Mr Temple manages a well diversified $400 million portfolio that tracks the S&P 500 index closely (i.e the portfolio'sheath is 1). He intends to buy insurance to protect his portfolio against a drop of more than 7% in value over the next 3 months. Assume that the level of S&P index is currently 1500, the risk-free rate is 4% per annum, the dividend yield of the portfolio is 4%, the dividend yield of the index is 5%, and the volatility of the index is 35% per annum.

a) how much does the insurance cost if it were in the form of European put options?

b) propose an alternative portfolio insurance strategy in (a) by using another type of derivative on the S&P 500 index. Specify the position in the proposed derivative that is required to provide the nsurance.