Pair Trading (NSE)

Two stocks that share the same economics (two private banks, two oil marketing companies) can drift apart for weeks, then close the gap. A pair trade is long the cheap one and short the rich one, sized so the market move cancels out. This works only if the gap is statistically mean-reverting (cointegrated). A high correlation is not enough.

1. Run it

python3 scripts/pairs.py test HDFCBANK ICICIBANK --csv-dir stocks/      # one pair, full statistics
python3 scripts/pairs.py screen --members members.csv --csv-dir stocks/   # all same-sector pairs
python3 scripts/pairs.py signal BPCL HPCL --csv-dir stocks/ --exit 0.5    # rules + in-sample trades
python3 scripts/pairs.py plan BPCL HPCL --csv-dir stocks/ --lots-csv fo_mktlots.csv \
    --ban-list fo_secban.csv --margin-a 120000 --margin-b 110000          # India execution

Without --csv-dir, prices come from Yahoo (pip install yfinance). Create offline CSVs with ../technical-analysis/scripts/ta.py fetch --symbol TCS --out stocks/TCS.csv. Only a date and a close column are needed; a volume column turns on the liquidity filter. Use split and bonus-adjusted closes. --members is a symbol,sector CSV. Common options: --lookback 500 sessions (0 = all), --end YYYY-MM-DD (re-test an earlier window), --window 60 (z-score), --entry 2 --exit 0 --stop 3.5, --adf-lag N or --max-lag N, --splits 3, --max-half-life 40, --json. Screen adds --min-bars 250 --min-turnover 10 (₹ crore a day) --min-corr 0.5 --top 20.

2. What it computes

Statistic	How
Correlation	Pearson correlation of daily log returns on common dates
Hedge ratio β	OLS of ln A on ln B. Hold ₹β of B against each ₹1 of A. Also reverse OLS and total least squares
Cointegration	Engle-Granger: ADF (no constant) on the OLS residuals, lag by AIC (Schwert maximum) or fixed
Critical values	MacKinnon (2010) Table 2, N = 2 with constant: ≈ −3.90 / −3.34 / −3.04 (1/5/10%) plus a T-adjustment. These are stricter than plain Dickey-Fuller values (≈ −2.86 at 5%) because β was fitted
p-value	MacKinnon (1994) asymptotic surface. Use it for ranking; the critical values decide
Half-life	AR(1) on the spread: s_t = c + φ·s_{t−1}; half-life = ln 0.5 / ln φ sessions
z-score	(spread − 60-session mean) / 60-session sd
Stability	β in 3 consecutive sub-periods; drift ≤ 25% of β = stable, > 50% = unstable

Both regression directions are tested. A pair counts only if both reject the unit root.

3. Reading the result

• Candidate: rejected at 5% or better both ways, half-life 1–40 sessions (--max-half-life; 3–20 fits a monthly futures cycle best) and β stable. Then look at the z-score.
• Half-life sets the trade. A 5-session half-life suits a 1–3 week trade inside one futures month. A 40-session half-life means several rollovers and more charges for the same reversion.
• z ≥ +2: A is rich against B, so short the spread (sell A, buy B). z ≤ −2: long the spread. |z| beyond 3.5: do not add. The relationship may be breaking, often because of news.
• High correlation without cointegration (common in a sector rally) means the stocks move together day to day, but the gap can trend for months. Do not trade it as mean reversion.

4. Signals (in-sample)

signal enters at |z| ≥ 2 once |z| has reset inside the band. It exits when z returns to 0 (or ±0.5 with --exit 0.5), stops at |z| ≥ 3.5, and time-stops after 2× the half-life (--max-hold, --time-stop-mult). Each trade is returned as % of gross notional. The trade list is in-sample: β, the test and the half-life all come from the same data, so the hit rate is an optimistic upper bound and excludes costs. Check out of sample: run test with --end six months back, then see whether the pair still holds on the newer data.

5. Executing in India (plan)

• The short leg. Cash-market shorts must be covered the same day. A short left undelivered goes to the exchange auction and pays a close-out penalty. Multi-day pairs therefore use stock futures: both legs (default), or --legs cash-long to buy the long leg for delivery and short the other leg in futures. SLB (stock lending) exists but is thin.
• Whole lots. A stock-futures lot is several lakh rupees, so β rarely maps to whole lots. plan rounds the B leg, reports the residual mismatch in % and ₹, and lists the lot combinations with the tightest hedge. With --legs cash-long, the delivery leg is sized in shares.
• Lot sizes: --lot-a/--lot-b, or --lots-csv with NSE's fo_mktlots.csv (one column per contract month). NSE revises lot sizes periodically, and corporate actions adjust them. If the file shows a different size in a later month, the plan flags it: re-size the hedge when you roll.
• Margin: --margin-a/--margin-b (₹ per lot from your broker), otherwise --margin-pct 25 of contract value per leg. Margin is summed leg by leg. A long/short across two different stocks is not a recognised spread, so do not count on a hedge margin benefit. Futures are marked to market daily, so keep a buffer.
• Charges come from ../trading-costs/scripts/charges.py (futures STT 0.05% on the sell side since Apr 2026). The plan counts one round trip per leg plus one per roll, and futures carry (the long leg pays it, the short earns it).
• Rollover: stock futures expire on the last Tuesday of the month, or the previous trading day if that is a holiday (from ../fno-options-analysis/scripts/options.py). They are physically settled. The plan lists roll-by dates within the expected hold (2× half-life). Near expiry, it switches to the next month.
• F&O ban: a stock enters the ban when OI crosses 95% of MWPL, and stays until it falls below 80%. In a ban you can only reduce, so you cannot open the pair or roll the leg. Pass --ban-list (NSE fo_secban.csv), --banned SYM, or --mwpl-a/--mwpl-b (%). See indian-market-structure.

6. Classic Indian pairs to test (not recommendations)

HDFCBANK/ICICIBANK, KOTAKBANK/AXISBANK, SBIN/BANKBARODA, TCS/INFY, HCLTECH/WIPRO, BPCL/HPCL (IOC as a third), ULTRACEMCO/SHREECEM, TATASTEEL/JSWSTEEL. They share sector, regulation and macro drivers. That makes them worth testing, not cointegrated by default. Re-test every quarter.

7. Pitfalls

• Structural breaks: mergers and demergers end relationships. HDFC Ltd merged into HDFC Bank in July 2023, which ended the classic HDFC/HDFCBANK pair. A demerger (Jio Financial out of Reliance, 2023) leaves a price gap in unadjusted data. Results, management changes and regulatory actions can break a pair for good. A stop is for that case, not for noise.
• Corporate actions: use adjusted closes for splits and bonuses. A large special dividend shows up as a spread jump on the ex-date.
• Look-ahead: in-sample signals use tomorrow's β today. Expect worse results live.
• Multiple testing: 10 bank stocks give 45 pairs. At 5%, about 2 will pass by chance. Apply a Bonferroni-style bar (0.05 / 45 ≈ 0.001), which screen reports, and confirm on a later window.
• Short samples: under about 250 sessions, the test has little power and β is noisy.
• Results season: a quarterly result on one leg alone can blow through the stop. Know both dates.

Related skills

Size the risk-to-stop rupee figure with position-sizing; compare broker costs in trading-costs; ban and margin rules in indian-market-structure; expiries in fno-options-analysis; sector backdrop in sector-rotation.

Output

Pair A / B: N sessions [from → to] | corr r | β (OLS / TLS) | EG t = x vs 5% crit y → reject? p≈
Half-life H sessions | z now Z → zone | β stability: stable/drifting/unstable | verdict
Signal (in-sample): trades n, hit rate h%, avg r% | now: flat / open / signal
Plan: SELL A fut n lots / BUY B fut m lots | mismatch ±x% | margin ₹ | charges ₹ | roll by date
Risks: F&O ban, lot revision, results dates, structural break

Educational analysis, not investment advice.