Please help with question 8-10

Question 8 1 pts A portfolio manager has a portfolio worth 1 million dollars and decides to hedge the market risk using 5&P futures on a 4-month horizon. If the portfolio beta is 0.8. what is the optimal dollar position in the futures that the investor will take to eliminate market risk? (The position would be positive if the manager goes long in futures and negative if the manager shorts the futures.) Question 9 1 pts Considera put option on a stock with exercise price K = $90 and maturityT = 1 year. The stock's current price is S = $100, the volahlity is 20%, and the dividend yield is 3%. The risk-free rate is 2%, and the expected return of the stock is 5%. The volatility, the dividend yield, and the riskvfree rate are all annual values. To answer this question, follow the three steps as described below. {a} Determine the stock and bond holdings of the replicating portfolio. You may use that the value of the put is 3.7849 and the delta of the put is {12737. (b) Now, suppose that the price jumps up to S = $110 instantaneously. Compute how the value of the replicating portfolio above changes. (c) Using the Excel spreadsheet, compute the new value of the put option. What is the difference (in absolute value} between the new value of the put option in (c) and the value of the replicating portfolio in (b)? Use 3 decimal places for your answer. Question 10 1 pts Considera portfolio that consists of two at-the-money call options (the strike price is the same as the stock price). The first call option is on Stock 1, whose price is 100 and volatility is 15%. The second call opn'on is on Stock 2, whose price is 200 and volatility is 25%. The correlan'on between the stock returns is 0.3. Neither stock pays any dividends, and the maturity of both options is T = 5 years. The risk-free rate is 2%. The volatilities and the rlskvfree rate are all annual values. Assuming that the average daily change in the option position is approximately zero. what is the 5% daily Delta VaR of the portfolio in dollars? Use 3 decimal places for your