Stat arb

The idea

Find instruments that usually move together. When they drift apart, buy the cheap side, sell the rich side, and wait for the gap to close.

The book is built to make money from the gap, not from the market going up. It is called arbitrage. It is not risk-free.

What the long record shows

In the mid-1980s Nunzio Tartaglia's quantitative group at Morgan Stanley traded pairs of stocks whose prices tended to move together. The group disbanded in 1989 after a couple of poor years. The most cited academic study, by Gatev, Goetzmann and Rouwenhorst, appeared as an NBER working paper in 1999 and was published in 2006. It matched stocks by the distance between their normalised price paths. Over 1962 to 2002, the profits typically exceeded conservative estimates of trading costs.

Do and Faff (2010) extended the test to 2009 and found the decline in profits continued. The strategy still performed strongly in long stretches of turbulence, such as the 2000 to 2002 bear market and the 2007 to 2009 crisis, when in their reading mispricing grew by more than the risk of holding it. They traced a large share of the decline to worsening arbitrage risks, meaning fundamental, noise-trader and synchronisation risk, all of which can prevent or delay convergence or impose losses first. Greater market efficiency, including more hedge funds chasing the same trades, explained only part of it. A later study by the same authors found that pairs converge less often when the two firms' own cash flows are volatile, and that market-wide changes in that volatility help explain a substantial part of the decline since the 1990s.

Once commissions, market impact and short-selling fees are counted, Do and Faff (2012) found pairs trading, and a reversal strategy that ranks stocks against their industry peers, largely unprofitable after 2002. Publication adds its own pressure. McLean and Pontiff found that return predictors weaken once academics publish them, and the stocks involved then trade more, carry more short interest and move more closely with other published strategies. The decline was larger in portfolios of stocks with low idiosyncratic risk, where arbitrage costs less.

Correlation versus cointegration

Correlation measures whether two returns move together from one day to the next. It says nothing about whether the gap between the two prices stays bounded. Two tokens can both track bitcoin's daily moves closely while one drifts lower for months. As Krauss's survey of the literature points out, securities that are correlated on returns need not share any equilibrium, so nothing forces a divergence to reverse.

Cointegration is the stronger claim. It says some weighted mix of the two prices is stationary, so shocks to the gap fade over time. Clegg and Krauss cite evidence that the property of being cointegrated does not persist. They argue that any change in a company's fundamental value is a permanent shock to the spread, and that spreads absorb a steady stream of them, from management changes and legal actions to credit-rating moves.

Wide screens make the problem worse. Test a thousand candidate pairs at a 5% significance level and around fifty can be expected to pass by chance, even if no true relationship exists. Those chance passes are the pairs most likely to fail once capital is on them. A test passed on history is a hypothesis about the next regime.

Why regime matters

The relationship is measured on history. When the regime changes, the relationship can change with it, and a gap that used to close can keep opening.

The signal says the trade is cheaper. The risk says the relationship has broken. The risk has to win.

Where it breaks

Crowding. Many desks hold the same kind of trade and unwind it at the same time. August 2007 is the standard example: quantitative equity books lost heavily in a few days, with no news in the stocks themselves to explain it.

Leverage. The gaps are small, so the books are often levered. A gap that widens before it closes can force the exit at the worst point.

Costs. The edge per trade is thin. Fees, funding, and slippage decide whether it exists at all.

Lessons from equity history

Khandani and Lo show that quantitative long/short books were hit on 7 and 8 August 2007 with little movement in equity or bond markets, and kept losing on 9 August when the S&P 500 fell nearly 3%. On 10 August much of the move reversed. Managers who cut risk mid-week locked in their losses and missed part of the rebound. In the authors' simulation of a leveraged contrarian strategy, a book with the credit lines to hold on all week would have recovered most of the damage by Friday.

The same paper offers likely reasons for the force of the unwind. Over the prior decade, assets in long/short equity had grown, the profitability of these strategies had fallen, and managers had added leverage to keep returns where investors expected them. The authors suggest the trigger was a sudden liquidation by a multi-strategy fund or proprietary desk, possibly in response to margin calls on a deteriorating credit portfolio. In a 2008 follow-up, they found the unwind began in July, with turnover concentrating from late July in stocks at the extremes of common valuation and momentum factors. The footprint was in the data about two weeks before the worst days.

Twin shares show how long a gap between two claims on the same cash flows can stay open. Royal Dutch and Shell Transport owned their operating group 60:40 for nearly a century, so their prices should have held a fixed ratio. A Reserve Bank of Australia study found the ratio deviated from parity by about 9.5% on average, in absolute terms, over 1980 to 1995, and still by about 4.7% from September 1999 to 2002, after academics had published the anomaly. Long-Term Capital Management held a US$2.3 billion position in the pair and lost money on it when the gap widened sharply in 1998. The gap finally closed through a corporate action, when the two companies unified under one parent in July 2005.

A book long Volkswagen preference shares and short the ordinary shares was betting that the voting premium between them would narrow. On 26 October 2008 Porsche disclosed a position of 74.1% of Volkswagen's voting stock through shares and cash-settled options. With the state of Lower Saxony holding about a fifth, little ordinary stock was left for short sellers to buy. Two days later the ordinary shares rose above EUR 1,005, briefly making Volkswagen the world's most valuable listed company, while the preference shares edged lower, as Allen, Haas, Nowak and Tengulov document. The premium had widened steadily since about late 2005 as Porsche built its stake, yet nothing in that history pointed to a jump of that size.

What is different in crypto

The largest cross-exchange gaps in crypto have been about moving fiat money across borders. Makarov and Schoar found the bitcoin price in Korea averaged more than 15% above the US price from December 2017 to early February 2018, and the gap reached 40% for several days. Gaps between exchanges in the same country typically stayed under 1%. On the same exchanges, the ether-to-bitcoin rate differed far less, which points to the fiat leg and capital controls as the barrier. At the time, Korean residents moving more than US$50,000 abroad in a year had to document the reason to the authorities.

These gaps also carry market direction. Makarov and Schoar found they opened and closed together across countries and widened when bitcoin rose quickly, so a book betting on them to close was in effect short the rally. Crépellière, Pelster and Zeisberger found the gaps shrank sharply from April 2018 onward and were hard to exploit after that, in data running to the end of 2021. Hautsch, Scheuch and Voigt show that cross-exchange gaps line up with periods of slow blockchain settlement, and are smaller between exchanges with low default risk. Settling on-chain leaves the arbitrageur exposed to price moves while the transfer confirms, and settling off-chain leaves it exposed to a venue failing, so the residual gap is a price for waiting or for trusting the venue.

Some crypto gaps have no working arbitrage route. The Grayscale Bitcoin Trust suspended redemptions in October 2014, and shares bought from the trust carried a six-month holding period. Its 2022 annual report states that, for these reasons, there was no arbitrage mechanism to keep the shares closely linked to the bitcoin price, and records premiums of up to 142% and discounts of up to 49% to the trust's holdings between May 2015 and December 2022. The discount was 45% at the end of 2022 and 8% at the end of 2023, so most of it closed before any redemption route existed. Redemptions began when the shares listed on NYSE Arca on 11 January 2024, the day after the SEC approved spot bitcoin exchange-traded products, and the sponsor reports closer tracking since.

Stablecoin pegs are relationships too, and they break when the arbitrage route shuts. On the evening of Friday 10 March 2023, Circle said it could not withdraw US$3.3 billion of USDC reserves, about 8% of the total, from Silicon Valley Bank. Minting and redemption ran on US banking hours, so Circle's primary market, which normally holds USDC at a dollar, was shut for the weekend. USDC traded as low as 86 cents, Dai fell with it through its USDC peg stability module, and USDT traded slightly above a dollar as holders sought safety. The peg returned after the US authorities' backstop announcement on Sunday evening and Circle's resumption of redemptions on Monday 13 March, as a Federal Reserve note sets out.

A USDC against USDT pair looked like one of the tightest relationships in the market until one leg's redemption route closed. Access to that route is narrow, and a Federal Reserve study notes that fiat-backed issuers limit minting and redemption to approved customers. Ma, Zeng and Zhang count about six agents redeeming Tether for cash in an average month, against 521 for USDC, and find that coins with fewer arbitrageurs trade further from a dollar on normal days. They also argue that efficient arbitrage amplifies run risk, because it lets holders sell with less price impact. How tightly a peg trades on a normal day says little about how it behaves under stress.

Reading crowding early

Crowding can show up in correlations before it shows up in losses. Lou and Polk built such a measure for momentum, using the unusual return correlation among the stocks the strategy trades after stripping out common factors, and found that high readings were followed by strong reversals in momentum stocks. McLean and Pontiff's finding that published strategies start to move together points the same way. Hanson and Sunderam use short interest to estimate how much capital is chasing value and momentum strategies, and find that capital is most limited when the strategies perform best.

Four warning signs follow for a stat arb book. The residuals of supposedly unrelated pairs start to move together. The book's legs start to line up with standard value or momentum portfolios. Turnover concentrates in names at the extremes of common signals, as it did in late July 2007. In crypto, a perpetual short leg that starts paying funding signals that demand to be short is outweighing demand to be long.

The trade looks most attractive when capital is scarcest. Shleifer and Vishny argued that arbitrage run with other people's money can stop working in extreme conditions, when prices sit furthest from fundamentals. Nagel shows that the expected reward for supplying liquidity rises sharply with the VIX in turmoil, and Mitchell, Pedersen and Pulvino found that when specialised arbitrageurs lose capital they turn into sellers and the price rebound takes months. Multi-strategy funds with spare capital added to positions, yet a large fraction of multi-strategy funds sold, which the authors link to barriers inside a firm that leave a desk with mark-to-market losses short of capital. Sizing has to assume a gap can widen further before anyone with spare capital steps in.