Problem 3 Suppose that a portfolio is worth $60 million and a stock index stands at 1,200. Suppose that the portfolio has a beta of 0.5 with respect to an index, the risk-free interest rate is 5% per annum (i)What is the number of put index option contracts (size -100) and the appropriate strike price needed to provide protection against the value of the portfolio falling belon S54 million in one year's time? Show how the insurance works if the value of the portfolio value were to drop by 20% to $48m (ii) Problem 3 Suppose that a portfolio is worth $60 million and a stock index stands at 1,200. Suppose that the portfolio has a beta of 0.5 with respect to an index, the risk-free interest rate is 5% per annum (i)What is the number of put index option contracts (size -100) and the appropriate strike price needed to provide protection against the value of the portfolio falling belon S54 million in one year's time? Show how the insurance works if the value of the portfolio value were to drop by 20% to $48m (ii)