The Forward Rate Is Not a Forecast: Fama and Bliss

Here is a claim that sounds obviously true, was taught as gospel for decades, and is largely false.

The expectations hypothesis says that a forward rate is the market's forecast of a future interest rate. If the one-year rate, one year from now, is quoted at 5 percent in the forward market, that is because the market expects the one-year rate to be 5 percent in a year. Long bonds yield more than short bonds because rates are expected to rise. It all hangs together, it is intuitive, and it says something comforting: the yield curve is a crystal ball, and you can read the future off it.

Eugene Fama and Robert Bliss took this seriously enough to test it properly. The answer they got reoriented the entire study of bond returns.

The problem: two very different reasons a forward rate can be high

Suppose the two-year yield is well above the one-year yield, so the forward rate for the second year is high. Why?

Story A, the expectations story. Investors think short rates are going to rise. To be willing to lock up money for two years instead of rolling over one-year bonds, they need to be paid the higher rates they expect to see. The forward rate is a forecast.

Story B, the risk premium story. Investors do not expect rates to rise at all. They simply demand extra compensation for holding a longer bond, because long bonds are risky: if rates move against you, a long bond loses much more than a short one. The forward rate is high not because of a forecast, but because of a fee the market is charging for taking duration risk.

These two stories make different, testable predictions, and they had never been cleanly separated over long horizons. Fama and Bliss designed the test that separates them.

The key idea via analogy: is the extra yield a prediction or a payment?

The test is deceptively simple. Take the forward-spot spread: how much higher the forward rate is than today's short rate. That is the "extra yield" being offered.

Now ask that number to predict two different things.

Test one. Does the spread predict that short rates will rise? If Story A (expectations) is right, a high spread should be followed by rising rates. If the forward market is a forecast, it should forecast.

Test two. Does the spread predict that you will earn an excess return by buying the longer bond and holding it for a year? If Story B (risk premium) is right, a high spread means the market is paying you extra for taking duration risk, and if you take that risk you should collect it.

The analogy: a shop is offering a big discount on umbrellas. Two explanations. Either everyone knows a storm is coming and the price reflects that forecast (Story A), or nobody is sure and the shop is just paying you to take inventory risk off their hands (Story B). To find out which, check two things: did it actually rain, and did people who bought umbrellas make money?

Fama and Bliss ran both tests, and here is what they found.

At short horizons, the forecast fails and the risk premium wins. Over the next year, a high forward-spot spread does a poor job of predicting rising short rates. What it does predict, and predict well, is that you will earn an excess return by holding longer bonds. The extra yield is not information about the future. It is a payment for bearing risk, and the payment is predictable in advance.

That is a direct rejection of the expectations hypothesis. The forward rate is not a forecast; it is dominated by a time-varying risk premium.

But at longer horizons, the forecast starts to work. Fama and Bliss found something subtler and often forgotten. Over horizons of several years, the forward-spot spread does contain real information about where rates are going. Rates mean-revert slowly, and the forward curve picks that up. So the crystal ball is not shattered, it is just useless at the horizon everyone was pointing it at.

And the risk premium is not constant. It moves, and it moves with the business cycle: high in bad times, when investors are nervous and demand a lot to hold risky duration, and low in good times, when they are relaxed. That is the finding that later work built on.

Why it mattered

• It killed the expectations hypothesis as a working assumption. Not as a theory people had doubts about, but as the default lens through which everyone read the yield curve. After Fama and Bliss (and Campbell and Shiller, arriving at the same destination by a different road), you could no longer read the forward curve as a pure forecast without embarrassment.
• It established that bond risk premia are predictable. This is the load-bearing result. If excess bond returns can be forecast from information available today, then the compensation for duration risk is not a constant. It swings. That single fact spawned an entire literature, and it is what Cochrane and Piazzesi refined into a much sharper predictor eighteen years later.
• It broke the interest rate models. Every affine model of the era hard-wired the risk premium to be proportional to the amount of risk, meaning it could only move when volatility moved. Fama and Bliss showed the premium moves for reasons that have little to do with volatility. That mismatch is precisely why those models forecast so badly, as Duffee later demonstrated, and it is why Duffee's "essentially affine" fix was necessary.
• The Fama-Bliss regression became a standard test. Regressing excess bond returns on the forward-spot spread is now the canonical way to test the expectations hypothesis in a new market or a new sample. It is a permanent fixture of the toolkit.
• The Fama-Bliss discount bond dataset they constructed became a standard research input in its own right, used for decades.
• It has a direct trading implication. If a high forward spread predicts excess returns, then the shape of the curve is a timing signal for how much duration to hold. Carry and roll-down strategies, and the systematic fixed income factors that asset managers run today, are the commercial descendants of this observation.

The honest limitations

• The regressions are statistically treacherous. Predicting one-year returns using overlapping data from a few decades of history gives you far fewer genuinely independent observations than the sample size suggests. The forward-spot spread is highly persistent, which is exactly the setup where regression tests are known to be biased and standard errors understated. The predictability is real, but the statistical evidence is weaker than the t-statistics in the table imply, and a substantial econometric literature exists to argue about precisely this.
• Predictable does not mean tradeable. The risk premium is compensation for real risk. Harvesting it means being long duration when everyone else is scared, and it will hurt, exactly when it is most tempting to stop. A predictable premium is not free money; it is a payment for enduring pain.
• It is a fact, not an explanation. Fama and Bliss establish that the premium varies. They do not say why. Is it rational compensation that rises when investors are genuinely more risk-averse, in bad times? Is it a behavioural mistake? Is it institutional, pension funds and insurers being forced to buy long bonds regardless of price? The paper cannot tell you, and neither, entirely, can anyone since.
• Sample dependence. US Treasuries, mostly a period of high and falling inflation. A large part of the "excess return to duration" over the past forty years came from a once-in-a-generation forty-year decline in interest rates. Whether the premium behaves the same way in a rising-rate world is a question the sample cannot answer.
• Fama himself never renounced efficiency. It is worth noting that a predictable risk premium is entirely consistent with efficient markets. Fama's own reading is that this is rational, time-varying compensation for risk, not a market failure. The behavioural reading is available, but the paper does not require it.

The one-line takeaway

Fama and Bliss showed that a high forward rate mostly does not mean the market expects rates to rise. It means the market is paying you extra to hold duration, and that payment is predictable, which is the fact that broke the expectations hypothesis and launched the study of bond risk premia.