Cointegration Baskets (Multi-Leg Stat Arb)

Thesis (edge)

Classic pairs trading hedges one stock with one other stock. The problem is that no single peer is a clean hedge. A refiner is not just a refiner: it is part energy price, part currency, part local demand. Hedging it with one other refiner leaves a lot of unrelated noise in the spread, and that noise is what stops you out.

The basket version fixes this by hedging the target against a weighted combination of several related names. If three or four peers together explain the target's moves better than any one of them alone, then what is left over after you subtract the basket is a cleaner, more stationary residual. That residual is the thing you actually trade: when it stretches unusually far from its normal level, you bet it comes back.

The edge is not magic. It is the simple observation that companies exposed to the same underlying drivers cannot drift apart forever without a real reason. When they do drift apart for no reason you can name, that gap tends to close.

Where it works (regimes)

• Works well: calm to normal markets, inside tight industry groups, where the names share genuine economics and news flows through all of them at once.
• Works badly: when one leg gets a real, permanent shock. A takeover bid, an accounting scandal, a product recall or a regulatory ban does not mean revert. The spread is supposed to move, and it will not come back.
• Works badly: in violent risk-off moves, when correlations jump toward one and previously distinct names all trade as a single macro instrument. Your carefully fitted weights were estimated in a different world.
• Watch out for: long stretches where the whole style is crowded. When many funds hold the same peer-group spreads, a forced unwind at any one of them pushes every spread the wrong way at the same time, which is exactly what happened to quant market-neutral books in August 2007.

Signals

Keep the math light. The pieces you need are:

• The spread. Take the target's price and subtract the weighted basket of hedge names. What is left is the spread. Weights come from a regression of the target on the peers, fitted on a training window.
• The z-score. Ask how unusual today's spread is compared to its own recent history. Roughly two standard deviations away is a common entry trigger. Use a rolling window so the score adapts.
• The half-life. This is the honest question: if the spread is stretched, how long does it typically take to close half the gap? If the answer is longer than you are willing to hold, do not take the trade. Half-life is your reality check on whether the basket is tradable at all.
• A stationarity check. Before trusting any basket, confirm the residual actually behaves like something that reverts, rather than something that wanders off. If the spread wanders, the whole setup is an illusion.

Entry is a stretched z-score. Exit is the z-score coming back near zero, a stop if it stretches much further, or a time limit if nothing happens.

Portfolio construction

• Neutrality: size the legs so the basket is roughly dollar neutral and beta neutral against the market. Many desks also neutralise sector and size, so the residual is not secretly a factor bet.
• Diversify across baskets: the single most reliable improvement is running many independent baskets rather than a few large ones. One basket is a coin flip. Fifty loosely related baskets is a business.
• Position sizing: scale each basket by the volatility of its own spread, so a jumpy spread gets less capital than a quiet one. Cap the weight of any single basket and any single underlying name, since one name can appear as a leg in several baskets and quietly build a concentrated exposure.
• Rebalance: refit weights on a fixed schedule (monthly is common) rather than continuously. Constant refitting makes the hedge chase noise and drives turnover through the roof.

Risk model

The main risk is boring to say and expensive to learn: the relationship you fitted was never real, or it stopped being real. Everything else follows from that.

• Divergence risk: the spread widens past your stop and keeps going. You lose on the way out, then it may revert after you have been forced to close.
• Single-leg event risk: an acquisition bid on one leg repriced overnight. No hedge protects you. This is the classic way a market-neutral book takes a real loss.
• Crowding and forced unwinds: when the trade is popular, drawdowns are correlated across the whole industry, and liquidity vanishes at exactly the moment you want it.
• Borrow risk: the short legs may become hard to borrow, expensive, or recalled. A recall forces you to close a leg and leaves the rest of the basket unhedged.
• Leverage: because each spread has small expected moves, the temptation is to lever up. That converts a modest strategy into a fragile one. Set gross exposure limits and honour them.

Costs & implementation

This strategy trades a lot, and it trades many legs at once, so cost discipline decides whether it survives.

• Every leg is a cost. A five-name basket means five spreads to cross on the way in and five on the way out. Costs scale with the number of legs, the edge does not.
• Short borrow: general collateral names are cheap, but the interesting spreads often involve names that are not. Check borrow availability and fee before the basket is even eligible for trading.
• Impact: trade only names where your intended size is a small fraction of daily volume. If you have to work the order over a day, the spread may have already reverted before you are fully on.
• Execution: use limit orders and be patient. This is not a strategy that pays you for aggression. If you cannot get the whole basket on, consider not trading it rather than sitting half-hedged.
• Data: you need clean, corporate-action-adjusted prices. A missed split turns into a fake spread blow-out and a very real loss.

Failure modes

• Data mining the basket. Search enough combinations of peers and you will always find a beautiful-looking stationary spread that means nothing. This is the single biggest killer here, because the number of possible baskets is enormous.
• Look-ahead in the weights. Fitting hedge weights using the full sample, including the period you then test on, produces spectacular backtests and terrible live results.
• Ignoring the half-life. A spread that reverts over two years is not a trading strategy, it is a hope.
• Treating a broken leg as a bargain. Adding to a losing spread because it is now even more stretched is how blow-ups happen. Sometimes the market knows something you do not.
• Ignoring borrow and financing. Many published pairs and basket results look fine only because they silently assume free shorting.
• Capacity denial. The edge lives mostly in mid and small caps, which is exactly where capacity is smallest. It does not scale the way you want it to.

Our Notes & Suggestions

Start with economics, then use statistics to confirm. Baskets picked because they make sense (same industry, same commodity, same customer base) hold up far better than baskets picked because a screen said the spread looked stationary. Statistics should be a filter on economic ideas, not a substitute for having one.

Insist on out-of-sample discipline. Choose the baskets, the weights and the thresholds on training data, then leave them alone in the test period. If performance collapses out of sample, that is the truth, not a sign you need to tune more.

Finally, be honest that this is a crowded, decaying space. The simple versions of the trade have been well known for over thirty years and much of the easy money has been arbitraged away. What remains lives in careful universe selection, disciplined cost control and having the risk framework to survive the periods when spreads refuse to come back.