Forward Rates from the Curve
Forward Rates from the Curve
A forward rate is the interest rate that the market implies for lending during a future period. If today's 1-year spot rate is 2% and the 2-year spot rate is 3%, we can infer what the market expects the 1-year rate to be one year from now. This inferred rate is the 1-year forward rate, one year ahead (often written as 1f1, meaning 1-year forward rate starting 1 year in the future).
Forward rates are extracted directly from the observed spot curve through a simple calculation. They are not quoted directly in the market; no one trades a contract that says "the interest rate one year from now will be X%." But the market's collective willingness to trade short and long bonds reveals what the market implicitly expects future rates to be. By comparing spot rates at adjacent maturities, we can back out forward rates.
Understanding forward rates is powerful because it tells you what the market expects for future monetary policy and economic conditions. If forward rates are rising (each successive year's implied rate is higher than the previous year's), the market expects rates to go up. If forward rates are flat or falling, the market expects rates to stay steady or fall. Forward rates are not forecasts—the market can be wrong—but they represent a consensus expectation distilled from the prices of billions of dollars of securities trading daily.
Key takeaways
- Forward rates are implied future short-term rates extracted from the current spot curve using arbitrage relationships.
- The 1-year forward rate starting 1 year from now (1f1) is calculated as: (1 + s2)^2 / (1 + s1) - 1, where s1 and s2 are the 1-year and 2-year spot rates.
- Forward rates tell you what the market expects for future interest rates; a rising forward curve implies expected rate increases; a flat forward curve implies stable rates.
- Forward rates are not perfect forecasts of actual future spot rates, but they are the best-informed forecast available from market prices.
- The difference between the forward rate and the actual future spot rate reflects changes in expectations (or term premium changes) that occur between today and the future date.
Calculating Forward Rates from Spot Rates
The relationship between spot rates and forward rates is built on the principle of no-arbitrage. If you can borrow or lend for 2 years at the 2-year spot rate, you should not be able to make a risk-free profit by instead borrowing for 1 year at the 1-year rate and rolling over into another 1-year loan in the future.
Here is the arbitrage logic. Suppose:
- 1-year spot rate (s1) = 2%
- 2-year spot rate (s2) = 3%
If you invest $1,000 for 2 years at the 2-year rate, you get: $1,000 × (1.03)^2 = $1,060.90
Alternatively, if you invest for 1 year at the 1-year rate and roll into another 1-year investment, you need the second-year 1-year rate (the forward rate, 1f1) to be: $1,000 × (1.02) × (1 + 1f1) = $1,060.90 $1,020 × (1 + 1f1) = $1,060.90 1 + 1f1 = 1.0401 1f1 = 4.01%
So the market is implying a 1-year rate of approximately 4.01% starting one year from now. Why? Because the 2-year spot rate (3%) is the geometric average of today's 1-year rate (2%) and the expected 1-year rate one year from now (4.01%). Investors locking in 3% for 2 years are accepting a blended return: 2% for the first year and 4.01% for the second year.
The general formula for a forward rate is:
(1 + sn)^n = (1 + sm)^m × (1 + fm,n)^(n-m)
where sn and sm are spot rates at n and m years, and fm,n is the forward rate for (n - m) years starting m years from now.
What Forward Rates Tell You About Expectations
A rising forward curve—where successive forward rates are higher—signals that the market expects interest rates to rise in the future. In the example above, the implied 1-year forward rate 1 year from now (4.01%) is much higher than today's 1-year rate (2%). The market is expecting a significant increase in rates over the next year.
By contrast, if spot rates were flat at 3% (1-year = 3%, 2-year = 3%), the forward rate would also be flat at 3%. The market would be signaling no expected change in rates.
If spot rates were inverted (1-year = 4%, 2-year = 3%), the forward rates would fall. The market would be signaling expected decreases in future rates. For example: $1,000 × (1.03)^2 = $1,000 × (1.04) × (1 + 1f1) 1,060.90 = 1,040 × (1 + 1f1) 1f1 = 1.98%
The forward rate of 1.98% is much lower than today's 4%, indicating the market expects rates to fall sharply.
Reading Forward Rates in Different Market Conditions
In 2017–2019, the Fed was in a tightening cycle, raising rates gradually. The spot curve was upward-sloping: 2-year Treasury yielded 1.5%, 10-year yielded 2.5%. The forward curve was also upward-sloping; forward rates rose, indicating the market expected ongoing rate increases. Market participants expected the Fed to continue hiking rates into 2019. This expectation was reflected in rising forward rates across the 1f1 (1-year forward 1 year out), 2f1 (1-year forward 2 years out), etc.
In late 2018, economic data weakened and equity markets sold off sharply. The Fed abruptly shifted from a tightening bias to a "patient" stance and eventually cut rates three times in 2019. The forward curve compressed and then inverted. Forward rates fell across the board. Investors who had positioned for rising rates based on the forward curve faced losses. The lesson: forward rates represent market expectations at a point in time, but those expectations can shift rapidly.
In 2022, after the Fed raised rates to 4.25%–4.50%, the forward curve was flat to declining. Forward rates were not much higher than current rates, indicating the market expected the Fed to hold rates steady or cut. This turned out to be accurate; the Fed cut rates starting in September 2024. The forward curve had correctly implied that the tightening cycle was ending.
Forward Rates and the Investment Decision
For bond investors, forward rates provide useful information for positioning. If you believe the forward curve is too high—that is, the market is overestimating how much rates will rise in the future—you can position for falling forward rates by buying longer-duration bonds. If you believe the forward curve is too low—that is, the market is underestimating future rate increases—you can position for rising forward rates by selling longer-duration bonds or staying short.
A practical example: In late 2021, forward rates implied the Fed would raise rates to 2.5% by the end of 2023. Many investors believed this was too low; they thought the Fed would need to raise rates to 3.5% or higher to combat inflation. Those investors bought short-term bonds or avoided bonds altogether, anticipating that longer-term bonds would decline in value if their beliefs were correct. When inflation did spike and the Fed raised to 5%+, longer-term bonds suffered significant losses. Those who trusted the forward curve were caught unprepared.
This illustrates that forward rates are not omniscient. They reflect the collective view of the market at a point in time, but they can be systematically biased. During the low-inflation 2010s, forward rates persistently underestimated the temporary inflation spike that came in 2021–2022. During the 2008–2015 period of high uncertainty, forward rates overestimated the pace of rate increases post-crisis.
Extracting the Entire Forward Curve
The forward curve can be built at any horizon. The 1-year forward starting 1 year out (1f1) is just one point. You can also calculate the 1-year forward starting 2 years out (1f2), 3 years out (1f3), and so on. You can calculate 2-year forwards, 5-year forwards, or any combination.
A complete forward curve shows the market's expected trajectory of interest rates far into the future. A rising forward curve suggests rising rates are expected; a flat forward curve suggests rates are expected to stabilize; a falling forward curve suggests falling rates are expected.
In the 1960s–1990s, long-dated forward rates (5-year forward 10 years out, for instance) were believed to converge to the long-run equilibrium real interest rate (around 2% inflation-adjusted). But in recent decades, with central bank intervention and structural changes in the global economy, this convergence is less reliable. Forward rates 10 or 20 years out are less informative about genuine economic expectations and more contaminated by term premium, liquidity effects, and central bank policy anchors.
For practical investors, the most useful forward rates are those in the 1–5 year horizon. These reflect genuine market expectations about the next few years of Fed policy and economic growth. Forward rates beyond 5 years are useful as part of the full curve picture, but they should be interpreted cautiously.
Flowchart: Using Forward Rates for Portfolio Positioning
Forward Rates vs. Actual Future Rates
It is important to note that forward rates are not perfect predictors of actual future spot rates. Over long periods, forward rates do a reasonable job forecasting the average direction of rate changes. But over shorter periods (1–2 years), actual rates often diverge from implied forward rates.
If the 1-year forward rate one year out is 4%, the 1-year rate one year from now might turn out to be 3.5% or 4.5%. The difference reflects either a change in expectations (the Fed shifted its policy path) or a realization that the term premium was different than what was priced in the forward curve. Over decades, forward rates have a modest but positive correlation with subsequently realized rates. But the correlation is not perfect, and surprises are common.
This is why forward rates are useful as one input to an investment decision but should never be the only input. Combine forward rate analysis with fundamental economic analysis, Fed guidance, inflation expectations, and other signals to form your own view. If your view differs from what the forward curve implies, you can position accordingly, accepting the risk that you may be wrong.
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Forward rates are derived purely from the assumption of no-arbitrage between spot rates at different maturities. But there is an alternative interpretation: the slope of the yield curve might reflect more than just rate expectations. It might also reflect compensation for risk—the term premium—as described by liquidity preference theory.