Answer all parts of this question a) The price of a six-month zero coupon bond is 98.03. The price of a 1.5-year bond that pays a coupon of 2 every six months is 95.15. The price of an additional 1.5-year bond that pays a Coupon of 5 every six months is 103.51. The price of a 2-year bond that pays coupon of E2 every six months is 84.63. The face value of each bond is 100. Calculate the yield to maturity for each bond assuming semi-annual compounding. Subsequently, express the obtained yields in terms of continuously compounded rates. In what circumstances can you interpret the yield to maturity as a (certain) rate of return on a bond? (10 marks) b) Using the relevant information from part (a), calculate the continuously and semi-annually compounded zero rates for the 6-month, 1-year and 1.5-year maturities and the respective forward rates for the periods within. (10 marks) OEPORAOMuoR c) Using the relevant information from part (b), calculate the value of a forward rate agreement (FRA) that enables the buyer to earn a semi-annually compounded interest rate of 9% for a 6- month period starting in 12-months on a principal of 50 million. Design a strategy to take advantage of possible arbitrage opportunities and calculate the final profit. (10 marks) d) Describe which factor or factors affect a bond's price sensitivity. Consider a portfolio of zero coupon and coupon bearing bonds. If a small parallel rise of the zero rates is imminent, which bonds would be ideal to sell just before the rise? Explain your answer. (10 marks) e) An equity investor holds a stock portfolio worth 10,000,000. The correlation coefficient between the returns of the portfolio and the FTSE 100 index is 0.8, the standard deviation of the portfolio returns is 0.45, whereas the standard deviation of the index returns is 0.25. Assume that the current level of the index is 6,300 and that a futures contract on the stock index is traded. The contract is worth 10 times the level of the index. ASsume that the delivery date of the contract is 18 months from now, which coincides with your hedging horizon and the continuously compounded interest rate is 5% per year. Construct the minimum variance hedge of the investor's stock portfolio using the stock index futures. Provide two calculations: without and with taking into account the effects of marking to market. Answer all parts of this question a) The price of a six-month zero coupon bond is 98.03. The price of a 1.5-year bond that pays a coupon of 2 every six months is 95.15. The price of an additional 1.5-year bond that pays a Coupon of 5 every six months is 103.51. The price of a 2-year bond that pays coupon of E2 every six months is 84.63. The face value of each bond is 100. Calculate the yield to maturity for each bond assuming semi-annual compounding. Subsequently, express the obtained yields in terms of continuously compounded rates. In what circumstances can you interpret the yield to maturity as a (certain) rate of return on a bond? (10 marks) b) Using the relevant information from part (a), calculate the continuously and semi-annually compounded zero rates for the 6-month, 1-year and 1.5-year maturities and the respective forward rates for the periods within. (10 marks) OEPORAOMuoR c) Using the relevant information from part (b), calculate the value of a forward rate agreement (FRA) that enables the buyer to earn a semi-annually compounded interest rate of 9% for a 6- month period starting in 12-months on a principal of 50 million. Design a strategy to take advantage of possible arbitrage opportunities and calculate the final profit. (10 marks) d) Describe which factor or factors affect a bond's price sensitivity. Consider a portfolio of zero coupon and coupon bearing bonds. If a small parallel rise of the zero rates is imminent, which bonds would be ideal to sell just before the rise? Explain your answer. (10 marks) e) An equity investor holds a stock portfolio worth 10,000,000. The correlation coefficient between the returns of the portfolio and the FTSE 100 index is 0.8, the standard deviation of the portfolio returns is 0.45, whereas the standard deviation of the index returns is 0.25. Assume that the current level of the index is 6,300 and that a futures contract on the stock index is traded. The contract is worth 10 times the level of the index. ASsume that the delivery date of the contract is 18 months from now, which coincides with your hedging horizon and the continuously compounded interest rate is 5% per year. Construct the minimum variance hedge of the investor's stock portfolio using the stock index futures. Provide two calculations: without and with taking into account the effects of marking to market