Yield curve theories

M7.03 §4.10 already introduced, by name and in narrative form, the three classic explanations for why the curve is shaped the way it is: the expectations hypothesis, liquidity-preference theory (Hicks), and market-segmentation/preferred-habitat theory (Modigliani–Sutch). That module decomposed a long spot yield into an expected-future-short-rate piece plus a term premium. This module extends the identical logic to the forward rate you just derived, because a forward rate is precisely where the three theories make their sharpest, most testable claims.

• Pure expectations hypothesis. The forward rate is exactly the market's expected future short rate for that period, with no premium at all: f(m₁, m₂) = E[s(m₁, m₂)]. Under this theory alone, a rising forward curve is a pure, literal forecast that short rates will rise, and nothing else is going on.
• Liquidity-premium theory. The forward rate embeds the expected future short rate plus a premium that compensates investors for the extra interest-rate risk of committing further out: f(m₁, m₂) = E[s(m₁, m₂)] + φ(m₂ − m₁), where φ is typically positive and increasing in how far out the forward period sits. This is the quantitative form of M7.03's term premium, and it is why a forward curve can rise even when the market genuinely expects flat short rates, the rise can be pure premium, pure expectation, or (almost always, in practice) some blend of both, and a forward rate alone cannot tell you which without an independent premium estimate.
• Market-segmentation / preferred-habitat theory. This theory denies that any single expectations-plus-premium equation need hold at all. Different investor classes have structural mandates that confine them to specific maturity "habitats", banks and money-market funds cluster at the short end, insurers and pension funds are required to hold long-duration paper to match long liabilities, and the rate in each habitat is set by the supply and demand within that habitat, not by any economy-wide forecast. A persistent spread that never fully arbitrages away, even though nothing about credit risk has changed, is this theory's signature. State Development Loans (SDLs) are the clean India illustration: SDLs typically trade at a spread over the G-Sec curve of matching maturity, order-of-magnitude tens of basis points, and meaningfully regime- and state-dependent, so verify current levels rather than anchoring on any single figure, driven in real part by captive, mandate-constrained demand (insurers and provident/pension funds with statutory or prudential incentives to hold specific paper) that does not costlessly reallocate into G-Secs just because the spread looks generous. That is preferred-habitat operating in real time, not a pure credit-risk story (SDLs are not risk-free, but the spread is wider and stickier than a pure default-risk read would predict).

Which theory should you use to read a forward curve?

No single theory is "the" answer, professionals read a forward curve as a blend of all three, and the honest position (M7.03's own closing discipline, extended here) is to name which piece of a given forward-rate move you can actually attribute to expectations versus premium versus habitat-driven supply/demand, rather than defaulting to the pure-expectations read because it is the simplest one.