Forward rate for the second six months

Question

The six-month interest rate is $5\%$ and the one-year rate is $10\%$ (both annualised). What rate is implied for borrowing from six months to one year?

Short answer

$15\%$ with continuous compounding. The forward rate solves $0.05\times0.5+f\times0.5=0.10\times1$ , giving $f=15\%$ . With simple annualised rates instead, $1+0.5f=\tfrac{1.10}{1.025}$ , so $f\approx14.6\%$ .

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q4.1, p.148; 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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