FRM Part II · FRM Exam Part II · Expectations, Risk Premium, Convexity and the Shape of the Term Structure
The one-year spot rate is 2.00% and the market's one-year forward rate starting in one year is 3.00%. The one-year forward rate starting in two years is 4.00%. All rates are annually compounded. What is the three-year spot rate, rounded to two decimals?
The three-year spot rate is about 3.01%. Multiply the growth factors 1.02, 1.03 and 1.04 to get 1.092624, then take the cube root. The simple average of 3.00% understates it slightly because compounding is ignored.
- A3.00%
- B3.01%Correct
- C2.99%
- D4.00%
Explanation
Three-year growth factor = 1.02 × 1.03 × 1.04 = 1.092624. The cube root is about 1.03009, so the spot rate is about 3.01%. The 3.00% option is the arithmetic average of the rates, which ignores compounding and is slightly too low.
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