How Fund Expenses Affect NAV Over Time

Every day, the scheme's expenses are accrued before a unit value is struck, so the value a holder sees is already net of them. On a unit standing at Rs 35.00, a ratio of 1.65 per cent a year removes about Rs 0.001582 a unit a day, roughly 0.0045 per cent of the value. Repeated daily, that invisible deduction is the whole distance between a gross return and a net one.

One scheme carries this guide from end to end. Girnar Asset Management Limited, an invented asset manager, runs the Girnar Large Cap Equity Fund. The fund holds net assets of Rs 4,200 crore against 120.00 crore units in issue, so its net asset valueThe value of one unit, worked out after the day's accruals have been set against what the scheme holds. (NAV) is Rs 4,200 crore divided by 120.00 crore units, or Rs 35.00 a unit exactly. Its expense ratio is 1.65 per cent of net assets a year. Kalyani Bhagat runs the portfolio and Sohail Merchant heads operations.

Unit values and how one is struck are settled elsewhere, and taking the annual ratio apart down to the amount charged in a single day is covered separately. A holder meets that daily amount in exactly one place, the value of the unit itself. The charge never appears as a line anybody pays. It appears as a value slightly lower than it would otherwise have been. Holders look for it on a statement and cannot find it.

A kitty in a shared flat works the same way. Four people put money into one pot every month, and the electricity bill is paid straight out of the pot before anybody counts what is left. Nobody is ever handed an electricity bill of their own, nobody signs anything, and asked what they paid for power last year most of them could not say. The four of them paid it. The money came out before anybody counted. A scheme's expenses work in exactly that way, one day at a time, and the counting is what carries the result.

The case record does not settle one point, so an assumption has to be declared before the arithmetic starts. The value of Rs 35.00 a unit is treated throughout as the value at the end of the stated year rather than at the start. The record gives the value and the year without saying which end the value sits at, so one end is chosen, stated here, and the choice is repeated wherever it changes an answer. The choice changes exactly one answer, and that answer is worked out in full below.

What does one day's expense accrual do to a unit value?

The smallest visible piece comes first. The Girnar Large Cap Equity Fund charges 1.65 per cent of net assets over a year, and 1.65 per cent of Rs 4,200 crore is Rs 69.30 crore. Spread across 365 days that is about Rs 0.1899 crore a day for the scheme as a whole. Dividing the day's amount by 120.00 crore units gives about Rs 0.001582 a unit. Against a unit value of Rs 35.00 that is about 0.0045 per cent. The daily amount is the number every later figure is built from, and its most important property is that it is far too small to see.

Hold the market still for a moment and let nothing else happen. A unit that would have been worth Rs 35.001582 at the end of the day is worth Rs 35.000000 instead. The day's deduction is an accrualAn amount recognised as owed by the scheme and taken into the value before the unit value is published, rather than billed to anybody afterwards., taken into the value before the value is published. Print the two numbers on a scale that runs from zero to Rs 35.00 and they land on the same pixel. The market moves the value by amounts hundreds of times larger in both directions, so no holder could compare a published value with yesterday's and pick the charge out of the movement.

A number invisible on any given day still lands with full force once it is repeated, and the only honest way to show it is to stop looking at days and start looking at the year. Before the year is worked out, a prediction is worth committing to.

What does a full year of accruals come to per unit?

Now let the days add up. Three hundred and sixty five accruals of about Rs 0.001582 come to about Rs 0.5774 a unit. Take the other route and work straight from the ratio: 1.65 per cent of Rs 35.00 is Rs 0.5775 a unit. Two completely different routes, one climbing up from a daily amount and one reading straight off the annual ratio, land on the same figure, and that agreement is what confirms the mechanism rather than leaving it merely believed.

A careful reader will spot the Rs 0.0001 between the two and wonder, so it is worth naming rather than hiding. The gap is rounding and nothing else. The unrounded daily amount is Rs 0.001582191780821 and a bit, and 365 of those come to exactly Rs 0.5775. The Rs 0.001582 used above is that figure cut off at six decimal places, and cutting it off loses about seven hundredths of a paisa a year. Where a rounded number is multiplied by 365, its rounding is multiplied by 365 too. Nothing about the mechanism moved.

The same figure scales back up to the level of the scheme rather than the unit. Rs 0.5775 a unit across 120.00 crore units comes to Rs 69.30 crore, the year's charge the build started from. The arithmetic closes in both directions, and closing in both directions is the property to demand of any cost figure from any source.

Why is a published scheme return already a net return?

Here the day's accrual stops being an arithmetic curiosity and starts deciding how every performance figure is read. The day's expenses are taken into the value before the value is struck. So every single unit value the Girnar Large Cap Equity Fund publishes has already had its own day's charge taken out of it. Whether it covers a month or the stated yearThe single twelve month period the case figures cover, which is the only period any of them describes., a return computed from those values is therefore a net returnA return computed from values that already carry the scheme's charges, so nothing further is deducted from it afterwards. before anybody does anything to it.

The Girnar Large Cap Equity Fund returned 13.4 per cent net for the stated year, measured value to value, against 12.1 per cent for its stated benchmark, and the word net travels with that 13.4 every single time it is written. One scheme, one year, one measurement. A completed year is a record rather than a forecast, and no arithmetic performed on it produces next year's number.

The practical consequence is a subtraction that must never be performed. Taking 13.4 per cent and knocking 1.65 per cent off it to find what the holder kept charges the expense ratio twice: once inside the values that produced the 13.4, and once again by hand. The holder kept 13.4 per cent for that year. There is nothing left to take off.

What would the same year have looked like before the charge?

A holder keeping 13.4 per cent net raises the obvious next question. Before the charge came out, what did the portfolio actually do? Adding the ratio back gives about 15.05 per cent as the gross returnA return measured before charges are taken off, which has to be labelled as such before it can be set beside anything. for the stated year. The 15.05 per cent is an approximation, and it is stated as one rather than dressed up as a measurement.

The reason it is approximate can be stated exactly. Adding 1.65 back to 13.4 charges the ratio once, on one value, at one moment. The real accrual is taken every day on whatever the value happened to be that day, and the value climbed through the stated year, so the later accruals were taken on larger values than the earlier ones. There is a second convention that backs the charge out multiplicatively instead of adding it, and on this record that route gives about 15.3 per cent rather than 15.05. Both are defensible. Neither is a measurement of what the portfolio did. Both routes survive one assertion and one only: the gross figure for the stated year sits somewhere a little above 15 per cent.

Take the assumption declared at the top and use it. If Rs 35.00 is the value at the end of the stated year and the year's net return was 13.4 per cent, the value at the start was Rs 35.00 divided by 1.134, or about Rs 30.8642. Run that opening value forward at about 15.05 per cent gross and it closes near Rs 35.5093. The distance between the two closes, about Rs 0.5093 a unit, is what the charge accounts for on that convention.

Where does the whole worked year land, line by line?

Every figure produced so far goes into one build, where the agreements and the disagreements fall in the right places. Each line below is worked from the case record rather than quoted, and the assumption about which end of the year the Rs 35.00 belongs to is carried through every line that depends on it.

Two lines in that build describe the same 1.65 per cent and give different answers, and that is not an error to be tidied away. Charging the ratio on the closing value of Rs 35.00 gives Rs 0.5775 a unit. Charging it on the opening value of Rs 30.8642 gives Rs 0.5093 a unit. Both readings are honest, they differ by Rs 0.0682 a unit purely because the value moved through the year, and a figure quoted without naming which value it was charged on has not really been stated at all.

What does the charge do to a unit value across many years?

A charge that is proportional to the value gets charged again on whatever is left, so it does not simply add up year after year. The charge compoundsA change applied repeatedly to a base that has already been changed by the earlier applications., and that is why the annual figure sounds trivial while the long figure does not. The same arithmetic drives the gap between two plans of one scheme. The same scheme is available with an expense ratio of 0.85 per cent and one of 1.65 per cent, a gap of 0.80 percentage points a year, and the difference between the two is the distribution commission rather than a different portfolio. The holdings are identical.

The single model this sequence uses, and no other, runs as follows. A gap of 0.80 points a year means the cheaper unit value runs ahead of the dearer one by a factor of 1.008 every year. Both are expressed in unit values rather than percentages. Both start at Rs 35.00, and the market does whatever it does to both of them equally.

The gap is worth about Rs 0.00077 a unit a day on a Rs 35.00 value, under a tenth of a paisa. Twenty years of it ends up worth about Rs 6.05 a unit, roughly 17.3 per cent measured against the dearer holding's ending value. That is the whole reason the annual number is the wrong number to reason with. The dragThe amount by which a charge reduces what a holder keeps, measured across a stated period rather than on any one day. is not the annual figure multiplied by the years; it is the annual factor raised to the years.

The dearer plan buys advice and service from a distributor, and what that service is worth to a particular holder is simply not in this record. The arithmetic above is the whole of what the numbers say. A holder who bought service and paid for it did not lose money to a leak, and neither choice deserves contempt. Which plan suits whom belongs to a separate discussion about advice.

Does a ratio taken in daily slices remove exactly that ratio?

No. A careful reader who finds the discrepancy unaided starts to doubt everything around it, and saying so plainly matters. Each day's slice is taken on a value that yesterday's slice already reduced, so the later slices are taken on marginally smaller values than the earlier ones. Holding the value flat at Rs 35.00 and running the year properly, the charge removes about 1.6365 per cent rather than 1.6500 per cent, leaving Rs 34.4272 a unit rather than Rs 34.4225.

The difference is about 0.0135 percentage points, or about forty seven ten thousandths of a rupee a unit, and nothing established so far moves because of it. It is worth about Rs 56,70,527 across all 120.00 crore units of the Girnar Large Cap Equity Fund, which sounds substantial until it is set against the Rs 69.30 crore the year's charge comes to, where it turns out to be under one per cent of that. Naming a discrepancy and sizing it is what makes an account checkable; rounding an inconvenience quietly away is what makes one impossible to check.

Notice what this does to the simulation above. The panel takes one three hundred and sixty fifth of the year's charge each day, the flat route, and says so on screen. The flat route is the right convention for showing an amount accumulating and the wrong convention for claiming an exact annual drag. Naming which convention a panel uses is the same discipline as naming which value a ratio was charged on.

What happens when a scheme return is set beside another number?

A comparison is where all of this arithmetic finally bites, and the reach of that is wider than anything above. A scheme return is net. A figure arriving from anywhere else may be gross, may be costless, may cover a different period, and nothing in the way it is printed announces which. Two such figures set side by side can be ranked backwards while every individual number is perfectly correct.

Work the case the record gives. A discretionary mandate returned 14.2 per cent gross for a stated year, with fees of 1.88 per cent charged separately from the assets rather than deducted inside them. Taking those fees off leaves 12.32 per cent net. The Girnar Large Cap Equity Fund returned 13.4 per cent net for a stated year. Put 14.2 against 13.4 and the mandate wins. Put 12.32 against 13.4, the only pairing where both figures mean the same kind of thing, and the ranking turns over completely. The two figures did not change; the basis did, and the basis was doing all the work from the beginning. How that mandate is run and how its fees are agreed belong to a separate discussion of discretionary portfolio management. The only thing borrowed here is the pair of numbers.

The same trap has a quieter version that catches even careful readers. The Girnar Large Cap Equity Fund is measured against a stated benchmark that returned 12.1 per cent for the stated year. An index is not something anybody can hold, and nobody pays anything to track it in the abstract, so a benchmark index carries no costs whatsoever. The familiar gap of 1.3 points therefore subtracts a net figure from a costless one, and that pairing is not like for like either. Put both on one basisWhether a figure is stated before or after charges, which decides whether two figures can honestly be set beside each other. and the gross equivalent of the scheme sits a little above 15 per cent against the benchmark's costless 12.1. The honest gap is then close to three points rather than 1.3. More than twice the headline, and in the scheme's favour.

One check on that comparison cannot be closed from this record, and the correct move is to record it as open rather than to assume. A scheme return includes the income the scheme received. An index may be computed on price movement alone or with income treated as reinvested, and the record here does not say which convention the stated benchmark uses. Until somebody establishes that, the three point figure is a finding with a loose end in it, and pretending otherwise would be exactly the failure at issue.

How does a service desk use this on a working day?

Sohail Merchant, who heads operations at Girnar Asset Management, reports that one question arrives more often than any other on the service line. A holder has read that the scheme charges 1.65 per cent, has gone through a statement line by line, and cannot find the charge anywhere. The holder wants to know whether they were charged at all, and quite reasonably suspects something is being hidden.

The answer that works is not a reassurance, it is an arithmetic walk, and it takes about ninety seconds. There is no line because there is no bill. The charge came out of the scheme before the value was struck, at about Rs 0.001582 a unit on a day when the value was Rs 35.00, or about 0.0045 per cent of that value. Multiplied by 365 that is about Rs 0.5775 a unit for the year, exactly 1.65 per cent of Rs 35.00. A holder who can reconcile the small number against the headline number stops looking for a hidden line and starts reading the value as what it already is: a number net of everything.

The same arithmetic does a second job for anybody comparing records rather than answering a phone. Before ranking anything, write the basis beside each figure in the margin. Net, gross, costless index, fees inside, fees outside, and the period each one covers. Most comparisons that produce a surprising ranking turn out to have a mismatch sitting in that margin, and finding it takes a minute against the hours somebody would otherwise spend explaining a result that was never there.

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.