The portfolio has a beta of 1.8, and you have determined that its alpha will be 1.2%. You have also determined that the standard deviation of the residuals, upon performing an index model regression on your portfolio, is 6%. You are uncertain about how the market will perform during this time and are concerned that an adverse movement could destroy your portfolios alpha. As a result, you wish to hedge your portfolios market exposure using S&P 500 e-mini futures contracts. The S&P 500 is currently 1,890, and the S&P 500 e-mini multiplier is $50. The rate of return on T-bills is 3% p.a.

a) How many contracts must you enter, in order to hedge your market exposure over the coming month? In your answer, also indicate whether you should buy or sell the contracts

b) What is your position in the futures contracts, at the end of the month?

c) Calculate the hedged proceeds from your portfolio and show that your alpha has been preserved.

d) What is the standard deviation of your portfolio, expressed as an annual figure, after hedging?