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FRM Part I · FRM Exam Part I · Modeling Non-Parallel Term Structure Shifts and Hedging

A bond portfolio has key rate '01s of USD 150 at the 2-year point and USD 450 at the 10-year point, and no other exposure. A trader wants to hedge both key rates using 2-year and 10-year instruments whose key rate '01s are: Instrument A (2-year) USD 50 at the 2-year point and 0 at the 10-year point; Instrument B (10-year) USD 0 at the 2-year point and USD 90 at the 10-year point. To neutralize both exposures, the trader should:

Short 3 units of Instrument A and short 5 units of Instrument B. Each instrument only affects one key rate, so divide the exposure by the instrument's '01: 150/50 equals 3 and 450/90 equals 5. Shorting offsets the portfolio's positive exposure to falling rates.

  1. AShort 3 units of A and short 5 units of BCorrect
  2. BLong 3 units of A and long 5 units of B
  3. CShort 5 units of A and short 3 units of B
  4. DShort 3 units of A and long 5 units of B

Explanation

Units of A needed: 150/50 = 3. Units of B needed: 450/90 = 5. The portfolio has positive exposure (gains when rates fall), so the hedge must be short both instruments to offset. Swapping the quantities (5 and 3) divides by the wrong instrument sensitivity.

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