January 22, 2010 | Case Study

Liquidity in Three Dimensions

A new model reveals quantity to be as important a variable as price and time in investors’ optimal trading strategies.


Investors and market watchers have traditionally analyzed liquidity, or the overall ease with which assets can be traded, as a two-dimensional tradeoff between price and time: An investor either accepts a worse-than-desired price in order to trade a set quantity immediately, or she waits to execute the trade later at a better price.

But this canonical price-time tradeoff might not always offer the best approach to understanding liquidity, Professor Laurie Hodrick says. “The tradeoff might actually be between quantity and time. Or the tradeoff may be between quantity and price,” she says. In such instances, liquidity reflects not only the dimensions of price and time, but also quantity.

“We think of the mutual-fund portfolio manager as the archetypal investor, limited by both what she needs to attain and the ease with which she can attain it,” Hodrick explains. For example, timing will be a key consideration for a fund manager facing redemptions — when investors want to cash out shares. The manager will not necessarily sell a given set of assets at whatever price she can get — she will look at her portfolio and current market prices and, based on that, pick and choose what and how much to sell.

“Contrast that with the idea of ‘this exact amount of this exact asset is the amount I have to sell — no more, no less,’” Hodrick says. “Depending on how binding other constraints are, if the terms are bad enough a portfolio manager may not trade some assets at all. It may simply be that when she runs the optimization, her most rational course might be to not trade.”

For some types of investors, quantity may not be an important factor. For example, a value investor will be much more concerned with long-term value and price. But for others, quantity is a dominant consideration. Hodrick worked with Pamela Moulton, PhD ’03, of Fordham University to create a model of investor dynamics that incorporates quantity as a variable in asset trading.

“Our model explores a three-dimensional concept of liquidity: ‘I want it, I want it now, I want it at a good price,’” Hodrick says. The model yields new insights about liquidity and other considerations that all investors — from the sophisticated active portfolio manager to the relatively uninformed index-fund manager — take into account in their attempts to optimize their trades. “Things that looked funny under previous models now look very consistent with rational, maximizing behavior.”

Consider, for example, index reconstitution, which is wholly predictable because there is no asymmetric information — a portfolio manager is simply replicating an index of securities without regard to what he may know about the particular assets that make up the index. But even reconstitution creates important liquidity considerations for portfolio managers, who often trade illiquid securities in advance of reconstitution. This may cause tracking error (under- or over-performance compared with the index) because it produces variations that don’t perfectly replicate the index. “But the managers are anticipating what they need to trade, obtaining the desired quantity at what they regard as a good price,” Hodrick says. “This is a behavior that earlier models did not allow for.”

Including quantity as a decision variable illuminates how investors try to optimize their portfolios. “Changing one choice variable in the investor’s maximization can make you think differently about many things,” Hodrick says. “It affects everything and everyone. It changes how prices are set by market makers. The informed investor faces different prices because of the uninformed investor’s maximization. The equilibrium in the market as a whole can look very different.”

Laurie Simon Hodrick is the A. Barton Hepburn Professor of Economics in the Faculty of Business in the Finance and Economics Division at Columbia Business School.

Read the Research

Laurie Simon Hodrick, Pamela Moulton

"Liquidity: Considerations of a Portfolio Manager"

View abstract/citation  Download PDF  

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