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# P1.T4.908. Interest rate factors and the DV01-based hedge (Tuckman Ch.4)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Describe an interest rate factor and identify common examples of interest rate factors. Define and compute the DV01 of a fixed income security given a change in yield and the resulting change in price. Calculate the face amount of bonds required to hedge an option position given the DV01 of each.

Questions

908.1. Your colleague Peter is building a model that will estimate the sensitivity of your firm's bond portfolio to interest rate changes. He is evaluating six different models. Each of his candidate models shocks the rate, but each assumes a different interest rate factor as the model's core assumption. These are the six candidate interest rate factors:

I. Yield to maturity; aka, yield
II. 2-, 5-, 10, and 30-year spot (aka, zero) rates
III. 2-, 5-, 10, and 30-year par yields
IV. Six month forward rates across the entire 30-year curve
V. Level and slope
VI. The continuously compounded, instantaneous rate, r(t)

Which of the six are usable (i.e., viable) interest rate factors?

a. Only I. and VI. are usable interest rate factors
b. Only I., II. and III. are usable interest rate factors
c. Only IV, V. and VI. are usable interest rate factors
d. All six are usable interest rate factors

908.2. Consider a 9-year bond with a semi-annual 10.0% coupon that has a current price of $119.780 and a yield of 7.000%. If the yield drops to 6.850%, the bond's price increases to$120.900. If this is the case, then which of the following is nearest to the bond's dollar value of '01 (DV01)?

a. -0.0121
b. 0.0121
c. 0.0747
d. 1.1200

908.3. On May 28, 2018, a market maker sells $200.0 million face amount of TYU0C 120, which are call options with a strike of 120 on 10-year U.S. note futures contracts; aka, TYU0. The table below shows selected price-rate pairs for the options, TYU0C 120, and the futures contracts: When the market maker sells the$200.0 million face amount of the option, TYU0C 120, the seven-year par rate is 3.77%. Which is nearest to the face amount of futures, TYU0, that the market maker should purchase to hedge the written option position?

a. $12.5 million b.$25.0 million
c. $1,600.0 million d.$1,712.50 million