FRM Part I · FRM Exam Part I · Mortgages and Mortgage-Backed Securities
An MBS has a price of 100. When yields are shifted down by 50 basis points and prepayment assumptions are re-run, the model price is 101.20. When yields are shifted up by 50 basis points, the model price is 98.60. What is the effective duration of the MBS?
The effective duration is 2.60. It equals the price when yields fall minus the price when yields rise, divided by twice the initial price times the yield change: (101.20 − 98.60) / (2 × 100 × 0.005) = 2.60. Prepayments are re-estimated in each scenario.
- A1.30
- B2.60Correct
- C2.00
- D5.20
Explanation
Effective duration = (P- − P+) / (2 × P0 × Δy) = (101.20 − 98.60) / (2 × 100 × 0.005) = 2.60 / 1.00 = 2.60. Using a 1.00% shift instead of 0.50% would give 1.30, a wrong-step-size error.
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