Forward Rates Are Not Forecasts: Read the Yield Curve’s Reinvestment Hurdle

A one-year zero-coupon rate of 4% and a two-year rate of 3.5% can both be correct. The shorter investment pays more per year, but it guarantees that rate for only half the investment horizon. To compare the alternatives, the useful question is not “Which displayed yield is higher?” It is “What return would I need in the second year for rolling short investments to match locking in two years?”

In the simplified example below, that hurdle is 3.0024%. It is a rate implied by today’s prices, not a promise that next year’s policy rate, deposit rate or bond yield will equal it. This distinction matters when a yield-curve chart is used to justify either staying in cash or extending maturity.

Start with cash flows, not the slope of the chart

Assume the same currency, the same credit quality and zero-coupon instruments held to maturity. Rates compound annually; dates are exactly one and two years away. There are no taxes, fees, defaults or bid–ask spreads. These are invented inputs for calculation, not current market quotations.

Investing 10,000 for two years at 3.5% produces 10,000 × 1.035² = 10,712.25. Investing for one year at 4% produces 10,400. The second investment must turn that 10,400 into 10,712.25. Therefore the one-year rate starting one year from today is:

f₁,₂ = 1.035² ÷ 1.04 − 1 = 3.0024038…%

Subtracting 4% from 3.5% gives a slope of minus 0.5 percentage points, not the forward rate. Nor is 3.5% simply the arithmetic average of the two one-year rates: the first year’s interest is reinvested.

The rate you lock today and the rate you discover next year are different

A forward fixes terms now for a future period. Rolling a one-year holding without a hedge leaves that future rate unknown. The two choices have different risk even when the initial curve makes their projected proceeds look identical.

The 25-cent shortfall at 3% is rounding, not a market inefficiency. A realized second-year rate above the unrounded hurdle makes the rolling strategy outperform in this example; a lower rate makes it underperform. That comparison does not require a forecast. It tells you what forecast would have to prove correct.

If the money is needed after one year, however, the comparison no longer holds. The two-year instrument would have to be sold before maturity at an unknown price. Matching the horizon is essential: certainty of the maturity payment is not certainty of the resale value.

Discount factors reveal the financing behind the formula

Let P(0,T) be today’s price of one unit paid at date T. Here P(0,1) = 1/1.04 = 0.96153846 and P(0,2) = 1/1.035² = 0.93351070. For a one-year future interval, 1 + f₁,₂ = P(0,1)/P(0,2).

A synthetic forward loan makes the economics tangible. Buy a claim paying 10,000 in year one for 9,615.38 today. Finance that purchase with a two-year borrowing whose single repayment is 10,300.24. Initial cash flows offset; the remaining schedule is a receipt of 10,000 in year one and repayment of 10,300.24 in year two. The implied interest is approximately 3.0024%.

This replication assumes borrowing and investing are available on the same curve. A household deposit and an unsecured corporate loan do not meet that condition. Funding spreads, collateral and transaction costs can prevent the theoretical schedule from being executable. A calculated forward is therefore not automatically a quote you can trade.

Why an implied rate is not a policy forecast

Bond prices reflect expectations, but also compensation for bearing interest-rate risk and the supply and demand for particular maturities. Central-bank term-structure models try to separate expected short rates from term premia; that separation is model-dependent, not another observable price on the screen. Liquidity and credit differences can add further distortions when instruments are mixed.

Even an overnight-indexed swap curve needs careful interpretation. A rate covering an interval is not necessarily the policy rate immediately after a particular central-bank meeting. Mapping it into a meeting outcome requires the instrument’s averaging or compounding rules, calendar and assumptions about other possible rate paths.

The same interpretive problem appears in breakeven inflation rates: a market-implied number can be useful without being a pure forecast. The question is what else is priced into the instruments used to construct it.

A forward rate can rise while the short spot rate falls

Keep the two-year spot rate at 3.5%, but lower the one-year spot rate from 4% to 3.75%. The second-year implied rate becomes 1.035²/1.0375 − 1 = 3.2506%. It rises by roughly 24.82 basis points even though the one-year rate has fallen by 25 basis points.

There is no contradiction: with the two-year compounded return unchanged, a smaller return in year one must be offset by a larger implied return in year two. This is a controlled arithmetic comparison, not a prediction of how an actual market would respond to a rate cut. Reading a forward move without checking both ends of its interval can reverse the economic story.

Check the quote, then calculate the decision threshold

1. Identify the contract and horizon. Record currency, issuer or collateral basis, start date and end date. Do not substitute a coupon bond’s yield to maturity for a zero-coupon spot rate.
2. Check conventions. The example uses annual compounding. For continuously compounded zero rates, the interval rate is (z₂T₂ − z₁T₁)/(T₂ − T₁). A simple-interest quote instead uses [P(0,T₁)/P(0,T₂) − 1]/δ, with the contractual year fraction δ.
3. Distinguish an interval from a point. The Bank of England’s published forward curve is instantaneous and continuously compounded. Its point at two years is not the same object as a one-year investment starting in two years. Convert conventions before comparing numbers.
4. Use net cash flows. If rolling alone incurs a fee of 20 at the start of year two, only 10,380 is reinvested. Matching 10,712.25 then requires 10,712.25/10,380 − 1 = about 3.2009%, not 3.0024%. Include any costs on the long alternative too.
5. Write down what would overturn the conclusion. A changed funding spread, early withdrawal, different tax treatment or a second-year rate below the net hurdle can change the ranking. Update the comparison when those inputs change.

The defensible conclusion is narrow and useful: today’s curve supplies a break-even reinvestment rate under specified assumptions. It does not settle which strategy will win, and it does not convert a bond-market price into certainty about the central bank.