Download Investment Valuation and Portfolio Management: Hedging with Durations and more Study notes School management&administration in PDF only on Docsity! Investment Valuation and Portfolio Management (E2093) Vit Bubak (Tutorial 2 and 3) More on Hedging with Durations Q1) Using duration (DUR) to form a Riskless Hedge Position Jane holds $1,000,000 (face value) of 10-year zero-coupon bonds with a yield to maturity of 8% compounded semiannually. How can she perfectly hedge this position with a short position in 5-year zero-coupon bonds with a yield to maturity of 8% (compounded simiannually)? What would have happened if the position in the 10-year zero coupon bonds was left unchanged? Hint: You can use the following formulas: ( ) (0.0001 0.0001 0B B H HDUR P DUR P× × − × × =) dr dP P DUR 1−= Q2) Changing the duration of Pension Fund Assets As the new manager of the pension fund, assume you have computed that the fund’s liabilities amount to amount an EUR 8bil market value obligation with a duration of 12 years. Unfortunately, while the fund has EUR 9bil in assets, their duration, largely composed of bonds, is only eight years. This means that a steep decline in interest rates may increase the present value of the obligations by EUR 1bil more than such a decline increases the value of the fund’s assets. While keeping a EUR 1bil surplus in the pension fund, how can a self-financing investment in 5-year Treasury notes, with a duration of 4 years, and 30-year Treasury bonds, with a duration of 10 years, eliminate this problem? Hint: Remember that the duration of a portfolio is a (weighted) combination of all of the portfolio’s assets/liabilities durations… Homework II. (Questions) Exercise I. Assume you manage a $29 mil portfolio with three types of bonds, including: 1) long position in 30-year T-Bonds, face value $5 mil, DV01 of $ 0.20 per $100 face value, 2) long position in 10-year T-Notes, face value $8 mil, DV01 of $ 0.08 per $100 face value, 3) short position in 5-year T-Notes, face value – $16 mil, DV01 of $ 0.02 per $100 face value. a) Compute the DV01 of this portfolio. b) Is the DV01 negative or positive? What does the positive/negative mean here? c) What is the impact of an 85 bp change in the interest rates on portfolio’s value? Exercise II. Assume that changes in the yields of various maturity bonds are identical. a) How much of a 5-year bond (coupon 6%, IR = 8% compounded semiannually, M = $10.000) should you purchase to perfectly hedge the interest rate risk of the portfolio from (exercise I.)? (Note: Perfect hedge means that DV01 equals zero!) b) What would have to happen with the coupons of our 5-year bond to make the price of the bond more sensitive to interest rate movements? Would they have to increase or decrease? (Hint: How does DUR (or DV01) react to changes in coupons?) c) If the DV01 for our 5-year bond goes up, will we need more/less of it to hedge the portfolio? Exercise III. Imagine you hold $2.5 mil face value in 10-year zero-coupon bonds. The bonds have a yield to maturity of 8% compounded semiannually. a) What amount (face value as well as present value) of a 5-year zero-coupon bond with the yield to maturity of 6% compounded semiannually would you need to purchase/sell to fully hedge your position? (Hint: Use hedging with durations!) b) When you purchase a bond, do you buy or sell a debt? If you buy/sell a debt, do you gain/lose with positive changes in interest rate(s)? 1
