How a Scheme's Assets and Liabilities Move Its NAV

A scheme's net asset value moves when either side of its books moves. Holdings and amounts owed to the scheme sit on one side, amounts the scheme owes sit on the other, and the running charges accrue there every day whether or not the market moved. The Girnar Large Cap Equity Fund accrues about Rs 18,98,630/- a day, about Rs 0.0015822 a unit.

Assets, liabilities and the idea of accrual are all settled elsewhere. Take those three ideas into a place most readers have never opened: the books of a pooled scheme, on an ordinary Tuesday, with nothing dramatic happening. A scheme having two sides is unremarkable. One item on the second side grows every single day without anybody deciding it should, and that growth is the only reason the figure a holder reads can drift downward on a day when nothing else happened at all.

One scheme carries this guide from end to end. Girnar Asset Management Limited, an invented fund house, runs the Girnar Large Cap Equity Fund, an open ended equity scheme with net assetsWhat a scheme holds and is owed, less everything it owes, at the moment the figure is struck. of Rs 4,200 crore and 120.00 crore units outstandingThe total count of units in issue across every holder of the scheme on that day. The count is the divisor, and it changes only when units are created or cancelled.. Divide the first by the second and one unit stands at Rs 35.00 exactly. The scheme carries a stated expense ratioThe running charge against a scheme, quoted as a percentage of its assets a year rather than as a bill to anybody. of 1.65 per cent of net assets a year, and the holding is spread across 3,80,000 folios. Kalyani Bhagat manages the portfolio and Sohail Merchant heads operations.

Three things are settled elsewhere. The first is that a scheme strikes one figure for the day, after the day is over, out of its own books rather than out of a market quote. The second is that which day's figure attaches to a particular application is a separate question with its own conditions, covered separately. The third is that what the scheme chooses to hold, and why, sits with portfolio thinking. The books that the once-a-day computation actually runs on are opened below, one side at a time.

What actually sits on the two sides of a scheme's books?

Two columns and one subtraction. On one side is everything the scheme holds and everything it is owed. On the other is everything it owes. Take the second from the first and what is left is net assets. Net carries its ordinary meaning here, and a scheme gives the word no special sense it would not have anywhere else. Net assets divided by units outstanding gives the figure per unit that gets published.

Consider a small catering business the night before a wedding. The business holds ingredients, hired crockery and cash in a tin. The caterer is owed the balance on last week's function. The caterer owes the vegetable supplier, and owes staff for the shift they have already worked even though payday is Friday. Nobody would call the value of the business the ingredients alone. Everything owed is netted off, including the wages that have piled up but not gone out, and what remains is the value of the business to its owner. A scheme does the identical subtraction, on a much larger pool, once every dealing day, and the only unusual feature is that one of its liabilities regrows overnight on its own.

What is on the asset side, and what does this record leave unsaid?

Three categories cover almost all of it, and categories are as far as the naming can go. First, the securities the scheme has bought, carried at a valued amount for the day. Second, cash the scheme is holding and has not put to work. Money arrives and leaves continuously, so some cash sits in every scheme at every moment. Third, amounts owed to the scheme but not yet in its hands. Such an amount is a receivableAn amount somebody owes and has not yet handed over. The entitlement already exists, so the amount counts as an asset. in the ordinary sense of the term: income that has been declared and will arrive, or the proceeds of something sold where the money has not settled yet.

Now the honest part, and it matters more than the categories do. The Girnar Large Cap Equity Fund's net assets stand as one figure of Rs 4,200 crore with no breakdown behind them, so no rupee amount attaches to any of those three categories. Not a holdings split, not a cash percentage, not a receivables number. A plausible split could be made up. Arithmetic assembled to fill a gap reconciles to nothing, and teaches nothing true. The categories are real and the split is absent.

What sits on the liability side, and why is a charge nobody has paid sitting on it?

The liability side holds the obvious things first. Amounts the scheme owes and has not yet paid out are a payableAn amount owed and not yet settled. A payable reduces what is left over even though the money is still sitting in the account. in the ordinary sense, and they include money due to holders who have redeemed and are waiting for it. Then it holds the item everything here turns on: the charges that have run against the scheme and have not been paid across yet.

An accrualRecognising an amount when it is incurred rather than when it is paid. The obligation exists the moment the day is worked, not the moment the money moves. is a familiar idea, applied here in an unfamiliar place. Electricity in a household is being consumed at this moment. Nobody is standing at the meter and nobody has sent a bill, and the amount owed is nonetheless larger than it was an hour ago. The obligation is real before any bill exists. An accrued liabilityAn obligation recognised in the books before any payment is made, because the day that created it has already been worked. in a scheme works the same way. The scheme has had a day of being managed, of having its records kept, of having its securities held, and the amounts owed for that day are recognised at the end of that day. An accrued charge is a liability the moment the day has been worked, even though not one rupee has left the scheme, and that is precisely why it lands on the second column and therefore on the published figure.

How much does the scheme accrue in one single day?

Three divisions, worked through here rather than quoted. A ratio without a base is not a number at all, so the ratio comes first with its base named in the same breath. The Girnar Large Cap Equity Fund carries 1.65 per cent of net assets a year, and its net assets are Rs 4,200 crore. Multiplying: 0.0165 times Rs 4,200 crore is Rs 69.30 crore for the year, or Rs 69,30,00,000/- written out in full.

Now the first division. Rs 69,30,00,000/- across 365 days is Rs 18,98,630.14, or about Rs 18,98,630/- a day. In crore that is about Rs 0.1898630 crore, and it is worth writing the extra digits out rather than stopping at Rs 0.1899 crore, for a reason that becomes visible one division later. The 365 day divisor is used here purely to make the illustration reproducible; how a scheme actually spreads its charges across a period is an operational and regulatory matter settled elsewhere.

Now the second division. Rs 18,98,630.14 goes across 120.00 crore units, or 1,20,00,00,000 units, and the result is Rs 0.0015822 a unit for the day. Rs 0.0015822 is roughly one and a half thousandths of a rupee, about a sixth of one paisa, on a unit standing at Rs 35.00, and it is the entire distance between the figure a holder saw yesterday evening and the figure they will see this evening if literally nothing else changes. Expressed as a share of the base rather than in rupees, it is 0.0045205 per cent of net assets a day, which is simply 1.65 divided by 365.

Do the two routes to the per unit charge actually agree?

The two routes agree, and not approximately. Route one worked from the whole scheme downward: Rs 4,200 crore, times 1.65 per cent, divided by 365, divided by 120.00 crore units. Route two never touches the scheme total at all. The second route starts at one unit standing at Rs 35.00. Take 1.65 per cent of Rs 35.00, or Rs 0.5775 a unit for the year, and divide by 365. The answer is Rs 0.0015822 a unit a day, digit for digit the same. The two routes are the same multiplication and division performed in a different order.

Now the trap, and it is worth more than the agreement. Taking the rounded daily figure of Rs 0.1899 crore and dividing it by 120.00 crore units gives Rs 0.0015825 rather than Rs 0.0015822. The difference is about three ten-millionths of a rupee. In money that is nothing, but it changes the sixth decimal place and it is not the same number. The two genuine routes give exactly Rs 0.001582191 a unit and the rounded route gives Rs 0.0015825, so the correct statement is that the two agree exactly while the third is a rounding artefact, and calling all three the same figure would be the kind of small dishonesty that quietly destroys a reader's ability to check anything. Carry the digits until the last step, then round once.

Why does no money ever leave a holder's bank account?

Because the charge was never addressed to the holder. The charge runs against the scheme, and the scheme settles it out of its own assets. Nobody raises an invoice against a folio. No standing instruction is set up. No mandate is signed. The holder is never asked to approve the amount, and there is no month in which a payment fails because a balance was short.

Here is the everyday version. On a prepaid mobile pack, a slice of the balance disappears each day for the plan in force. Nothing is paid on day fourteen. There is no transaction, no debit from a bank account, no confirmation to approve. The amount was taken from the pool already handed over, so the balance is simply smaller than it was. A scheme does the same thing on a much larger pool, and that pool is divided among everyone rather than belonging to one holder.

No money leaves a holder's bank account for this charge in any month of any year, no bill is raised against them, and their approval is never sought, and those three facts together are the complete explanation for why so many people are certain they are not paying it. They are paying it. Holders pay it in the only currency a pooled scheme can charge in: a slightly smaller share of a slightly smaller pool. The mechanism that makes the charge painless is exactly the mechanism that makes it invisible.

Why can a holder not find the charge on a statement?

Because there is no row on which it could sit. Look at what a statement actually carries. A statement carries a folioThe account number under which one holder's units in a scheme are recorded and every transaction on them is listed. number, the name of the scheme, the number of units held, a figure per unit, and the two multiplied together. Every transaction row on it is an event: money came in and units were created, or units were cancelled and money went out. The charge is neither. The charge created no units and cancelled none, and it moved no money into or out of the folio.

The charge moved the second number, the figure per unit, downward by a small amount before that figure was ever printed. So the statement is not concealing it and is not omitting it. The charge is not missing from the statement. The charge is inside the only number on the statement that could carry it, and a holder who reads twelve statements and finds nothing has conducted a correct search and received the correct result. The place it is disclosed is the scheme's own documents, where the ratio is stated as a ratio, which is a different document doing a different job.

What happens to each side when prices move?

The two sides do not respond to the same things, and that asymmetry is why the published figure behaves the way it does. Those holdings are carried at a valued amount, so when their prices move the asset side moves with them, in full and immediately. The liability side largely does not. Amounts owed on settlements do not change because prices did. Redemption proceeds already fixed do not change. The day's accrued charge is struck on the value of the assets, so it does move a little, by roughly 0.0045205 per cent of the change rather than by the whole of it.

And the divisor does not move at all. Units outstanding of 120.00 crore are a count of units in issue, not a value. A day of violent price movement leaves that number exactly where it was, and the per unit figure therefore tracks what the scheme holds very closely. Units change only when units are created or cancelled, which happens because people bought or sold, never because prices did. One asymmetry is worth holding on to above all others: prices move the numerator hard, barely touch the small correction, and cannot touch the denominator.

Does the accrual stop when the market falls?

No, and it does not need to be dramatic about it either. The charge is struck on the value of the assets, so when the assets are smaller the charge is smaller in exactly the same proportion. Proportion is a real and often overlooked piece of protection: nobody is charging a fixed rupee amount against a shrinking pool. Work it. If net assets fall by a fifth from Rs 4,200 crore to Rs 3,360 crore, the year's charge falls from Rs 69,30,00,000/- to Rs 55,44,00,000/-, and the daily accrualThe single day's slice of the running charge, recognised against the scheme at the end of that day. falls from about Rs 18,98,630/- to about Rs 15,18,904/-. Every one of those falls by the same fifth.

A proportion of a positive number is a positive number, so the charge never becomes nothing: the accrual approaches zero as the assets fall and arrives there only if the assets do. On a day when what the scheme holds gains nothing and loses nothing, the accrual is the only thing that moved, and the figure per unit ends the day lower than it started by exactly that amount. A drift of that kind is not a fault in the design and not a hidden penalty. A running charge is exactly this.

What does one day and then one whole year actually look like?

The condition comes first. Everything except the charge is held completely still. Such stillness never happens in any real year, and it serves one purpose only: to isolate a single effect. In an actual year the movement in what the scheme holds is far larger than anything below. The size difference is precisely why the accrual goes unnoticed.

Start of day one. Net assets of Rs 4,200 crore over 120.00 crore units is Rs 35.00 a unit exactly. The day is worked, and the day's charge of Rs 0.0015822 a unit accrues. The per unit valueNet assets divided by units outstanding, which is the single figure a scheme publishes for the day. ends the day at Rs 34.998418, or Rs 34.9984 rounded to four decimals so the movement stays legible in a sentence. How many decimal places a scheme actually declares its figure to is set by the Securities and Exchange Board of India (SEBI).

Now run 365 of those days with nothing else moving. The accumulated charge is Rs 0.0015822 times 365, or Rs 0.5775 a unit. Rs 35.00 less Rs 0.5775 is Rs 34.4225. Check it from the other end. The year's charge of Rs 69.30 crore takes net assets from Rs 4,200 crore to Rs 4,130.70 crore, units are untouched at 120.00 crore, and Rs 4,130.70 crore divided by 120.00 crore is Rs 34.4225. The two ends meet exactly. Nowhere across those 365 days did the holder pay anything, receive a bill, approve a deduction or see a line appear anywhere, and the entire year's charge arrived as a figure per unit that is six paise and a fraction lower than where it started.

What does it mean to say the published figure is already net?

Already net means the subtraction has already happened before the number is published, and that every figure built on top of that number inherits the subtraction without having to repeat it. The day's accrued charges land on the liability side, net assets are what is left after they land, and the division by units happens last. So the figure a holder reads for the Girnar Large Cap Equity Fund on any evening is the figure after the day's charge, not before it.

The sequence is not a presentation convention and not a choice anybody made about how to display something. The sequence is simply the order in which the arithmetic runs, and that order decides how every return computed from those figures has to be read. A return measured from one published figure to another published figure is already netDescribes a figure from which the charges have been taken before it was published, so no further deduction belongs on top of it. of the running charge across the whole period. Nothing further is deducted from it afterwards, and anybody who subtracts the expense ratio from such a return a second time has taken the same charge twice. Equally, anybody comparing such a figure with a number computed on a different basis has to say which basis each one is on before the comparison means anything. Comparisons of that kind, and the arithmetic of what a charge costs over a long holding, are both covered separately.

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.