Zero sum game
The principle that every derivative long has a matching short, so one side's gain is exactly the other side's loss and the net value of all derivative positions is zero.
In plain language
A derivative is only a contract between two people with opposing views about the price of something else.
The seller of gold futures thinks prices will fall; the buyer thinks they will rise. When the price moves, whatever one gains, the other loses. Add the two positions together and you get zero.
That is what the workbook means by a zero sum game: in a derivative market there is a "long" position of a buyer and a corresponding "short" position of a seller, so "by definition, the net economic value of all derivative positions should be zero". No new asset and no new underlying is created by writing derivative contracts on it.
How it works
Take the workbook's own forward on 10 grams of gold at Rs 30,000, one year out:
| Gold price at maturity | Buyer | Seller | Sum |
|---|---|---|---|
| Rs 30,000 (unchanged) | 0 | 0 | 0 |
| Rs 35,000 | + Rs 5,000 | − Rs 5,000 | 0 |
| Rs 25,000 | − Rs 5,000 | + Rs 5,000 | 0 |
The workbook's comment on the outcomes: "one of the two parties tends to lose, while the other gains", because neither knew the future price.
The same holds for options, once the premium is counted. The premium is simply a transfer from buyer to writer, so it cancels too.
Why it matters: the derivative market transfers risk — the primary objective the workbook gives for any derivative contract — but it does not create wealth. Gains to hedgers who got protection, or to speculators who guessed right, are paid for by the other side of the same contracts.
A worked example
The workbook's option example: Arvind buys a Nifty call from Salim, strike Rs 10,000, premium Rs 100.
Case 1 — Nifty settles at Rs 10,200. Arvind exercises.
Arvind: +200 (buys at 10,000 what is worth 10,200) − 100 premium = +Rs 100
Salim: +100 premium − 200 (sells at 10,000 what is worth 10,200) = −Rs 100
Sum = 0
Case 2 — Nifty settles at Rs 9,800. Arvind does not exercise.
Arvind: −Rs 100 (premium lost)
Salim: +Rs 100 (premium kept)
Sum = 0
Scaling it up, with illustrative numbers: if 40,000 such contracts are open and the Nifty settles at 10,200, the buyers as a group gain Rs 40 lakh and the writers as a group lose exactly Rs 40 lakh. Nothing in between leaks away except brokerage and taxes, which make the game slightly negative sum for the two traders taken together.
Why NISM asks about it
Chapter 6 (Derivative Markets), section 6.2.1 "Zero Sum Game in Futures", is the first of the chapter's underlying concepts, placed before settlement mechanism, OTC versus exchange-traded, and arbitrage. It connects to the gold forward (section 6.1) and the Arvind–Salim option example (section 6.3.3). Expect a straight statement question: "the net economic value of all derivative positions is..." — zero — or "derivative contracts create a new underlying asset: true or false?" — false.
Common exam traps
- Zero sum does not mean nobody profits. It means every profit is matched by an equal loss on the other side.
- No new asset is created by a derivative contract. The underlying is the same gold or the same index.
- The option premium does not break the rule. It is paid by one party and received by the other.
- It is a statement about derivative positions. The workbook's point is that the contract adds no new asset; the underlying gold or index is unchanged by it.
- Transaction costs make the combined result slightly negative, not positive.
- Risk transfer is the purpose, not wealth creation: a hedger can "lose" on the derivative and still be better off because the underlying exposure gained.
Where this is taught
- Series XXI-B · Chapter 5: Derivativesintroduced here
- Series XXI-A · Chapter 5: Derivativesintroduced here
- Series X-A · Chapter 10: Understanding Derivativesintroduced here
- Series XII · Chapter 6: Derivative Marketsintroduced here
Related terms
- HedgingTaking a derivative position that moves opposite to an exposure you already have, so gains on one offset losses on the other and the future rate is locked in at a known level.
- DerivativeA contract whose value is derived from the value of something else — the underlying — rather than from anything the contract itself owns or produces.
- Forward contractA bilateral, over-the-counter agreement between two parties to buy or sell an asset on a fixed future date at a price agreed today — customised to suit them, and binding on both.
- Futures contractA standardised forward traded on an exchange, where the exchange fixes every term except the price and the clearing corporation guarantees settlement, so neither side carries the other's default risk.
- OptionA contract giving the buyer the right, but not the obligation, to buy or sell the underlying at a stated price on or before a stated date, in exchange for a premium paid to the writer.
- SwapA derivative in which two parties agree to a specified exchange on future dates — typically one pays a fixed interest rate and receives a floating one on an agreed principal that never itself changes hands.
- Cash settlementSettling a derivative on expiry or exercise by exchanging the price difference, without delivering the underlying asset. SEBI mandates physical settlement for stock derivatives, not index derivatives.