You are the portfolio manager in charge of a portfolio whose current value is $ 5,000,000. You need to make sure that the portfolio value remains unchanged in the next few days. The portfolio beta is 1.5 and its dividend yield is the same as the S&P 500 index's dividend yield. You choose to use a Protective Put with a strike price of 1250. a) Compute the Put's DELTA, and use the result to compute the optimal number of put options contracts needed for the hedge. b) Now assume that one day later, the S&P 500 index falls to 1150. Compute the losses on your portfolio after the index falls by assuming that CAPM holds exactly as expected, as well as the gains on the option contracts. Show the resulting net value of your holdings. 1.5 portfolio beta: SIGMA of S&P 500 index: 20% 1200 3% b) Fall in the value of the S&P 500 index: spot value of S&P 500 index: annual dividend yield: annual riskless rate: time to expiration: 3% 0.25 Initial Portfolio Value: Change in Portfolio due to Change in Index: Change in Portfolio Value: New Portfolio Value: Old Price for the Put Options: New Price for the Put Options: Change in Value of Option Contracts: Net Change in Value of the Holdings: Resulting net Value of the Portfolio = (thanks to hedging) You are the portfolio manager in charge of a portfolio whose current value is $ 5,000,000. You need to make sure that the portfolio value remains unchanged in the next few days. The portfolio beta is 1.5 and its dividend yield is the same as the S&P 500 index's dividend yield. You choose to use a Protective Put with a strike price of 1250. a) Compute the Put's DELTA, and use the result to compute the optimal number of put options contracts needed for the hedge. b) Now assume that one day later, the S&P 500 index falls to 1150. Compute the losses on your portfolio after the index falls by assuming that CAPM holds exactly as expected, as well as the gains on the option contracts. Show the resulting net value of your holdings. 1.5 portfolio beta: SIGMA of S&P 500 index: 20% 1200 3% b) Fall in the value of the S&P 500 index: spot value of S&P 500 index: annual dividend yield: annual riskless rate: time to expiration: 3% 0.25 Initial Portfolio Value: Change in Portfolio due to Change in Index: Change in Portfolio Value: New Portfolio Value: Old Price for the Put Options: New Price for the Put Options: Change in Value of Option Contracts: Net Change in Value of the Holdings: Resulting net Value of the Portfolio = (thanks to hedging)