What a Fund Actually Costs a Holder Over Twenty Years

The cost of holding a scheme is not the charge in one year; it is the charge repeated on a value that is itself compounding. Two plans of one scheme at 0.85 per cent and 1.65 per cent differ by 0.80 percentage points a year, and after twenty years the cheaper one holds about 17.3 per cent more, measured against the dearer one.

What does a charge take out of a holding entered below?

The panel's opening settings, written out

A figure that lives only inside a script cannot be checked by anybody who is not sitting at it, so here is the opening instance in ordinary words. Rs 1,00,000/- goes in at the start and Rs 5,000/- goes in every month for twenty years. The total put in is Rs 13,00,000/-. The assumption typed into the return field is 10.00 per cent a year before any charge, and the plan held charges 1.65 per cent a year.

On those settings the holding ends at Rs 34,07,726/-. With no charge at all against the same money it would have ended at Rs 42,92,684/-. The charge taken across the twenty years adds up to Rs 4,47,514/-. The gap it opened is Rs 8,84,958/-, very nearly twice as much. The difference between those two, Rs 4,37,444/-, is not a charge anybody levied. Rs 4,37,444/- is what the money already taken would have gone on earning had it stayed in the scheme, and that missing earning is the whole reason a small annual ratio is not a small thing.

The ratio charged never moved off 1.65 per cent for a single day of that, and the charge taken in year twenty is Rs 54,292/- against Rs 2,296/- in year one, about twenty-four times as large. Five rows of the panel's own twenty are shown here so the arithmetic can be read without running anything; the panel prints all twenty and rebuilds them from whatever is entered.

The exit load is the part most readers expect to hurt. Only the Rs 57,219/- of units bought inside the last twelve months are still within the load period on the day the holding is redeemed, so on these settings the load takes Rs 572/-. Set that Rs 572/- against the Rs 8,84,958/- the ratio opened up. The charge a holder can see on the way out is roughly one fifteen hundredth of the charge they never see at all. Move the holding period from one year to twenty and the load stays exactly where it is. The gap climbs from Rs 2,390/- to Rs 8,84,958/-. A load is levied once on a slice. A ratio is levied every year on everything.

Here is what sits underneath that. A charge running against a scheme's assets every day is not an event anybody can point at. Nothing leaves a bank account, no line appears on a statement, and the unit value looked up in the evening has already had it taken out. So the only way to see the cost of a fund over time is to convert the annual figure into the number of years the units are actually meant to be held for. Converting the annual figure is one line of arithmetic, it takes about twenty seconds, and almost nobody runs it.

Three things are already settled. A scheme carries a charge that runs against its assets every day. Converting that charge into a daily figure is set out under fund loads. A percentage of an amount grows in rupees when the amount grows, and that is ordinary arithmetic. And there are two expense ratiosThe charge that runs against a scheme's assets every day, expressed as a percentage a year. on one scheme sitting behind an identical portfolio.

Girnar Asset Management Limited runs the Girnar Large Cap Equity Fund, an open ended equity scheme, and offers it in two plans. The direct planThe version of a scheme whose charge carries no distribution commission. carries an expense ratio of 0.85 per cent a year. The regular planThe version of the same scheme whose charge includes a commission paid to a distributor. carries 1.65 per cent a year, and the difference is entirely a distribution commission paid to a distributor. Kalyani Bhagat manages one portfolio for both of them. There is no second set of holdings, no second set of trades and no second decision anywhere: the securities are the same securities in the same weights. The two plans differ in the charge and in nothing else. Every figure below rests on that one fact. Neither ratio is a ceiling or a typical charge. Only the 0.80 percentage points between them do any work below.

Start with something easy to picture. Two identical flats sit on two floors of one building, same builder, same fittings, same lift that breaks in the same week, and one of them pays Rs 800/- a year more in maintenance. Nobody moving in would think about that twice, and nobody would be foolish for not thinking about it. Twenty years later neither household has lived differently in any way a photograph could capture, and one of them has handed over a sum they never sat down and discussed.

What does a cost figure like this actually compute?

The arithmetic computes one thing. The difference between two charges applied to one portfolio, across a stated number of years. Not what the scheme will earn. Not what a holder will end up with. Not whether the dearer plan is worth what it costs. The number forecasts nothing at all, and that is not a limitation to apologise for: it is the whole reason the answer can be trusted.

Consider what the arithmetic needs before it will produce anything. The arithmetic needs the two ratios, printed in the scheme documents, and the number of years, a decision belonging to the holder and nobody else. The list stops there. No return, no market view, no benchmark, no inflation figure, no view on the manager. A short list of inputs is exactly what makes a figure repeatable by a stranger who has no reason to trust the person who produced it.

Set that against the question most readers actually have: how much will the holding be worth at the end? Answering that needs a return for a future period, and a return for a future period is not knowable. A reader needs rupees, so the panel above still works in rupees. The return in it is typed by the reader and named as theirs in every line it produces. The gap between the two plans is the one figure here that needs no such assumption from anybody.

Why does one year of charge understate what holding costs?

Because the charge is not a fee paid once. The charge is a percentage of a value, taken again the next year on a value already reduced by it, and again the year after on a value reduced twice. A leak in a tank is not the water lost today; it is the water lost today plus everything that would have been sitting on top of it a decade from now.

Two separate things are happening and they push the same way. A percentage of a larger amount is a larger amount. As the value held across the holding periodThe length of time the units are actually held, which is the horizon a charge should be judged over. rises, the rupees taken each year rise with it. The ratio has not changed by a hair. The second is quieter and matters more: money taken in year three is not in the scheme in year four, so it earns nothing more, and neither does the amount it would have earned. The money that is no longer there is what compoundsA change applied repeatedly to a base that has already been changed., and the missing money is why the cost of holding is a curve rather than a slope.

One distinction trips people here, and it repays a slow reading. Nobody is claiming the charge gets bigger as a percentage. It does not. 0.80 percentage points a year is 0.80 percentage points a year in year one and in year thirty. The accumulated consequence of applying that unchanged ratio over and over to a moving base is what grows. The ratio is constant and the outcome is not, and holding both of those together at once is most of the work.

What is the model, and can it be repeated independently?

Here it is, whole. The regular plan charges 1.65 per cent a year and the direct plan charges 0.85 per cent, so the direct plan keeps 0.80 percentage pointsWhat a gap between two percentages is counted in. 1.65 against 0.85 is a gap of 0.80 percentage points. more of the value every year. Turn that into a ratio and the direct plan's value stands at 1.008 times the regular plan's at the end of each year. Ratios multiply, so after any number of years the ratio is 1.008 raised to that number, and the gap is that figure less one.

An exponent left implied is an exponent nobody checks, so the exponent here is written out. Twenty years is 1.008 multiplied by itself twenty times. The product is 1.172764. Taking away one leaves 0.172764, or about 17.3 per cent. Any calculator with a power key will do it, and a number produced first hand sits differently in the mind from a number handed over.

One honest note. There is more than one defensible way to arrange this arithmetic, and the alternatives land within a few tenths of a point of each other at twenty years, so one convention is fixed and used everywhere, in the panel above as well as here. A reference carrying two answers for one gap has a defect, whichever answer is the better one.

Why does the gap not need a view about what the scheme earns?

The cancelling that follows is the centre of the whole argument, and it is worth slowing down for. Both plans hold the same securities in the same weights, bought on the same days at the same prices by the same manager. Whatever the market did over the period, good, bad or sideways, it happened to both of them in exactly the same proportion. Dividing one plan's value by the other's puts that shared experience on the top and the bottom of the fraction, where it disappears. The charge is what is left, and only the charge.

The everyday version is two people cycling the same road in the same wind. The wind is fierce and behind them, or fierce and against them, and it does not matter which. The question is not how fast either of them went. The question is how far apart they ended up, and that needs only the one thing that differed between them. The wind cancels. The cancelling happens whether the wind was kind or cruel, and which it was never has to be established.

Notice what that asymmetry buys. A cost gap requires nobody to know the future, so a cost gap can be stated honestly when a return cannot. It also marks where scepticism belongs elsewhere: any comparison that survives without a forecast stands on firmer ground than one that needs a forecast to work.

What do five, ten and twenty years actually come to?

Every one of these is computed by raising 1.008 to the number of years and taking away one. The whole column can be reproduced on any calculator in about a minute.

The distance between the first row and the fourth row is the point, so read the two together. In year one the difference is 0.80 per cent. Most people would wave that away without a second thought, and they would be making a perfectly ordinary judgement in doing so. Twenty years of that same unchanged figure is about 17.3 per cent of the terminal valueWhat a holding is worth at the end of the period being examined. being examined. 0.80 per cent a year sounds like nothing and 17.3 per cent does not, and they are the same fact stated over two different lengths of time.

Look also at the tenth row against the twentieth. Ten years gives about 8.3 per cent and twenty gives about 17.3, so the second decade adds more than the first did, and nothing in the charge changed to cause it. The second decade is the same ratio applied to a wider gap. A curve does that. A straight line never does.

Which value is the gap measured against?

Here is where two careful people produce two different numbers and both are right. At twenty years the direct plan stands at 117.28 against the regular plan's 100.00. Measured against the regular plan's ending value, the wedge between them is about 17.3 per cent. Measured against the direct plan's ending value, the identical wedge is about 14.7 per cent. One divided by 1.172764 is 0.8527, and what is missing from one is 0.1473. A gap quoted without saying which value it is measured against has not actually been stated.

Shopping makes the same point. A shirt marked down from Rs 1,000/- to Rs 800/- is 20 per cent off the old price, and the old price is 25 per cent above the new one. Same two prices, same one gap, two true percentages, and which one appears is decided only by which number was divided by. Quoting the larger figure, staying quiet about the base and leaving the other one to be assumed is misleading.

What does the gap look like in rupees, with nothing assumed about returns?

Percentages slide off people, so the figure is better put in rupees. Putting the figure in rupees takes care. A rupee figure at the end of twenty years would need a value at the end of twenty years, and a value needs a return. A return has to be assumed rather than computed. The conservative route is to hold the value flat and let the ratios do the work.

On a value held at Rs 1,00,000/-, the regular plan's 1.65 per cent is Rs 1,650/- for the year and the direct plan's 0.85 per cent is Rs 850/-. The difference is Rs 800/- a year, on every Rs 1,00,000/- held. Repeat that on a value that never moves and twenty years comes to Rs 16,000/-. A value that grows carries a proportional charge that grows with it, so the flat figure understates the gap on purpose. Rs 16,000/- is the floor of the answer rather than the answer.

Rs 16,000/- is not what the difference will be. Rs 16,000/- is the smallest the difference can be, on a holding of that size held for that long, and the figure got there without anybody assuming anything about markets. Knowing which side of the truth a number sits on is worth more than a sharper number whose direction of error nobody can name.

How does anyone use this on a working day?

Start with the holder, the person the charge is least visible to. Sohail Merchant runs operations for Girnar Asset Management, and the unit value his team puts out each evening has already had that day's charge taken off it. Nothing is billed. No debit appears. There is no fee line to find, so a holder who scrolls a statement looking for one will not find it. The only place this cost ever becomes visible is in arithmetic somebody chooses to run, and the habit below matters more than the number it produces.

The habit is three moves, and they are the same three at an advice desk, on a fund research team reviewing a scheme, or at a kitchen table working out a household position on a Sunday.

There is a fourth move that is really a refusal. Never hand anybody a rupee figure for the ending gap without saying whose assumed return produced it. The panel above will compute one, and it puts the reader's own assumption into the sentence every time. Naming the assumption is the whole difference between an illustration and a forecast.

What does this arithmetic refuse to settle?

The arithmetic refuses to settle which plan to hold, and the refusal is a named part of the method rather than a caveat parked at the bottom. One side of the trade has been computed in full: the difference in charge is 0.80 percentage points a year, about 17.3 per cent of the ending value at twenty years measured against the regular plan, and Rs 800/- a year on every Rs 1,00,000/- held flat. The other side is the value of the advice and the service that the distribution commission buys. No figure for that value exists above, and none exists in general. The value of that advice is different for a reader who has never held units before and a reader who has held them for thirty years.

One side is arithmetic and the other is a judgement about a particular household's situation, and nobody can add those together from outside it. Resolving that trade would amount to advice; the arithmetic is stated and stops there. A holder in the regular plan is buying something, is not being robbed, and has not been foolish. Neither choice is anybody's business but the holder's.

The general proposition that cost is among the most dependable things a holder keeps hold of, in a world where almost nothing else about a scheme can be known in advance, is associated with John C. Bogle and set out in his book Common Sense on Mutual Funds, first published in 1999. The name belongs with the proposition. The arithmetic above is run on a made up scheme rather than on anything in that book.

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