The magic alpha of dark liquidity and partial diversity

In an earlier post, I highlighted an article about dark liquidity and dark books. The Park Paradigm’s new post on dark liquidity prompted me to take another look at it with regard to CASTrader.

What are dark liquidity and dark books?

Very simply, it is liquidity (trading) that is hidden behind the walls of an organization. If you and I both have an account at Broker A, and I happen to be buying Stock A when you are selling an equal amount, the broker could simply match our trades, without ever going to the exchanges - the two trades, their liquidity and volume are “dark,” e.g. not public. Theoretically, there is minimal or no friction on the trade, and the broker can pocket the savings instead of the exchanges. To have dark liquidity, you must have internal trades that represent opposing viewpoints.

How else is dark liquidity useful?

Say you are investing using several diverse trading algorithms that buy and sell a specific security at different times. To the extent these algorithms make money, but have differing opinions, you can pocket the friction savings yourself.

Dark Liquidity Math

I will invent a use of the term diversity to define the amount of time your set of trading algorithms differ with each other on the direction of the market. Full Diversity would be where the algorithms are never in agreement, for example: one is long while the other is short. There is no net trade here, no net profits, and 100% dark liquidity is available. This is analogous to chaos. Zero Diversity would be algorithms in complete agreement, for example, all algorithms are 100% long. Here, there is a net buy-and-hold trade, and no dark liquidity is possible. Your algorithms are completely ordered. Although dark liquidity can save a lot of frictional trading costs as you tend towards the Full Diversity case, Partial Diversity is the continuum between full and zero diversity where things can get really interesting. Consider the case of two algorithms (A and B) trading stock XYZ over the course of a year. Furthermore, A and B and are either in cash or 100% long mode, but they are never long at the same time. Also assume that cash pays no interest and Algorithms A and B share the same cash pool:

Option 1: Hypothetical XYZ buy-and-hold return: 10%
Option 2: Trading Algorithm A @ 6% return, and Trading Algorithm B @ 6% return

Which has the higher return, assuming no friction and no taxes? Option 2 consists of two algorithms with mediocre returns. If you said Option 1 though, you’re wrong. Option 2 has the higher return, due to the Partial Diversity. The returns from Algorithm A and B in this hypothetical are multiplicative due to the magic of compounding: 1.06 * 1.06 = 1.124 or 12.4%. Option 2 beats Option 1 by two percentage points. Note that this example implies that although A and B are never in the market at the same time, they must be both out of the market at least some of the time (otherwise they could never beat buy-and-hold). To the extent A is buying when B is selling, there is dark liquidity potential, although in this example it is meaningless since friction is assumed to be zero anyway.

Finding Algorithm A and B that perform in the future like the example on a real stock or index is a difficult adventure. Nevertheless, the example illustrates how Partial Diversity can pay off if you can achieve it. Neither A nor B probably look all that attractive individually using conventional performance measures, but together, the whole is greater than the sum of the parts relative to buy-and-hold. It’s important to note that you could envision an example where A and B are in the market the same number of days and with the same returns as the above example, but they have zero diversity and in that case Option 2 returns 6%. Thus, you cannot measure the performance of trading algorithms individually using conventional measures, rather they must be measured in combination to see their benefits (of partial diversity). To my knowledge, none of the researchers seem to grasp the importance of this concept and may routinely discard promising trading patterns. Equal Sharpe Ratios do not necessarily have equal utility! More to the point, finding algorithms that beat the market individually isn’t the holy grail.

How do we maximize the magic of dark liquidity and partial diversity? Answer: find as many diverse trading algorithms with an edge as you can, even if they don’t beat the market, and let them share cash as much as possible (to achieve compounding), and create a dark internal market they can trade in. You’ll likely be creating partial diversity and hopefully generate some alpha as in the example. Algorithms that were only marginally beneficial due to high frictional costs are attractive simply for their added liquidity, which can then be turned “dark” and harvested as alpha. As the example illustrates, even algorithms that don’t beat buy-and-hold can potentially add value.

This is exactly how I’m coding CASTrader in the quest for alpha. I’m coding as many diverse traders as possible that trade on a dark market. Only the net trade will show up on the exchanges.

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