FRM Part II · FRM Exam Part II · Expectations, Risk Premium, Convexity and the Shape of the Term Structure
The one-year spot rate is 3.00% and the market's expected one-year rate one year from now is 4.00%. Ignoring risk premium and convexity, what is the approximate two-year spot rate (annual compounding)?
Compound the one-year spot of 3% with the expected one-year rate of 4%: 1.03 times 1.04 is 1.0712, and its square root minus one is about 3.50%. This is the geometric average of the two one-year rates under pure expectations.
- A3.50%Correct
- B3.00%
- C4.00%
- D3.70%
Explanation
Two-year spot = sqrt(1.03 x 1.04) - 1 = sqrt(1.0712) - 1, about 3.499%, which rounds to 3.50%. 3.00% and 4.00% each ignore one leg of the investment, and 3.70% has no basis in the data.
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