NAV vs Unit Price: A Computed Value and an Agreed One

Net asset value is computed from a scheme's own books once for each day. A unit price is what two parties agree. In an open ended scheme there is no second party, so the applicable value is what a holder transacts at. Where units change hands on an exchange instead, the agreed price can sit above or below the value struck for that day.

Two numbers, both in rupees, both to two decimals, often printed one under the other on the same screen. Nothing in how they look reveals that they were made in completely different ways. The identical presentation is the whole difficulty, and it is why so many otherwise careful readers treat the two numbers as versions of one thing. The two are not versions of one thing, they are two different kinds of number, and almost every confusion on this subject comes from mixing the kinds up.

A net asset valueWhat a scheme holds, less what it owes, divided by the units in issue, worked out once for each dealing day. is a computation. Somebody adds up what the scheme holds, subtracts what it owes, divides by the units in issue, and writes down the answer. Nobody sits on the other side of that arithmetic. A unit priceThe amount at which one unit actually changed hands between a buyer and a seller in a particular bargain., in the sense a market uses the phrase, is an agreement. Somebody wanted to sell, somebody wanted to buy, they wanted different numbers, and they settled on one. The settled number is the price.

A household version comes before the finance version. A family sits with the receipts and works out that the gold in the house is worth Rs 4,20,000/- at today's rate. The Rs 4,20,000/- is a computation, and it exists whether or not anybody ever offers a single rupee for any of it. A neighbour then offers Rs 4,12,000/- for the lot and the family agrees. The Rs 4,12,000/- is a price, and it exists only because two people met and settled. The computation did not move when the offer arrived, and the offer was not produced by the computation. Both numbers are correct. The computation and the price answer different questions.

One scheme carries the comparison. Girnar Asset Management Limited, an invented asset manager, runs the Girnar Large Cap Equity Fund, an open endedA scheme that takes money in and pays money out continuously, making and unmaking units against itself rather than passing a fixed stock of them around. equity scheme with net assets of Rs 4,200 crore and units outstandingThe count of units in issue on a given day, which is the divisor in the strike. of 120.00 crore. Divide the first by the second and the figure for the day is Rs 35.00 per unit exactly. Kalyani Bhagat manages the portfolio and Sohail Merchant heads operations.

Three things are settled elsewhere. Separate treatments cover how the figure is struck out of a scheme's books, the day's figure that attaches to an application, and what a unit is as a legal interest. The treatment of the strike also deals at length with a related claim. A higher figure is not dear and a lower one is not cheap. A value that is computed and a price that is agreed are separate things, and the gap between them shows up plainly on a day when both exist at once.

What is the difference between a computed value and an agreed price?

The difference is in the machinery that makes them, not in the shape they come out in. Run the two machines side by side and the point becomes hard to miss. Into the first machine go the things the scheme holds, the amounts it is owed and the amounts it owes. Out comes one number, by division. Into the second machine go one person's willingness to sell and another person's willingness to buy. Out comes one number, by settlement. The two machines have no part in common.

Notice what that means for how the numbers behave. The arithmetic can be done on an empty afternoon, so a computed figure exists on every dealing day whether or not a single unit moves. An agreed price exists only when a bargain is actually struck, and if nobody deals all day there is no price for that day at all, only the last one somebody happened to agree to. One of the two is produced on a schedule and the other is produced by an event. The scheduled one is always there and the other one sometimes is not.

Think of a wedding caterer quoting for four hundred guests. The caterer has a costing sheet: so much rice, so much oil, so much labour, so many hours. The costing sheet produces a number, and it produces the same number whether the wedding happens or not. The amount actually written on the contract after an hour of talking is a different number, and it came from talking. The costing sheet and the contract sit on separate sheets of paper, so nobody would confuse them. In a scheme they sit on the same screen.

Who sets each of the two, and out of what?

The computed figure is set by the scheme, out of the scheme's own records. The parties involved are the asset manager that keeps the books, the trustee company that oversees the arrangement, the custodian that holds what the scheme has bought and the registrar and transfer agent that keeps the unit count. Not one of them is trying to arrive at a number that somebody else will accept. Each of them is trying to arrive at the number the records produce.

The agreed price is set by whoever is dealing that minute. The agreed price is opinion end to end: an opinion about the worth of a holding, an opinion about how badly the other side wants to deal, an opinion about what will happen next. One of the two is an accounting output and the other is a market output, and no amount of care in producing the first one turns it into the second.

There is one place judgement does enter the computed figure, and it is worth naming honestly rather than pretending the arithmetic is spotless. Deciding what each holding is worth today is a policy question, and the policy sits in the scheme's own documents against requirements the Securities and Exchange Board of India (SEBI) sets. The valuation policy is covered under the strike. Everything downstream of that valuation, the adding, the subtracting and the division, is arithmetic that two competent people would run identically.

The confusion with a listed share usually starts in the same place. A share price is a quote: it is what the last two people agreed, and it moves whenever two more people agree something else. A scheme's figure is a division: net assets over units, once for the day. A quote is set by a market and a division is set by a pool, and reading one as though it were the other is the single most expensive habit a reader brings to this subject. A further consequence follows, and the treatment of the strike makes the case in full. No scheme's figure is comparable with any other scheme's. The two divisions were struck over different pools and different unit counts.

When are the two the same thing?

In an open ended scheme, almost always, and for a reason worth stating precisely. When a holder applies to the Girnar Large Cap Equity Fund, nobody sells that holder their units. The scheme makes new ones and hands them over. When a holder goes out, nobody buys those units from them. The scheme takes them back and unmakes them. The making and unmaking of units, creation and cancellationMaking new units against a scheme when money comes in, and unmaking them when money goes out, so the count of units in issue rises and falls., is what the whole open ended arrangement rests on.

The consequence follows. If the scheme itself is on the other side of the transaction, then there is no counterpartyThe other party to a bargain, the one whose agreement is needed before a price exists. in the ordinary sense. There is nobody with a different view about the number, nobody to hold out for a better one, nobody to walk away. With no second party there is nothing to agree, and where there is nothing to agree there can be no agreed price. The applicable value simply is what a holder transacts at.

Two qualifications, both of them pointers rather than lessons. The scheme may apply a load on the way out. A load changes what a holder receives without changing the computed figure at all, and loads are covered separately. And which day's figure attaches to a given application depends on conditions SEBI sets about timing and the receipt of funds. Those conditions are covered at the start of this sequence. Neither qualification disturbs the claim being made: the number was not negotiated with anybody.

When do the two come apart?

The moment units of a scheme can change hands between two people instead of being made and unmade against the scheme. Such a bargain becomes possible where units of a scheme are listed and dealt on an exchange. The instant a second party exists, the whole apparatus of agreement comes back: a buyer with a number in mind, a seller with a different number in mind, and a settlement somewhere between the two.

Now watch what that bargain does to the scheme. The answer is nothing. The scheme is not a party to it. The scheme did not make any units and did not unmake any. Its records show that a certain number of units moved from one holding to another, and its count of units in issue is exactly what it was that morning. When the day ends and the figure is struck, the same arithmetic runs on the same books. The scheme is not a party to the bargain, does not see the price and does not use it, and the figure it strikes for that day is computed exactly as it always is.

The shopkeeper version runs the same way. A shopkeeper weighs the stock in the shop on Monday evening and the sheet says Rs 2,40,000/-. Down the road, two other people buy and sell a shop like it for less than that sheet says this stock is worth. The sheet does not change. The sheet was never a report of what anyone would pay; it was a report of what the shopkeeper counted.

What is a premium, and what is a discount?

Two names for the same gap, pointing in opposite directions. A price above the computed value is a premiumA price sitting above the value computed for the same day, stated as an amount or as a share of that computed value. to it. A price below the computed value is a discountA price sitting below the value computed for the same day, stated as an amount or as a share of that computed value. to it. The two words do nothing else. Each marks which side of the computed figure the agreed price landed on, and how far away it landed.

A percentage without a base is not a number, so sizing the gap means naming the base in the same breath. A worked case runs from an assumed exchange price of Rs 34.30 on a day when the computed value was Rs 35.00. The gap is Rs 35.00 less Rs 34.30, or Rs 0.70 per unit. As a share of the computed value the gap is Rs 0.70 over Rs 35.00, or 2.0 per cent exactly. So the price sat at a 2.0 per cent discount to the computed value, and the words to the computed value are not decoration; they are the base.

Both words describe the gap and neither of them explains it, and a reader who hears the word discount and thinks bargain has been handed a name and has mistaken it for an argument. The word says nothing about why the two numbers differed. The word does not say the units are worth more than they fetched. It does not say anyone was mistaken. Discount is a measurement with a direction attached.

What does this look like on one actual holding?

The working runs in two passes, and the second pass is a device rather than a description. The Girnar Large Cap Equity Fund is open ended, so its units are not dealt on an exchange and there is no exchange price for them anywhere in this record. The second pass assumes one, purely so that the arithmetic of a gap can be shown on figures already established.

Pass one, the open ended case. The scheme has net assets of Rs 4,200 crore and 120.00 crore units in issue, and Rs 4,200 crore over 120.00 crore units is Rs 35.00 per unit exactly. An application of Rs 1,00,000/- attaching to that figure gives 1,00,000 divided by 35.00. The answer is 2,857.142857 and continues without ending. The scheme records units to three decimals, so it writes 2,857.143 units. Nobody quoted anything and nobody negotiated anything: an amount of money was divided by a computed figure, and the answer was the unit count.

Held against the figure it came from, that unit count shows the three decimal convention biting. 2,857.143 units at Rs 35.00 is Rs 1,00,000.005 exactly. Not about Rs 1,00,000/-, and not Rs 1,00,000/- with a bit of rounding waved at it. Exactly Rs 1,00,000.005, half a paisa more than the money that went in. The half paisa cannot be stated to the nearest paisa without silently choosing whether to round it up or down, and no rounding rule settles that choice. The residue is an artefact of recording units to three decimals, nothing more, and it is stated rather than smoothed over.

Pass two, the assumed exchange case. Assume units of a scheme changed hands at Rs 34.30 on a day when Rs 35.00 was computed for that scheme. The gap is Rs 0.70 per unit, and on a base of Rs 35.00 that gap is 2.0 per cent, a discount to the computed value. Apply that to the same 2,857.143 units. At an assumed Rs 34.30 they come to Rs 98,000.0049 exactly, about Rs 98,000/- and, unlike the first product, not landing on a half paisa. Check the difference both ways: Rs 1,00,000.005 less Rs 98,000.0049 is Rs 2,000.0001, and 2,857.143 units at Rs 0.70 is also Rs 2,000.0001. The two routes agree to the last digit.

Now be strict about what that arithmetic establishes, because it is less than it looks. The working establishes the size of the gap and the language for describing it. It establishes nothing whatever about why the gap was there, whether it would close, whether either number was right, or whether anybody was better off on either side of the bargain. The arithmetic is complete and the explanation is absent, and a reader who supplies the missing explanation out of instinct has gone past what the arithmetic shows.

Why does nothing close the gap on its own?

Prices converge for one reason only: somebody can make money by moving between them, and in doing so pushes them together. If units can be bought cheaply in one place and turned into something worth more in the other place, people will do it until the difference stops being worth the trouble. Profit is the entire mechanism, and the mechanism has a precondition.

The precondition is a route. Where units can be created or cancelled against the scheme itself, a route between the agreed price and the computed value exists, and the gap gets worked on. Where no such route exists, there is nothing to do about the gap except look at it, and it can sit where it is for as long as it likes. The presence or absence of that route is the whole explanation for why some gaps close and some do not, and no property of the gap itself reveals which case applies. How such an arrangement actually works, and who is permitted to use it, is covered elsewhere and is not explained here.

A street example makes the shape of it obvious. Onions cost Rs 30/- a kilo in the wholesale market and Rs 45/- a kilo two lanes away. Where buying in the first place and selling in the second is permitted, somebody with a cart will close that gap, and it will not last. Where the second lane sits inside a compound that goods may not enter, the gap can survive for years, and nothing about the size of the gap says which of those two lanes is in view.

How do the two compare, row by row?

Set them against each other on the criteria that decide how a number can be used, and the pattern is not a mixed one. Every row separates them. The two figures differ on who makes them, on what goes into them, on how often they exist, on whether they can be argued with, on whether everyone gets the same one and on what moves them, and a pair of numbers that differs on every criterion is not two versions of one thing.

One row deserves a second look, the one about how often the figure exists. Where a scheme's units are not dealt at all on some day, there is no agreed price for that day and the last one somebody happened to agree to may be days old. The computed figure, meanwhile, was struck that evening as usual. Two numbers on a screen can therefore be describing two different days without saying so, and nothing in their presentation flags it.

Which figure answers which question?

Both are correct and neither is better, so the question is not which to trust but which one was asked. For what a holding is worth on the scheme's records, the computed value answers: 2,857.143 units at Rs 35.00 is Rs 1,00,000.005. For what somebody would hand over for it right now, where a market for it exists, only an agreed price answers, and on the assumed Rs 34.30 that came to Rs 98,000.0049.

Neither figure is the better number, and asking one of them the other's question is the whole of the error at issue here. The computed value placed in a valuation of a holding is doing its job. Placed in a sentence about what the holding would fetch at four o'clock this afternoon, it is being asked something it was never built to answer. The reverse is just as true: an agreed price in a statement of what the scheme's records hold is an intruder.

And there is a trap sitting underneath even the first of those. A holder who reads the computed figure and concludes they can transact at it, right now, at the moment of looking, has taken one step too many. Which day's figure attaches to an application depends on when the application and the money reach the scheme, on conditions SEBI sets and revises. Those conditions are covered at the start of this sequence, and the lesson worth carrying away is this: the computed figure states what a holding is worth on the records, not what can be had on demand.

Girnar Asset Management Limited, the Girnar Large Cap Equity Fund, Kalyani Bhagat and Sohail Merchant are invented.
Educational material. Not advice on any investment, tax, budget or market position.