Bond Positions, Expectations, and the Yield Curve

Abstract

Abstract: This paper implements a structural model of the yield curve with data on nominal positions and survey forecasts. Bond prices are characterized in terms of investors' current portfolio holdings as well as their subjective beliefs about future bond payoffs. Risk premia measured by an econometrician vary because of changes in investors' subjective risk premia that are identified from portfolios and subjective beliefs but also because subjective beliefs differ from those of the econometrician. The main result is that investors' systematic forecast errors are an important source of business cycle variation in measured risk premia. By contrast, subjective risk premia move less and more slowly over time. JEL classification: E4, E5, G1 Key words: expectations, surveys, interest rates, portfolio choice, asset positions, term structure, yield curve Working Paper 2008-2 January 2008 I Introduction There is a large literature that tries to understand the dynamics of the yield curve through the behavior of optimizing investors. For example, consumption-based asset pricing models start from the fact that, when investors optimize, bond prices can be expressed in terms of investors' beliefs about future asset values and consumption. Model-implied bond prices then consist of expected discounted future bond payoffs, minus a risk premium that depends on the covariance of future bond returns with consumption. Empirical implementation of this idea requires the modeler to postulate a probability distribution that represents investor beliefs. In practice, this distribution is typically supplied by a stochastic process of asset values and consumption, often constrained by cross- equation restrictions implied by the economic model. This paper proposes an alternative approach to implement a structural model of the yield curve. We start from the fact that, when investors optimize, the prices of bonds can be expressed in terms of the distribution of their future payoffs together with current realized investor asset positions. We construct measures of both objects, using survey expectations of yields as well as data on outstanding nominal assets in the US economy. Model-implied bond prices again depend on expected payoffs minus risk premia, where the latter are identified from beliefs and portfolio holdings. Our model allows for three sources of time variation in expected excess bond returns measured by an econometrician. First, there is time variation in the subjective volatility of investors' consumption growth (or their return on wealth), which we identify from portfolio data. Second, there is time variation in the conditional covariance of bond returns with investors' continuation utility (or investment opportunities), a property of investors' subjective belief. Finally, risk premia measured by an econometrician can vary over time if investors' subjective beliefs do not agree with those of the econometrician. The main result of this paper is that, at least in the model we consider, this third source of time variation in measured expected excess returns is the most important one. We consider a group of investors who share the same Epstein-Zin preferences and hold the same subjective beliefs about future asset payoffs. Our analysis proceeds in four steps. First, we estimate investors' beliefs about future asset values, combining statistical analysis and survey forecast evidence. Second, we produce a measure of investor asset positions, using quantity data from the Flow of Funds accounts and the CRSP Treasury database. Third, we work out investors' savings and portfolio choice problem given beliefs to derive asset demand, for every period in our sample. Finally, we find equilibrium asset prices by setting asset demand equal to investors' observed asset holdings in the data. We thus arrive at a sequence of model-implied bond prices of the same length as the sample. …