Implied rate for year two from spot rates

Question

The annually compounded one-year spot rate is $7.15\%$ and the two-year spot rate is $7.60\%$ . What one-year forward rate, starting one year from today, is implied by these numbers?

Short answer

About $8.05\%$ . Investing for two years at the two-year rate must equal rolling one year at $7.15\%$ then one year at the forward rate, so $1+f=\tfrac{1.076^2}{1.0715}\approx 1.0805$ . The forward sits roughly as far above the two-year rate as the one-year rate sits below it.

Adapted from Crack, Heard on the Street, Q3.8, p.34; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Duration and Convexity: Measuring and Managing Interest Rate Sensitivity
Forward and Futures Prices: Cost-of-Carry, Known Income, and Continuous Yields

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