Intrinsic Value and Time Value: One Number, Two Parts

A premium splits into two parts. Intrinsic value is what the contract would hand over if the end date landed today, and it never drops below nil. Time value is the whole of the rest, and it is a leftover rather than a figure anybody worked out. One part can be computed from two numbers already in hand; the other needs a premium supplied from elsewhere.

The two parts of a premium are not two ingredients that somebody added together to arrive at it. One of them is a calculation performed on two numbers already sitting on the table. The other is whatever survives once that calculation has been taken away from a premium that came from elsewhere. Read the pair as a figure and a remainder rather than as two ingredients, and most of the nonsense written about the second one stops being possible.

Everything below runs on one invented pair of contracts, and every rupee in it is made up for teaching. A reference asset stands at a price of Rs 2,000.00/-. The asset throws off nothing whatsoever to whoever holds it, and financing runs at 6.50 per cent across a year. A call and a put are both written on it at a strikeThe number agreed at the outset and printed in the contract itself. The strike is the yardstick every later reading is taken against, and it stays put for the whole term. of Rs 2,000.00/-, and both run twelve months. The call premium is Rs 180.00/-, given rather than produced by any model here, and the put premium of Rs 57.93/- gets worked out from it further down.

What exactly is intrinsic value?

Intrinsic value is what the contract would hand over if the end date landed today. The definition stops there. Read it twice. It carries a hypothetical that people quietly drop. Nobody is claiming the end date has arrived. Nobody is claiming it will arrive with the price where it is now. The figure answers a question of the form "if the music stopped right here, what would this contract hand over", and it answers it with arithmetic on two numbers.

For the call, those two numbers are the strike and whatever the reference asset costs. The call is a right to buy at Rs 2,000.00/-. Where the reference asset changes hands in the open at Rs 2,130.00/-, buying at Rs 2,000.00/- is worth Rs 130.00/- and the intrinsic value is Rs 130.00/-. Nobody pays Rs 2,000.00/- for a thing available at Rs 1,600.00/-, so where the reference asset stands at Rs 1,600.00/-, a right to buy at Rs 2,000.00/- is worth precisely nothing. The intrinsic value is Rs 0.00/-, and it is not minus Rs 400.00/-.

For the put, the two numbers are the same and the direction is reversed. The put is a right to sell at Rs 2,000.00/-. At a price of Rs 1,600.00/- that right is worth Rs 400.00/-, so the put's intrinsic value is Rs 400.00/-. At Rs 2,130.00/- the right to sell at Rs 2,000.00/- is worth nothing, so the put reads Rs 0.00/-. Two contracts, one arithmetic, mirrored in the strike.

Intrinsic value never falls below nil, and the reason is the one fact this whole subject rests on. Whoever bought holds a right, whoever wrote carries the matching duty, and the two are nothing like each other. Only the buyer decides whether the right gets used. What the buyer holds is a right rather than a duty, so nobody can compel a purchase at Rs 2,000.00/- while the reference asset sits on offer at Rs 1,600.00/-. Ignoring the contract is always on the table and carries no extra bill, so the figure settles on nil and stays there. The floor is not a convention somebody adopted to keep the numbers tidy. The floor is the asymmetry showing up as a shape.

Consider a coupon a shop handed out last month that allows a fan to be bought for a fixed amount any time before Diwali. If the shop is now selling that fan for less than the coupon amount, the coupon is worth nothing today. The coupon is not worth a negative amount. The buyer simply ignores it and pays the shelf price, and the coupon costs nothing more for the privilege of being ignored. A coupon resting at nothing is intrinsic value resting on its floor, in a shop rather than on a contract.

And what exactly is time value?

Time value is the premium less the intrinsic value. The definition ends there, and dressing it up any further is how readers end up believing things about it that are not true.

The definition does not say time value is a charge for the remaining life of the contract. The definition does not say somebody levied it, or that a fee schedule produced it, or that it appears anywhere on any document. A contract note, a statement, a confirmation, any sheet of paper connected with an option, carries a premium. Nobody ever charged a time value, so none of those documents carries a line reading "time value". A premium exists, and what a reader does afterwards is a subtraction.

Because time value is defined by subtraction, it exists only where a premium already exists, and its size is therefore never anybody's calculation. Time value is a residue. The word residue is doing real work here. A residue is what a process leaves behind, and its size is learned by measuring what went in and what came out, not by computing it directly from anything.

Here is the everyday version. Somebody buys a small shop as a going concern. The buyer counts the stock on the shelves and values the fittings, and those two numbers are theirs to check, in their own handwriting, with the stock in front of them. Then they look at what they actually paid, take the countable part away from it, and give the leftover a name. The leftover is real, in the sense that money genuinely changed hands for it. But nobody wrote a cheque labelled with that name, no line on the sale deed carries it, and its size depends entirely on what the shop was sold for. Nobody ever measured the leftover, only inferred it. Change the sale price and the leftover changes with it.

Time value works the same way and inherits the same weakness. On the call here, the premium is Rs 180.00/- and the intrinsic value is Rs 0.00/-, so the time value is Rs 180.00/-. Every paisa of that Rs 180.00/- was reached by subtraction. Subtraction is the whole of its provenance, and it could not be otherwise: a premium has to arrive from somewhere before there is anything to subtract from.

What do the two actually share?

Take the overlap before the differences. The overlap is wider than most readers expect, and three of the four items on it are places where readers routinely go wrong.

First, both are parts of one number. The premium is the number. Intrinsic value and time value are two portions of it, and the portions were arrived at by drawing a line, not by adding two things. The sentence "the premium is made up of intrinsic value plus time value" is arithmetically true and psychologically misleading. The plus sign invites a picture of two separately sourced amounts arriving and being totalled. Nothing of the kind happened.

Second, both are readings taken at a moment rather than amounts anybody has received. Neither of them has moved between any two parties, ever. The only sums that genuinely moved on this pair of contracts are the two premiums, Rs 180.00/- for the call and Rs 57.93/- for the put, and both moved once, at the start. Every other figure on these two contracts is a description of a position, not a record of a payment.

Third, and this is the one that costs people money, neither of them is a payoff and neither of them is a profit. A payoff means the amount a contract settles for when its date arrives. A profit is that payoff after what was paid for the contract has been counted. Intrinsic value is neither. Intrinsic value is what the contract would hand over if the end date landed today, a hypothetical about a date that has not arrived, and it has not subtracted a single paisa of the premium. Asserting that gap has never once been enough, so a whole section below works it at a price.

Fourth, both are stated on one reference asset, at one strike, for one end date. The restriction sounds obvious until somebody puts the time value from one contract next to the intrinsic value of another and draws a conclusion. Two figures on two different contracts have nothing to say to each other. The split is only meaningful inside one contract at one moment.

Where do the two genuinely differ?

Here is the finding, and it is not what most readers guess. The two quantities do not differ mainly in what they measure. The two quantities differ in how each one is obtained, and once that difference is seen, a great deal of confused talk about options becomes easy to sort.

Intrinsic value is a calculation on two figures anybody holds. The calculation needs the price of the reference asset and the strike, and nothing else in the world. Not a rate, not a date, not a premium, not a model, not a screen. One comes off the other in the right direction, stopping at nil, and the figure is finished. The intrinsic value line in the first drawing runs across the whole width of the picture for that reason: at every price on that axis, the figure exists and anybody can produce it.

Time value cannot be obtained that way at all, and the reason is structural rather than a shortage of effort. Time value is the premium less the intrinsic value. Producing it needs a premium first. Producing a premium needs something absent from this working example: a reading of the ground the reference asset could cover before the year is out, and the chances riding on each part of it. There is no such reading here. There is no history, no distribution and no measure of movement anywhere in it, and supplying one quietly would mean inventing the single most important input in the subject and presenting the invention as arithmetic.

So intrinsic value can be stated at every price, and time value can be stated at exactly two moments: today, where a premium was handed over, and the end date, where it is nil for a reason that needs nothing this example lacks. The gap is not an apology for the working example. The gap is the result. Every option anybody has ever held has this property; this pair of contracts simply makes it impossible to hide behind a screen full of numbers.

And it leaves behind a reading habit worth keeping. A quoted time value is a subtraction somebody performed on a premium they obtained from somewhere. The subtraction is trivial and cannot be wrong. Everything that could be wrong is upstream, in the premium. So the question to ask about any time value is never "how was that calculated" but where did the premium come from.

One move of the control and the point stops being an argument. Two numbers already in hand are enough to produce the left bar, so it redraws at every single setting, cleanly, with a figure printed on it. The two bars beside it never acquire a height anywhere except at Rs 2,000.00/-, and they do not fade or taper on the way out. There is nothing to draw, so the bars simply stop. The blank is the honest picture of what an option premium is: one part of it is arithmetic anybody can perform, and the rest of it is a number that had to come from somewhere else.

What happens to both parts on the end date?

There is exactly one moment at which the whole comparison dissolves, and it is the last one. When the end date arrives, a premium is worth its intrinsic value and not one paisa beyond. Time value is Rs 0.00/- at every price on that date. There is no remainder, no residue and nothing left to name.

The collapse to nil holds no matter what the missing figure turns out to be, and that makes it the one statement about time value that can be made without a premium. The logic needs no model at all. Time value is the premium less whatever the contract would hand over if the end date landed today. When the end date does land, that condition stops being a hypothetical and becomes a fact. No interval is left for anything further to occur in, so a contract is worth exactly what it settles for, and the two numbers close on each other. The subtraction leaves nil not because anybody decided it should, but because it has run out of anything to leave.

Now the boundary, in the same breath. Readers over-read this statement more than any other on the subject. The end-date rule says where time value ends up and says nothing whatever about how it gets there. It does not say time value falls at a steady rate. The rule does not say time value halves at any point. No path, no curve and no schedule is described, and none can be drawn from this working example: drawing one would need a premium at some second moment, and there is not one. The route is covered separately. The destination is all that is settled.

Where can both parts be stated at once?

Today, and here is the working. The reference asset sits at Rs 2,000.00/- while both contracts carry a strike of Rs 2,000.00/-. The two matching figures are deliberate. Both contracts got written at the moneyA contract where the level agreed at the outset and the going price of what it references land on one and the same number, so it settles for nothing if the term ends today., and that is precisely what the phrase means. One figure was not copied into the other by accident. A reader who wonders whether it is a typing error stops trusting the rest of the arithmetic, so the coincidence is worth stating out loud.

One more thing about that Rs 2,000.00/-. The price of the reference asset is exposureThe amount of the reference asset a position stands against. Exposure is a size rather than a bill: nobody has handed it over, and it is not what the position cost., meaning the value the contracts reference, rather than an amount anybody paid. Nobody has parted with Rs 2,000.00/-. The only sums that left anybody's hands are the two premiums.

So work it. The call's intrinsic value is the price less the strike, floored at nil: Rs 2,000.00/- less Rs 2,000.00/- is Rs 0.00/-. The put's is the strike less the price, floored at nil: also Rs 0.00/-. Then the time values fall out by subtraction. The call's is Rs 180.00/- take away Rs 0.00/-, or Rs 180.00/-. The put's is Rs 57.93/- take away Rs 0.00/-, or Rs 57.93/-. Two contracts, and both premiums land entirely inside the half that nobody calculated.

Sit with the reading for a second. The split corrects a picture most people carry without noticing. A reader who thinks of a premium as mostly intrinsic value with a little time value sprinkled on top has, without knowing it, only ever looked at contracts that were already ahead. At the money the split is as lopsided as a split can possibly be: one part takes everything and the other takes nothing. Nothing unusual is happening. The strike and the price are level, so the contract would pay nothing if the end date arrived now, so the whole premium is the other thing.

What is the gap between the two premiums actually made of?

Now something the name "time value" gives no warning of.

Both intrinsic values today are Rs 0.00/-. The entire difference between the two premiums is therefore a difference between two time values, with nothing else in it. The call costs Rs 180.00/-, the put costs Rs 57.93/-, and the gap is Rs 122.07/-. Every paisa of that gap is time value against time value.

So what is it made of? Take the price of the reference asset and subtract the present valueWhat an amount due at a later date is worth if it had to be settled today. Money in hand can earn something in the meantime, so the earlier figure is smaller. of the strike. A strike of Rs 2,000.00/- falling due in twelve months, brought back at 6.50 per cent a year, is Rs 1,877.9343/-. Take that off and Rs 2,000.00/- leaves Rs 122.0657/-. The two routes land on the same place.

The two routes agree to the paisa, and they do not agree exactly. Rs 122.07/- and Rs 122.0657/- stand forty three hundredths of one paisa apart, and the reason is dull and worth knowing: the put premium got trimmed to Rs 57.93/- so that a human being can write it down and work with it. Round a figure and a small residue appears in every sum it enters. Claiming an exact equality that the rounded figures cannot deliver would train a reader out of the habit of checking.

Here is the finding. The Rs 122.0657/- carries nothing in it concerning the distance the reference asset could cover. The figure is the price with the present value of the strike taken off it. The cost of money across one year is the whole of what remains. A good part of what gets called time value is financing rather than anything about movement, so naming the two parts of a premium says nothing whatever about what produced either of them. The label describes where a number sits inside a subtraction. The label does not describe where the number came from.

If that feels like a trick, consider the shape of it away from contracts. A forward priceWhat it costs to arrange today for delivery at a later date, worked out from the price now plus the cost of carrying it until then. Arithmetic, not a forecast. on this same reference asset takes Rs 2,000.00/- and carries it a year at 6.50 per cent, giving Rs 2,130.00/-. The Rs 130.00/- of carry in that figure is not an opinion about where the price is going. The Rs 130.00/- is the cost of holding the thing for a year. The same cost is sitting inside the gap between the two premiums here, wearing a different name.

Which of these figures are payoffs, and which are profits?

Slow down here. The confusion between a payoff and a profit is the one that actually costs people money.

Put the reference asset at Rs 2,130.00/- on the end date. Three readings sit at that one price and they are three different numbers.

The call's intrinsic value is Rs 130.00/-: the price less the strike, floored at nil. On the end date, the amount the call would hand over if the end date landed today and the amount it actually hands over are one figure, so that same Rs 130.00/- is also the call's payoff. Two words, one figure, and the fact that they collapse on that date is exactly why people mix them up everywhere else.

The profit at that same price is minus Rs 61.70/-. The premium of Rs 180.00/- left at the start of the year, and carrying it forward at 6.50 per cent to the same date makes it Rs 191.70/-. Set Rs 191.70/- against a payoff of Rs 130.00/- and the position is down Rs 61.70/-. The position is in the moneyA position that would collect something if the end date arrived this instant. The phrase says the contract pays, not that the holder is ahead. and losing money at the same moment, and both statements are true.

Standing in the money and standing ahead are two separate claims, and on this contract they part company by a wide margin. That margin is not a rounding wrinkle. The call has to travel Rs 130.00/- past the strike merely to reach the point where the loss is only Rs 61.70/-.

The two break-evenThe price that leaves a position square, neither up nor down, after everything handed over for it has been counted in. readings say the same thing more precisely. Published diagrams almost always print only the first, so both are set out below.

Rs 11.70/- is not a large number, but the habit behind it is the point. The second reading counts something real: money handed over a year earlier could have been doing something else in the meantime, and a break-even that ignores that is quietly reporting a slightly better position than the one actually held.

The whole pair, worked from three inputs

Everything above comes out of three numbers, and collecting them makes the arithmetic checkable against itself. The reference asset stands at a price of Rs 2,000.00/- and throws off nothing whatsoever to whoever holds it. Financing runs at 6.50 per cent across a year, and that year is the term of both contracts. The call premium is Rs 180.00/-, given rather than modelled. From those three the put premium of Rs 57.93/- is derived, and everything else follows.

The third row across is the one to read before anything else. Four prices, four nils, and the row is printed rather than described because a row of nils looks like an omission when it is only read about. The collapse of time value on the end date is that row in one line.

And read the last two rows against each other. The only difference between the payoff row and the profit row is one subtraction that happens once, so the two rows have the same shape and sit Rs 191.70/- apart at every price. The call turns from a loss into a gain somewhere between Rs 2,130.00/- and Rs 2,400.00/-, and the two break-even readings above say precisely where.

One line on what the table holds. Not one figure in it is an amount that has moved between anybody. The only sums that moved on this pair are the two premiums of Rs 180.00/- and Rs 57.93/-, at the start. Everything else is a description of what the contracts would do at prices that have not happened.

How does anybody read this away from a textbook?

Someone holding an option position gets a statement, and the statement carries a current worth for the position. The figure is a premium, sourced from somewhere. The split is what lets a reader ask the right question about it.

An analyst reading a set of quoted premiums does exactly one thing first: works out the intrinsic value from the price and the strike. The analyst can check that part alone, in ten seconds. Subtract it and what is left is the part that came from a model, a screen or another person's judgement. None of that is a criticism of the leftover. The point is where the checkable boundary lies. Everything upstream of the premium is somebody else's work, and treating it as though it were arithmetic is how a reader stops noticing when it changes.

A treasurer at a small manufacturer who has bought protection against a price move reads it the same way for a different purpose. When the board asks for the protection's worth today, the honest answer separates the two parts. Part of it would pay out if the year ended today, and that part can be shown from the price and the level the firm fixed. The rest of what somebody would give for the contract is what that buyer thinks the remaining time is worth, and that figure belongs to the buyer rather than to the treasurer. A separated answer survives a follow-up question. A single blended number does not.

The household version needs no contracts at all. A wedding hall was booked eleven months ago at a rate fixed then, for a date next year. If somebody now offers to take the booking over, part of what they are paying for is measurable by the holder: the gap between the rate locked then and the rate that hall goes for today. The rest of their offer is what they think the date itself is worth to them, and it is not written on the receipt, nobody itemised it, and its size depends entirely on what they offer. The first part can be checked. The second can only be observed.

The practical value of the split is not that it explains a premium. The split draws a line between the part of a quoted figure that can be verified and the part that can only be received.

So which of the two deserves watching?

Readers come to the split carrying that question, so it deserves a plain answer rather than a shrug at the end.

The question cannot be answered from the split alone. The reason has nothing to do with caution. An honest answer needs three separate things, and the split supplies none of them. One is a view on the ground the reference asset could cover over the coming year, with the chances riding on each part of it. No such figure appears in this working example. Another is the situation of the person asking, and no general account of the two parts can take that in. The last is what holding the contract and unwinding it would cost. That figure turns on the collateral a writerThe party on the obligation side of the contract. The writer took the premium at the start and must perform if the other side chooses to use the right. places and on the charges of dealing, both set by an authority named below rather than stated.

The split is worth more than a recommendation would be, and it is portable. The split says what each of the two quantities is. One of them is arithmetic anybody can perform on figures already held, and the other is a leftover from a number somebody handed over. Neither of them is a payoff and neither is a profit. And it supplies the question to put to any time value anybody quotes.

Splitting a premium into two parts is an act of description, and a description of what a number is made of says nothing about what the number will do.

The reference asset, both contracts, both premiums and every rupee figure here are invented.
Educational material. Not advice on any investment, tax, budget or market position.