We construct a general equilibrium model with incomplete markets and borrowing constraints, in order to study the term structure of real interest rates. Agents are subject to both aggregate and idiosyncratic income shocks, which latter may force them into early portfolio liquidation whilst in recession. We derive a closed-form equilibrium with limited agents heterogeneity (despite market incompleteness), which allows us to derive analytical expressions for bond prices and returns at any maturity. The desirability of bonds as liquidity makes the aggregate bond demand downward-sloping. One consequence of this is that a larger bond supply raises both the level and the slope of the yield curve.