Problem 2 (20 points): Consider a l-factor model with factory. For today's value of y=5%, your portfolio's value is V(0.05)=$ 1,000,000. However, a small increase in y to y=5.02% will lead to the $5,000 drop in the portfolio's value to V(0.0502)=$995,000, while at y:4.98% your portfolio's value will be V(0.0498)= $1 07,000. a) (6 points) Find DV01, Duration, and Convexity of your portfolio. b) (3 points) Using the rst-order Taylor approximation, estimate by how much the value of your portfolio will change when the factor increases to 5.1%. Round your answer to the nearest dollar. c) (3 points) Using the second-order Taylor approximation, estimate by how much the value of your portfolio will change when the factor increases to 5.1%. Round your answer to the nearest dollar. d) (5 points) You would like to use short-term xed income securities (call them cST\") with Duration=3 and Convexity=12. What is the dollar value of such securities you need to short? Using the second-order Taylor approximation, by how much the value of your hedged portfolio (in S) will change i'fy will increase to 5.1%? Round your answers to the nearest dollar. 6) (3 points) If, in addition to ST securities in part (d), you can also use long-term xed income securities (call them \"LT\") with a Duration=9 and Convexity=80, what will be your best hedging strategy? Specify the dollar value of ST and LT securities you will buy or sell to construct such hedging portfolio. Round your answers to the nearest dollar (note: do not be afraid if your answer will be in hundreds of millions of dollars) Problem 3 (14 points): Assume the term structure of forward rates is at and they are equal to 5%. The factor y is the forward rate (such one-factor model is called \"parallel yield shift\" model and in class we called the duration D in this special case by Dana, i.e., D=Dmod). Assume you own a perpetuity with $1M annual payments paid semi-annually (i.e., it pays $500,000 every six months). a) (4 points) Find the current value of this perpetuity, its DVOI, Duration. and Convexity. Round your answer to the nearest cent. By how much the value of your perpetuity will change if interest rates increase to y=5. 1% (round your answer to the nearest dollar)? b) (5 points) You have decided to hedge your perpetuity using 20year zero-coupon bonds. How many bonds you should sell (remember that the bond's face value is $100). Round your answer to the nearest integer number of bonds. c) (3 points) Given the hedge you have constructed in part (b), by how much the value of your hedged position will change if interest rates increase to y=5.1%? Use the integer number of bonds from part (b) and round your answers to the nearest dollar. (1) (2 points) If, in addition to the 20year zero-coupon bonds, you would be able to use 5-year zero-coupon bonds, would you be able to construct a better hedge? Explain why (no calculations are necessary)
