No-arbitrage bounds
The band around the fair futures price, created by transaction costs, taxes and margins, within which a mispricing is too small to arbitrage profitably — so prices can sit there undisturbed.
In plain language
The cost of carry model says that if a futures contract trades away from its fair price, arbitrageurs will pounce until the gap closes. In a frictionless world that would pin the futures price exactly to fair value.
Real markets have friction. Margins, transaction costs (commissions) and taxes all have to be paid to execute the arbitrage. The workbook says these cost components "create distortions and move the markets away from equilibrium" — and specifically that they create no-arbitrage bounds.
Inside the bounds, a mispricing exists but cannot be profitably exploited, so arbitrage will not take place. For arbitrage to be triggered, the futures price must fall outside the no-arbitrage bounds in either direction.
How it works
Picture the fair price as a line, with a band drawn above and below it.
- Above the upper bound, the futures price exceeds fair value by more than the cost of doing the trade, and cash and carry arbitrage — buy spot, sell futures — pays.
- Below the lower bound, reverse cash and carry arbitrage — sell spot, buy futures — pays.
- Between the bounds, nothing pays, so nothing happens.
Width. The workbook says "practically, every component of carrying cost contributes towards widening of these no-arbitrage bounds", and that the wider the bounds, the farther the markets are from equilibrium. For markets to be efficient, costs should be as low as possible; lower costs narrow the bounds and ensure efficient price alignment.
Different for different people. Borrowing costs, return expectations and so on differ between participants, so fair values and no-arbitrage bounds differ too. The workbook suggests that this may be exactly what makes trading happen continuously.
The model ignores them. The cost of carry model's stated assumptions include no transaction costs, no taxes and no margin requirements. The fair price it produces is therefore the centre of the band, not a price at which arbitrage necessarily becomes profitable. Chapter 3 says an arbitrage is feasible "only if it provides net cash inflow after transaction costs, brokerage, margin deposits, etc."
A worked example
The workbook's gold arbitrage (Chapter 3, section 3.7). Spot gold Rs 62,130 per 10 g; cost of financing, storage and insurance for three months Rs 100; three-month futures Rs 62,280.
Fair futures price = 62,130 + 100 = Rs 62,230
Gross arbitrage gain = 62,280 − 62,230 = Rs 50 (workbook: no transaction costs considered)
Now add friction (illustrative). Suppose brokerage, taxes and the cost of margin for the round trip come to Rs 70 per 10 g, and assume the same cost applies to the reverse trade.
Upper bound = 62,230 + 70 = Rs 62,300
Lower bound = 62,230 − 70 = Rs 62,160
| Futures price | Position vs bounds | Net result of arbitrage |
|---|---|---|
| Rs 62,280 | Inside | 50 − 70 = −Rs 20 — no trade |
| Rs 62,350 | Above upper | 120 − 70 = +Rs 50 — cash and carry |
| Rs 62,100 | Below lower | 130 − 70 = +Rs 60 — reverse cash and carry |
The workbook's Rs 50 opportunity disappears once costs are counted.
How wide are real bounds? The workbook's Chapter 6 cost example — one lot of index futures sold at 17,500, lot size 50, contract value Rs 8,75,000 — totals Rs 769.97 in brokerage, STT, exchange fees, SEBI and IPFT charges and GST. That is 769.97 ÷ 50 = 15.40 index points for the futures leg alone, before the cash-market leg is paid for. A futures contract trading 10 points rich is not an arbitrage for that trader.
Why NISM asks about it
Chapter 3, section 3.7 (Futures pricing), introduces no-arbitrage bounds under "Cost of transaction and no-arbitrage bounds", right after cash and carry and reverse cash and carry arbitrage, and notes that bounds differ across participants. Section 3.9 repeats that arbitrage is undertaken only if it yields a net inflow after costs. Expect conceptual questions: what creates the bounds, what happens inside them, and whether wider bounds mean a more or less efficient market.
Common exam traps
- Inside the bounds, arbitrage does not take place — even though the futures price differs from fair value.
- Wider bounds = farther from equilibrium = less efficient. Lower costs narrow them.
- The fair price excludes costs; the bounds are built from them. They are not the same thing.
- Bounds differ between participants, because their costs and borrowing rates differ.
- Above the upper bound → cash and carry (buy spot, sell futures); below the lower bound → reverse cash and carry.
- The cost of carry model assumes away transaction costs, taxes and margins; the bounds are what those assumptions hide.
Where this is taught
Free preparation for NISM Series VIIIRelated terms
- Securities Transaction TaxA central government tax collected by the exchange on the sell side of every futures and option trade — 0.05% of futures traded value, 0.15% of option premium, and 0.15% of settlement price on exercise.
- ArbitragerA participant who locks a profit by entering opposite transactions in two markets at once — carrying no exposure and taking no view, and in the process pulling the two prices back together.
- ArbitrageSimultaneously buying and selling an asset, or a replica of it, in different markets to profit from a price discrepancy — a trade that aims to lock in a profit rather than bet on direction.
- Cost of carryThe cost of holding an asset until a future date — financing interest plus storage, less any income it pays. It links spot to futures: fair futures price = spot + cost of carry − inflows.
- Cash and carry arbitrageBuying the underlying in the cash market and simultaneously selling futures when futures trade above their fair price, carrying the asset to expiry to lock in the mispricing.
- Reverse cash and carry arbitrageSelling the underlying in the cash market and simultaneously buying futures when futures trade below their fair price — the mirror image of cash and carry, and it needs stock to sell.
- Spot priceThe price at which the underlying asset trades in the cash market for immediate delivery — the anchor from which futures prices, basis, moneyness and final settlement are all measured.