Introductory Context
"Quantitative intraday arbitrage strategy across same-index ETF pairs on the National Stock Exchange. Modeling executable quote spreads and Authorized Participant creation bounds."
The Law of One Price: Arbitrage Across Same-Index ETF Pairs
On the National Stock Exchange (NSE), multiple asset management companies issue Exchange Traded Funds (ETFs) that track the exact same underlying benchmark index. For example, NIFTYBEES (Nippon India), SETFNIF50 (SBI Mutual Fund), ICICINIFTY (ICICI Prudential), and HDFCNIFTY (HDFC AMC) all hold the exact same 50 constituent stocks of the Nifty 50 Index in identical market-cap weights.
Because each ETF trades independently on the secondary order book with different market makers and retail order flows, transient supply-demand imbalances cause temporary pricing discrepancies. When one Nifty ETF's bid price exceeds another Nifty ETF's ask price by more than a costed threshold κ, a risk-free Same-Index ETF Arbitrage opportunity exists.
• The Executable Arbitrage Condition
Short Rich ETF 1 & Buy Cheap ETF 2 when:
Bid(ETF 1) ≥ Ask(ETF 2) × κ
where κ > 1.0 (e.g. κ = 1.002) is the all-in cost threshold incorporating brokerage, exchange turnover fees, STT, and latency buffers.
Mathematical Model & Unwind Conditions
Let P^{bid}_i and P^{ask}_i represent the executable inside quotes on ETF 1 and ETF 2:
P^{bid}_1 ≥ P^{ask}_2 × κ
Simultaneously sell ETF 1 at the bid and buy ETF 2 at the ask with matched dollar notionals (Q_1 × Bid_1 + Q_2 × Ask_2 = 0).
P^{bid}_2 ≥ P^{ask}_1
Close both legs when the executable spread normalizes, locking in the locked basis profit.
Authorized Participant (AP) NAV Creation & Redemption
In addition to secondary exchange order-book trading, institutional Authorized Participants (APs) keep ETF market prices anchored to fundamental Indicative Net Asset Value (iNAV):
- Cash Premium Arbitrage: When ETF Market Price > iNAV, APs buy the underlying 50 cash stocks on NSE, deliver the basket to the AMC in Creation Units, receive new ETF units, and sell them into the market.
- Cash Discount Arbitrage: When ETF Market Price < iNAV, APs buy cheap ETF units on the market, redeem them with the AMC for the underlying stock basket, and sell the stocks on the exchange.
- Fill-or-Kill (FOK) Requirement: In electronic pairs arbitrage, both legs must be executed simultaneously via Fill-or-Kill orders. If one leg fails to fill, the position must be aborted immediately to prevent unhedged directional market risk.
Execution Hazard: Stale Quotes & Lagged Snapshots
Apparent arbitrage crosses observed in delayed market feeds are almost always stale quote illusions. If one ETF order book has not updated after a sudden market move, attempting to execute will result in immediate rejection or adverse fills.
Educational and Research Simulator Only
This strategy documentation is for educational and quantitative backtesting purposes only. High-frequency ETF arbitrage requires sub-millisecond execution and direct AMC authorized participant facilities.