3. You're given with the following information of a portfolio consisting of stocks such that the covariance between Rs and Rf, denoted as Cov(Rs, Rf) = 0.371, 0, = 0.63, where the Rs is the rate of return in your stock portfolio, Rf is the percentage price change of stock index futures price, a) Suppose the overall value of the portfolio right now is $10 millions. Suppose there is no applicable put or call for your portfolio. However, there exists stock-indexed futures contract to apply. Let the current stock-index futures price be 850, with a multiplier as 100 per contract, how many futures contract should you apply if you want to apply the minimum-variance hedging portfolio? Does it mean that this portfolio is completely risk-free? b) Now suppose that your portfolio's beta is 1.45 what is your minimum-variance futures position now? c) Suppose the correlation coefficient between Rs and Rf is 0.916, what is the VaR of your stock-index futures contract in a) if your confidence level is 95% and the rates of return are all distributed normally? What is the VaR of your hedged portfolio now after you apply the stock index futures on your original portfolio? d) Now suppose that you want to perform Delta Hedging by using the futures contract. Let the risk-free interest rate be 4%. What is your futures position now if the stock index did not pay dividends? e) Suppose that you only want to hold the portfolio for 3 months. Let the volatility of the stock index be 35% while assuming that the portfolio you have mimics the stock index so that they have similar betas. Suppose the futures contract is maturing in 8 months, what is the optimal numbers of futures contract you should have? f) Suppose you also consider a put option for your portfolio, in additional to the futures position. Let the put option on the stock index have the strike price as 825 with the maturity as 3 months. Each option's contract size is 100 times of the index. The current stock index level is 842, what is the fair price of this option? (Hint: the volatility of the portfolio is feasible using the information given in the problem and that is in question c)). g) Find the delta and gamma for the option in f). Let the gamma for the stock-indexed futures be 5.87, what are you optimal hedging positions or hedging ratios now in using both the futures contract and option? 3. You're given with the following information of a portfolio consisting of stocks such that the covariance between Rs and Rf, denoted as Cov(Rs, Rf) = 0.371, 0, = 0.63, where the Rs is the rate of return in your stock portfolio, Rf is the percentage price change of stock index futures price, a) Suppose the overall value of the portfolio right now is $10 millions. Suppose there is no applicable put or call for your portfolio. However, there exists stock-indexed futures contract to apply. Let the current stock-index futures price be 850, with a multiplier as 100 per contract, how many futures contract should you apply if you want to apply the minimum-variance hedging portfolio? Does it mean that this portfolio is completely risk-free? b) Now suppose that your portfolio's beta is 1.45 what is your minimum-variance futures position now? c) Suppose the correlation coefficient between Rs and Rf is 0.916, what is the VaR of your stock-index futures contract in a) if your confidence level is 95% and the rates of return are all distributed normally? What is the VaR of your hedged portfolio now after you apply the stock index futures on your original portfolio? d) Now suppose that you want to perform Delta Hedging by using the futures contract. Let the risk-free interest rate be 4%. What is your futures position now if the stock index did not pay dividends? e) Suppose that you only want to hold the portfolio for 3 months. Let the volatility of the stock index be 35% while assuming that the portfolio you have mimics the stock index so that they have similar betas. Suppose the futures contract is maturing in 8 months, what is the optimal numbers of futures contract you should have? f) Suppose you also consider a put option for your portfolio, in additional to the futures position. Let the put option on the stock index have the strike price as 825 with the maturity as 3 months. Each option's contract size is 100 times of the index. The current stock index level is 842, what is the fair price of this option? (Hint: the volatility of the portfolio is feasible using the information given in the problem and that is in question c)). g) Find the delta and gamma for the option in f). Let the gamma for the stock-indexed futures be 5.87, what are you optimal hedging positions or hedging ratios now in using both the futures contract and option