Why the Forward Rate Exceeds 20%

This interview question focuses on interpreting spot and forward interest rates in a fixed income term structure. The candidate is given two constant-maturity yields over different horizons and an approximate forward rate implied over the remaining period. They are then asked to justify, in intuitive language rather than algebra, why the correct forward rate must exceed that naive estimate. The setting is typical of sell-side and buy-side fixed income roles, particularly those involving curve construction, derivatives pricing, or relative value trades where spotting inconsistency between spot and forward rates is essential.

To answer well, the candidate has to connect the idea of multi-period compounding to forward rate logic, and distinguish clearly between arithmetic averages and the growth rate relevant for returns. The interviewer is looking for comfort with geometric compounding, no-arbitrage reasoning, and the ability to explain forward-spot relationships without relying purely on formulas. Strong answers highlight how compounding magnifies higher rates over time and therefore forces the implied later-period rate to overshoot a simple average-based back-of-the-envelope estimate.

What it tests

Whenever you compare average interest rates over multiple periods to the rate that would apply over a subinterval (such as a forward rate), you must account for the compounding effect: interest is earned not only on the original principal but also on previously earned interest. This means that the total return over several periods is governed by the geometric average of the rates, not the arithmetic average. The arithmetic average always overstates the growth rate compared to the geometric average unless all rates are equal. This is because compounding amplifies the effect of higher rates and dampens the effect of lower rates, so to match a higher average rate over a longer period, the forward rate for the later interval must be even higher than the simple difference would suggest. This principle underlies why forward rates derived from spot rates must compensate for compounding to avoid arbitrage opportunities.