Please answer question 1, thank you!!!!!

Assume that you are managing an equity portfolio worth $5,000,000, and you are considering hedging your portfolio over the next three months. The hedging instrument is the S&P 500 index futures which matures in four months. The contract has been written on $250 times the index. Right now, the index is 1990, while the S&P futures price is 1980. Your portfolio has a beta value of 0.85. The risk-free rate of interest is 2%, and the dividend yield on index is 2% per annum. Discuss your hedge strategy and compute the expected value of your hedged portfolio, assuming that the index falls to 1850 in 3 months and the futures price is 1815. Suppose that Treasury bills maturing in 3 months, 6 months, and 1 year are selling for $99.75, 99.25 and 98.75, respectively; and a Treasury note maturing in 1 and half years paying a 4% semiannual coupon is selling at par. Construct the forward curve for periods extending out to 1.5 years. Interpret what these rates are telling you. Suppose that a financial institution has agreed to pay 6-month LIBOR and receive 3.5% per annum (with semiannual compounding) on a notional principal of $200 million. The swap has a remaining life of 1.25 years. The LIBOR rates with continuous compounding for 3-month, 9-month, and 15- month maturities are 2.25%, 2.35%, and 2.5%, respectively. The 6-month LIBOR rate at the last payment date was 2% (with semiannual compounding). Compute the value of the swap in terms of FRAs. It is August 2 and a fund manager with $20 million invested in government bonds is concerned that interest rates are expected to be highly volatile over the next 3 months. The fund manager decided to use the December T-bond futures contract to hedge the value of the portfolios. The current futures price is 94-04. Each contract is for the delivery of $100,000 face value of bonds. Suppose that the duration of the bond portfolio in 3 months will be 7.40 years. The cheapest-to-deliver bond in the T-bond contract is expected to be a 20-year 8% per annum coupon bond. The yield on this bond is currently 6%, and the duration will be 8.20 years at maturity of the futures contract. Discuss how the fund manager would hedge and show how he can avoid the interest rate risk. Suppose that Stock X is currently selling for $85. but the price can change over the next 2 months in a binomial stochastic Process by a 40% matching volatility. There is a European stock call option with an exercise price of $80. The risk-free rate of interest today is 2.5% Compute the option delta and the price for the call by using the risk neutral valuation method. Consider a 6-month put with a strike price of $44 on a stock whose current price is $40. Assume that there are two time steps, and in each time, step the stock price either moves by 10% or moves down by 10%. We also suppose that the risk-free rate of interest is 2%. Compute the value of the put using the recombining binomial tree under the assumption that the option is European and under the assumption that the option is American. Suppose that an investor buys a 3-year corporate bond and a 3-year CDS to buy protection against the issuer of the bond defaulting. The probability of a reference entity defaulting during a year conditional upon no earlier default is 2%, and the continuously compounding risk-free LIBOR is 2%. Assume also that the CDS buyer pays 2.25% of the notional principal every year The CDS buyer is expected to recover 80% of the face value of the bond. Middle-of-the-year bankruptcy is not Assume that you are managing an equity portfolio worth $5,000,000, and you are considering hedging your portfolio over the next three months. The hedging instrument is the S&P 500 index futures which matures in four months. The contract has been written on $250 times the index. Right now, the index is 1990, while the S&P futures price is 1980. Your portfolio has a beta value of 0.85. The risk-free rate of interest is 2%, and the dividend yield on index is 2% per annum. Discuss your hedge strategy and compute the expected value of your hedged portfolio, assuming that the index falls to 1850 in 3 months and the futures price is 1815. Suppose that Treasury bills maturing in 3 months, 6 months, and 1 year are selling for $99.75, 99.25 and 98.75, respectively; and a Treasury note maturing in 1 and half years paying a 4% semiannual coupon is selling at par. Construct the forward curve for periods extending out to 1.5 years. Interpret what these rates are telling you. Suppose that a financial institution has agreed to pay 6-month LIBOR and receive 3.5% per annum (with semiannual compounding) on a notional principal of $200 million. The swap has a remaining life of 1.25 years. The LIBOR rates with continuous compounding for 3-month, 9-month, and 15- month maturities are 2.25%, 2.35%, and 2.5%, respectively. The 6-month LIBOR rate at the last payment date was 2% (with semiannual compounding). Compute the value of the swap in terms of FRAs. It is August 2 and a fund manager with $20 million invested in government bonds is concerned that interest rates are expected to be highly volatile over the next 3 months. The fund manager decided to use the December T-bond futures contract to hedge the value of the portfolios. The current futures price is 94-04. Each contract is for the delivery of $100,000 face value of bonds. Suppose that the duration of the bond portfolio in 3 months will be 7.40 years. The cheapest-to-deliver bond in the T-bond contract is expected to be a 20-year 8% per annum coupon bond. The yield on this bond is currently 6%, and the duration will be 8.20 years at maturity of the futures contract. Discuss how the fund manager would hedge and show how he can avoid the interest rate risk. Suppose that Stock X is currently selling for $85. but the price can change over the next 2 months in a binomial stochastic Process by a 40% matching volatility. There is a European stock call option with an exercise price of $80. The risk-free rate of interest today is 2.5% Compute the option delta and the price for the call by using the risk neutral valuation method. Consider a 6-month put with a strike price of $44 on a stock whose current price is $40. Assume that there are two time steps, and in each time, step the stock price either moves by 10% or moves down by 10%. We also suppose that the risk-free rate of interest is 2%. Compute the value of the put using the recombining binomial tree under the assumption that the option is European and under the assumption that the option is American. Suppose that an investor buys a 3-year corporate bond and a 3-year CDS to buy protection against the issuer of the bond defaulting. The probability of a reference entity defaulting during a year conditional upon no earlier default is 2%, and the continuously compounding risk-free LIBOR is 2%. Assume also that the CDS buyer pays 2.25% of the notional principal every year The CDS buyer is expected to recover 80% of the face value of the bond. Middle-of-the-year bankruptcy is not