Bond Risk Premia and Return Predictability

If the expectations hypothesis were literally true, a steep yield curve would carry no trading signal at all — it would simply mean short rates are expected to rise, and holding a long bond versus rolling short-term cash would earn the same expected return either way. Decades of data say otherwise. When the curve is unusually steep, long-maturity bonds go on to outperform, on average, over the following year. The curve's slope is forecasting excess returns, not just future short rates — evidence that the "extra" yield on a steep curve is compensation for risk, and that compensation moves around over time.

The regression that started it

Fama and Bliss showed that the spread between a forward rate and the current short rate, $f_{t,n} - y_{t,1}$, predicts the excess return of an $n$-year bond held for one year:

$$rx_{t+1}^{(n)} = \alpha + \beta \left(f_{t,n} - y_{t,1}\right) + \varepsilon_{t+1}$$

Under the expectations hypothesis, $\beta$ should be zero — the forward-spot spread should only forecast where the short rate is heading, contributing nothing to excess returns. Empirically $\beta$ comes out well above zero and often close to one, meaning almost the entire forward-spot spread is return-predictive rather than rate-predictive.

Worked example: turning a spread into a forecast

Say the five-year forward-spot spread ($f_{t,5} - y_{t,1}$) is currently 1.20%, and historical fitting gives $\alpha \approx 0$ and $\beta \approx 0.8$ for this maturity.

$$\widehat{rx}^{(5)} = 0 + 0.8 \times 1.20\% = 0.96\%$$

The model forecasts about 0.96% of excess return on the five-year bond over the coming year, above what you'd earn just rolling one-year cash. If instead the pure expectations hypothesis held ($\beta = 0$), that same 1.20% spread would forecast zero excess return — all of it would be "explained" by an expected rise in short rates. The gap between $\beta = 0.8$ found in the data and $\beta = 0$ predicted by the simple theory is the empirical case for a real, forecastable term premium.

Now suppose a year passes and the five-year bond actually returns 1.40% in excess of cash. The realized term premium for that period was 1.40%, close to the 0.96% forecast — the forecast doesn't have to be exact, only informative on average across many such periods, which is what the regression's statistical significance is certifying.

Why the premium moves at all

If the term premium were a constant, it would just be a fixed markup and the expectations hypothesis's logic would still roughly hold up to a constant shift. What the data actually show is that the premium is time-varying: it rises in recessions and around periods of high uncertainty (investors demand more compensation for duration risk when the macro outlook is murky) and compresses during calm, low-volatility stretches. Cochrane and Piazzesi later showed that a single "tent-shaped" combination of forward rates across the whole curve, not just the one at the traded maturity, captures even more of this predictability than the two-point Fama-Bliss spread alone.

Where it shows up

This is the empirical foundation for systematic bond risk-premia and carry strategies: going long steep parts of global curves and short flat ones, informed by exactly this kind of spread regression. It is also the reason central-bank watchers distinguish "the market expects rate cuts" from "the market is being paid a risk premium to hold duration" — conflating the two is a common and costly misreading of the curve.

The same logic extends across countries: a systematic global bond strategy can rank sovereign curves by their forward-spot spreads and take relative positions accordingly, treating each country's curve steepness as an independent signal about that market's compensation for duration risk, much like a cross-sectional value strategy ranks stocks by valuation rather than trading a single name in isolation.

Key terms

• Excess return — a bond's holding-period return minus the return from rolling short-term cash over the same period.
• Forward-spot spread — the gap between a forward rate and today's short rate; the standard predictor variable.
• Term premium — the average compensation, above expected future short rates, for holding duration risk.
• Expectations hypothesis — the (empirically rejected in its pure form) claim that forward rates are unbiased forecasts of future spot rates.