Liquidity might come at cost: The role of heterogeneous preferences

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Highlights

  • Heterogeneous risk preferences indeed generate trade, but not monotonically.

  • Turnover and liquidity increase with heterogeneity to a maximum and then decline.

  • Higher liquidity increases share-redistribution and hence average RRA volatility.

  • Thus, liquidity is costly, as it increases Sharpe ratio and stock price volatility.

  • The model generates turnover levels comparable to real data, at reasonable RRAs.

Abstract

Asset-pricing models with volume are challenged by the high turnover-rates in real stock markets. We develop an asset-pricing framework with heterogeneous risk preferences and show that liquidity and turnover increase with heterogeneity to a maximum, and then decline. With U.S. parameters, turnover exceeds 55%. Liquidity is costly since it facilitates a large share redistribution across agents, causing changes in average risk aversion, which increases Sharpe ratio variability, and hence stock return volatility. Illiquidity and its risk are minimized at moderate heterogeneity levels, highlighting an "optimal" heterogeneity level, yet, there is no "optimal" combination between liquidity level and Sharpe ratio variability.

Section snippets

The economic setting

Assume a single bond and a single risky asset trade in frictionless financial markets under information symmetry. The riskless bond has a price Bt and it yields a constant rate of return r, following the process:dBt/Bt=rdt.

The risky asset is an open-ended mutual fund that holds the market portfolio of stocks. It is a claim on the aggregate dividend, Δ, generated by an exogenous process:dΔt/Δt=μΔdt+σΔdzt,where both μΔ and σΔ are given constants. The stock has an exogenously-given standard

The motivation to trade

This section is devoted to deriving optimal intertemporal trade by each investor type, aiming to express volume and liquidity in closed form. Bilateral trading volume emerges in our setup through agent heterogeneity, measured by the dispersion of RRAs about the market price of (variance) risk. The formal derivation is based on (20), where two mutually-exclusive optimal rebalancing strategies imply conditional buy or sell orders for shares; conditional on the direction of price change (see

The determinants of volume

These building blocks allow the exploration of the ways volume and liquidity vary with key parameters. Our first step is deriving closed-form expressions for optimal rebalancing of volume between t and t  +  dt by each investor type, C and T (henceforth, “trade plans”). Trade plans differ from bilateral volume, as the latter is the minimum between the two trade plans, in absolute terms.

Calibration and simulation procedures

In this section, we explain the procedures and parameters we use to construct the simulated markets. The simulations allow us to explore both time series and cross-sectional implications of heterogeneity. Unlike the previous analysis, here we construct the 16 RRA combinations (“markets”) by creating an RRA_factor, aiming to focus attention on less extreme RRA levels. The factor starts at 0.975 and declines 39 BPS from one combination to the next, until it equals 0.39. Because our RRAs must

Cross-sectional predictions for sharpe ratio variability

In this section, we return to the debate on the role that changes in heterogeneity play in causing variations in Sharpe ratio. We explore how the Sharpe ratio and its volatility vary along a cross-section of heterogeneity. In Xiouros and Zapatero (2010) and Chan and Kogan (2002), Sharpe ratio variability necessarily increases with heterogeneity, which is measured as the variance across agents' RRAs. Because we measure trade as the smaller (in absolute terms) between both trade plans, trade is

Cross-sectional predictions for turnover and liquidity

In this section, we explore how levels and volatilities of turnover and liquidity vary across levels of heterogeneity. All time-series simulations are conducted in a way similar to the previous analysis, except that in these analyses the averages and medians are measured across 100 sample paths of 250 periods in each market state. The results incorporate the market-specific σπT that was computed recursively until convergence. Prediction 4 explores the linkages between heterogeneity and market

Conclusions

In this paper, we analyze the extent to which heterogeneity motivates trade in an asset pricing model under information symmetry with time-separable, power utilities. Two uniquely defined investors have RRAs that bracket the market price of risk, where heterogeneity is measured by the dispersion between both RRAs. Investors’ optimal portfolio rules imply intertemporal bilateral trade, thus average RRA in the market changes stochastically, but is perfectly correlated with expected stock returns.

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    We thank Yakov Amihud, Gideon Saar (the Editor), Fernando Zapatero, and two anonymous referees for valuable suggestions and insights. We are indebted also to Zvi Afik, Doron Avramov, Scott Cederburg, David Feldman, Dan Galai, Arieh Gavious, Eugene Kandel, Michel Robe, Itzhak Venezia, and Zvi Wiener. We thank participants of the Midwest Economic Theory Conference, Lansing, MI, the Far Eastern Meeting of the Econometric Society, Beijing, and the Finance Department Research Seminar at the Hebrew University, Jerusalem. We assume full responsibility for any remaining errors. The opinions expressed in this article do not necessarily reflect the position of the Israel Securities Authority.

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