Fair value
Also written Theoretical futures price · Fair value of a futures contract
The theoretical futures price — spot plus the cost of carrying the commodity to expiry — at which a buyer is indifferent between buying today and buying forward.
In plain language
A futures price is not a forecast. Most of it is arithmetic.
If you need a commodity in four months you can buy it now and carry it, or buy the future. Fair value is the futures price that makes those two routes cost exactly the same. Above it, buying spot and storing is cheaper. Below it, buying the future is cheaper.
That is why the workbook calls it the price that is fair to both the buyer and the seller of the contract: at fair value neither side has a free lunch, and there is no arbitrage to take.
How it works
The simple additive form is Fair value = Spot price + Cost of carry, and cost of carry is finance cost plus storage plus insurance over the holding period.
Where the money cost is compounded rather than applied simply, the workbook gives three versions and expects you to know which to use:
- annual compounding —
F = S x (1 + r)^n mtimes a year —F = S x (1 + r/m)^(m x n), withm = 2for semi-annual,4for quarterly,12for monthly- continuous (daily) compounding —
F = S x e^(r x n), withe = 2.71828
The continuous form is the one used when no storage cost is involved — it prices the futures contract purely as money invested at r for n years.
What sits between fair value and the traded price is convenience yield, which pulls the futures price down by Y.
The formula
Fair value = Spot price + Cost of carry
Annual compounding F = S x (1 + r) ^ n
m-times compounding F = S x (1 + r / m) ^ (m x n)
Continuous compounding F = S x e ^ (r x n)
S : spot price r : cost of financing, per annum
n : years to expiry m : compounding frequency per year
A worked example
Three of the workbook's own valuations, side by side.
1. Simple carry, with storage. Spot Rs 2,500, holding period 90 days, interest 6% p.a., storage 1% p.a.
Finance cost = 2,500 x 0.06 x (90/365) = Rs 36.98
Storage = 2,500 x 0.01 x (90/365) = Rs 6.16
Cost of carry = Rs 43.14
Fair value = 2,500 + 43.14 = Rs 2,543.14
2. Simple carry on gold. Spot Rs 1,20,000 per 10 grams, cost of carry 12% p.a., four months:
F = 1,20,000 + (1,20,000 x 12% x 4/12) = 1,20,000 + 4,800 = Rs 1,24,800
3. The same four months, compounded. Spot Rs 50,000 per 10 grams, financing 12% p.a.
| Compounding | Working | Fair value |
|---|---|---|
Monthly (m = 12) | 50,000 x (1.01)^4 = 50,000 x 1.040604 | Rs 52,030 |
| Continuous | 50,000 x e^0.04 = 50,000 x 1.04081 | Rs 52,040 |
Ten rupees per 10 grams separates them — Rs 1,000 on a one-kilogram gold contract, purely from the compounding convention.
Why NISM asks about it
Chapter 3 (Commodity Futures), section 3.5, which is the most calculation-heavy section in the paper. The chapter's own sample question — spot gold Rs 50,000 per 10 grams, cost of carry 12% per annum, three-month fair value — answers Rs 51,500, straight from S + S x r x n. Expect one or two arithmetic questions, plus a conceptual one on what a buyer should do when the spot-futures difference is larger or smaller than the cost of carry.
Common exam traps
- Convert the tenor to years before using
n. Four months is4/12, ninety days is90/365. The workbook uses 365 days, not 360. - Simple carry and compounded carry give different answers — Rs 52,000 against Rs 52,030 against Rs 52,040 on the same gold. Read which the question asks for.
mis the compounding frequency, not the number of periods. Monthly compounding for four months ism = 12andn = 4/12, giving the exponent 4.- The continuous form assumes no storage cost. Do not use
S x e^(r x n)on a commodity where the question hands you a warehousing charge. - Fair value is theoretical. The traded futures price differs from it, and the gap is where convenience yield and arbitrage live.
- If the spot-futures difference is greater than the cost of carry the buyer is better off buying spot and storing; if less, better off buying the future. Candidates routinely flip this.
Check yourself
1.The ICAI guidance note requires that all derivatives are recognised on the ______ and measured at fair value.
- a)Balance sheet
- b)Income statement
- c)Cash flow statement
- d)Speculative statement
Show the answer
Answer: (a) Balance sheet
(This is a sample question from the NISM workbook.)
The reasoning is worth holding on to, because it is what makes the rule inevitable rather than arbitrary. A futures contract may cost nothing to enter — no premium, only margin — yet from the moment it is struck it creates enforceable rights and duties. An accounting system that showed nothing until settlement would leave an entire derivative book invisible to a reader of the accounts.
And "fair value" has a specific meaning here: ⚠️ "FAIR VALUE in the context of derivative contracts REPRESENTS THE EXIT PRICE — the price that would be PAID TO TRANSFER A LIABILITY or RECEIVED WHEN TRANSFERRING AN ASSET to a knowledgeable, willing counterparty." And "THE EXTENT AND AVAILABILITY OF COLLATERAL SHOULD BE FACTORED IN."
Note also that recognition is unconditional: the Note applies to its four categories of contract ⚠️ "WHETHER OR NOT USED AS HEDGING INSTRUMENTS." Hedge accounting is an additional, optional treatment on top — not a precondition for the derivative appearing on the balance sheet at all.
2.The cost of 10 grams of gold in the spot market is Rs 50,000 and the cost of financing is 12% per annum compounded monthly. Using F = S × (1 + r/m)^(m × n), what is the fair value of a 4-month futures contract?
- a)Rs 50,500
- b)Rs 52,030
- c)Rs 56,000
- d)Rs 56,730
Show the answer
Answer: (b) Rs 52,030
With m = 12 and n = 4/12 years:
- F = 50,000 × (1 + 0.12/12)^(12 × 4/12)
- F = 50,000 × (1.01)^4
- F = 50,000 × 1.040604
- ⚠️ F = Rs 52,030
Watch the exponent — this is where the marks go. m × n = 12 × (4/12) = 4, which means four monthly compounding periods, not twelve. Anyone who writes (1.01)^12 has quietly converted a four-month contract into a one-year one, and lands near option (d) at Rs 56,730.
For comparison, the same gold under continuous compounding:
Compounding 4-month fair value Monthly (m = 12) Rs 52,030 Continuous, F = S × e^(r×n) Rs 52,040 The continuous figure is always the higher of the two, because interest starts earning interest at every instant rather than once a month. Note also that the continuous formula is used to calculate the futures price of a commodity when no storage costs are involved — it prices financing alone.
And the conversions to memorise: semi-annual means m = 2, quarterly means m = 4.
3.From an accounting point of view, which of the following is a type of hedge?
- a)Fair value hedge only
- b)Cash flow hedge only
- c)Net investment hedge only
- d)Fair value hedge, cash flow hedge and net investment hedge
Show the answer
Answer: (d) Fair value hedge, cash flow hedge and net investment hedge
(This is a sample question from the NISM workbook.)
"From the accounting point of view there are THREE TYPES OF HEDGES, viz. FAIR VALUE HEDGE, CASH FLOW HEDGE AND NET INVESTMENT HEDGE."
The phrase "from an accounting point of view" is doing real work in this question. Elsewhere in the syllabus hedges are classified quite differently — as long hedge and short hedge, by the direction of the futures position. Those are market categories. The accounting categories ask a different question: what is being protected, and is it already on the balance sheet?
Accounting hedge What it protects ⚠️ Fair value hedge "The risk of a FAIR VALUE CHANGE OF ASSETS AND LIABILITIES ALREADY RECOGNIZED IN THE BALANCE SHEET, OR A FIRM COMMITMENT THAT IS NOT YET RECOGNIZED" ⚠️ Cash flow hedge "The risk of CHANGES IN HIGHLY PROBABLE FUTURE CASH FLOWS OR A FIRM COMMITMENT IN A FOREIGN CURRENCY" ⚠️ Net investment hedge Hedges of net investments in foreign operations, requiring separate disclosure The first two are worked through in the Company Z copper example, where the same futures contract produces two entirely different sets of entries depending on whether it is designated against existing inventory or against forecast sales.
Where this is taught
- Series IV · Chapter 9: Accounting and Taxation of IRDintroduced here
- Series XVI · Chapter 3: Commodity Futuresintroduced here
- Series XIX-C · Chapter 14: Valuationintroduced here
- Series XIX-D · Chapter 11: Valuationintroduced here
- Series I · Chapter 9: Accounting and Taxation of ETCDintroduced here
- Series XIX-A · Chapter 11: Valuationintroduced here
- Series XVI · Chapter 9: Accounting and Taxation
Related terms
- ConvergenceThe principle that futures and spot prices meet at maturity, because at that single point in time there can be no difference between them.
- 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.
- Cost of carryStorage cost plus the interest to finance holding the asset until delivery, less the income earned on it.
- ContangoA market in which the futures price sits above the spot price, normally because the futures buyer is paying for the cost of carrying the commodity through to delivery.
- Convenience yieldThe rupee benefit of physically holding a commodity rather than holding a futures contract on it — the term that lets a futures price fall below spot plus carry.
- IPEV GuidelinesThe international best-practice guidelines for valuing unlisted private equity and venture capital investments at fair value, setting out seven widely used methods for valuing a portfolio company.