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

Discount factors are d(1) = 0.9600 and d(2) = 0.9100. What is the implied one-year forward rate starting one year from now, with annual compounding?

The implied one-year forward rate one year ahead is 5.49%. It equals the ratio of the one-year to the two-year discount factor, 0.96/0.91 = 1.0549, minus one. This is the return needed to grow the one-year value into the two-year value.

  1. A5.49%Correct
  2. B9.89%
  3. C4.17%
  4. D5.00%

Explanation

The forward rate is f = d(1)/d(2) - 1 = 0.96/0.91 - 1 = 5.49%. Using 1/d(2) - 1 gives 9.89%, which is the two-year total return. Using 1/d(1) - 1 gives 4.17%, the one-year spot rate. Subtracting the factors gives 5.00%, which uses the wrong base.

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