Preferred-habitat theory is the view that investor clienteles favor specific bond maturities, so demand shocks local to one maturity move its interest rate. When the US Treasury announced long-bond buybacks in January 2000, thirty-year yields fell 58bps within three weeks while two-year yields rose 9bps. In Vayanos and Vila's "A Preferred-Habitat Model of the Term Structure of Interest Rates" (2021), the Fama-Bliss coefficient spans zero to one. It is zero when arbitrageurs are risk neutral and one when they are infinitely risk averse, in the one-factor model.
What the Study Found
The one-factor Fama-Bliss coefficient is γFB = (κr − κr)/κr > 0, and adding a demand factor lets it exceed one. A unit short-rate shock raises the forward rate for maturity τ by e^(−κ*r τ). The expected short rate at that horizon rises by the larger e^(−κr τ). In a numerical two-factor example, the first principal component explains 94.61% of return variation and is flat across maturities. Short-rate shocks explain 99.92% of variation for the one-year bond but only 4.79% for the thirty-year bond.
"We show that the preferred-habitat view of the term structure generates a rich set of implications for bond risk premia, the effects of demand shocks and of shocks to short-rate expectations, the economic role of carry trades, and the transmission of monetary policy."
Vayanos and Vila (2021), A Preferred-Habitat Model of the Term Structure of Interest Rates, abstract of the 2009 NBER working-paper version.
Methodology
The paper is a theoretical model, not an empirical study, so it uses no dataset, sample, or time period. The short rate follows an exogenous Ornstein-Uhlenbeck process, and each clientele demands only the zero-coupon bond matching its maturity. Arbitrageurs trade every maturity and maximize a mean-variance objective over instantaneous wealth changes, with risk-aversion coefficient a. This page summarizes the November 2009 NBER working-paper version (No. 15487), the full text on file.
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| Thirty-year yield change, 2000 buyback | −58bps | Within three weeks of the January 2000 announcement |
| Five-year and two-year yield change | −9bps and +9bps | Same window; effect confined to long maturities |
| Buyback program scale | 45 reverse auctions, average 14% of each targeted issue | March 2000 to April 2002, maturities 10 to 27 years |
| Fama-Bliss coefficient (one-factor) | γFB = (κr − κr)/κr > 0 | Proposition 2, Δτ → 0 |
| Forward-rate response to short-rate shock | e^(−κ*r τ) < e^(−κr τ) | Proposition 3; forward rates under-react |
| First principal component, two-factor example | 94.61% of variation | Flat across maturities; equals 0.44rt + βt |
| Short-rate share of return variation | 99.92%, 92.20%, 65.22%, 18.50%, 4.79% | One-, five-, ten-, twenty- and thirty-year bonds |
| Demand decrease, three-factor example | Forward rates rise up to seven years (ks), three years and longer (kℓ) | Shocks at five and twenty years; effect more local than in two-factor model |
| Preferred-habitat demand | yt,τ = α(τ)τ(Rt,τ − βt,τ) | Eq. (4); demand rises linearly in the bond's yield |
| Risk-neutral mean reversion | κ*r = κr + aσr² ∫ α(τ)Ar(τ)² dτ | Proposition 1; κ*r > κr whenever a > 0 |
Low vs High Arbitrageur Risk Aversion
| Measure | Low risk aversion (a ≈ 0) | High risk aversion (a ≈ ∞) |
|---|---|---|
| Demand-shock location affects | Magnitude only | Magnitude and relative effect across maturities |
| Short-rate shock, long forward rates | Same direction, A′r(τ) ≈ e^(−κr τ) | Opposite direction (Corollary 2) |
| Campbell-Shiller γCS | Close to one, increasing in τ | Can be negative, decreasing in τ |
| One-factor Fama-Bliss γFB | Zero when risk neutral | One when infinitely risk averse |
Why This Matters
The model explains how central-bank bond purchases or Treasury issuance can move long yields without changing expected short rates. Short-rate policy reaches long maturities through arbitrageurs' carry trades, so its pass-through weakens when arbitrageur capital is scarce. In those conditions, buying long-term bonds directly may influence long rates more than moving the short rate. A steeper curve caused by weaker bond demand predicts larger premia than one caused by a falling short rate.