One of your high net worth clients (Jessica William-Matthew) has just received an inheritance of $50,000,000. Jessica is risk averse and has asked you to invest this money into an equity portfolio which is slightly less risky than the US market. In addition, Jessica wants to ensure that this money will benefit her children and her children’s children, her one requirement is that she wants to limit the downside risk that she has on this investment to $45,000,000 over the next twelve months.

a) You construct a portfolio consisting of two million shares equally split across 200 stocks which has a beta of 0.9 and dividend yield of 2.55% per annum with simple compounding. Current market conditions indicate that the S&P 500 index stands at 2500 with a dividend yield of 3.10% per annum with simple compounding and volatility of 15% annually. Further, the risk-free rate is 1% per annum with simple compounding. Detail the insurance strategy that will meet Jessica’s requirement.

b) The average transaction cost to purchase the shares in the equity portfolio is 0.1% of the value purchased. How much money does Jessica have to transfer to us (the bank) today to setup the index portfolio and insurance strategy? For the purposes of part (b) only and calculating the cost of the insurance strategy, assume the dividend yield on the index and the risk-free rate when expressed as simple rates are approximately the same as the continuously compounded rates.

c) Jessica has also asked you to simulate the insurance strategy. She wants to know how much money she makes or loses if the S&P 500 increases by 20% in twelve months. She also asks you to explain the outcome of the strategy.

d) In addition, Jessica wants to know how much money she makes or loses if the S&P 500 decreases by 40% in twelve months. Again she asks you to explain the outcome of the strategy.