Introductory Context
"Quantitative multi-cluster statistical arbitrage strategy on Indian equities. Residualizing returns against sector dummy matrices for pure industry-neutral alpha."
Institutional Stat-Arb: Industry-Neutral Residual Mean-Reversion
In single-cluster mean-reversion, all stocks in the universe are de-meaned against a single broad market return. However, in real-world markets, stocks belong to distinct economic sectors and industries (e.g. Private Banks, IT Services, Pharmaceuticals, Metals). If the Banking sector rallies +4% due to an RBI rate cut while the IT sector drops -3% due to US tech earnings, single-cluster models will incorrectly treat Banking stocks as"overpriced" and IT stocks as"underpriced."
Multi-Cluster Statistical Arbitrage solves this structural flaw. By categorizing the Nifty 500 universe into K distinct industry clusters (via GICS classifications or K-Means statistical clustering), the algorithm strips out industry factor returns via Dummy Matrix Regression (R = Λf + ε). The strategy trades strictly within-cluster idiosyncratic residuals (ε_i), ensuring complete sector neutrality.
• Cluster-Demeaned Residual Formula
For stock i belonging to Industry Cluster A:
ε_i = R_i - Mean_Return(Cluster A)
Within every single cluster A: ∑ ε_i = 0. The resulting portfolio is 100% dollar-neutral within every individual industry.
The Dummy Loadings Matrix & OLS Equivalence
Let Λ be the N × K one-hot dummy matrix where Λ_{iA} = 1 if stock i belongs to cluster A, and 0 otherwise:
Λ⊤Λ = diag(N_1, N_2, ..., N_K)
Because every stock belongs to exactly one cluster, the Gram matrix is diagonal. Ordinary Least Squares (OLS) factor estimation collapses identically to simple within-cluster de-meaning.
D_i = -γ × ε_i ⇒ ∑ D_i × Λ_{iA} = 0
Dollar holdings D_i are directly proportional to negative residuals. Capital is long and short within Banking, within IT, within Metals—never net long an entire sector.
Indian Equity Universe Construction (Nifty 500)
On the National Stock Exchange, multi-cluster stat-arb is executed across major industry groups:
- Cluster Minimum Size (N_min ≥ 5): Each industry must contain at least 5 liquid constituent stocks to ensure the cluster mean is statistically robust. Clusters with fewer than 5 names are excluded.
- Point-in-Time Industry Taxonomy: Stock industry assignments are updated on a quarterly basis. Using current industry classifications to backtest historical periods introduces look-ahead bias.
- Holding Horizon: Daily formation (1-to-5 day lookback) with 1-to-5 day holding periods, executed via liquid F&O stock futures or cash equity market-on-open (MOO) orders.
Risk Factor: Single-Stock Earnings Shocks
A stock reporting disastrous quarterly earnings (e.g. an unexpected 30% profit drop) will plummet -15% intraday. Multi-cluster models will classify this large negative return as a massive mean-reverting residual and attempt to buy the stock. Quantitative desks must implement an Earnings Blackout Window (freezing trades 3 days before and after results).
Educational and Research Content Only
This strategy documentation is for educational and quantitative backtesting purposes only. Statistical arbitrage requires low-latency execution and sophisticated borrow management.