The Cochrane-Piazzesi Return Forecasting Factor
A single combination of forward rates across the whole yield curve that predicts next year's bond returns far better than any one forward rate or yield spread on its own.
If long-term bond yields simply reflected expected future short rates, forward rates would be useless for predicting bond returns beyond that expectation. But Cochrane and Piazzesi found that a specific weighted combination of forward rates across maturities from 1 to 5 years — not any single yield or spread — predicts the following year's excess bond returns with unusually high explanatory power, often an R² well above what a single forward rate achieves alone.
The Cochrane-Piazzesi factor is one number built from a specific weighted blend of forward rates across the curve, and that single number forecasts next year's bond risk premium better than any individual yield, spread, or forward rate does by itself.
What the factor looks like
The factor is estimated by regressing average excess bond returns (across maturities) on the full set of forward rates, then using the resulting weights as a fixed recipe going forward. Unlike a slope factor (which just looks at long yield minus short yield), the Cochrane-Piazzesi weights typically form a tent shape — small or negative on the shortest and longest forwards, largest on the middle maturities — which is not the shape anyone would have guessed from theory alone.
Because this single factor consistently outperforms simpler predictors in-sample, it is widely used in academic term-premium research, though practitioners note the same tent shape can be unstable and overfit to the sample period it was estimated on.
Practice in interviews
Further reading
- Cochrane, J. and Piazzesi, M., 'Bond Risk Premia' (2005)