Tim Iacono very aptly titles a post about the much-discussed "liquidity" in world markets, Hard to Define and Measure. I have long thought the notion of liquidity was ill-defined and under-theorized. Never fear, because, as usual, I have *the answer!*

In loose talk, liquidity usually has something to do with the quantity or availability of money. From this perspective, liquidity means a high monetary base, low interest rates, and/or easy access to credit for prospective borrowers. The academic literature usually operationalizes liquidity in terms of the bid-ask spread and price impact. In a liquid market, the bid-ask spread is narrow, and price-impact small. (Price impact refers to the amount prices change disadvantageously when one attempts to buy or sell a commodity.)

My proposal is that liquidity should be defined very simply as *certainty of valuation of an asset with reference to some currency or commodity*. An asset whose value in dollar terms is 100% certain is perfectly liquid in dollars. An asset whose value is completely random or unknown would be perfectly illiquid in dollars.

This definition maps very nicely to the academic stand-ins for liquidity. One needs only assume the usual no arbitrage condition to see this. Suppose there were a market (in dollars) for $10 bills. The dollar value of a $10 is trivially certain. What would the bid-ask spread be in this market? If a market maker could consistently sell ten dollar bills for $10.001 or buy ten dollar bills for $9.999, the market-maker could make infinite, risk free profit by doing so in volume. The bid-ask spread on $10 bills must quickly converge to zero to prevent a tear in the fabric of the financial universe. Similarly, suppose I have a zillion $10 bills to sell. Will the price move against me? In a world without informational frictions or transaction costs, no. If some market shyster, seeing that I'm desperate to sell, offers only $9.999 a piece, some other entrepreneur, eying a perfect arbitrage, will quickly offer $9.9995, until the price converges to $10 nearly instantaneously. You can see all of this in action in the real world. If you ask to "sell" a ten-spot (that is to make change) most store owners will buy it for you for precisely 10 one dollar bills. If you have a hundred thousand tens, a bank will purchase that truck-load for one million dollars. (This sort of purchase is called a "deposit".)

The relationship between an informational definition of liquidity and the popular notion of "lots of money sloshing around" is more subtle, but very much worth teasing out. In addition to requiring the no arbitrage condition, we'll make two additional assumptions. We'll presume that as the quantity of a currency increases, so too do transaction volumes in that currency. (This is equivalent to the conventional monetarist assumption that money velocity is resistant to change.) We'll also presume that market transaction prices vary continuously, and that the rate at which prices change over short periods of time is bounded and not sensitive to changes in the quantity of money. Under these assumptions, an increase in the availability of money also leads to an increase in informational liquidity. Why? Because given a current price, a prospective buyer or seller of an asset is fairly certain as to a near-future realizable price, since transactions are frequent and the rate at which prices change is bounded. A current price represents a fairly certain near future value in the currency at issue. From an informational perspective, it's not the extra money that represents the liquidity, but the frequent, near-continuous transactions provoked by the ready availability of the currency. I like to think of the sort of liquidity caused by extra money as "sample rate liquidity", in that it decreases the uncertainty of valuation by increasing the sample rate of the fluctuating values.

I think that an information definition of liquidity can be made precise, and that many fruitful avenues for research that could be derived from it. If one assumes that markets are efficient, and that market prices reflect but do not alter the value of underlying assets, one can consider transactions to be samples of a noisy signal. Each trade price represents a sample, and the size of the trade is a measure of sample accuracy. From signal theory we know that for any signal whose maximum frequency in the Fourier transform is bounded, there is a sample rate that is sufficient to reconstruct the signal perfectly, such that further sampling would be pointless. If one views financial markets as decision-making institutions, devices whereby economies tease out information about the true value of potential enterprises and investors then devote scarce resources to the most useful, then a bound on the liquidity required to fully value an asset over time represents a bound on useful liquidity. If one also presumes the existence of "noise traders", entities who engage in transactions for reasons detached from a valuation of the asset being traded, and presumes that noise trading is sensitive to money availability, a bound on informationally useful liquidity should become a normative bound to central banks or other currency issuers, as increases in the availability of a currency beyond this bound increases noise without contributing to asset valuation, increasing the likelihood that an economy will devote scarce resources to erroneously valued projects. Similarly, insufficient "sampling rate liquidity" could lead to "aliasing", where the underlying signal and its sampled reconstruction may bear little resemblence to one another. Between aliasing and noise-trading, there should be an informationally optimal level of "sample rate liquidity", and potentially an informationally optimal level of money and credit for a given stock of tradable assets and a maximum frequency of "real" value fluctuations.

There is much more to go from here. Suppose, counter to our assumption above, the rate at which prices fluctuate is in fact sensitive to the quantity of money and credit availabilty. Then conventional measures of liquidity, like the bid-ask spread, might either expand or decline in response to increased money, depending on a race between the increased slope of the price time-series and the increase in the frequency of transactions. In either case, this is a bad situation, as increased market activity, rather than more precisely valuing resources is simply decreasing the precision which with resources can be valued. I think a real world analysis would show that the effect of money and credit are non-uniform, that there are times and circumstances where additional money is likely to improve the informational resolution of markets, and times when it is likely to magnify noise, and that with a bit of effort, theoretical and empirical, these regions could be usefully characterized. I don't think Taylor-rule-style monetary regimes even begin to capture this dynamic. Readers of this blog will be unsurprised to know that I think we are presently in a region wherein "lots-of-money-sloshing-around" is creating the appearance of liquidity (narrower spreads, less price impact) without the *sine qua non* of genuine liquidity: additional information or certainty about the real-economic value of the assets being exchanged and priced.

Steve Randy Waldman — Wednesday January 10, 2007 at 9:38pm | permalink |