Ebook Transaction Cost Can Have A First-Order Effect on Liquidity Premium
Transaction costs are prevalent in almost all financial markets. Extensive research has been conducted on the optimal consumption and investment policy in the presence of transaction costs (e.g., Constantinides (1986), Davis and Norman (1990), Koo (1992a), Liu and Loewenstein (2002), Liu (2004)). As shown in these studies, the presence of transaction costs significantly changes the optimal consumption and optimal investment strategy. For example, an investor no longer trades continuously and even a small transaction cost can dramatically decrease the frequency of trading to save transaction costs.
However, the utility loss is found to be small by most of the existing literature. In particular, in his seminal paper Constantinides (1986) finds that the liquidity premium (i.e., the maximum expected return an investor is willing to give up in exchange for zero transaction cost) is small relative to the transaction cost, even for a suboptimal trading strategy and thus concludes that transaction costs are of second-order effect for asset pricing.
One of the common assumptions of the existing literature on optimal consumption and investment with transaction costs is that the investment opportunity set is constant. For example, Constantinides (1986), Davis and Norman (1990), Liu and Loewenstein (2002), and Liu (2004) all assume that not only the expected stock return, the return volatility but also the liquidity (transaction cost) are constant throughout the investment horizon. Intuitively, with a constant investment opportunity set, an investor does not need to trade much and thus the transaction costs incurred is small.
Empirical research, however, documented a great deal of evidence against the constant investment opportunity set hypothesis. For example, Campbell (1991) and Lewellen (2003) find that expected returns on equities change over time. Schwert (1989) and Campbell and Hentschel (1992) conclude the volatilities of stock returns also vary substantially over time. Fama and French (1988) and Poterba and Summers (1988) conclude that there is a mean reversion component in stock prices. In addition, large liquidity shock may also appear from time to time (e.g., 1987 crash, 1998 LTCM event).
Taking into account the stochastic nature of the investment opportunity set may qualitatively change the well-known conclusion of Constantinides (1986) that the transaction costs are of second-order effect. This conjecture follows from a simple intuition that if the investment opportunity set changes stochastically, an investor would need to rebalance more often and thus would incur higher transaction costs. Following this intuition, in this paper we build a model similar to Constantinides (1986) and Davis and Norman (1990), but with a regime switching for fundamental parameters that include expected return, volatility, and liquidity.
Specifically, we consider the optimal consumption and investment problem for a small investor (i.e., no price impact) who derives constant relative risk averse (CRRA) utility from intertemporal consumption and bequest. The investor can invest in one stock and one risk-free asset. In contrast to most of the existing literature, we assume that the investment opportunity set is not constant and there are two regimes with different fundamental parameters. One regime switches to the other regime at the first jump time of an independent, regime dependent Poisson process.
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