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

A Eurodollar futures contract maturing in 4 years implies a rate of 5.00%. The underlying rate covers the period from year 4 to year 4.25. The annual volatility of the short-term rate change is 1.2% (0.012). Using the convexity adjustment forward rate = futures rate − 0.5σ²t₁t₂, what is the forward rate?

The forward rate is 4.8776%. The convexity adjustment is 0.5 × 0.012² × 4 × 4.25, which is 12.24 basis points. It is subtracted from the 5.00% futures rate because daily settlement makes the futures rate higher than the forward rate.

  1. A4.8776%Correct
  2. B5.1224%
  3. C4.7552%
  4. D4.9388%

Explanation

The adjustment is 0.5 × 0.012² × 4 × 4.25 = 0.5 × 0.000144 × 17 = 0.001224, or 12.24 bp. The forward rate is 5.00% − 0.1224% = 4.8776%. Omitting the 0.5 factor gives 4.7552%. Adding the adjustment instead of subtracting it gives 5.1224%.

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