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Derivatives Foundation · CoreTrack
1Derivatives, Hedging & Structured Products
iDerivative Fundamentals
DerivativesLong PositionMark to MarketThe UnderlyingThe Derivative ContractHow Derivatives Transfer Financial…
iiForwards and Futures
The Futures ContractLong and Short PositionsThe Spot PriceThe Forward ContractSpot Price vs Forward PriceThe Futures PriceForward and Futures PositionForward vs FuturesHow to Read Futures Margin and Mark-to-MarketHow Futures Margin and Mark-to-Market WorkDeliveryRolloverOpen InterestOpen-Interest ChangeBasis vs Basis RiskHedge Ratio vs Hedge Effectiveness
iiiOptions
OptionsThe Call OptionThe Strike PriceThe Put OptionOption DeltaOption Buyer and Option WriterCollar and Protective PutCall and Put OptionsHow to Map What…How to Take an…Exercise Price and Strike PriceOption Price DriversThe Expiration DateIntrinsic Value and Time Value
ivOption Strategies and Payoffs
Option SpreadsOption PayoffVertical and Calendar SpreadsHow to Map an Option PayoffMaximum GainThe Iron CondorThe Covered CallMaximum LossStraddle and Strangle
vVolatility and the Greeks
The Implied Volatility SurfaceThe Option GreeksHow an Option Payoff…What an Implied Volatility…How Delta, Gamma, Theta…How Option Volatility Surfaces…Delta HedgingTime DecayHistorical VolatilityImplied Volatility vs Historical Volatility
viSwaps and Rate Derivatives
The Interest Rate SwapSwap Rate and Forward RateThe SwapThe Currency SwapInterest Rate Swap and Currency SwapThe Payment DateThe Reset DateThe Swap CurveThe Swap Payment CalculatorHow to Map a…Cross-Currency BasisDay Count ConventionsDerivative and UnderlyingExchange Traded and Over the CounterFixed Leg and Floating LegHow to Read a Derivative ContractHow to Map a Derivative ExposureHow to Read Derivatives Market DataHow to Map Derivative…How to Write a Derivative Research NoteHow to Run a…How to Maintain a Derivatives Decision Log
viiHedging Application
The HedgeHedge RatioHedge or SpeculationFraming a Hedge ObjectiveExposureOffsetBasis RiskHedge Risk or Counterparty RiskThe Hedged Item
viiiStructured Products
What a Structured Product IsStructured Product and Mutual FundHow to Take a…Participation RatePrincipal Protection and Capital Guarantee
ixClearing, Margin and Settlement
The Settlement PriceThe Three MarginsInitial, Variation and Clearing MarginPhysical and Cash SettlementHow a Position Moves…Market SurveillanceCounterparty RiskNettingNetting and SettlementPosition LimitsPosition Limits and MarginMarket ManipulationHow Corporate Actions Can…
xDerivatives Discipline and Cases
Derivative ResearchOpen Interest DataPost-Mortem and Performance Marketing,…Market Observation and Trade SignalScenario Analysis and ForecastReading Derivatives Data When…What a Derivatives Post-Mortem…

The Forward Contract: Bilateral, Customised and Unmargined

A forward contract binds two named parties directly to trade the reference asset on a later date at a price fixed today. Nobody stands between them, so each carries the other side of the promise for the whole term. Every term is negotiated rather than fixed by an exchange, nothing is posted at the start, and all of the money moves on one day at the end.

Two parties who want a price now for a transaction later can simply agree one. Agreeing that price is the whole idea, and a forward contract is that agreement with nothing whatever added to it. What has been left out matters more than anything put in: there is no exchange to standardise the terms, there is no party in the middle to replace the two promises with its own, and there is no collateral anywhere to stand behind them. Taken seriously, those three absences produce every property of a forward contract, including the one property that made somebody build the standardised version.

What does a forward contract bind each side to do?

Start with the promises. Everything else is decoration on top of them. The forward buyer must take delivery of a single unit on the agreed date and must pay the forward price for it. The forward seller must hand that single unit over on the same date and must accept that same price. There is no third clause hiding underneath. Each side is committed the instant the number is written down, and when the date comes round neither may back out of what it committed to.

Notice what that rules out. Neither party holds a right, a choice or an entitlement of any kind here. Neither may look at the price on the day, decide it has gone against them, and quietly step away. If the reference asset has collapsed, the forward buyer still buys at the agreed price. If it has doubled, the forward seller still sells at the agreed price. The arrangement is symmetrical in obligation even though it will be violently unsymmetrical in outcome. Carry that distinction carefully. The instrument that does hand one side a choice is a genuinely different animal and is covered separately.

Now the part readers routinely skip. Nothing at all moves on the day the agreement is struck. There is no premiumA sum handed over at the start to acquire a position. A forward contract carries none. paid to enter a forward contract. Neither side is buying anything from the other on that day. The two parties are exchanging promises, and promises are free to make. The agreement happens today and the money happens later, and on the day it is struck the position has cost nobody a single rupee. The absence is the design, not a gap in it.

Now the version visible from any street, and it repays a moment before any arithmetic starts. A household that has just fixed the price of next winter's firewood with the supplier down the lane has struck a forward contract. No wood has moved. No money has moved. Both sides have simply written a number down and agreed to be held to it. And yet something real has happened. If firewood is dearer in December that household is in a different position from the neighbour who agreed nothing, and if it is cheaper the household has bound itself to overpay. Nobody has bought anything yet. Everybody is committed.

Try it out

A forward buyer and a forward seller agree today to trade one unit of the reference asset in a year at a fixed price. How much money changes hands on the day they agree?

Who stands between the two parties?

Nobody. The word bilateral carries exactly that much content, and it deserves unpacking rather than nodding at. Most of the consequences below begin there. There is no exchange in this arrangement. There is no clearing corporationThe institution that steps into a trade done on an exchange and becomes each side's replacement for the other. None is present in this arrangement. that has substituted itself for either promise. There is a forward buyer, a forward seller, and a line between them, and that is the complete structure.

Concretely, that means the forward buyer is carrying the forward seller by name for the whole term, and the forward seller is carrying the forward buyer by name for the whole term. Not carrying a market, not carrying an institution, not carrying an abstraction. Carrying one specific business, with one specific balance sheet, whose ability to perform on one specific day in the future is the only thing standing between the forward buyer and a worthless piece of paper. The word for that specific business is the counterpartyWhichever party happens to be standing at the far end of a signed agreement. The word points at one named business, not at a market., and on a forward contract there is no being vague about which business that is.

ONE PROMISE, TWO NAMED PARTIES, AND NOTHING IN BETWEEN THEM THE FORWARD BUYER Bound to buy one unit on the agreed date, at Rs 2,130.00/-. THE FORWARD SELLER Bound to sell one unit on the agreed date, at Rs 2,130.00/-. one promise, direct NOBODY HERE no clearing corporation Each side is carrying the other side by name for the whole term. Neither can hand the agreement to somebody else, because nobody else negotiated it. If the forward seller cannot perform on the date, the agreement was worth exactly what the forward seller was worth, and not one rupee more.
A forward contract is one promise running directly between two named parties with nobody in the middle, so each side carries the other side by name for the whole term.

Followed through, a second property appears immediately. The forward buyer cannot close the position by dealing with somebody else. On an exchange, selling what was bought ends the matter. The party faced was never the party bought from in the first place. On a forward contract that route fails. The promise was made to one named business, and that business has not agreed to release anybody from it. There are exactly two routes out, and they are worth drawing because readers assume there is a third.

WANTING OUT OF A FORWARD CONTRACT: TWO ROUTES, AND NO THIRD WANTING OUT ROUTE ONE: UNWIND IT Go back to the same forward seller and agree the agreement is over. It needs their agreement, and they may want paying for it. ROUTE TWO: STRIKE A SECOND ONE Agree an opposite forward with a third party. The prices offset, but the holder now carries two agreements and two parties who might not perform. There is no route three, because nobody else negotiated this exact agreement. On the exchange traded kind, covered separately, a third route exists. Not here.
Getting out of a forward contract has exactly two routes: agree an unwind with the same party, or strike a second offsetting agreement and carry two parties instead of one.

Route one is the unwindEnding an agreement early by getting the same party to agree it is over, rather than by handing it to somebody else.. Going back to the forward seller, both sides agree the arrangement is finished, and money changes hands to reflect whichever way the reference asset has moved since. An unwind requires the forward seller's consent. A party who has to want to give consent can charge for giving it. Route two is to strike a second, opposite forward with a third party. Economically the prices offset. Structurally things are worse rather than better. The second agreement leaves two parties who might fail, instead of one.

Feel this one from the street. A stall outside a single office building has agreed its whole winter stock with one supplier, at a fixed price, for delivery in November. The stall's agreement cannot be handed to the shop next door. The shop next door did not negotiate it and does not want it. And if the supplier shuts up shop in September, the agreement was worth exactly what the supplier was worth. The supplier turned out to be worth nothing. The stall did not lose money on the price. The stall lost the whole arrangement, and it lost it on a day when it had no time left to replace it.

Try it out

A forward buyer wants out of the agreement six months before the date. What is the one thing they cannot do?

What is negotiated, and what does the fit cost?

Everything is negotiated, and the word is meant literally. How much of the reference asset, what exactly counts as the reference asset for delivery purposes, on what date, delivered by what method, and against what security if any, are all decided between the two parties and written down by them. There is no template. There is no exchange publishing a specification that both sides simply accept. If the two of them want an odd quantity settling on an odd date, they can have it. The only two people who have to agree are already in the room.

Negotiating every term buys an agreement that fits the exact amount and the exact date somebody actually needs, with nothing left over. A business with a known payment falling due on the eleventh of a particular month can fix a price for exactly that day and exactly that quantity. Nothing has to be rounded to a lot size. Nothing has to be rolled because the nearest available date fell short. The fit is perfect because the fit was built to measure.

FIVE TERMS: NEGOTIATED HERE, FIXED IN ADVANCE ON THE OTHER KIND THE TERM ON A FORWARD CONTRACT ON THE EXCHANGE TRADED KIND How much negotiated fixed in advance Of what exactly negotiated fixed in advance On what date negotiated fixed in advance Delivered how negotiated fixed in advance Against what security negotiated fixed in advance The fit is exact, and that is precisely why nobody else wants the agreement. Two consequences of one design decision, seen from either end.
Every term that is negotiated between the two parties on a forward contract is fixed in advance by the exchange on the standardised kind, and that single difference produces both the perfect fit and the impossibility of handing the agreement on.

The fit costs the agreement its audience: nobody else wants it, so it cannot be handed on. The perfect fit and the dead end are not a benefit and a drawback sitting side by side. The two are one design decision seen from either end. An agreement built to one buyer's exact requirement is, by construction, an agreement that no second buyer needs, and the tighter the fit the smaller the pool of people who would take it on. Standardisation exists to create that pool, and it pays for the pool by making the fit approximate. One or the other is available; both together are not.

One routing note before the arithmetic. Where the reference asset is a currency or a rate rather than a physical thing, the arrangements under which such a bilateral agreement may be entered into at all are set by the Reserve Bank of India at rbi.org.in. The arrangements move. Each such requirement is set out below beside the authority that settles it.

Try it out

The reference asset costs Rs 2,000.00/- now, financing costs 6.50 per cent a year, and it hands its holder nothing across the whole year. Before any arithmetic is shown, what should a fair price be for a transaction one year out?

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The Forward Price: where does Rs 2,130.00/- come from?

The forward price is built rather than quoted, and the build runs below so that no such number need ever be accepted on trust again. Three inputs and no more. The reference asset costs Rs 2,000.00/- for delivery now, and that figure is a price. Financing costs 6.50 per cent a year, and the period matters as much as the number. And across that year the reference asset returns nothing whatever to whoever is sitting on it. The absence belongs in the same breath as the other two inputs. A payment reaching a holder would change the answer.

Now reason about what somebody with the reference asset in a year would have had to do. Anybody wanting it could buy it today at Rs 2,000.00/- and borrow the money to do it. Apply 0.065 to Rs 2,000.00/- and a year of financing weighs Rs 130.00/-. Set that weight back on top of the Rs 2,000.00/- they started from, and having the reference asset in hand a year from now has cost them Rs 2,130.00/-. So Rs 2,130.00/- is the forward price, and it is a price rather than a premium, a payoff or a profit.

ONE PRICE TODAY, CARRIED FORWARD TO A DATE ONE YEAR OUT Rs 2,000.00/- spot price, for delivery now ONE YEAR OF FINANCING AT 6.50 PER CENT A YEAR adds Rs 130.00/- of carry Rs 2,130.00/- forward price, for delivery then Apply 0.065 to Rs 2,000.00/-, then set the Rs 130.00/- it weighs back on top. No payment reaches a holder during the year, so nothing is ever taken away from that.
The spot price of Rs 2,000.00/- becomes the forward price of Rs 2,130.00/- by adding one year of financing, and there is no other ingredient anywhere in the step.
The forward price, as a build
$$ F \;=\; S \,+\, S \times r $$
Fthe forward price, a price agreed today for a transaction one year from today
Sthe spot price of the reference asset today, Rs 2,000.00/-
rthe financing rate over that one year, 6.50 per cent a year, written as 0.065
What it says in wordsThe forward price is the spot price with one year of financing set on top of it. Nothing is taken away anywhere in the expression. This reference asset hands its holder nothing during the year.

Now the test that shows why it has to be that number rather than a nearby one. Suppose a forward seller offered to sell forward at Rs 2,100.00/-. Anybody could then borrow Rs 2,000.00/-, buy the reference asset today, hold it for the year, deliver it into that agreement, collect Rs 2,100.00/-, and repay a loan that has grown to Rs 2,130.00/-. The assembly leaves them Rs 30.00/- short, so nobody does it in that direction. Turn it round: the party who assembles the position for Rs 2,130.00/- and delivers it into an agreement struck at anything above Rs 2,130.00/- pockets the difference for certain, with no view about the reference asset required. A forward sale struck beneath Rs 2,130.00/- makes a present of the shortfall to whoever runs that assembly, and the gift is the entire reason the number sits where it does. The word for that assembly is arbitrageAssembling one position out of cheaper parts and delivering it into a dearer promise, so a difference is pocketed without waiting to see what happens., and it is the reasoning rather than the term that does the work here.

  1. Borrow Rs 2,000.00/-for one year, with financing at 6.50 per cent a year.
  2. Buy the reference asset todayat its spot price of Rs 2,000.00/-, and hold it. The reference asset hands its holder nothing during the year, so nothing comes back in.
  3. Deliver it on the agreed dateinto the forward that was sold, and collect the forward price.
  4. Repay the borrowing.The loan has grown to Rs 2,130.00/-. If the forward price was Rs 2,130.00/- the position is exactly square, and it was square from the day it started.

The forward price is a cost, not an opinion. The difference between a cost and an opinion carries a good deal of the rest of this subject. Not one of the four steps above required anybody to hold an opinion on the direction the referenced thing is travelling in. Nobody was asked what they expected. Nobody was asked what they hoped. The number came out of a borrowing rate and a purchase price, and it would be the identical number if every party involved were privately certain that the reference asset was about to halve.

Try it out

The financing rate falls from 6.50 per cent a year to nil and nothing else changes at all. Predict where the forward price goes.

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Why can the forward price never sit below the spot price here?

Because of one property of the reference asset, stated more than once already. Across the whole year this reference asset returns not one paisa to whoever holds it, so holding it throws off nothing that could be set against the financing, and the carry is therefore positive at every financing rate above nil. Take the build apart again and look for the subtraction. There is no subtraction. There is a spot price and there is a financing cost, and the second is added to the first. A quantity that is only ever added cannot make the total smaller than the thing it was added to.

One thing could flip the arithmetic, and it is worth naming plainly. If the reference asset paid something to its holder during the year, that payout would subtract from the carry, and a payout large enough to exceed the financing would put the forward price below the spot price. The holder would be compensated for holding, rather than only charged for it. Nothing about that case is exotic or unusual, and readers meet it constantly in the world.

RAISE THE FINANCING RATE AND THE UPPER LINE LIFTS. IT NEVER DROPS BELOW. the forward price, in rupees 2,050 2,100 2,150 2,200 2,250 SPOT Rs 2,000.00/-, held fixed FORWARD PRICE rises with the rate carry Rs 130.00/- at a rate of nil the two meet, at Rs 2,000.00/- 0.00 3.25 6.50 9.75 13.00 the financing rate, per cent a year Nothing on these figures takes the upper line below the lower one, because a holder of this reference asset receives nothing during the year.
The forward price rises with the financing rate and meets the spot price of Rs 2,000.00/- exactly where financing costs nothing, and on these figures nothing can push it below that line.
Try it out

Could the forward price on these figures ever sit below Rs 2,000.00/-?

How Forward Contracts Work: what happens between the day it is struck and the day money moves?

Three moments, and nothing whatever between them. Three moments are the honest summary of the whole life of a forward contract. Readers who have met the exchange traded kind first arrive expecting activity that never comes, and find the emptiness genuinely surprising.

Moment one is the day of agreement. The forward price of Rs 2,130.00/- is fixed and written down. Nothing moves. No cash, no reference asset, no collateral, no record of value anywhere. Moment two is the entire stretch in between, however long it runs, and the thing to understand is that it is empty. The reference asset can travel wherever it likes. The agreement is not revalued. Nothing is collected from the side that is behind and nothing is paid to the side that is ahead. Moment three is the final date, and the whole of the arrangement executes at once: the forward buyer pays Rs 2,130.00/- and the forward seller delivers one unit of the reference asset, or the two settle the difference in cash if that is what they negotiated.

THREE MOMENTS, AND THE LONG EMPTY STRETCH IS THE TEACHING cash that has moved so far Rs 2,130.00/- nil nil nothing is collected, nothing is paid, nothing is even recorded DAY OF AGREEMENT price fixed at Rs 2,130.00/- ANY DAY IN BETWEEN however far the price travels THE FINAL DATE one unit against Rs 2,130.00/- The whole of the money moves on one day, and the gap before it is where the risk lives.
On a forward contract the price is fixed on one day, nothing at all moves through the term however far the reference asset travels, and the whole of the money moves on the final day.

Sitting in that empty stretch is an unrecorded and uncollateralised gain on one side and an exactly equal loss on the other, and the gain grows as the reference asset moves away from Rs 2,130.00/-. The forward buyer struck at Rs 2,130.00/- with the reference asset now at Rs 1,600.00/- is behind by Rs 530.00/-. Nothing has recorded that. Nothing has collected it. The forward seller who is ahead by exactly Rs 530.00/- has received nothing and has no claim on anything until the final date arrives. Both facts are simply sitting there, agreed and unactioned.

WHAT ONE SIDE WILL OWE ON THE FINAL DATE, AND NOBODY COLLECTS IT EARLY amount owed on the final date, in rupees 100 200 300 400 500 struck at Rs 2,130.00/- nothing is owed either way the forward buyer will owe this much and nothing collects it the forward seller will owe this much and nothing collects it 1,630 1,880 2,130 2,380 2,630 the settlement price of the reference asset on the final date, in rupees Both arms grow without limit and neither is settled until the final date arrives.
The amount one side will owe on the final date grows as the reference asset moves away from the struck price of Rs 2,130.00/-, and nothing in the arrangement collects any part of it before that day.

Here is the consequence almost no reader reaches unaided: the bigger the move, the more the losing side owes, and therefore the more reason that side has not to perform, and nothing whatever in the arrangement pushes back on that. The risk is not merely present. The risk is correlated with exactly the circumstance in which it would matter. A small move leaves a small obligation that anybody could meet. A large move leaves a large obligation, concentrated on whichever party is least able to meet it precisely because the same move has probably hurt them elsewhere too. The correlation is why somebody eventually built the standardised, cleared and margined version of this agreement, and that version is covered separately.

What the forward buyer receives on the final date
$$ \Pi \;=\; S_T \,-\, F $$
Πthe payoff to the forward buyer on the final date, in rupees, positive when received and negative when paid
STthe settlement price of the reference asset on the final date
Fthe forward price agreed at the start, Rs 2,130.00/-
What it says in wordsThe forward buyer receives the settlement price less the price they agreed to pay. Because nothing was handed over at the start, the payoffWhat a position hands over on the day it settles, counted before anything spent getting into it is knocked off. and the profit are the same figure on this contract, and letting that coincidence slip teaches a reader to blur the two everywhere else.
Try it out

Halfway through the term the reference asset has fallen to Rs 1,600.00/-. How much money has moved between the two parties so far?

What is posted, and what follows from posting nothing?

Nothing is posted. The word for that is unmargined. The word gets used so casually that its two consequences are rarely held together, so it is worth saying plainly before unpacking it. No collateralCash or securities parked with somebody else so that a promise has something behind it if the promise is broken. is lodged by either side at the start, none is lodged as the reference asset moves, and none is topped up when one side falls behind.

The first consequence is that no cash leaves either party before the final date, so the arrangement costs nothing at all to carry. Costing nothing to carry is a genuine advantage, and it is why plenty of businesses use exactly this shape. A business that has fixed a price for a payment falling due next year has not had to find any money to do it. Its working capital is untouched. Nothing sits idle in an account somewhere waiting for a date that has not come.

The second consequence is that nothing stands behind the promise, so the whole of the risk is the other party's ability and willingness to perform on one day. There is no buffer. There is no fund. There is nobody who has already taken the money and would pay out of it. There is a signature and a business, and the value of the first depends entirely on the health of the second on a date that may be a year away.

The two consequences are one design decision seen from two sides, and the standardised version of this contract, covered separately, is simply what results when somebody refuses to accept the second in exchange for giving up the first. Read together, the trade is obvious. Post nothing, and the counterparty is carried. Post something, and the cost of posting it is carried. There is no arrangement in which neither is carried, and the whole of the next stretch of this subject is an examination of what the second choice actually looks like when it is engineered properly.

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Who actually uses this, and what do they do with it?

Three seats, and it is worth being concrete about each. The shape looks abstract until somebody is seen handling it.

The first seat is a business with a known future payment. Its problem is not that it wants to take a view on the reference asset. Its problem is precisely the opposite. It wants to stop having a view at all. A business with no view can quote a price to its own customers and not be embarrassed by a move it did not choose. A bilateral forward fixed at the exact quantity and the exact date removes the uncertainty completely. The forward introduces in exchange a named party who has to be there on the day, and a good treasurer treats that substitution as the actual decision rather than as a formality attached to it.

The second seat is a lender or a credit team looking at a business that has forward contracts on its books. The credit team is not asking for today's value of the position. The credit team is asking how large the unrecorded obligation could get, and who is on the other end of it. An uncollateralised forward is a credit exposure dressed as a price agreement, and the credit question is the one that decides whether it matters. Two words earn their keep in that seat. A forward for forty units at Rs 2,130.00/- carries a notionalThe headline size an agreement is measured against. The notional scales what is owed; it is not a sum anybody hands over. of Rs 85,200.00/-, a sum that stays entirely on paper and reaches nobody's bank account. The exposureHow much of the referenced thing a promise actually moves with, priced at what that thing is worth now. that moves with the reference asset is forty units at the current Rs 2,000.00/-, or Rs 80,000.00/-. Reporting one of those and calling it the other misdescribes the arrangement by Rs 5,200.00/- while sounding entirely precise.

The third seat is an analyst reading a forward price out of somebody's disclosure. The temptation is to write down that the price implies a view, and the disciplined move is the one in the reading routine below: carry the spot price at the financing rate for the period and see whether the gap is already fully accounted for. If it is, there is nothing left over to interpret, and the correct sentence in the note is that the arrangement is priced at carry rather than that anybody expects anything.

Try it out

A forward for forty units is struck at Rs 2,130.00/- while the reference asset stands at Rs 2,000.00/-. Which figure is the notional?

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How to analyse a Forward Contract: which questions, and in what order?

Six questions in a fixed order. The order matters more than it looks. Each answer narrows what the next question can mean, and taking the six out of order is how people end up interpreting a price before they know what it is a price of. No mechanism is explained by the routine. The six questions are a reading procedure, and everything they need has already been built above.

SIX QUESTIONS IN A FIXED ORDER, AND THE FOURTH IS THE ONE NOBODY ASKS 1 What exactly is referenced, and how much of it? Quantity and description, before anything else at all. 2 What is the date? One date, negotiated, and no other day means anything. 3 What is the forward price, and what is the spot price today? Here, Rs 2,130.00/- against Rs 2,000.00/-. 4 What financing rate is embedded in the gap between those two? Rs 130.00/- over Rs 2,000.00/- is 6.50 per cent for the year. 5 Who is on the other side, and what happens if they cannot perform? Nothing stands behind the promise, so this question is not optional. 6 Does it end in delivery of the reference asset, or in cash? Negotiated between the two parties, and it changes what has to be ready. Reading the rate out of the two prices checks the forward price, rather than merely accepting it.
The reading routine is six questions in a fixed order, and the fourth one reads the financing rate back out of the two prices, which is how a forward price gets checked rather than accepted.

Question four is the one nobody performs, so it gets the arithmetic spelled out. An agreement arrives at Rs 2,130.00/- while the reference asset stands at Rs 2,000.00/-. The gap is Rs 130.00/-. Dividing Rs 130.00/- by the Rs 2,000.00/- it was struck on gives 0.065, or 6.50 per cent for the year. The 6.50 per cent is the rate the agreement has embedded in it, and reading it out is the difference between checking a forward price and simply believing one.

The financing rate, read backwards out of the two prices
$$ r \;=\; \frac{F - S}{S} $$
rthe financing rate embedded in the agreement, over the period from today to the agreed date
Fthe forward price written into the agreement, Rs 2,130.00/- here
Sthe spot price of the reference asset today, Rs 2,000.00/- here
What it says in wordsThe gap between the two prices, divided by the spot price the gap was struck on, is the financing rate the agreement contains. On these figures the answer is 6.50 per cent for the year, and it carries its period because a rate without one is not a rate.

The rate read out is good for two things. If the rate read out is roughly what money costs the party concerned, the agreement is priced at carry and there is nothing further to interpret. If it is materially different, something real has been learned: either the reference asset is not what was assumed, or the agreement contains something other than plain financing, or somebody has quoted a price nobody would run the four steps against. Any of those is worth knowing, and none of them is available to a reader who never divided.

Try it out

A forward agreement arrives at Rs 2,130.00/- when the reference asset stands at Rs 2,000.00/-, for a date one year out. What financing rate is embedded in it?

The failure: reading a financing cost as somebody's forecast

The gap between the two prices is where the number is produced, and where the misreading does the most damage. Somebody sets Rs 2,130.00/- beside Rs 2,000.00/-, does the division in their head, and writes down that the referenced thing is expected to gain 6.50 per cent across the twelve months. Nothing whatever in the arrangement carries that claim. Almost everybody does it on first contact, and, expensively, so do analysts who put a forward price into a note as though it reported somebody's view.

The misreading costs more than one wrong sentence. The cost is every conclusion stacked on top of that sentence. A financing cost gets recorded as information. A gap between two dates gets read as direction. And a reader who has learned the habit will carry it onto assets that do pay something while they are held, meet a forward price sitting below the spot price, and record a prediction of a fall. A forward price below a spot price is not that either.

THE NOTE A READER WRITES, AND THE LEDGER THAT DISPOSES OF IT Forward Rs 2,130.00/- over spot Rs 2,000.00/-, so a 6.50 per cent rise is expected what a reader writes down on first contact, and it is wrong SETTLEMENT PRICE ON THE FINAL DATE WHAT THE FORWARD BUYER PAYS OR RECEIVES Rs 1,600.00/- minus Rs 530.00/- Rs 2,000.00/- minus Rs 130.00/- the price did not move, and it still costs the carry Rs 2,130.00/- nil the forecast came true to the rupee, and it earns nil Rs 2,400.00/- plus Rs 270.00/- Every row is the settlement price less Rs 2,130.00/-, and no belief enters any of them. Change the financing rate and every row moves, without one word said about the asset.
A forward buyer struck at Rs 2,130.00/- pays minus Rs 130.00/- when the reference asset settles unchanged at Rs 2,000.00/-, and earns nil when it settles at exactly the price the misreading called a forecast.

Three separate arguments dispose of it, and it is worth carrying all three because different readers are convinced by different ones. The first is the arithmetic in the ledger above. Suppose the forecast reading were correct. Suppose the reference asset arrived at the year's end at exactly Rs 2,130.00/-, the very number the agreement was struck at. The forward buyer would then walk away with nothing at all: no gain, no loss, nil. A prediction accurate to the last paisa would have earned its holder nothing whatsoever, a strange property for a prediction to have. And if the reference asset simply sits where it started at Rs 2,000.00/-, the forward buyer pays minus Rs 130.00/-, losing the carry precisely because the carry was the whole of what the number ever was.

The second is the free money test. If Rs 2,130.00/- were an opinion rather than a cost, somebody who held a different opinion could simply agree a lower price. But then the party on the other side would borrow, buy the reference asset today, hold it, deliver it and repay Rs 2,130.00/-, pocketing the difference with no view about anything required. Opinions can differ. Costs cannot be disagreed with, and that asymmetry is why the number is pinned where it is.

The third is the direction of dependence. Change the financing rate and the forward price moves, immediately and mechanically, without one word being said about the reference asset by anybody at all. Something that responds to a borrowing rate and ignores every belief in sight is not a statement about beliefs. The control below runs that test, and the run takes about four seconds.

Nobody who made this error was careless. The number genuinely looks like a view, nothing on any screen anywhere says otherwise, and the arithmetic that would settle it is arithmetic nobody prompts. The habit therefore has to be a conscious one: before a forward price is read as anything at all, the spot price is carried at the financing rate for the period to see whether the whole of the gap is already spoken for.

Play with it

Move the financing rate, and change nothing else at all

One control changes arithmetic, and only one: the financing rate for the year. The spot price is held at Rs 2,000.00/- while that control moves, and a holder of the reference asset receives nothing across the year. Nothing is therefore ever taken away from the shaded block at any point in the range. A second control changes only how the same picture is described, and touches no number. Both bars are drawn on one shared scale, so their lengths may be compared directly.

Financing: 6.50 per cent a year
RAISE THE RATE AND ONLY THE SHADED BLOCK GROWS. THE UPPER BAR NEVER MOVES. SPOT Rs 2,000.00/- FORWARD Rs 2,130.00/- carry Rs 130.00/- nil Rs 2,260.00/-, the top of this shared scale Read as a price: Rs 2,130.00/- is the only figure either side may transact at. No financing, so no block, and the two bars are level at Rs 2,000.00/-. Educational illustration. Invented asset, invented figures, and not a pricing tool.

Financing
6.50%
Carry for the year
Rs 130.00/-
Forward price
Rs 2,130.00/-
Gap over spot
6.50%

One unit of the reference asset. The spot price is Rs 2,000.00/- and is held fixed while the control moves. One year to the agreed date, with simple carry over that year and no compounding inside it. Both are stated rather than assumed. Holding the reference asset returns nobody anything, so the lower bar never falls short of the upper one. A referenced thing that did throw off a payment would take that payment away from the carry and could push the lower bar underneath. The range of nil to 13.00 per cent a year is illustrative, is symmetric about the worked default of 6.50 per cent a year, and carries no claim about what financing costs anywhere.

Six questions, one order, each narrowing the next. See where the forward price fits.

Who sets the terms left blank here?

India

Who decides what, and where they publish it

Six things below are decided by an authority, not by arithmetic. Each row names who decides and where they publish.

What is setWho decides it
The arrangements under which a bilateral forward on a currency or a rate may be entered into at allReserve Bank of India, rbi.org.in
What such a bilateral arrangement gets reported as, who it is reported to, and by whenReserve Bank of India, rbi.org.in
Who is allowed to carry a derivative position at all, and what has to be put in front of them before they doSecurities and Exchange Board of India (SEBI), sebi.gov.in
How long money, and the thing itself, take to move once a trade has been doneSEBI, sebi.gov.in
The conditions on which a position is treated as a hedge rather than as a position standing on its ownSEBI, sebi.gov.in
Which contracts finish by handing over the thing itself and which finish in cashSEBI, sebi.gov.in

Every one of the six moves. A value fixed on any one day becomes untrue the moment the authority revises the position. The site named in each row carries the current position. Nothing at all is posted on a plain bilateral agreement, so no margin appears among the six. Cross border conduct principles for cleared markets are published by the International Organization of Securities Commissions (IOSCO) at iosco.org, and what binds in India is the version SEBI has adopted.

Should anybody enter one of these?

The question is not one the arithmetic can settle. Four things would have to be on the table before anybody could answer it: what the position exists to do, what is already being held against it, who is standing on the far end, and what lands on whichever side is wrong on the day the money moves. Not one of the four is knowable from here, and three of them are properties of the reader rather than of the contract.

Following the arithmetic above is not a reason to go and sign one of these. Understanding how an agreement is put together and deciding to be a party to it are two entirely separate activities, and only the first has been performed here.

The taking apart above stops at the plain bilateral agreement. The standardised, cleared and margined version of the same contract is covered separately, and so is everything that follows from clearing it: the money moving day by day, what gets posted and topped up, and what a clearing corporation does when a member fails. The two prices set one against the other, and the two contracts set one against the other, are each covered separately. Delivery of the reference asset, moving a position on to a later date, and the count of contracts outstanding are covered separately, and none of the three applies to a bilateral agreement in the same form. Anything that lets one side decline to perform is a different instrument entirely and is covered separately. The markets in the referenced things themselves, and how a set of holdings is put together, are settled elsewhere and are used here rather than rebuilt. Holding this reference asset returns nobody anything, so no forward price on it sits below the spot price. A reference asset that pays its holder is a different case and is covered separately. Every arrangement, reporting duty, eligibility condition, settlement timing, hedge treatment and delivery method touched above belongs to the authority named beside it.

References

SourceWhat it settlesWhere
Securities and Exchange Board of IndiaExchange traded contracts and everything attached to them: eligibility to carry a position, how quickly money and goods move, hedge treatment, and delivery against cash finish.sebi.gov.in
Reserve Bank of IndiaBilateral arrangements struck on currencies and on rates, and the reporting that attaches to them.rbi.org.in
International Organization of Securities CommissionsCross border conduct principles behind cleared markets. What binds in India is the version SEBI has adopted.iosco.org
Working paper repositoriesWhere the no free money reasoning behind a carry price is set out in its original form.ideas.repec.org
Preprint archiveWorking papers on the pricing of forward contracts.arxiv.org

The reference asset, its Rs 2,000.00/- spot price, the 6.50 per cent a year it costs to finance and both parties to the agreement are invented.
Educational material. Not advice on any investment, tax, budget or market position.

Covered in this topic

Subtopics

Forward PriceHow Forward Contracts WorkHow to analyse a Forward Contract
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