Skip to content

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

Annual effective spot rates are 5% for one year, 5.5% for two years and 6% for three years. What is the three-year par yield (annual coupons, redeemed at par)?

The three-year par yield is 5.96%. It equals one minus the three-year discount factor, divided by the sum of the three annual discount factors. Since earlier coupons are discounted at lower spot rates, the par yield falls slightly below the three-year spot rate of 6%.

  1. A5.50%
  2. B6.00%
  3. C5.96%Correct
  4. D5.80%
  5. 5.65%

Explanation

v1 = 0.952381, v2 = 1/1.055^2 = 0.898452, v3 = 1/1.06^3 = 0.839619, so the sum is 2.690452. Par yield = (1 - 0.839619)/2.690452 = 0.160381/2.690452 = 5.96%. The answer of 6.00% is the three-year spot rate, which is higher than the par yield on an upward sloping curve.

Did you get it right without looking?

One question tells you little. A timed set on Term structure of interest rates shows your real accuracy, how long you take and where you lose marks.

Practise Term structure of interest ratesFree diagnostic mock

More Term structure of interest rates questions