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FRM Part I · FRM Exam Part I · Interest Rate Futures

Using the convexity formula forward rate = futures rate - 0.5 x sigma^2 x T1 x T2, a 2-year Eurodollar futures (T1 = 2.0, T2 = 2.25) is quoted at 95.00 and the annual rate volatility sigma is 1.2% (0.012). Assuming the futures rate is 5.00%, what is the approximate forward rate?

The forward rate is about 4.9676%. The convexity adjustment is 0.5 times 0.012 squared times 2.0 times 2.25, which equals 0.0324%. Subtracting it from the 5.00% futures rate gives 4.9676%. Adding it would use the wrong sign.

  1. A4.9676%Correct
  2. B4.9856%
  3. C4.9676% is wrong; the answer is 5.0324%
  4. D4.9676 basis points

Explanation

Adjustment = 0.5 x 0.012^2 x 2.0 x 2.25 = 0.5 x 0.000144 x 4.5 = 0.000324, or 0.0324%. Forward = 5.0000% - 0.0324% = 4.9676%. Adding the adjustment gives 5.0324%, which has the wrong sign.

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