1-Year Forward Rate Starting Year 2

This fixed income interview question focuses on extracting a one-year forward rate from a small set of given spot rates. The setup is a simple, default-free yield curve with annual compounding, where you know the rate for investing today over one year and the rate for investing today over two years. You are asked to infer the implied rate that must prevail between the end of year one and the end of year two so that an investor is indifferent between locking in for two years now or rolling over after one year. Variants of this appear frequently in rates trading, fixed income research, and entry-level quant roles.

To answer correctly, a candidate must translate the no-arbitrage idea into the appropriate compounding relationship and manipulate it cleanly to isolate the unknown forward rate. The problem leans on understanding term structures, spot versus forward rates, and geometric (rather than arithmetic) compounding. Interviewers watch for quick, accurate setup of the equation, correct handling of exponents, and an intuitive explanation of why the equality between the two investment strategies must hold.

What it tests

The core structure behind forward rate problems is the law of no-arbitrage applied to compounded returns: the return from investing over a longer period at a known spot rate must match the return from rolling over shorter-term investments at their respective spot and forward rates. This leads to the geometric compounding relationship, where the multi-period spot rate is the geometric average of the constituent spot and forward rates. The reason this pattern holds is that, in efficient markets, any mismatch between these compounded returns would allow riskless profit, which cannot persist. Thus, the forward rate is not simply an arithmetic difference but is determined by the compounding structure of interest rates over time. This ensures that the value of investing for two years at the two-year spot rate equals investing for one year at the one-year spot rate and then reinvesting for another year at the forward rate.