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

A manager holds a bond portfolio with KR01s (gain per 1bp fall) of USD 3,000 at the 2-year and USD 9,000 at the 10-year key rates, and zero at other key rates. She wants to neutralise both exposures using a 2-year zero-coupon bond with KR01 of USD 190 per USD 100,000 face value (only 2-year exposure) and a 10-year zero-coupon bond with KR01 of USD 780 per USD 100,000 face value (only 10-year exposure). Approximately what positions in face value should she take?

She should short about USD 1.58 million face of the 2-year zero and about USD 1.15 million of the 10-year zero. The required offset is 3,000/190 and 9,000/780 units of USD 100,000, and shorting is needed because the portfolio is long both key rate exposures.

  1. AShort about USD 1.58 million of 2-year and short about USD 1.15 million of 10-yearCorrect
  2. BLong about USD 1.58 million of 2-year and long about USD 1.15 million of 10-year
  3. CShort about USD 15.8 million of 2-year and short about USD 11.5 million of 10-year
  4. DShort about USD 1.15 million of 2-year and short about USD 1.58 million of 10-year

Explanation

2-year: 3,000/190 = 15.79 units of USD 100,000 = USD 1.58 million face. 10-year: 9,000/780 = 11.54 units = USD 1.15 million face. Since the portfolio is long exposure, she must short both. Longs have the wrong sign, and swapping the sizes mismatches the maturities.

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