The signs of tacit collusion in the dividend play trade

Game theory and real-world data point to a different understanding of how arbitrage in markets works

When academics at the London Business School conducted a study into a multi-million-dollar arbitrage trade known as the “dividend play” last year, they were surprised to find arbitrageurs left half the potential profit on the table. What was more: at various times, only single trading firms seemed to be trying to make money.

The findings, published in the Journal of Finance in December last year, confound standard models of arbitrage, which assume trading firms will chase all available chances for a near-riskless profit, starting with the most lucrative. 

In a follow-up working paper, the team draws on game theory to create a model to explain what might be going on. What they conclude might change how practitioners think about how markets work.

In real life, “it’s like traders are not stepping on each other’s toes”, says Anna Pavlova, a professor of finance at London Business School, who led the research.

The researchers propose a new model that hinges on what game theorists call a tacit collusion equilibrium – a form of co-operation among market participants that requires no explicit agreement and can arise naturally from traders seeking to maximise long-term profit.

The academics acknowledge in the paper they have only indirect evidence of this happening. But the research findings serve as a “cautionary tale”, they suggest, about the potential presence of such effects in broader markets.

Arbs at play

The dividend play trade sees market participants write huge volumes of call option contracts immediately before the dividend of the underlying stock comes due.

The arbitrage works because some investors fail to exercise options in time and miss out on a profit by doing so. At the same time, the clearing house assigns exercise notices randomly. Writers of options that are not assigned avoid the obligation to deliver the underlying stock and effectively realise a windfall gain. 

By writing vast numbers of options, arbitrageurs can raise their odds of holding the unexercised, money-making contracts. Between November 2019 and June 2023, the trade offered potential profits of $340 million, the researchers estimate. 

Little of what the data shows matches conventional wisdom about how these markets should function

In their study, the academics document as much as an 80-fold increase in trading in certain options on the last day before stocks pay a dividend. For the most actively traded option – SPY – volumes spiked as high as 53-times larger. 

It's possible to tell how many firms are trading the arbitrage by tracking the signatures of different players in transaction level data, Pavlova explains. Trades of the same size in the same contract happen within millisecond bursts, she says, leaving a footprint that points to activity coming from individual market participants.

Little of what the data shows matches conventional wisdom about how these markets should function. 

Theory says that if some market participants fail to harvest near-riskless profits, others will step in. In half of the contracts where arbitrage took place, though, only a single trading firm seemed active. 

When the researchers looked at the most profitable arbitrage opportunities in isolation, where activity ought to be greatest, they observed the same pattern of profits left unearned and single traders dominating in specific contracts.

“There should be a pecking order,” Pavlova says, which is to say: more profitable contracts should see more incidences of arbitrage. “There’s not.”  

The new model, then, posits that market participants learn over a sequence of iterations to stick to certain markets and steer clear of those where others are active. 

“If you have two arbitrageurs that enter the same contract, both pay fixed costs and that creates inefficiency,” explains Svetlana Bryzgalova, assistant professor of finance also at London Business School, who worked on the research with Pavlova. “If they co-ordinated their action, they’d decide to split the markets – one arbitrageur to trade in one market and the other to enter the other market. With repeated interactions, the equilibrium can emerge even without any explicit co-ordination.”

The half of profits left unharvested probably results from arbitrageurs avoiding contracts in which market makers already hold short positions, which would make it harder for a trader to shift the windfall odds in their favour.

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The tacit collusion idea, if correct, could apply in other markets too, the academics suggest. One possible candidate would be the trading of credit default swaps, which meets the criteria for the model to make sense: an opaque market with high barriers to entry, a limited number of players and repeated interactions between them. 

Fixes

As for the dividend play itself, the trade has attracted controversy in the past because it likely transfers wealth from less-informed, mostly retail, investors to the market’s bigger players. 

In 2014, a Securities and Exchange Commission rule change made it impractical for traders to buy and sell the same contract simultaneously, hindering their ability to execute the arbitrage trade. 

The researchers say arbitrageurs have found a way around the change, though, by trading long and short positions in options with neighbouring strikes. 

Regulators could end this by requiring retail brokerages to report the early exercise value of options to investors. Another alternative, the academics suggest, might be to make exercise automatic on last cum-dividend dates when profitable, with investors able to opt out. A third measure could be for the clearing house to replace the random assignment of exercise notices with an order favouring original options writers over dividend play arbitrageurs.

Dividend play traders inflate trading volumes and to no end, the researchers conclude. “This trade doesn’t correct any market inefficiency and its size creates operational risk,” Pavlova says.