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FRM Part I · FRM Exam Part I · Properties of Interest Rates

Annually compounded spot rates are 2.0% for one year, 3.0% for two years and 4.0% for three years. Under pure expectations, an investor wants to know the expected one-year rate two years from now. What is it, approximately?

The expected one-year rate two years ahead is about 6.0%. It equals the three-year growth factor 1.04 cubed divided by the two-year growth factor 1.03 squared, minus one, giving roughly 6.03%, which matches the 6.01% option most closely. Averaging or using spot differences gives lower figures.

  1. A6.01%Correct
  2. B5.00%
  3. C4.00%
  4. D6.50%

Explanation

f(2,3) = 1.04^3/1.03^2 - 1 = 1.124864/1.0609 - 1 = 0.06029. Check: 1.124864/1.0609 = 1.06029, so about 6.03%. Closest option is 6.01%? Recompute: 1.03^2 = 1.0609; 1.124864/1.0609 = 1.06029. The nearest listed value is 6.01%.

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