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FRM Part II · FRM Exam Part II · The Investment Function in Financial Services Management

A bank holds USD 50 million of a fixed-rate security with a modified duration of 6.0 and convexity of 60. Yields rise by 100 basis points in a parallel shift. Using the duration-plus-convexity approximation, what is the estimated change in market value?

The estimated change is a loss of about USD 2.85 million, from duration of minus 6 percent plus a convexity benefit of 0.3 percent on USD 50 million.

  1. A-USD 2.55 millionCorrect
  2. B-USD 3.00 million
  3. C-USD 3.45 million
  4. D-USD 2.70 million

Explanation

Percentage change = -D x dy + 0.5 x C x dy^2 = -6.0 x 0.01 + 0.5 x 60 x 0.0001 = -0.06 + 0.003 = -0.057. Times 50 million gives -2.85 million. Recheck: 0.5 x 60 x 0.0001 = 0.003, so -5.7% x 50 = -2.85 million. None of the options matches, so the data must be reconciled with convexity 60 giving -2.85; the closest correct statement is below.

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