Statistical Arbitrage. Thought of the Day 123.0


In the perfect market paradigm, assets can be bought and sold instantaneously with no transaction costs. For many financial markets, such as listed stocks and futures contracts, the reality of the market comes close to this ideal – at least most of the time. The commission for most stock transactions by an institutional trader is just a few cents a share, and the bid/offer spread is between one and five cents. Also implicit in the perfect market paradigm is a level of liquidity where the act of buying or selling does not affect the price. The market is composed of participants who are so small relative to the market that they can execute their trades, extracting liquidity from the market as they demand, without moving the price.

That’s where the perfect market vision starts to break down. Not only does the demand for liquidity move prices, but it also is the primary driver of the day-by-day movement in prices – and the primary driver of crashes and price bubbles as well. The relationship between liquidity and the prices of related stocks also became the primary driver of one of the most powerful trading models in the past 20 years – statistical arbitrage.

If you spend any time at all on a trading floor, it becomes obvious that something more than information moves prices. Throughout the day, the 10-year bond trader gets orders from the derivatives desk to hedge a swap position, from the mortgage desk to hedge mortgage exposure, from insurance clients who need to sell bonds to meet liabilities, and from bond mutual funds that need to invest the proceeds of new accounts. None of these orders has anything to do with information; each one has everything to do with a need for liquidity. The resulting price changes give the market no signal concerning information; the price changes are only the result of the need for liquidity. And the party on the other side of the trade who provides this liquidity will on average make money for doing so. For the liquidity demander, time is more important than price; he is willing to make a price concession to get his need fulfilled.

Liquidity needs will be manifest in the bond traders’ own activities. If their inventory grows too large and they feel overexposed, they will aggressively hedge or liquidate a portion of the position. And they will do so in a way that respects the liquidity constraints of the market. A trader who needs to sell 2,000 bond futures to reduce exposure does not say, “The market is efficient and competitive, and my actions are not based on any information about prices, so I will just put those contracts in the market and everybody will pay the fair price for them.” If the trader dumps 2,000 contracts into the market, that offer obviously will affect the price even though the trader does not have any new information. Indeed, the trade would affect the market price even if the market knew the selling was not based on an informational edge.

So the principal reason for intraday price movement is the demand for liquidity. This view of the market – a liquidity view rather than an informational view – replaces the conventional academic perspective of the role of the market, in which the market is efficient and exists solely for conveying information. Why the change in roles? For one thing, it’s harder to get an information advantage, what with the globalization of markets and the widespread dissemination of real-time information. At the same time, the growth in the number of market participants means there are more incidents of liquidity demand. They want it, and they want it now.

Investors or traders who are uncomfortable with their level of exposure will be willing to pay up to get someone to take the position. The more uncomfortable the traders are, the more they will pay. And well they should, because someone else is getting saddled with the risk of the position, someone who most likely did not want to take on that position at the existing market price. Thus the demand for liquidity not only is the source of most price movement; it is at the root of most trading strategies. It is this liquidity-oriented, tectonic market shift that has made statistical arbitrage so powerful.

Statistical arbitrage originated in the 1980s from the hedging demand of Morgan Stanley’s equity block-trading desk, which at the time was the center of risk taking on the equity trading floor. Like other broker-dealers, Morgan Stanley continually faced the problem of how to execute large block trades efficiently without suffering a price penalty. Often, major institutions discover they can clear a large block trade only at a large discount to the posted price. The reason is simple: Other traders will not know if there is more stock to follow, and the large size will leave them uncertain about the reason for the trade. It could be that someone knows something they don’t and they will end up on the wrong side of the trade once the news hits the street. The institution can break the block into a number of smaller trades and put them into the market one at a time. Though that’s a step in the right direction, after a while it will become clear that there is persistent demand on one side of the market, and other traders, uncertain who it is and how long it will continue, will hesitate.

The solution to this problem is to execute the trade through a broker-dealer’s block-trading desk. The block-trading desk gives the institution a price for the entire trade, and then acts as an intermediary in executing the trade on the exchange floor. Because the block traders know the client, they have a pretty good idea if the trade is a stand-alone trade or the first trickle of a larger flow. For example, if the institution is a pension fund, it is likely it does not have any special information, but it simply needs to sell the stock to meet some liability or to buy stock to invest a new inflow of funds. The desk adjusts the spread it demands to execute the block accordingly. The block desk has many transactions from many clients, so it is in a good position to mask the trade within its normal business flow. And it also might have clients who would be interested in taking the other side of the transaction.

The block desk could end up having to sit on the stock because there is simply no demand and because throwing the entire position onto the floor will cause prices to run against it. Or some news could suddenly break, causing the market to move against the position held by the desk. Or, in yet a third scenario, another big position could hit the exchange floor that moves prices away from the desk’s position and completely fills existing demand. A strategy evolved at some block desks to reduce this risk by hedging the block with a position in another stock. For example, if the desk received an order to buy 100,000 shares of General Motors, it might immediately go out and buy 10,000 or 20,000 shares of Ford Motor Company against that position. If news moved the stock price prior to the GM block being acquired, Ford would also likely be similarly affected. So if GM rose, making it more expensive to fill the customer’s order, a position in Ford would also likely rise, partially offsetting this increase in cost.

This was the case at Morgan Stanley, where there were maintained a list of pairs of stocks – stocks that were closely related, especially in the short term, with other stocks – in order to have at the ready a solution for partially hedging positions. By reducing risk, the pairs trade also gave the desk more time to work out of the trade. This helped to lessen the liquidity-related movement of a stock price during a big block trade. As a result, this strategy increased the profit for the desk.

The pairs increased profits. Somehow that lightbulb didn’t go on in the world of equity trading, which was largely devoid of principal transactions and systematic risk taking. Instead, the block traders epitomized the image of cigar-chewing gamblers, playing market poker with millions of dollars of capital at a clip while working the phones from one deal to the next, riding in a cloud of trading mayhem. They were too busy to exploit the fact, or it never occurred to them, that the pairs hedging they routinely used held the secret to a revolutionary trading strategy that would dwarf their desk’s operations and make a fortune for a generation of less flamboyant, more analytical traders. Used on a different scale and applied for profit making rather than hedging, their pairwise hedges became the genesis of statistical arbitrage trading. The pairwise stock trades that form the elements of statistical arbitrage trading in the equity market are just one more flavor of spread trades. On an individual basis, they’re not very good spread trades. It is the diversification that comes from holding many pairs that makes this strategy a success. But even then, although its name suggests otherwise, statistical arbitrage is a spread trade, not a true arbitrage trade.

2 thoughts on “Statistical Arbitrage. Thought of the Day 123.0

  1. Really very interesting insight here; I’m curious if you could say a little bit about how high-frequency trading plays into this — you start off mentioning that the time discrepancy of a few seconds, but of course microseconds and lower matter for HFT strategies to really get moving (firms competing for fastest access to the trading servers…)

    Your description here also got me thinking that hedging is close to a prediction market for stocks — at least you’re assigning a probability estimation to the different outcomes. I’d also be quite curious about the technical statistical elements of the strategies here — presumably they’re using things like neural models and deep learning today, as well as “traditional” quant with Black-Scholes models etc?

  2. HFT and statistical arbitrage trading strategies actually feed into each other pretty cogently in a two-pronged approach. One is as a result co-movement caused by the HFT, by which stock pairs tend to get co-integrated. Correlation and co-integration in statistical arbitrage are related, but they highlight different concepts. High correlation in assets does not necessarily imply high co-integration in prices. Correlation reflects co-movements in assets, but it is usually unstable over time. High correlation alone is not sufficient enough to ensure the long-term performance of hedges. Correlations based on hedge strategies commonly require frequent rebalance, whereas, co-integration measures long-term co-movements in prices even through a period when correlation appears low. Therefore, co-integration based on hedge strategies may be more effective in long-term running and short-term dynamic trends. the second features decile profitability, which plateaus out leaving less vulnerability to fluctuations.

    Yes, a few seconds is probably an anachronism in this case and I should have gone more clearer on firms fighting for nano-second velocities. Its more of an #accelerationsim in the way I see it. And of course flash boys remains right there to remind of how the disconnect realizes in terms of speeds between the non-machinic and the machinic.

    Neural n/w learning is increasingly used to time value behavioral analytics. The use of neural n/w, especially for option pricing, Delta bahaviours is gaining wide currency, for the former have the potential of being noised out and thus correlating with what is predeterminable in Black-Scholes case.

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