Equity Cash-and-Carry Futures Arb
Equity cash-and-carry arbitrage compares an index future with the cost of buying its underlying equity basket and financing it to expiry. If the future is sufficiently rich, buy cash equities and sell futures. If it is sufficiently cheap, buy futures and short or otherwise finance the basket. The contractual payoff anchors the trade, but the executable threshold is wider than the textbook basis.
With continuous funding rate r, dividend yield q, and time T:
F_theoretical = S * exp((r - q) * T)
For a real index, replace q with forecast cash dividends at their ex-dates and use the desk’s incremental financing and stock-borrow curves. The full carry framework is covered in equity index futures basis.
Build the all-in threshold
The rich-futures trade sells the future at bid and buys each stock at ask. It must also fund the cash basket, receive dividends, meet margin, and execute the eventual unwind. A conservative comparison is:
sell-future edge = F_bid - (cash_ask + funding - dividends + fees + impact)
The reverse direction uses future ask, cash bid, stock borrow, and the risks of dividend payments on the short. A published index spot value is not a basket price. Use current constituent weights, bid/ask quotes, corporate-action adjustments, and stale-price flags.
| Cost component | Long cash / short future | Long future / short cash |
|---|---|---|
| Financing | pay funding | invest cash or post collateral |
| Dividends | receive forecast dividends | pay manufactured dividends |
| Stock loan | usually none | can dominate economics |
| Equity execution | buy at ask | sell at bid |
| Futures execution | sell at bid | buy at ask |
import math
def fair_future(spot, rate, dividend_yield, years):
return spot * math.exp((rate - dividend_yield) * years)
def rich_future_edge(future_bid, basket_ask, funding, dividends, costs):
return future_bid - basket_ask - funding + dividends - costs
The code is a sensitivity calculator, not an execution engine. Dividends should be modeled per constituent and ex-date, with uncertainty for special dividends, withholding, and corporate actions. Funding should reflect the marginal rate and collateral convention rather than a generic policy rate.
Execution and residual risk
Enter the future and cash legs as a coordinated program. Partial fills leave exposure to a moving basis and market beta. Set a maximum unhedged notional, dynamically hedge completed cash fills, and reserve an impact budget that grows with participation rate. The close can offer high liquidity but also contains index-fund demand, auction risk, and benchmark competition.
| Condition | What breaks | Response |
|---|---|---|
| Reconstitution | weights and demand shift | use announced effective basket |
| Ex-dividend cluster | carry jumps | reconcile dates and entitlement |
| Volatility shock | spread/impact widens | enlarge buffer or pause |
| Hard-to-borrow name | reverse cash-and-carry fails | exclude or price loan conservatively |
Futures are marked to market daily, whereas the cash basket’s financing and settlement occur on their own schedules. Liquidity and margin calls can therefore arrive before the convergence P&L. Stress the position for futures variation margin, dividend forecast error, index constituent halts, and a sudden inability to borrow the basket.
Expiry and validation
Near expiry, futures converge to the settlement index under that contract’s rules. Settlement may use an opening special quotation rather than the prior close, creating auction exposure. Decide in advance whether to unwind before the calculation window, roll the future, or deliver through final convergence. A trade that is profitable on midpoint data may be negative once entry, exit, and margin funding are included.
Walk-forward testing needs historical constituent files, contemporaneous quotes, point-in-time dividend forecasts, financing assumptions, and realistic basket execution. Decompose realized P&L into basis convergence, dividend error, funding, borrow, and trading costs. That attribution reveals whether the edge was true carry arbitrage or an accidental directional index bet.
The same economics support index arbitrage and program trading; cash-and-carry is simply the expiry-focused form of the broader basket-versus-future relationship.
Key takeaways
- Equity futures fair value is spot plus financing minus actual expected dividends.
- Use executable basket bid/ask and desk-specific funding, not a published spot index.
- Partial fills, dividends, and margin create material residual risk.
- The arbitrage band expands sharply when stock liquidity, borrow, or balance sheet is scarce.