Please solve it in 30 minutes

ch 18, 2022 (in 99 days). Panel A: S&P 500 index: S&P 500 index 4,687.94 0.70% Level Risk-free rate (continuously compounded) Dividend yield (continuously compounded) 1.28% Panel B: European options on the S&P 500 index: Strike Price 4,685 March Call Midpoint Price Delta 166.90 0.510 March Put Midpoint Price 175 Delta -0.484 Each S&P 500 options contract is for 100 times the value of the S&P 500 index. Annualized volatility implied in March options is 18%. Panel C: S&P 500 Micro E-mini futures: March Micro E-mini futures 4,686.25 Price Each Micro E-mini futures contract is for 5 times the value of the S&P 500 index. Panel D: American options on the S&P 500 Micro E-mini futures: Strike Price 4,685 March Call Last price 180.00 March Put Last price 167.75 16. S&P 500 futures hedging and target strategies (34 points) Next, suppose that you are a portfolio manager. On December 9, 2021, your portfolio is worth $500,000. It consists of three stocks: 40% of the portfolio is invested in the Apple stock market beta of 1.12), another 40% in the Tesla stock (market beta of 1.51), and the remaining 20% in the Rivian stock (market beta of 1.71). a) (10 points) What is the market beta of your portfolio? Market beta of your portfolio: b) (12 points) Suppose that you are optimistic about the market's prospects and want to increase your portfolio's beta to 2.0. How many Micro E-mini futures contracts do you need to buy or sell in this situation? Hint: if you were unable to do calculations under a., assume that the beta of your portfolio is 1. Answer: a c) (12 points) Suppose that you believe your portfolio has a positive alpha, and you want to create a pure alpha strategy. How many E-mini futures contracts do you need to buy or sellin this situation? Hint: If you were unable to do calculations under a., assume that the beta of your portfolio is 1