What a Term Structure Can—and Cannot—Tell You

The conclusion of this series is about how to use an equity-premium term structure without mistaking it for an observed market constant. The combined evidence supports a horizon-aware view: the compensation attached to equity cash flows can change with the date of payment, the firms or portfolios being compared, and the economic state in which the estimate is made. The practical judgment is not to replace one universal number with another, but to ask whether a quoted premium is the right object for the cash flows and risks under consideration.

A curve is a map of timed compensation

The most useful mental model is a chain rather than a number. Equity value is built from expected cash flows. Those cash flows arrive at different dates. Each date is discounted using a risk-free component and an equity-risk component. The equity-premium term structure is the schedule of those risk components across horizons. It is a map of how required compensation is assigned through time.

That map has three dimensions that should not be separated. The first is the horizon: how does compensation differ between near-term, intermediate, and distant cash flows? The second is the conditioning set: are we describing the aggregate market, a firm characteristic, an industry, or a particular economic state? The third is precision: how strongly does the evidence support each point on the curve? A long-horizon estimate with a narrow confidence band can deserve more weight than a short-end estimate that is largely extrapolated, even if the short end looks more dramatic.

The two estimation routes make different parts of this map visible. The New York Fed approach uses heterogeneous firm cash-flow forecasts and observed prices. It asks how a common but characteristic-sensitive discount curve can explain firms whose expected value arrives on different cash-flow clocks. The ECB approach uses one pricing kernel to price bonds and a broad stock index. It asks how the current state of inflation, payout yield, and real-rate factors changes expected excess stock returns at different horizons. One emphasizes cross-sectional composition; the other emphasizes state-dependent dynamics.

Neither route produces a direct meter reading of investors’ required return. The New York Fed curve is inferred after specifying how ROE, sales growth, and shareholder cash flow evolve, how long the transition to steady state takes, and how the curve is shaped. The ECB curve is inferred after specifying a four-factor state process, an affine pricing kernel, a reinvestment convention, and restrictions linking real and nominal assets. Those assumptions are not defects to be hidden. They are the mechanisms that make the otherwise unobservable curve estimable.

This is also why an aggregate upward slope can coexist with opposing curves below the aggregate. In the New York Fed benchmark, the 15-year premium is about 8.3% and the normalized 15-minus-5-year slope is about 7.5 percentage points. Yet the same study finds a slope near −4.2% for firms in the top book-to-market quartile and about −3.6% for speculative-grade firms after the relevant interaction is applied. These results do not say that the aggregate estimate is wrong. They say that the aggregate is a weighted combination of firms whose cash-flow timing and required compensation differ.

A simple aggregation example clarifies the point. Imagine a market made of two groups. Group A receives much of its expected value from cash flows in the next few years and has an upward-sloping curve. Group B depends more on distant outcomes and has a flat or inverted curve. If Group A is larger or receives more weight, the market curve can rise even while Group B’s curve falls. The market slope is then a statement about the weighted whole, not a rule governing every component. Changing the weights or the composition changes the object being summarized.

The same logic applies across time. The 2026 estimates become flatter in bad times: under the NBER recession classification, the normalized slope falls from roughly 7.5% in good times to 3.8% in bad times, and the 15-year premium falls from about 8.3% to 6.3%. The curve remains upward sloping because short and intermediate premia rise sharply while the long end falls only slightly. A market can therefore experience substantial stress without every horizon repricing in the same direction or by the same amount.

The affine evidence provides a complementary way to express this state dependence. Its conditional curve can be upward sloping, downward sloping, or hump-shaped depending on the current state, while unconditional expected stock returns are flat across horizons in the model. There is no contradiction between “the curve today” and “the average curve across states.” A current state can tilt the compensation schedule even when averaging over the stationary distribution removes that horizon difference in expected stock returns.

The central synthesis is therefore not that one method has found the one true shape.