Explaining the Magnitude of Liquidity Premia : The Roles of Return Predictability , Wealth Shocks and State-dependent Transaction Costs ∗

Constantinides (1986) documents how the impact of transaction costs on per-annum liquidity premia in the standard dynamic allocation problem with i.i. d. returns is an order of magnitude smaller than the cost rate itself. Recent papers form portfolios sorted on liquidity measures and find spreads in expected per-annum return that are the same order of magnitude as the transaction cost spread. When we allow returns to be predictable and we introduce wealth shocks calibrated to labor income, transactions costs are able to produce per-annum liquidity premia that are the same order of magnitude as the transaction cost spread. A number of recent papers have found a difference in expected return across portfolios sorted on liquidity measures. While the finding of a difference is not surprising, the magnitude is, with expected return differences on the order of 6-7% per annum.1 The magnitude of the difference seems too large to be explained by realistic transaction costs. In particular, the seminal work of Constantinides (1986) documents how investor utility is largely insensitive to transaction costs when the investor solves the canonical problem of i.i. d returns calibrated to U.S. data, no non-financial income, and a constant proportional cost rate. For realistic proportional costs, Constantinides shows that the per-annum liquidity premium that must be offered to induce an CRRA investor to hold the transaction-cost asset instead of an otherwise identical no-transaction-cost asset is an order of magnitude smaller than the transaction cost rate itself. Constantinides also provides the intuition for this result. Investors respond to transaction costs by turning over their portfolios much less frequently than annually, because an investor’s value function is insensitive to quite large deviations from the optimal no-transaction-cost portfolio allocation. Our paper bridges the gap between this theoretical result and the empirical magnitude of the liquidity premium by examining dynamic portfolio choice with transaction costs in a variety of more elaborate settings that move the problem closer to the one solved by real-world investors. In particular, we allow returns to be predictable and we introduce wealth shocks, mainly labor income but also stationary multiplicative. When returns are predictable, we also allow the wealth shocks and the transaction cost rate to be state dependent. We find that adding these real world complications to the canonical problem can cause transaction costs to produce per-annum liquidity premia that are no longer an order of magnitude smaller than the rate, but are instead the same order of magnitude. In particular, return predictability and i.i. d. labor income growth calibrated to U.S. data are sufficient to obtain per-annum liquidity premia of the same order of magnitude as the cost rate, for realistic wealth-income ratios. For this reason, our results provide an important new insight into the effect of transaction costs on investor behavior. In particular, the effect of proportional transaction costs on the standard consumption and portfolio allocation problem with i.i. d. returns can be materially altered by reasonable perturbations that bring the problem closer to the one investors are actually solving. Moreover, since our