P1.T4.16. Hedging given DV01 or effective duration

David Harper CFA FRM

David Harper CFA FRM
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AIMs: Calculate the face amount of bonds required to hedge an option position given the DV01 of each. Define, compute, and interpret the effective duration of a fixed income security given a change in yield and the resulting change in price.

Questions:

16.1. A market maker sells (writes) $50 million face value of call options on underlying bonds when the interest rate is 4.0%. At this 4.0% rate level, the DV01 (dollar value of an '01) of the option, per 100 face value, is $0.030. At this 4.0% rate level, the DV01 (per 100 face value) of the underlying bond is $0.070. What is the market maker's hedge transaction?

a. Short $50.0 million face amount of underling bonds
b. Short $50 million face amount of call options on bond
c. Long $21.4 million face amount of underlying bonds
d. Long $50.0 million face amount of underlying bonds

16.2. A market maker sells (writes) $100 million face value of call options on underlying bonds when the interest rate is 4.0%. The price of the call options is $3.0 million and their (modified) duration is 80.0 years. At the same 4.0% rate, as the underlying bonds pay a 4.0% coupon, the price of the underlying happens to equal $100 par with a duration of 7.0 years. What is the market maker's hedge transaction?

a. Short $12.9 million of underlying bond
b. Short $24.0 million of underlying bond
c. Long $24.0 million of underlying bond
d. Long $34.3 million of underlying bond

16.3. At a rate of 4.00% a bond has a price of $107.93. If the rate drops by one basis point to 3.99%, the bond price increases to $108.00. What is an estimate of the bond's effective duration?

a. 5.83 years
b. 6.49 years
c. 7.21 years
d. 8.55 years

Answers:
 
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