The Term Structures of Equity and Interest Rates

Empirical studies of asset pricing have uncovered a rich set of properties of the time series of aggregate stock market returns, of the term structure of interest rates and of the cross-section of stock returns. Average returns on the aggregate stock market are high relative to short-term interest rates. Relative to dividends, aggregate stock returns are highly volatile. They are also predictable; the return on the aggregate market in excess of the short-term interest rate is predictably high when the price-dividend ratio is low and predictably low when the price-dividend ratio is high. The term structure of interest rates on U.S. government bonds is upward sloping, and excess bond returns are predictable by yield spreads and by linear combinations of forward rates. In the cross-section, stocks with low ratios of price to fundamentals (value stocks) have higher returns than stocks with high ratios of price to fundamentals (growth stocks), despite the fact that they have lower covariance with aggregate stock returns. These facts together are inconsistent with popular benchmark models and therefore represent an important challenge for theoretical modeling of asset prices. While there are large literatures that study equity markets and bond markets separately, there is relatively little existing work that models both the time series and cross section of equity and bond markets simultaneously. In this project, we seek to explain the aggregate market, the cross-section of stock returns, and term structure facts within a single model. To do so, we combine elements of tightly parameterized models based on parsimonious assumptions about preferences and endowments (as in consumption-based equilibrium models of stock returns) and modern term structure models that specify the stochastic discount factor directly without reference to preferences and endowments. We assume that only risk arising from aggregate cash flows is priced directly, thus maintaining the strict discipline about the number and nature of priced factors imposed by the equilibrium approach. We determine the parameters of the cash flow processes based on data from the cash flows themselves. This modeling approach maintains the parsimony that is typical of equilibrium models. However, rather than specifying underlying preferences, we directly specify the stochastic discount factor as in the SDF approach. Our goal is to introduce a small but crucial amount of flexibility in order to explain the facts listed in the first paragraph. Understanding the linkages between equity and bond markets is crucial for modern investment managers. The existing literature others little guidance on the risk-return tradeoffs and resulting portfolio allocations for managers who operate in both markets. The goal of this project to take a first step to fill this gap. We will address questions that are of direct relevance for practitioners such as how changes in the shape of the bond term structure might affect growth stocks relative to value stocks.