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FRM Part I · FRM Exam Part I · Interest Rates

A short-term interest rate futures contract matures in 4 years, and the underlying rate covers the period to 4.25 years. The futures rate is 5.00%, and the annualized standard deviation of the short-term rate change is 1.2%. Using the convexity adjustment forward rate = futures rate - 0.5 x sigma^2 x t1 x t2, the implied forward rate is closest to:

The forward rate is about 4.8776%. Daily settlement makes the futures rate higher than the forward rate, so the convexity adjustment of 0.5 x 0.012^2 x 4 x 4.25 = 0.1224% is subtracted from the 5.00% futures rate.

  1. A5.1224%
  2. B4.8776%Correct
  3. C4.7552%
  4. D5.0000%

Explanation

Adjustment = 0.5 x 0.012^2 x 4 x 4.25 = 0.5 x 0.000144 x 17 = 0.001224, or 0.1224%. The forward rate is 5.0000% - 0.1224% = 4.8776%. Adding the adjustment gives the wrong sign, and omitting the 0.5 gives 4.7552%.

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