Liquidity Premia and Transactions Costs

Abstract

Although transaction costs can alter optimal trading strategies significantly, standard literature (e.g., Constantinides (1986) among others) concludes that they only have a second-order effect on liquidity premia (i.e., the maximum expected return an investor is willing to exchange for a zero transaction cost). We show that this conclusion depends crucially on the assumption of a constant investment opportunity set. In a regime-switching setting where the investment opportunity set (such as expected return, volatility, and liquidity) varies stochastically, we explicitly characterize the optimal trading strategy in terms of two coupled ordinary differential equations with free boundaries; we prove a verification theorem for the obtained solution; and we provide an extensive analysis of the optimal trading strategy and liquidity premium. We find that contrary to the standard finding, transaction costs can have a first-order effect on liquidity premia. This result follows from a simple but fundamental intuition that if the investment opportunity set changes stochastically, the optimal stock investment target in the no-transaction-cost case also changes stochastically and an investor optimally rebalances more often to avoid being too far away from the moving target, which in turn results in the transaction cost having a greater effect. This result suggests that the presence of transaction costs can produce a significantly larger portion of the observed high risk premium than the literature on portfolio choice with a constant opportunity set and transaction costs indicates. However, we show that with reasonably calibrated parameters, the presence of transaction costs alone still cannot fully explain the magnitude of the equity premium puzzle, even when the investment opportunity set varies stochastically. Our new results follow from a simple but fundamental intuition that if the investment opportunity set changes stochastically, the optimal stock investment target in the absence of transaction costs also changes stochastically and as market conditions change an investor rebalances more often to avoid being too far away from the target if transaction cost rate is small and thus the relative impact of the transaction cost increases. This fundamental intuition also applies to the case where the investment opportunity set varies with a continuous state variable. Therefore jumps in the fundamental parameters in our model are not critical for our results and are employed only for tractability. Our model also has important implications for the resolution of the Equity-Premium Puzzle. We show that concerns over a potential liquidity crash, no matter how unlikely it is, can dramatically reduce investment in stock even when the current market is perfectly liquid and the expected excess return is high. Intuitively, an investor who has to liquidate her (leveraged) stock position in order to consume could risk insolvency when the market for the stock is illiquid. Thus, the sheer possibility of an unpredictable liquidity crash, no matter how small the probability is, would make leverage suboptimal no matter how high the equity premium is or how liquid the market is in normal circumstances. This suggests that the existence of liquidity risk may largely explain the Equity-Premium Puzzle. In contrast to the existing literature, this liquidity risk explanation does not require high risk aversion (e.g., Mehra and Prescott (1985)) or the separation of the risk aversion and the intertemporal rate of substitution (e.g., Epstein and Zin (1989)) or habit formation (e.g., Constantinides (1990)).