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Unformatted text preview: your total liabilities? (d) To finance the liabilities, you are asked to invest in a single zero coupon bond. What maturity zero coupon bond would you choose so that the equity of the owner is best protected against parallel shifts in the yield curve? You are not limited to whole numbers for the maturities. (Hint: For example you could use a bond with 2.768 years to maturity. 2.768 years to maturity is not the correct answer, however!) (e) Suppose that immediately after you make your investment, interest rates increase to 6% at all maturities. Would you expect the change in the value of your investment in the bond to be smaller or larger than any change in the value of your liabilities? Q7. Assume there are three default ­free bonds with the following prices and future cash flows: Cash flow Cash flow Cash flow Bond Price today Year 1 Year 2 Year 3 A 934.58 1,000 0 0 B 881.66 0 1,000 0 C 1,118.21 100 100 1,100 Consider a fourth bond (Bond D), which is zero coupon with maturity 3 years and face value 1000 and assume it is traded in a liquid market at the price 839.62. a. Can you evaluate Bond D, by a replication argument using a portfolio that contains Bonds A, B and C. b. Show that Bond D is underpriced and show what arbitrage strategy, you would follow to profit with no risk from the underpricing. Q8. You will receive $1 M in one year from now and will not need to use it until three years from now. You thus want to invest the $1M for two years. a. Suppose that you want to guarantee a rate today for your investment. What is relevant rate for such an investment? b. Suppose that the one year spot rate is 6% and the three year spot rate is 7%. Compute the rate in (a) c. Suppose that you are unable to contact a bank that offers the rate in (a). You can however trade zero ­coupon bonds. Explain how you can use zero ­coupon bonds (i.e., what bonds you use and how you trade them) to lock in the rate in (a). Q9. Consider an investment context where you can invest in the stocks of two companies: A and B. The expected returns and standard deviations of returns for the two stocks are as follows: Stocks Standard deviation A 8% 12% B Expected return 13% 20% Assume that the correlation of return of the two companies is 0.3. In addition to the two stocks, it is also possible to invest in a risk free security offering a return of 5%. The resulting tangency portfolio has an expected return of 11%. a) If you have $200M and that you want the highest expected return, provided that the standard deviation of your portfolio is 12%. Compute the amounts that you should invest is stock A, stock B and the risk free security as well as the resulting expected return....
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