19. We present some empirical evidence indicating that the forward rates are better predictors of future bond returns than of future rate changes in Antti Ilmanen, “Market’s Rate Expectations and Forward Rates,” Journal of Fixed Income (September 1996), pp. 8–22. This evidence also suggests that the current spot curve is a better predictor of the next-period spot curve than is the implied spot curve one period forward. These findings imply that the rolling yields are reasonable proxies for the near-term expected bond returns—although even rolling yields capture a very small part of the short-term realized bond returns. Note that the poorer the forwards are in predicting future rate changes, the better they are in predicting bond returns—because then the implied rate changes that would offset initial yield advantages tend to occur more rarely. Note also that some investors may not care whether the forwards’ ability to predict bond returns reflects rational risk premia or the market’s inability to forecast rate changes; they want to earn any predictable profit irrespective of its reason.

20. One common misconception is that the forward rates are used in the valuation of swaps, options, and other derivative instruments because the forwards are good predictors of future spot rates. In fact, the forwards’ ability to predict future spot rates has nothing to do with their usefulness in derivatives pricing. Unlike forecasting returns, the valuation of derivatives is based on arbitrage arguments. For example, traders theoretically can construct, by dynamic hedging, a riskless combination of a risky long-term bond and an option written on it. The price of the option should be such that the hedged position earns the riskless rate—otherwise, a riskless arbitrage opportunity arises. The forward rates are central in this valuation because the traders can lock in these rates for future periods in their hedging activity. This arbitrage argument implies that the yield-curve option pricing models should be calibrated to be consistent with the market forward rates in spite of the fact that the forwards are quite poor predictors of future spot rates.