Pricing a Global Measure of Liquidity Risk

Most of us are not willing to bear risk without compensation. For a long time, return volatility has been almost synonymous with financial risk, but now we know that this is not the only consideration. For instance, when we have an asset in our portfolio, no matter how volatile it is, we would like to be in a position to sell it at any time without incurring high penalties. We prefer assets for which we will always be able to get our money back if we suddenly need it or if the market experiences a downturn. Thus, it makes good sense to think that investors will require a relatively higher expected return if the asset they are holding is illiquid, i.e., difficult to trade.

Robert A. Korajczyk (Finance Department, Kellogg School of Management) and Ronnie Sadka (University of Washington; graduate of the Kellogg School’s finance doctoral program) provide statistical evidence supporting this intuitive idea in a paper forthcoming in the Journal of Financial Economics.

While the concept of liquidity is straightforward, many approaches have been followed for measuring it. For example, the volume of trade is clearly related to liquidity. Also, it is easy to realize that if you want to buy a stock at a given time, you have to be willing to pay a bit more than the sum you can pocket by selling the same asset at the same moment. This phenomenon is referred to as the bid-ask spread and represents a cost one must bear to carry out an immediate trade. The larger the spread, the more problematic trading becomes. Suppose one follows a certain strategy that requires frequently rebalancing a portfolio. High transaction costs of the type described above are a barrier to the profitable implementation of such a financial strategy. This is why we can consider the bid-ask spread as a measure of liquidity as it gives a sense of which cost one needs to bear to trade equity. It is no surprise that an investor may require a higher return to put her money on a share that may be costly to sell.

But what is the most correct measure of liquidity? That is a tough question, as both of the economic variables described above are good candidates, and they are not the only ones. Different measures of liquidity have been shown to have an impact on average returns. But, are there many liquidity premia—possibly one for every variable—or are we simply measuring the same phenomenon in different ways?

Such a question is important to understanding whether the conclusion that illiquid assets yield higher returns is supported by empirical evidence and if it can be relied upon for trading purposes. If instead this hinged on ad hoc measures of liquidity, one could wonder how sensitive the result is to the researcher’s choice of measure.

Korajczyk and Sadka propose an answer: a global measure of liquidity risk, which they studied while constructing monthly series on 4,055 common stocks traded between 1983 and 2000 in the New York Stock Exchange, and aggregating eight different measures of liquidity commonly used in this strand of the literature. The first four include:

• The average of the daily return (in absolute value) divided by the dollar volume.
• Turnover measured as the ratio of volume to shares outstanding.
• Quoted percentage spread, measured for each trade as the ratio of the quoted bid-ask spread to the bid-ask midpoint. The series is then averaged through the month for every stock.
• Effective percentage half-spread, measured for each transaction as the absolute value of the difference between the transaction price and the quote midpoint, divided by the bid-ask midpoint. Figures are then averaged through the month for every stock.

The next four measures are components of “price impact”, i.e. the reaction of transaction price to trading, obtained from a regression based on an extension by Sadka (2006) of a methodology devised by Glosten and Harris (1988):

• Permanent variable (correlated to traded volume) component of price impact.
• Transitory variable (correlated to traded volume) component of price impact.
• Permanent fixed component of price impact.
• Transitory fixed component of price impact.

Figure 1 shows the variable (λ_GH, the slope of the line labelled “Glosten-Harris”) and fixed (ψ, a discrete price change unrelated to the size of the trade) price impacts in a simplified diagram that plots change in stock price as a result of trading (Δp) against volume traded (q). Additional information about prices enables the authors to further decompose these price impacts into transitory and permanent. The proportionate transaction costs include quoted and effective spreads.

Figure 1:

Korajczyk and Sadka extracted the common, systematic components of liquidity by using a special form of factor decomposition. Following a standard approach in finance, they investigated separately the liquidity shocks that are common to the entire market and those that pertain to specific stocks and hence can be easily hedged by investing in a well-diversified portfolio. In fact, asset-pricing theory suggests that only the former should command a premium.

Korajczyk and Sadka find that most liquidity measures impact a broad array of assets in a common and long-lasting fashion, which suggests that they could really affect prices.

To assess to which extent liquidity affects returns, they considered the most widely used models in finance and introduced a liquidity factor. For instance, Fama and French (1993) found that large firms (in terms of market capitalization) earn, other things equal, lower returns than so-called small caps. The correlation of a single asset’s return with market returns, as represented by major stock indexes, is also another key ingredient to explain differences in various equities performance.

The idea is to see whether liquidity can add something to these generally accepted asset-pricing models. Supporting the claim of Korajczyk and Sadka, the data suggest that liquidity is, indeed, a driving force of the observed share returns. This, however, is not a novel concept. Their original contribution relies in addressing whether the eight measures of liquidity they use have an impact when considered in isolation or whether they have what might be called a “joint effect.”

The result is that the synthetic measure of liquidity they employ helps explain return patterns and at the same time seems to correctly and thoroughly sum up all the relevant information that the eight single variables contribute.

Thus one could say that the simple measures of liquidity, like the bid-ask spread, are all approximations to the true underlying liquidity factor that the statistical framework Korajczyk and Sadka developed singles out.

The main message is that liquidity affects assets and should not be overlooked by the practitioner or private investor. In fact, as is often the case in finance, one faces a trade-off between risk and return.

Further reading:

Fama, Eugene F. and Kenneth R. French (1993). “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics, 33(1): 3-56.

Glosten, Lawrence R. and Lawrence E. Harris (1988). “Estimating the Components of the Bid/Ask Spread.” Journal of Financial Economics, 21(1): 123–142.

Sadka, Ronnie (2006). “Momentum and Post-earnings-announcement Drift Anomalies: The Role of Liquidity Risk.” Journal of Financial Economics, 80(2): 309-349.