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

A 2-year zero-coupon bond paying 1 at maturity has a discount factor of 0.9000. What is the 2-year spot rate expressed with annual compounding?

The 2-year annual-compounding spot rate is 5.41%. The discount factor of 0.90 implies a two-year growth factor of 1/0.90 = 1.1111, and taking the square root gives 1.0541. Simple division by two would overstate it at 5.56%.

  1. A5.41%Correct
  2. B5.56%
  3. C11.11%
  4. D5.27%

Explanation

With annual compounding, d(2) = 1/(1+s)^2, so (1+s)^2 = 1/0.9 = 1.1111 and s = 1.1111^0.5 - 1 = 5.41%. Dividing the 11.11% total return by 2 ignores compounding and gives 5.56%. The 5.27% option is the continuously compounded rate.

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