Friday, May 28, 2010

Fictitious liquidity

Now you see it; now you don’t

My last posting closed with “Neither liquidity nor transparency is a God, but there are aspects of both that are needed for markets to function.” Transparency was discussed in “The false God of transparency.” Now, it’s time to discuss liquidity. The definition is essential to understanding my use of “fictitious liquidity” in the posting on transparency. Further, it explains the rather counter intuitive reference to liquidity and volatility in the last posting. Since this is central to what has been said on this blog, this posting will address it in three ways: (1) textbook, (2) operational, and (3) practical.

For textbooks, let’s use INVESTMENT ANALYSIS AND PORTFOLIO MANAGEMENT by Frank K. Reilly and Keith C. Brown as an example. After all, it is the textbook used to train many Certified Financial Analysts (CFAs) who become market participants. After discussing information, it defines liquidity as “… the ability to buy or sell an asset quickly and at a known price….”

It then goes on to define “price continuity” as a component of liquidity. It’s at that point that the discussion of liquidity gets telling. So, here’s the definition of price continuity “…that prices do not change much from one transaction to the next unless there is substantial new information available.” By making price continuity a component of liquidity, it ducks the question of whether information about liquidity is “substantial.”

That, as it turns out, is rather essential to the discussion of what liquidity is. Add price continuity, and one is no longer dealing with a concept. One is dealing with an objective. More importantly, from a behavioral perspective, liquidity becomes self-referential.

It also ignores the fact that money, for numerating trades, is not continuous. Is it saying “same price” in dollars, pennies, fractions of a penny?

It does say next trade; thus, defining time as whatever the market determines. That raises some questions: Is an asset liquid if it trades freely at the same price, but infrequently? Seems to me it could be boring, but liquid, but it could also be illiquid. Is the boring asset more liquid than an asset that turns over repeatedly each day but bounces around? Seems to me the textbook definition is just saying that it depends on how fast it bounces. It ducks the issue of clock time. As a consequence, it falls into the trap of implying instantaneous liquidity is necessary to liquidity. Liquidity has to address the issue of “by when” (i.e., time). Otherwise, the definition seems to be of little practical use.

Don’t get me wrong. I’m not disparaging what can be accomplished with continuous, instantaneous assumptions. Newton did some amazing things that advanced physics by working out how to use those assumptions. Besides calculus is fun for me; it creates an alternative universe all of its own. It has also facilitated some interesting and vital advances in finance and economics. But, eventually, one has to deal with the operational and practical.

The texts also incorporate the concept of depth. But, at this point we are really proceeding to what I’ve called the operational. Not surprisingly, it’s at this point the definition does get more substantive.

There is liquidity as in large pools of capital participating in the market. To my way of thinking, adding “a large numbers of counterparties” to the definition of liquidity without defining a legitimate counterparty makes the definition partially conditional. There is always some liquidity based on counterparties dependent on hedges. That generates counterparties without necessarily expanding the capital pool. It increases volumes that can be supported, but the increased volumes are ultimately based on leverage (i.e., larger volumes on the same capital base).

Arbitraging forward curve is a familiar illustration, but any form of statistical arbitrage or hedging strategy could do just as well. They illustrate the consequences of this fictitious liquidity. If the markets disconnect, the liquidity based on the arb can increase as the arbs place positions, but it can disappear if the hedge that allowed the leverage fails. In short, if the hedges fail, the difference between real and fictional liquidity surfaces. Thus, volumes only indicate liquidity under very specific conditions (i.e., if the hedges work). If my belief that there is no perfect hedge is correct, then failure is inevitable. It is this liquidity that I refer to as fictitious liquidity.

So, you ask: “Why is it fictitious? Just because it can go away, doesn’t mean it wasn’t real while it existed.” The issue of liquidity based on arbitrage or hedging isn’t new. It’s been discussed in the literature on financial markets. Terms like borrowed liquidity (i.e., liquidity borrowed across markets), and aggregated liquidity (i.e., combining the liquidity of two or more markets) have been applied. It has been celebrated as one of the breakthroughs of modern finance, and justifiably so. It increases the liquidity of each individual market.

Hedging and arbitrage would actually produce multiplicative liquidity if total liquidity were the sum of individual market liquidities. But, total liquidity isn’t the sum of individual market liquidities. Total liquidity would then be a product of total market activity. This is totally circular reasoning: liquidity makes trading possible and trading defines liquidity. That may be OK since the phenomena itself may be self-referential. But, the circular definition is one argument for calling it fictitious liquidity.

The liquidity could as easily be called leveraged liquidity. But, here’s where things get weird; to the extent hedges work, they cancel each other out. However, we have not canceled the liquidities across the markets. We accept that the liquidity is there as long as we believe it is there. Lose faith and unwind the hedge, and it is gone. So, I like fictitious.

“This is all terminology; how does it contribute to volatility?” One should remember the question about whether changes in liquidity are substantive information. That is the answer to how the usually stabilizing impact of liquidity can be destabilizing. Volatility isn’t about levels; it’s about change.

Economists are use to quasi self-referential systems. We talk of virtuous cycles and vicious cycles. But, economists, especially modelers, know that a specification that is self-referential can lead to an unstable or explosive model. One seeks to avoid models where the change in a variable is dependent on the level of the same variable or the change in the same variable, much less where the change in the rate of change is dependent on the change. The modeling solution is to build in mean reversion in some form or avoid self-referential specifications totally. That, however, doesn’t negate the fact that, to the extent liquidity is, in fact, self-referential, it produces a tendency toward instability (i.e., produces volatility).

Economists aren’t alone in having to deal with self-referential systems. In math, think chaos theory and fractals. For a pop culture example, think TIPPING POINT; HOW LITTLE THINGS CAN MAKE A BIG DIFFERENCE by Malcolm Gladwell, although it mixes in non-linear systems. Many disciplines (demographics, engineering, physics, evolutionary biology) have concluded self-referential systems tend to be volatile. So, we shouldn’t be too surprised if financial economics finds an example.

Now, let’s turn to the practical. In a practical sense, time is essential. For practical purposes, liquidity is the ability to move between assets when one wants. The assets may include money, often the focus of discussions of liquidity. Being able to move to the medium of general exchange extends the definition to include moving between investment and consumption. But, let’s leave the consumption/investment decision aside for now.

Once time is introduced, we need to have a practical definition of time. Time is never continuous in this context. Even at the nanosecond level it’s a bit on a computer. For someone trading fractions of a penny for fractions of a second, the units are very small. That’s fine if they’re basing it on the same information as other traders. However, if they’re trading between ticks, it gets downright dishonest. They remind me of the currency trader who took the ten thousandths of a penny dropped in accounting for foreign currency transactions, and deposited them in his bank account (he went to jail).

For other traders, seconds, minutes, hours, days, weeks, etc. are practical. For a person planning for retirement, multiple years could fit. A trade can be structured so that the practical definition is indefinite, good until canceled or executed, or good until unwound. Thus, a practical definition of time is very personal.

In practical time, price gaps (discontinuities) become a meaningless concept or just another way to say volatility. Once practical time is introduced, liquidity becomes the ability to exchange assets. Price disappears from the definition. That puts us at the mercy of supply and demand. What really exists is some number of buyers at each price and some number of sellers. Under this definition, buyers and sellers now define liquidity, but they will also determine price. Thus, by this definition, information about liquidity is “substantial.” So, under this definition liquidity is still self-referential and directly related to price.

This has implications for what people who retain the focus on price continuity mean. Essentially they’re saying they want the same price at transaction time as existed at some earlier point. There is no reason for the “same.” Buyers want lower; sellers want higher. There is also no reason for any specific time lapse. The more one is motivated to trade the shorter the time frame. It would seem the alternative definitions that incorporate price continuity are biased in favor of frequent trading. Since trading has a cost, it is legitimate to question the result from a capital allocation perspective.

Now a disclosure, I’m so comfortable with volatility that an observer might think I’m insensitive to its impact. I understand self-referential systems reasonably well, at least well enough to recognize one. But, that’s not insensitivity to the impact of the volatility produced by the self-referential nature of liquidity. The fictitious liquidity added to liquidity due to genuine counterparties (i.e., those willing to take a position in an asset) often adds to volatility. There is enough truth to the risk-equals-volatility logic to justify concern, especially since it influences the allocation of capital and even the capital formation verses consumption decision. I also recognize that many people don’t share my indifference. Further, some people are mislead into making bad investment decisions by their reactions to volatility. Other can trade it quite well.

Since volatility is a part of life, why single out inter-tick volatility (discontinuities) for special treatment. Gapping between ticks and between years is only different depending on whether the tick or the year is your trading time frame.

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