Why Forward Rates Differ from Expected Future Spot Rates
Summary
The document asks why forward interest rates, which are implied by current market prices, are often treated as forecasts of future spot rates. The answer explains that observed rates can reflect more than expectations: compensation for duration risk can raise yields, while the value of positive convexity can lower them. Consequently, a forward rate need not equal the market’s unbiased expectation of a future short rate.
It also names forward rate bias, the tendency for forwards to overstate subsequently realized rates, and notes that forward curves have not reliably predicted future bond yields and curve shapes. A separate response distinguishes forecast accuracy from pricing: bootstrapping reflects rates implied by executable market transactions, and a swap’s legs would offset if the projected forward curve were realized. These points are conceptual rather than a quantitative estimation procedure; the document gives no empirical sample or method for extracting the risk premium and convexity effects.
Key ideas
- Forward rates are market-implied equilibrium rates and are not necessarily forecasts of future spot rates.
- Observed rates can include expectations, a bond risk premium, and a convexity effect.
- Duration risk can add compensation to longer maturity yields, while positive convexity can work in the opposite direction.
- Forward rates may overstate later realized rates, a pattern described as forward rate bias.
- A forward curve can support pricing even when its forecasts prove inaccurate.
Tags
Full text
# Why AREN'T forward rates what the market expects of the spot rates? # Why AREN'T forward rates what the market expects of the spot rates? I know that for a swap for example, the swap rate is just what adopts equilibrium for both legs by no arbitrage, on the other hand for a FRA its just the same only with one period of time. Considering what most economist do which is saying that the forward rates are the expectations of the marke (at least here) why are these numbers (just values of equilibrium given today's spot rates) good predictors for anything? ## Answer by Helin (score 2, accepted) https://quant.stackexchange.com/a/19268 Strictly speaking, any risk-free interest rate can be composed into three components: - The rate expectations component is the market's "true" expectation for future interest rate. - A bond risk premium component: longer maturity bonds have higher duration risk than cash. Accordingly market participants will demand more compensation for taking on duration risk; i.e., they'll ask for a higher yield. This is why even if market expectation for rates for the next 100 years is completely flat, the yield curve will still typically be upward sloping. - A convexity bias component: longer maturity bonds are more positively convex, providing more return advantages when rates increase or decrease. Because of this "convexity advantage," investors are willing to accept a lower yield (all else equal). This is why the long end of the yield curve sometimes dip down. So simply put, forward rates do NOT represent market expectation of future interest rates – you must subtract bond risk premium and add back convexity bias. It is also well known that forward rates frequently overstate subsequently realized interest rates. This is known as "forward rate bias." ## Answer by Edward Watson (score 0) https://quant.stackexchange.com/a/46940 Forwards have never really been that accurate at predicting the future shape and yield of the the bonds that you're looking at. That being said the bootstrapping process represents real executable transactions. In the case of the swap if the forward curve upon swap execution is realized the returns on the swap will be zero for both legs.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.