Mailin Investment Trust manages a well-diversified $500 million equity fund. In March 2020, the Trust was concerned about a market decline, perhaps lasting until June. The March value of the portfolio the Trust manages was $500 million and the portfolio had a beta of 1.25. Suppose Mailin Investment Trust decided in March to maintain its portfolio beta at 1.25 if the market were greater than 2,500 in June, but have a beta of 0.5 if the market were less than 2,500.In March, the S&P 500 spot index was trading at 2,500 and a June S&P 500 spot call and put contracts with exercise prices of 2,500 and $100 multiplier were trading at 50.

a.Using the pricesensitivity model, determine how many S&P 500 call or put contracts the Mailin Investment Company would have needed in March in order to decrease her portfolio beta to0.50 in June if the market were less than 2,500 while keeping their portfolio at 1.25 if the market were greater than 2,500.

b. Show in a table the proportional changes in the S&P 500 in June from its March level of 2,500, the proportional changes in the portfolio, the values of the portfolio corresponding to the spot index, the call or put option values, the call or put position's cash flow, the option-hedged portfolio values, and the proportion changes in the option-hedged portfolio from its $500 million current value, proportion changes in the option-hedged portfolio value to the proportional changes in S&P 500. Evaluate for possible spot index values on the June expiration date of 1,750, 2,000, 2,250, 2,500, 2,750, 3,000, and 3,250.

c.Suppose Mailin decided that the cost of the options were too expensive and therefore decided to just lower her beta to 0.5 in June, irrespective of whether the market increased or decreased. Explain how Mailin could hedge with June S&P 500 futures contracts that in March were at f₀ = $2,500 (multiplier = $250).