Liquidity: considerations of a portfolio manager.

This paper examines liquidity and how it affects the behavior of portfolio managers, who account for a significant portion of trading in many assets. We define an asset to be perfectly liquid if a portfolio manager can trade the quantity she desires when she desires at a price not worse than the uninformed expected value. A portfolio manager is limited by both what she needs to attain and the ease with which she can attain it, making her sensitive to three dimensions of liquidity: price, timing, and quantity. Deviations from perfect liquidity in any of these dimensions impose shadow costs on the portfolio manager. By focusing on the trade-off between sacrificing on price and quantity instead of the canonical price-time trade-off the model yields several novel empirical implications. Understanding a portfolio manager's liquidity considerations provides important insights into the liquidity of many assets and asset classes.

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This paper examines liquidity and how it affects investor behavior, focusing on the considerations of a mutual fund portfolio manager. US mutual funds are the largest investor in US commercial paper with 47%, and they hold 35% of US tax-exempt debt, 27% of US equities, and about 10% of US corporate, Treasury, and agency debt (Investment Company Institute, 2008). Total mutual fund holdings worldwide equaled $26 trillion at year-end 2007. An understanding of the liquidity considerations of a portfolio manager therefore provides important insights into the liquidity of many assets and asset classes.

A portfolio manager seeks to optimize the performance of her portfolio relative to her performance benchmarks. In this pursuit, she is limited by both what she needs to attain and the ease with which she can attain it. This makes her sensitive to three dimensions of liquidity: price, timing, and quantity. Deviations from perfect liquidity in any of these dimensions impose shadow costs on the portfolio manager, making them key considerations in her portfolio decisions.

We define an asset to be perfectly liquid if a portfolio manager can trade the quantity she desires when she desires at a price not worse than the uninformed expected value. A few examples serve to motivate the three dimensions of liquidity and their shadow costs. Quantity may be the most important consideration for passive portfolio managers, such as those who are bound by prospectus to closely replicate an index. (1) As of year-end 2007, indexed assets equaled approximately 30% of the $4.85 trillion benchmarked to the Standard and Poor's (S&P) 500 Index (Journal of Indexes, 2005). Timing may be the most important consideration for portfolio managers liquidating asset holdings in response to significant mutual fund redemptions. Annual redemption rates have exceeded 25% each year over the past two decades and have been in excess of 50% (Investment Company Institute, 2008). (2) Price may be the most important consideration for active portfolio managers in pursuit of value.

Ours is a theoretical model with three risk-neutral agents, a liquidity provider, an informed trader, and an uninformed investor (the portfolio manager), all of whom are rational. The main innovation of our model is that we allow the uninformed investor to choose whether and how much to trade. In early papers on liquidity, Bagehot (1971) and Black (1971) describe liquidity as the trade-off between sacrificing on price and timing, assuming that a trader always trades her desired quantity. This assumption has been largely maintained in the subsequent theoretical literature, begun by Copeland and Galai (1983) and continued by Glosten and Milgrom (1985) and Easley and O'Hara (1987), with O'Hara (1995), for example, defining a liquid market as one that accommodates trading with the least effect on price. (3) Here we focus on the trade-off between sacrificing on price and quantity instead of the canonical price-time trade-off. (4)

We characterize when assets are and are not traded, allowing us to predict the extent of trading in primary and secondary markets, portfolio managers' trading patterns after stock splits, and trade-size clustering in response to changes in fund disclosure requirements. We find that bid-ask spreads for some quantities may be decreasing in the prevalence of informed traders, providing a novel explanation for the narrowing of spreads in response to increased hedge fund presence. Finally, we find that private information specific to an asset may be more valuable when portfolio managers have an intense desire to trade that asset. This provides a new interpretation of the well-documented effects of inclusion in the S&P 500 Index.