Fair value
Also written Theoretical futures price · Fair value of a futures contract · Fair value (of a derivative)
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.
Where this is taught
- Series I · Chapter 9: Accounting and Taxation of ETCDintroduced here
- Series XVI · Chapter 3: Commodity Futuresintroduced here
- Series XIX-D · Chapter 11: Valuationintroduced here
- Series IV · Chapter 9: Accounting and Taxation of IRDintroduced here
- Series XIX-A · Chapter 11: Valuationintroduced here
- Series XIX-C · Chapter 14: Valuationintroduced here
- Series XVI · Chapter 9: Accounting and Taxation
Related terms
- ConvergenceThe certainty that a futures price and the spot price of its underlying meet at expiry — because on the last trading day the contract settles at the cash market price, leaving no room for a difference.
- 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 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.
- 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.
- Amortized CostA debt security's purchase cost adjusted for the purchase discount or premium over its maturity — how a Category III AIF values unlisted securities with no ascertainable market, plus accrued interest.
- Law of one priceThe principle that identical assets cannot trade at different prices in two markets, beyond the transaction costs between them — because arbitrageurs would close the gap.
- Non-traded securityA security (other than money market and debt) not traded on any stock exchange for thirty days before the valuation date, which the AMC must then value in good faith rather than at a market price.
- Fair Value Through Profit or LossThe default Ind AS 109 measurement for a derivative not in a qualifying hedging relationship — recognised at fair value on the balance sheet, with every gain or loss taken straight to profit and loss.
- Unaffected share priceA target company's share price before a merger or acquisition is announced — the base over which an acquirer must pay a premium, and the price a merger arbitrageur measures the spread from.
- Market approachValuing a business from what the market pays for comparable businesses, using earnings and market multiples rather than the company's own projected cash flows.
- Cost approachValuing a business from its assets less its liabilities — by book value, by what it would cost to replace, or by what it would fetch if broken up and sold.
- Hedging instrumentIn hedge accounting, the derivative — a forward, future or option — used to reduce the risk of the hedged item, whose gains and losses are matched against that item under the ICAI Guidance Note.
- Cash Flow Hedging ReserveThe equity account in which the fair-value gains and losses of a derivative designated as a cash flow hedge are parked until the hedged forecast transaction hits profit and loss.
- Accounting mismatchThe gap between a derivative, measured at fair value, and the exposure it hedges, usually measured at cost — the very mismatch hedge accounting exists to offset.
- Exit priceThe ICAI Guidance Note's definition of fair value for a derivative — the price to sell or transfer the position to a willing counterparty today, factoring in available collateral.
- Prospective effectiveness testingThe forward-looking test, done at hedge inception and at every reporting date after, that checks whether a hedge is expected to offset nearly all of the change in the hedged item.
- ICAI Guidance NoteICAI's revised 2021 note on accounting for derivative contracts, effective for accounting periods beginning on or after 1 April 2021, requiring every derivative on the balance sheet at fair value.
- Base priceThe reference price a contract starts each trading day from — the theoretical futures price on the day it is introduced, and the previous day's daily settlement price on every day after.
- Interest rate parityThe principle that a currency pair's forward or futures price differs from spot by the two currencies' interest rate differential, so borrowing in one and lending in the other earns no riskless profit.
- 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.
- Post-money valuationA start-up's pre-money valuation plus the new money going in — the number that fixes what percentage of the company the incoming investor owns after the round.
- Price of Previous Transaction MethodAn IPEV valuation method that marks an AIF's whole holding in a company at the price of its latest follow-on investment; a first investment is carried at cost until a follow-on reprices it.
- Adjusted NAVThe value of an AIF measured as the cash investors would receive if every portfolio investment were realised at fair value on the valuation date, after taxes, fees, expenses, carry and other deductions.
- Milestone ValuationAn investor protection under which a venture investor pegs the company's valuation to technical or commercial targets in the business plan, so missed milestones can mean a lower valuation or delayed funding.