# 1009 – Some thoughts on Albert's new liquidity measure''

Albert Menkveld advocates in a recent blog for a new definition for liquidity taking and provision in the financial securities market. The basic idea is to look at whether an order—be it a market order or a limit order—adds to or alleviates the existing price pressure.

i.e.\ the difference between the current quoted price and the market history implied “true value” of the asset.

I think it is a cool idea. But there are several things perhaps worth elaboration. First, what is the “old” definition for liquidity taking or provision? The answer from conventional thinking is fairly simple: If one posts limit orders, s/he is providing liquidty and if one submits market orders, s/he is taking. (Clearly, by posting limit orders, one indicates his/her willingness to be traded at that price, hence provides liquidity. Similarly, by submiting market orders, one consumes existing liquidity and hence is taking liquidity.) Fairly straightforward.

Second, what is price pressure? One of the key insight from the trading literature is that the asset’s current trading price or quoted price does not always match to its expected true value conditional on all available information (yes, this is the semi-strong efficient price). The difference between the currently traded/quoted price and expected value is called the “price pressure”. To some extent, at least in my mind, such a price pressure can be thought of as a temporary mispricing of the asset, which, of course, arises for a reason. The key driver for the mispricing lies in the market intermediaries, i.e. the liquidity providers or the market makers, who are risk-averse and, hence, require a compensation for holding risky asset as inventory even for a very short period of time. This risk-premium perspective of price pressure for liquidity providers has a long history in the literature and probably goes back to Grossman and Miller (1988) who studies the 1987 crash. The 2010 Flash Crash serves a more concrete example, in which the 9\% evaporation of market value in twenty minutes was clearly an example of price pressure (which Albert and I argue in the revised version of our paper was due to the breakdown of cross-market arbitrage channel). Albert also has a recent paper with Terry Hendershott (Hendershott and Menkveld, 2014) showing how market makers use price pressure to adjust their inventory.

Second, now that we understand what price pressure is, it should also be clear that when price pressure strenghthens, market makers or liquidity providers are essentially demanding a higher compensation for bearing an additional unit of inventory. For example, the semi-strong efficient price might be $10.00 per unit of the asset after the last trade. The latest quotes, however, have been revised to$10.08 and $10.12$ (for bid and ask, respectively). If we look at the midquote, which is $10.10, a$0.10 price pressure exists. Now suppose a market maker posts a limit buy order at $10.10, which improves the previous best bid quote by two cents. For the sake of clear argument, assume that this limit buy order does not affect the efficient price, which remains at$10.00. According to the “old” definition, since this market maker is posting limit order, s/he is clearly providing liquidity. Is it so according to Albert’s new definition?

The answer is no. Note that after the new limit buy order is posted, the new price pressure, measured by the midquote, becomes ($10.10+$10.12)/2 - $10.00 =$0.11, seeing a one-cent increase from $0.10. Hence, as the price pressure strenghthens, the market maker actually takes liquidity, because s/he makes it more expensive to transfer one additional unit to the intermediary. That is the basic idea of Albert. It clearly stands on a very different side of the old tradition of how we understand liquidity taking and provision in the market. (Of course, the real art is how to estimate the semi-strong efficient price in a econometrically sound way. The existing technology in this aspect is known as the “state space model”; see, e.g., Koopman, Lucas, and Menkveld, 2008.) I am here to offer a slightly different thinking, which I would like to argue is more general and reconciles Albert’s new and the traditional definition of liquidty taking vs. provision. My starting point is to think from the counterparty’s point view, not the overall market’s (semi-strong) efficient price. Following the above example of the addition of a limit buy order, let’s consider its potential counterparty, i.e. a potential seller. My claim is that such a seller has a marginal valuation of the asset larger than or equal to$10.08, i.e. the best bid price before the new limit buy order. Clearly, if the seller values the asseet at a price lower than the best bid, s/he whould just go ahead and take that marginal unit. The fact that the $10.08 bid still stands there implies it is “too low”, lower than the potential seller’s marginal valuation. Hence, from such a seller’s point of view, there exists a “price wedge” (which in my view is another form of mispricing, similar to the price pressure above). If the seller’s marginal valuation turns out to be$10.11, then the price wedge is $0.03 for him/her. Now that there comes a new bid price at price$10.10, how does this seller’s price wedge change? Similarly, let’s assume for exposition clarity that the sellers marginal valuation is not affected by the new limit bid order (just like the efficient price is unaffected). Then clearly, from the seller’s perspective, the price wedge reduces, from $0.03 to$\$0.01 and, hence, the one posted the new limit buy order is providing liquidity to the seller, i.e.\ the counterparty. (If you go through the thinking a little bit more rigorously, it is not hard to see that along this line of thinking, you will always get a predicition of liquidity taking/provision consistent with the old traditional definitoin.)

The above two interpretations should make my point clear: The old definition and Albert’s new idea of liquidity taking/provision only differs in the choice of “reference”. The old definition considers the liquidity taking/provision from the perspective of the counterparty: How does the new buy (sell) order affects wedge between the potential seller’s (buyer’s) marginal valuation of the asset and the best bid (ask). Albert’s new idea instead looks at the market’s overall valuation: the difference between the (semi-strong) efficient price and the midquote (or the latest traded price); i.e. the price pressure.

So the conclusion is that depending on your choice of reference, the overall market might be thinking the previous order is taking liquidity, while that order’s natural counterparty might be thinking the opposite.

13:17, Mar 11, 2015
bzy@Flying over Indian Ocean from Melbourne back to Singapore