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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Term structure of interest rates

The annual effective spot rates are 4% for one year and 5% for two years. What is the two-year par yield, expressed as an annual coupon rate on a bond redeemed at par and paying coupons annually?

The two-year par yield is 4.98%. It is found by setting the bond price to par: c equals one minus the two-year discount factor, divided by the sum of the one- and two-year discount factors. Because the first coupon is discounted at the lower spot rate, the result sits just below 5%.

  1. A4.50%
  2. B4.98%Correct
  3. C5.00%
  4. D4.76%
  5. 5.25%

Explanation

Par yield c = (1 - v2)/(v1 + v2). With v1 = 1/1.04 = 0.961538 and v2 = 1/1.05^2 = 0.907029, the numerator is 0.092971 and the denominator is 1.868567, so c = 4.98%. Using 5.00% ignores that the first coupon is discounted at the lower 4% rate. 4.50% is just the simple average of the two spot rates.

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