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FRM Part I · FRM Exam Part I · Mortgages and Mortgage-Backed Securities

An MBS has a price of 100. If yields fall by 50 bps, its price rises to 102.00; if yields rise by 50 bps, its price falls to 97.00. What is its effective duration?

Effective duration is 5.0. It equals the price when yields fall minus the price when yields rise, 102 minus 97, divided by twice the initial price times the yield shift of 0.005, which gives 5 divided by 1.

  1. A4.5
  2. B5.0Correct
  3. C1.5
  4. D9.0

Explanation

Effective duration = (P- − P+)/(2 × P0 × Δy) = (102 − 97)/(2 × 100 × 0.005) = 5/1 = 5.0. Using 0.5 instead of 0.005 or dropping the factor of 2 gives wrong results; 4.5 mixes up the price change, and 9.0 is not derived from the data.

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