FRM Part I · FRM Exam Part I · Modeling Non-Parallel Term Structure Shifts and Hedging
A bond portfolio worth $50 million falls in value by $22,500 when only the 10-year key rate rises by 1 bp, with triangular interpolation to adjacent key rates. What is the portfolio's 10-year key rate duration?
The 10-year key rate duration is 4.5. The proportional value loss is 22,500 divided by 50 million, or 0.045 percent, and dividing by the 0.01 percent (1 bp) rate shift gives a sensitivity of 4.5.
- A0.45
- B45
- C2.25
- D4.5Correct
Explanation
Key rate duration = -(ΔP/P)/Δy. ΔP/P = -22,500/50,000,000 = -0.00045, and Δy = 0.0001. Duration = 0.00045/0.0001 = 4.5. Using a 10 bp shift instead of 1 bp would give 0.45.
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