13A.11 Risks and frictions of statistical arbitrage in India

13A.11.1Regime change and crowding#

• Regime change. Cointegration is a property of the process over a sample. Mergers, demergers, index reconstitutions, changes in regulation or in a company's business model change it, and the break can arrive in a single day. Monitor recursively (CUSUM, rolling EG) and treat a known corporate event as a pre-specified break date.
• Crowding. When many funds hold the same spreads, one fund's forced liquidation moves every such spread against the others, and their stop-losses and deleveraging continue the move. The spread may revert later, after the losers have been forced out. Shleifer and Vishny (1997) call this the limits of arbitrage: arbitrage capital is scarce precisely when mispricings are largest. 13A.13.1 is the canonical episode.

13A.11.2Costs#

A pair trade has four legs per round trip. M01 · 1.7 (worked example 3) puts the statutory and brokerage cost of a round trip in one Nifty futures lot at about 5.95 bp of notional (post-April-2026 STT). A pair round trip pays this on both legs, about 12 bp of the long-leg notional, before bid–ask spreads, impact and roll costs. The worked example of 13A.8 used $c = 20$ bp as an illustration. By Proposition 13A.11(c) the optimal band moves only as $c^{1/3}$, but the profit rate falls, and a spread whose stationary standard deviation is not many times $c$ is not worth trading.

13A.11.3Shorting constraints#

• Cash equities. A short sale in the cash market must be covered intraday unless the stock is borrowed through the securities lending and borrowing (SLB) mechanism (M01 · 1.6; M07 · 7.1.6). SEBI permitted short selling by all classes of investors and an SLB scheme in its circular of 20 December 2007 (SEBI circular MRD/DoP/SE/Dep/Cir-14/2007); the scheme began in 2008. Stocks traded in the F&O segment are eligible. SLB tenures of up to 12 months are reported (secondary: law-firm summary, 2025). Liquidity in SLB is thin for most names.
• Disclosure. Under SEBI's circular of 5 January 2024 on the short-selling framework (as summarised by several secondary sources; check the circular): naked short selling is not permitted; institutional investors must disclose upfront at order placement that a sale is a short sale, and may not square off intraday; retail investors disclose by the end of the trading day. SEBI's chairman announced a review of the short-selling and SLB frameworks in November 2025 (reported by Business Standard); as of the date of writing we have not found a final outcome.
• The practical short leg is a futures contract. Single-stock futures exist only for F&O stocks, expire monthly and must be rolled (M07 · 7.3 and 7.4.4: basis risk and roll cost). Index pairs use index futures.
• Lot sizes make hedge ratios discrete. As of 5 Nov 2026 the Nifty 50 futures lot is 65 and the Nifty Bank lot 30 (NSE F&O bhavcopy; M07 facts table). With illustrative levels of 24,500 and 55,500, one lot of each is ₹15.93 lakh and ₹16.65 lakh of notional. A log-price hedge ratio of 1.03 (Bank Nifty on Nifty) needs 1.077 Nifty lots per Bank Nifty lot; 1:1 leaves a 7.1% hedge error; the hedge error first falls below 2% at 11 Bank Nifty against 12 Nifty lots (about ₹3.7 crore gross). Problem 13A.15 does the search.

13A.11.4Data and execution#

• Use prices adjusted for splits, bonuses and (for total return) dividends (M01 · 1.10). An unadjusted bonus issue looks like a 50% crash in one leg, a spectacular false signal.
• Legging risk: the two legs fill at different times and prices. Index futures and liquid stock futures can be traded together as a spread on most platforms, but a fill on one side only is a directional position.
• Non-synchronous closes. MCX gold closes at 11:30 PM or 11:55 PM IST depending on US daylight time (M10 · 10.10); COMEX settles at a different time. A spread built from closing prices contains a timing error that looks like mean reversion.