Portfolio Choice with Many Risky Assets, Market Clearing and Cash Flow Predictability

Abstract

This paper examines portfolio allocations and market clearing prices when the representative agent can allocate across equity portfolios formed on the basis of characteristics like size and book-to- market and portfolio cash flows are predictable. The state space is discrete and price-consumption ratios are obtained portfolio by portfolio simply by inverting an economy-wide matrix and multiplying this matrix by a portfolio-specific vector. The economy-wide matrix has the dimensionality of the state space. The paper calibrates cash flow predictability to the data using the consumption-wealth fraction (cay) of Lettau and Ludvigson (2000a) and dividend yield (div) as state variables. Annual cash flow processes are calibrated for three stock portfolios and for the aggregate consumption stream. The economy's representative agent possesses a relative risk aversion coefficient of either 5 or 10.

When cash flow predictability is calibrated to the data using cay as the predictor and risk aversion is 5, equilibrium excess returns on the four assets are more volatile, more correlated with each other, and have higher means than in the equivalent economy with i.i.d. cash flows. Further, the conditional second moments for returns and the contemporaneous state variable are found to be highly state-dependent. The paper finds much smaller excess return predictability using cay in the calibrated economy than in the data, though the relation is positive in both. Conditional Sharpe ratios are virtually invariant to state.

While the representative agent's optimal portfolio is not very state-dependent, her hedging demands are quite large and her optimal portfolio is not minimum-variance. For example, her single-period allocation to the four risky assets is about 75% of the portfolio while her infinite-horizon allocation is 100%. The implication is that the conditional CAPM does not hold in the conditional economy with cay as the state variable. However, the spread in CAPM abnormal returns across the three book-to-market portfolios is an order of magnitude smaller in the calibrated economies than in the data. The spread in the data in 5.6% p.a. while the largest spread in the six calibrated economies considered is only 0.6% p.a. Finally, the paper has important implications for partial equilibrium analyses of dynamic portfolio choice.