The Bryce Investment Trust Company plans to liquidate part of its stock portfolio in June. The company is bullish but would like to set a floor on the portfolio sale as a defensive strategy. The portfolio it plans to sell is well diversified, has a beta of 1.5 , and is currently worth \(\$ 100\) million. The S\&P 500 index is currently at 2,250 and a June S\&P 500 spot put option with an exercise price of 2,250 and multiplier of \(\$ 100\) is currently at 50 .

a. Using the price-sensitivity model, determine how many S\&P 500 spot put contracts the Bryce Investment Trust Company would need in order to set a floor on the sale of its \(\$ 100\) million portfolio in June. What is the cost of the puts?

b. Show in a table the proportional changes in the S\&P 500 from its current level of 2,250 , the proportional changes in the portfolio, the values of the portfolio corresponding to the spot index, the put option values, the put position's cash flow, and the put hedged portfolio values on the June expiration date for possible spot index values of index values for possible spot index values starting at 1,980 with 30 point steps to 2,850 .