Pairs Mean Reversion Strategy

The idea in one sentence

Two related stocks usually move together — when their price gap stretches abnormally far, bet that it snaps back.

Financial background

Pairs trading is the original statistical arbitrage strategy, popularised by Nunzio Tartaglia’s quant team at Morgan Stanley in the mid-1980s. The premise: if two assets share a common economic driver — same sector, same supply chain, same macro exposure — their prices should track each other within a stable, mean-reverting band. When the gap (the spread) widens beyond its historical norm, one leg is temporarily mispriced relative to the other. Selling the rich leg and buying the cheap leg captures the convergence.

What makes it attractive:

  • Market-neutral by construction. Long one leg, short the other → broad market moves cancel out. The PnL depends on the spread converging, not on equity-market direction.

  • Self-financing. The short proceeds fund the long, so capital usage is low (modulo margin requirements).

  • Sector-bet hedged. Trading two oil majors against each other is not a bet on oil; it is a bet on relative pricing.

The classic textbook pair is two integrated oil companies (Exxon vs. Chevron), two large US banks (JPMorgan vs. Bank of America), or two index ETFs tracking the same underlying (SPY vs. IVV). Cointegration tests (Engle–Granger, Johansen) are typically used to select pairs; the strategy below assumes you have already chosen a pair worth trading.

Why it can stop working:

  • Structural break. A merger, regulatory shock, or business-model divergence permanently re-prices one leg. The spread is no longer mean-reverting — you are now holding a directional bet.

  • Liquidity vacuum. If one leg becomes hard to borrow, the short side is forced to cover at the worst possible time.

  • Crowding. Famous pairs (Pepsi/Coca-Cola, Ford/GM) are arbitraged so aggressively that the edge is razor-thin and erodes during quiet markets.

How it works

The strategy maintains a rolling z-score of the price spread between two instruments A and B:

spread[t]  = close_A[t] - close_B[t]
z_score[t] = (spread[t] - rolling_mean(spread, window))
             / rolling_std(spread, window)

The z-score measures how unusual today’s gap is relative to the recent past. A z-score of +2 means the spread is two standard deviations above its rolling mean — i.e. extreme divergence in one direction.

Two thresholds drive the trade:

  • entry_z — magnitude required to open a paired position (default 2.0).

  • exit_z — magnitude tight enough to close the position (default 0.5).

exit_z must be strictly less than entry_z, so positions only close after meaningful convergence.

Signal logic

The two legs are always traded atomically: every signal emission contains both legs in one MultiAssetStrategyOutput so the engine applies them as a single transaction.

Entry — spread too high (z_score > +entry_z)

A is rich, B is cheap. The strategy expects the spread to fall.

SELL A, BUY B

Entry — spread too low (z_score < -entry_z)

A is cheap, B is rich. The strategy expects the spread to rise.

BUY A, SELL B

Exit — convergence (|z_score| < exit_z)

The spread has tightened back inside the inner band. The strategy closes both legs simultaneously regardless of direction.

CLOSE A, CLOSE B

No signal — middle band (exit_z ≤ |z_score| ≤ entry_z)

The spread is wider than the exit threshold but not yet at the entry threshold. The strategy holds existing positions and does not open new ones — a hysteresis band that prevents whipsaw.

Worked example

Pair: AAPL and MSFT. Parameters: spread_window = 60, entry_z = 2.0, exit_z = 0.5.

Today’s snapshot:

close_AAPL = 180.00
close_MSFT = 420.00
spread     = 180.00 - 420.00 = -240.00

rolling mean(spread, 60) = -250.00
rolling std (spread, 60) =    4.00

z_score = (-240.00 - (-250.00)) / 4.00 = 10.00 / 4.00 = +2.50

Today’s spread (-240) is unusually high relative to the typical -250 ± 4 band. AAPL is rich vs. MSFT.

Because 2.50 > entry_z = 2.0:

Signal: SELL AAPL, BUY MSFT — bet the spread drops back toward -250.

Two weeks later, the spread has compressed back to -249 and the z-score is now +0.25. Because |0.25| < exit_z = 0.5:

Signal: CLOSE AAPL, CLOSE MSFT — convergence achieved, lock in the gain.

The confidence scales linearly with |z_score| / entry_z, capped at 1.0. A z-score of exactly entry_z triggers confidence 1.0; weaker entries from the schema are not possible because |z_score| ≤ entry_z would not have triggered an entry in the first place.

When it works well

  • Cointegrated pairs in stable regimes. Two firms in the same industry, with similar business mix, traded on the same exchange. The spread oscillates around a stable mean for years.

  • Liquid large-caps. Tight bid-ask, easy borrow, low slippage. Pairs trading is fundamentally a high-turnover, low-edge game; transaction costs eat returns fast.

  • Mid-volatility environments. Enough movement to generate 2σ events, not so much that the rolling mean shifts faster than positions can converge.

When it struggles

  • Structural breaks. A 2013-style spin-off (eBay/PayPal) or 2023-style banking shock (SVB) permanently re-prices one leg. The “mean” the strategy assumes no longer exists.

  • High-volatility crashes. Correlations break down — every spread widens at the same time, and the rolling-window estimates lag the new regime.

  • Asymmetric borrow costs. If shorting one leg is expensive (high HTB fee), the realised PnL is much worse than the model PnL.

  • Single-pair concentration. A diversified pairs book of 20+ uncorrelated pairs has a far smoother equity curve than betting on one pair, even a “perfect” one.

Key concepts

Spread

The price difference between the two legs (not a ratio, not log prices). This works when the two instruments have similar nominal price levels. For pairs with very different price scales (e.g. BRK.A vs. SPY), a log-spread or hedge-ratio formulation is more appropriate — outside the scope of this engine.

Rolling z-score

Standardises the spread against its own recent history rather than a fixed mean. This adapts gradually to slow drifts in the relationship while still flagging sharp dislocations.

Entry / exit hysteresis

Keeping exit_z < entry_z creates a dead band between ±exit_z and ±entry_z where the strategy neither opens nor closes. Without this, every wiggle around the threshold would trigger a re-entry. Typical ratios: entry_z = 2.0 with exit_z = 0.0 (close at the mean) or exit_z = 0.5 (close just inside the mean).

Atomic two-leg signals

Both legs always flip together, packaged in a single MultiAssetStrategyOutput. This ensures the engine never holds a half-built pair (long one leg without the offsetting short), which would convert the trade into an unintended directional bet.

Pair selection (out of band)

This engine assumes the user has already identified a pair worth trading. In production, pair selection typically uses:

  • Pearson / Kendall correlation — quick first filter (> 0.7).

  • Cointegration tests — Engle–Granger or Johansen — to confirm a stable long-run relationship.

  • Half-life of mean reversion — Ornstein-Uhlenbeck fit; reject pairs with half-life much longer than the holding-period budget.

Parameters

Parameter

Default

What it controls

instrument_a

required

First leg’s identifier (must match a key in candles_map)

instrument_b

required

Second leg’s identifier (must differ from instrument_a)

spread_window

60

Rolling window for the z-score mean and stdev

entry_z

2.0

Z-score magnitude required to open a paired position

exit_z

0.5

Z-score magnitude required to close an open position (must be < entry_z)

Tuning guidelines

  • More trades, smaller edge: lower entry_z (e.g. 1.5). Expect more whipsaws and more sensitivity to transaction costs.

  • Fewer trades, higher conviction: raise entry_z (e.g. 2.5–3.0). Holding periods lengthen; idle capital between signals is the cost.

  • Faster adaptation: shorten spread_window (e.g. 20–40). The mean tracks regime shifts more responsively but is noisier.

  • Slower, smoother: lengthen spread_window (e.g. 120–252). The mean is stable but takes longer to recognise a structural break.

  • Tighter exits: drop exit_z toward 0.0 to ride convergence all the way to the mean. Trades off larger per-trade gain against more time exposed.

References

  • Gatev, E., Goetzmann, W. N., & Rouwenhorst, K. G. (2006). Pairs Trading: Performance of a Relative-Value Arbitrage Rule. Review of Financial Studies, 19(3), 797–827.

  • Vidyamurthy, G. (2004). Pairs Trading: Quantitative Methods and Analysis. Wiley.

  • Engle, R. F., & Granger, C. W. J. (1987). Co-integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2), 251–276.