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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

The discount factor for 2 years is 0.9300 and for 3 years is 0.8900. What is the annually compounded forward rate for the year from t=2 to t=3?

The forward rate is 4.49%. The one-year forward from year 2 to year 3 equals the earlier discount factor divided by the later one, minus one. That is 0.93 divided by 0.89, minus 1, which is about 4.49%.

  1. A4.49%Correct
  2. B-4.30%
  3. C4.00%
  4. D12.36%

Explanation

The forward rate is d2/d3 − 1 = 0.93/0.89 − 1 = 4.49%. Inverting the ratio gives −4.30%, which is the wrong direction. The 4.00% option is the simple difference in discount factors, which is not a rate on the earlier cash flow. The 12.36% figure is 1/d3 − 1, a 3-year cumulative return.

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