NISM Series XVI Formula Sheet
Ten formulas, what each one is for, and a worked example.
Commodity futures differ from financial futures in one way: physical goods cost money to store, insure and finance. Series XVI builds its pricing and hedging questions around that.
These ten formulas cover it, with a worked short-hedge example.
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The 10 Formulas
1
Formula
Futures fair price (cost of carry)
Expression
F = S + Financing + Storage + Insurance − Convenience yield
Use it for
Theoretical futures price of a storable commodity.
2
Formula
Basis
Expression
Basis = Spot price − Futures price
Use it for
Local cash price relative to futures; drives hedge results.
3
Formula
Contract value
Expression
Futures price × Lot size
Use it for
Exposure per contract.
4
Formula
Mark-to-market
Expression
(Today's settlement − Previous settlement) × Lot size × Contracts
Use it for
Daily profit or loss settled in cash.
5
Formula
Effective price of a short hedge
Expression
Spot price at sale + (Futures sold − Futures bought back)
Use it for
What a producer actually receives after hedging.
6
Formula
Effective price of a long hedge
Expression
Spot price at purchase − (Futures sold back − Futures bought)
Use it for
What a buyer actually pays after hedging.
7
Formula
Hedge contracts
Expression
Quantity to hedge ÷ Lot size
Use it for
Contracts needed for a physical position.
8
Formula
Calendar spread
Expression
Far-month futures − Near-month futures
Use it for
Trading the difference between two expiries.
9
Formula
Call option payoff (long)
Expression
max(F_T − K, 0) − Premium
Use it for
Options on commodity futures.
10
Formula
Put option payoff (long)
Expression
max(K − F_T, 0) − Premium
Use it for
Producers buying protection against a price fall.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Futures fair price (cost of carry) | F = S + Financing + Storage + Insurance − Convenience yield | Theoretical futures price of a storable commodity. |
| 2 | Basis | Basis = Spot price − Futures price | Local cash price relative to futures; drives hedge results. |
| 3 | Contract value | Futures price × Lot size | Exposure per contract. |
| 4 | Mark-to-market | (Today's settlement − Previous settlement) × Lot size × Contracts | Daily profit or loss settled in cash. |
| 5 | Effective price of a short hedge | Spot price at sale + (Futures sold − Futures bought back) | What a producer actually receives after hedging. |
| 6 | Effective price of a long hedge | Spot price at purchase − (Futures sold back − Futures bought) | What a buyer actually pays after hedging. |
| 7 | Hedge contracts | Quantity to hedge ÷ Lot size | Contracts needed for a physical position. |
| 8 | Calendar spread | Far-month futures − Near-month futures | Trading the difference between two expiries. |
| 9 | Call option payoff (long) | max(F_T − K, 0) − Premium | Options on commodity futures. |
| 10 | Put option payoff (long) | max(K − F_T, 0) − Premium | Producers buying protection against a price fall. |
Worked Example: A Producer's Short Hedge
A gold producer sells futures at ₹72,000 per 10 g. At delivery, spot is ₹69,000 and the futures are bought back at ₹69,300.
- 1
Gain on futures
72,000 − 69,300 = ₹2,700.
- 2
Effective price
69,000 + 2,700 = ₹71,700.
- 3
Why not ₹72,000?
At close the basis was 69,000 − 69,300 = −₹300. The effective price is the futures price sold plus the closing basis: 72,000 − 300 = ₹71,700.
Free account, this exam preselected.
Hedges Remove Price Risk, Not Basis Risk
A hedge locks in the futures price, but the effective price still moves with the basis at closing. Questions that give spot and futures prices at both dates are testing basis.
FAQs
What is convenience yield?expand_more
The benefit of holding the physical commodity, such as keeping a factory running. It lowers the futures price relative to spot plus carry.
Is backwardation common in commodities?expand_more
It happens when near-term supply is tight, so spot or near-month prices sit above far-month prices.
Are commodity options on spot or futures?expand_more
On Indian exchanges, most commodity options are on futures contracts, and devolve into futures positions on exercise.
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