Why Supply and Demand Move the Yield Curve: Vayanos and Vila

Classical term structure theory contains a claim that, once you notice it, is quite hard to swallow.

It says the yield on a thirty-year bond depends only on expected future short rates and a risk premium. It does not depend on how many thirty-year bonds exist. It does not depend on whether pension funds are desperate to buy them. If the government suddenly issued a trillion dollars of thirty-year bonds, the theory says the thirty-year yield need not move, because bonds are all substitutes for one another and arbitrageurs will simply reshuffle.

Anyone who has worked in a bond market knows this is not how it feels. Supply matters. Demand matters. When a central bank buys hundreds of billions of long bonds, long yields fall. When an index rebalances, particular maturities go bid. The market behaves as though who wants what, and how much of it exists, is a first-order determinant of prices.

Dimitri Vayanos and Jean-Luc Vila wrote the model that makes that intuition rigorous. The working paper circulated for over a decade before its 2021 publication in Econometrica, and in the meantime it quietly became the intellectual foundation of quantitative easing.

The problem: the theory forbids what the market obviously does

The old idea that investors have a preferred habitat, a maturity they want for institutional reasons and will not readily leave, goes back to Modigliani and Sutch in the 1960s. Pension funds and life insurers have liabilities stretching decades out, so they want long bonds. Money market funds want very short paper. Banks want the middle.

It is an appealing story, but as economics it was incomplete. It described a preference. It did not explain how that preference turns into a price, and it did not explain why arbitrageurs, who supposedly stand ready to exploit any mispricing, do not simply flatten out the effect and restore the classical answer.

That is the gap: you need both habitat investors and arbitrageurs, and you need the arbitrageurs to be limited. Otherwise the model either has no price effects at all (unlimited arbitrage) or no discipline at all (no arbitrage).

The key idea via analogy: a sponge and a limited number of buckets

Vayanos and Vila populate their world with two kinds of participant.

The habitat investors. These are the pension fund that must own thirty-year bonds because it owes pensions in thirty years, the money fund that must own three-month paper, the insurer with a duration target. They are not price-insensitive fanatics, but they are sticky: they will demand more of their preferred maturity than of others, and they will not happily swap into a different part of the curve just because it looks slightly cheap. When their demand shifts, or when the government issues more of a particular maturity, they create localised pressure at one point on the curve.

The arbitrageurs. These are the hedge funds and dealer desks who will move across maturities to exploit a mispricing. They are the ones who are supposed to enforce the classical answer.

The crucial ingredient is that the arbitrageurs are risk-averse and finite. They do not have infinite balance sheets. Taking a position means bearing interest rate risk, and the more they take on, the more risk they carry and the more compensation they demand.

Here is the analogy. Think of the yield curve as a taut sheet. Habitat investors press down on it at particular points: a pension fund pressing at thirty years, a money fund pressing at three months. In the classical world, arbitrageurs are an infinitely stiff frame: press anywhere and nothing deforms. In Vayanos and Vila's world, the frame has give. Press hard at thirty years and the sheet dimples there, and, crucially, because the sheet is connected, the dimple spreads to the neighbouring maturities as arbitrageurs partially, but only partially, smooth it out.

That gives you both halves of what you want. Supply and demand have local effects (a shock at thirty years hits thirty-year yields most). But the arbitrageurs transmit those effects along the curve (it also moves the twenty-year and the ten-year, less so). Neither pure segmentation (where each maturity is an island) nor pure classical theory (where the curve is rigid) gets this right. The model does.

The same machinery explains how a shock to the short rate propagates to long rates: it does so through the arbitrageurs' carry trades, and the strength of that transmission depends on how much risk they are willing to bear. If arbitrage capital is scarce or arbitrageurs are frightened, the link between short rates and long rates weakens, and the curve becomes more susceptible to local supply and demand.

Why it mattered

• It is the theory behind quantitative easing. When a central bank buys long-dated government bonds, it is acting as an enormous habitat investor, removing duration risk from the market. In the classical model this should do essentially nothing to yields, which would make QE pointless. In the Vayanos-Vila model it lowers long yields, and by an amount that depends on how much duration is removed and how constrained the arbitrageurs are. Central banks needed a coherent account of why their flagship policy should work at all, and this is it.
• It legitimised "bond supply matters." A whole empirical literature (Greenwood and Vayanos on bond supply and returns, Krishnamurthy and Vissing-Jorgensen on the demand for Treasuries, the work on the scarcity value of safe assets) sits on this theoretical foundation. Debt management by treasuries, how much long versus short paper to issue, becomes a policy lever with real consequences for yields.
• It gives limited arbitrage a formal role in rates. The idea that arbitrageurs have finite capacity, and that markets are therefore not perfectly efficient, was well developed in equities. Vayanos and Vila built it properly into the term structure, and it explains a great deal that the frictionless models cannot: why particular maturities trade special, why the curve dislocates in a crisis, why yields can move on flow.
• It generates an underreaction result. Their calibration indicates that long rates underreact to forward guidance announcements about future short rates, relative to what a frictionless model would predict. That is a testable, policy-relevant implication with immediate practical bite for central bank communication.
• It reconciles theory with what practitioners always believed. Every bond trader knew supply and demand move yields. This paper is why they can now say so in a seminar without being corrected.

The honest limitations

• The habitat demand is assumed, not explained. The model takes it as given that certain investors want certain maturities. Where does that preference come from? Regulation, accounting rules, liability structures, mandates: probably all of these, but the model does not derive it, it posits it. That is a real gap, and it means the model cannot tell you when habitat demand will shift.
• Calibration is genuinely hard. How risk-averse are the arbitrageurs? How much capital do they have? How sticky are the habitat investors? These are the parameters that determine the size of every effect the model predicts, and none of them is directly observable. Different plausible calibrations give quite different answers about how much a given QE programme should move yields, which is an uncomfortable position for a theory whose main use is evaluating QE.
• Measuring the effect of QE is a nightmare in practice. Central banks announce bond purchases precisely when the economy is deteriorating, which is also when long yields would be falling anyway. Disentangling the pure supply effect from the signal about future policy that the announcement also carries is extremely difficult, and the empirical estimates of QE's impact on yields span a wide range. The model says the effect exists; how big it is remains contested.
• It is a partial equilibrium story. The arbitrageurs' risk aversion and capital are exogenous. In reality, arbitrage capital is itself endogenous and pro-cyclical: it evaporates in crises, exactly when the model's predictions matter most. A model where the frame's stiffness is fixed cannot capture the moments when the frame collapses.
• The effects may be transitory. Even if a large purchase moves yields on impact, it is a separate question whether the effect persists once capital flows in to exploit it. The model's steady-state effects and its short-run effects are different things, and policy discussion frequently conflates them.
• It complicates every other model. If yields depend on supply and demand, then reading expectations out of the curve, the thing every central bank and every forecaster does, is even harder than Fama and Bliss and Campbell and Shiller had already made it. The curve is now a mixture of expectations, a risk premium, and whoever happened to be buying. That is a more honest picture and a much less usable one.

The one-line takeaway

Vayanos and Vila built the model where the yield curve is set by the tug-of-war between investors who need a specific maturity and arbitrageurs whose capacity to smooth things out is finite, which is why bond supply and demand move yields, and why quantitative easing works at all.