Tracking Difference: The Gap, and What Is Inside It

A tracking difference is what a tracker returned less what its index returned, across the identical period. The Girnar Broad Market Index Fund came in at 12.12 per cent net across the stated year, against 12.40 per cent for the index behind it, leaving minus 0.28 percentage points. Split that figure and 0.20 points is the charge and 0.08 points is everything else.

The charge is not the whole of the gap, and the whole argument turns on that. The charge is most of the number, so almost every explanation of this measure stops one step earlier, at the charge. Most is not all. The Girnar Broad Market Index Fund charges 0.20 per cent of its own assets a year and its shortfall for the stated year was 0.28 points, so a reader told that a tracker falls behind by its costs is holding a rule that reaches a little over seven tenths of what happened and leaves the rest with nowhere to live. Every wrong story about a tracker begins in the 0.08 points the cost explanation cannot reach, so the gap is worth building in two parts rather than one.

The instrument above opens on that record: an index at 12.40 per cent for the stated year, a charge of 0.20 per cent of assets, and four residual lines loaded at 0.05 points of cash drag, 0.03 points for following index changes and 0.02 points of dividend timing, against 0.02 points of securities lending income credited back. The four residual lines net to the 0.08 points the record does hold, and with the charge they add to 0.28 points behind, leaving the scheme at 12.12 per cent net. The record itself divides its residual no further, so those four lines are the analyst's rather than the scheme's.

Girnar Asset Management Limited, an invented asset manager, runs the Girnar Broad Market Index Fund on a broad unnamed index. Kalyani Bhagat manages the equity scheme in the same range and Sohail Merchant heads operations. Every return below carries its period and the word gross or net, and the whole record is one year on one scheme.

What exactly is a tracking difference, and which way round is it computed?

A tracking difference is the tracker's return minus the index's return, in that order, over one stated period. Nothing else. With the scheme first and the index second, a scheme that ended behind carries a minus sign. The minus sign is the ordinary case, and the one worked here. Taken the other way round, every sign flips. A flipped sign is fine when the order is stated and quietly disastrous when it is not.

For the Girnar Broad Market Index Fund in the stated year the subtraction is 12.12 per cent net less 12.40 per cent. The answer is minus 0.28 percentage points. The 12.12 per cent is a net figure, meaning the chargeMoney taken out of a scheme's own assets to pay for running it, quoted here as a percentage of those assets for a year. has already come out of it. An index is a computation rather than a scheme, and nobody pays to hold a computation, so the 12.40 per cent has no charge inside it at all. The subtraction takes a figure a real cost has already reduced away from a figure that never carried one, so a gap is built into the arithmetic before any question of skill or care has been asked.

Two things travel with the number or the number says nothing. The first is the sign: minus 0.28 points and plus 0.28 points describe opposite years, and a difference quoted as nought point two eight with nothing in front of it has thrown away half its content. The second is the period. A gap across a year and a gap across three months are not comparable, and neither is an annual figure unless somebody says so. A tracking difference quoted without its sign and without its period is not a number a reader can use, and both are dropped constantly.

The gap is measured in percentage pointsThe unit that results from subtracting one percentage from another. Twelve per cent less eleven per cent is one percentage point, not one per cent. rather than in per cent. Saying the scheme fell 0.28 percentage points behind describes a subtraction that has already happened. Saying it fell 0.28 per cent behind invites a reader to take 0.28 per cent of something. Taking 0.28 per cent of something is a different sum with a different answer.

Why can a scheme that holds the index not just return the index?

Because one of the two things being compared is a business and the other is a sum. Think of a shop that promises to sell exactly what the wholesale price list says. The shop still pays for the shutter, the electricity and the person behind the counter, it still keeps a float in the till that is not stock, and when the wholesaler changes the list on a Tuesday it has to swap what is on its shelves, at a cost, on a day the list changed for free. The list has no shutter, no till and no shelves.

Four mechanical facts do the work, and none of them is anybody making a mistake. The scheme charges for its work against its own assets rather than billing a holder. The scheme cannot be in the market at every instant, so it holds some cash. An index is never subscribed to and never redeemed, so money reaches the scheme and leaves it on days the index has no such event. And when the index changes its constituentsThe individual securities an index is computed from. When the index changes which ones it counts, a scheme following it has to change what it actually holds. it starts counting different names from a stated date, while the scheme has to deal in real securities at real prices to match it.

Not one of those four is a fault, an oversight or a symptom, so a gap between a tracker and its index is the expected condition rather than a warning sign. The question is never whether a gap exists, but how large it is, how much of it was contracted in advance, and what the rest of it is made of.

What would a perfect tracker have returned for the stated year?

A reference point turns a single figure into a decomposition, so the reference point comes before the real number. A perfect trackerA reference scheme that matches its index exactly and charges what the real scheme charges. A perfect tracker is a measuring device, not a target and not an ideal. is an invented scheme that follows the index with no slippage of any kind and charges exactly what the real scheme charges. The perfect tracker holds no cash and receives no money on awkward days, and it changes what it holds at no cost when the index changes what it counts.

The arithmetic is one subtraction. The index returned 12.40 per cent for the stated year and the scheme charges 0.20 per cent of its own assets a year, so the perfect tracker would have returned 12.20 per cent net. The 12.20 per cent is not a target anybody promised. The figure is a measuring device whose only job is to separate the part of the gap that was contracted before the year began from the part that was not, and almost every treatment of this subject leaves that step out.

Once that figure exists, the real number has somewhere to be measured from. The Girnar Broad Market Index Fund actually returned 12.12 per cent net for the stated year, putting it 0.08 points below the perfect tracker's 12.20 per cent net. Two subtractions have now happened rather than one.

How does the 0.28 point gap split into charge and everything else?

Into 0.20 points and 0.08 points, and those two add back to 0.28 exactly with nothing left over. The smaller part is the one worth the closer look.

Take the two subtractions in order. The index at 12.40 per cent less the charge of 0.20 per cent of assets gives the perfect tracker at 12.20 per cent net. The perfect tracker at 12.20 per cent net less what the scheme actually managed, 12.12 per cent net, leaves 0.08 points. Add them: 0.20 plus 0.08 is 0.28, the gap the very first subtraction produced. The books close in both directions, and that is the only reason to trust either half.

Now the shares. Dividing 0.20 by 0.28 gives 0.714285 and a bit, or 71.4 per cent of the gap. Dividing 0.08 by 0.28 gives 0.285714 and a bit, or 28.6 per cent. The costs explain most of the gap and not all of it, so an explanation saying a tracker falls behind by its costs has stopped one step early.

The same subtraction reads easier in money than in points. On a holding of Rs 1,00,000/- across the stated year, the index figure ends at Rs 1,12,400/-, the perfect tracker at Rs 1,12,200/- and the scheme at Rs 1,12,120/-. The charge is the largest and most predictable part of a tracker's shortfall, and on this record it costs Rs 200/- of every Rs 1,00,000/- held for the year, with everything else costing a further Rs 80/- on top.

The whole build in rows. Every line can be repeated rather than taken on trust. The last two rows are the check.

What is actually inside the 0.08 points?

Three things, named, with no arithmetic dividing the figure between them. The first is cash: a scheme cannot be fully invested at every instant, and money sitting as cash does not earn what the index earns. The second is flow timingThe effect of money arriving into a scheme and leaving it on particular days. An index has no subscriptions and no redemptions, so it never has this at all.. Money comes in on a Tuesday and goes out on a Friday, and an index has no Tuesday or Friday of that kind. The third is the cost of following the index when it changes: the scheme has to deal in real securities to match, and dealing has a cost the index never carries.

Now the part a lot of writing about this subject gets wrong by being too helpful. The Girnar record splits the 0.08 points no further, so no share of it is assigned to cash, none to flow timing and none to index changes, and saying that plainly is part of the answer rather than a hole in it. Somebody who writes that roughly half of it was cash has invented a number that sounds like measurement. The missing split is also why the four residual fields in the instrument are left open: a split entered there makes the arithmetic work perfectly, and the split still belongs to whoever entered it.

If a household's electricity bill for a month is higher than usual by Rs 400/- and the reason is some mixture of the new cooler, the guests who stayed for a week and the two humid weeks in the middle, all three can be named honestly. Announcing that the cooler was Rs 250/- of it cannot be done unless somebody metered the cooler. Nobody metered the cooler here.

Does the gap survive if the charge is taken away entirely?

The gap survives, and that is how the claim gets proved rather than merely repeated. Run backwards: the scheme returned 12.12 per cent net for the stated year, so adding its charge of 0.20 per cent of assets back on gives about 12.32 per cent grossA figure stated before a particular cost has been taken out of it. The opposite of net, which is the figure after that cost.. The index returned 12.40 per cent. The difference is 0.08 points, arrived at from the opposite direction with the charge out of the picture.

Two cautions travel with that 12.32. Say approximate: a charge accrues against the scheme's assets day after day, so adding a year's worth back as one lump is a close approximation rather than an exact reversal. And say gross, every time. The 0.08 points is still there once the charge has been entirely removed, and that is what proves the residual was never a part of the charge in the first place.

One plain sentence for a reader who has met the figure 12.32 elsewhere. A discretionary mandate in the portfolio material is left with 12.32 per cent net after its own fees. The mandate is a different scheme on a different basis measured against a different thing. The match is a coincidence produced by arithmetic and nothing joins them.

What happens to the gap as the charge slides down to nothing?

The control below moves two things at once. The stacked bar is the shortfall built in the same two parts, and the marker is where the scheme's return lands against a fixed index line at 12.40 per cent. At a charge of 0.20 per cent of assets the scheme sits at 12.12 per cent net, with 0.28 points split 0.20 to 0.08. The charge can then be taken down. The residual segment never moves, so the charge segment shrinks away to nothing and the bar still refuses to close.

Can a tracking difference ever be positive?

Not from the charge, ever. A subtraction has one direction, so a charge of 0.20 per cent of assets can take 0.20 points off and can never put anything back. From the residualWhat is left of a difference once the part that can be named and priced has been taken out of it. Here, the gap that is not the charge., though, yes. Cash sitting idle hurts in a rising period and helps in a falling one. Money arriving on a good day helps and on a bad one hurts. Dealing to follow an index change costs money, but the price the scheme got can land on either side of the price the index assumed.

One part of the gap has a fixed sign and the other does not, and that is exactly why the two behave so differently from one period to the next. A tracker ending a period slightly ahead of its index is possible and is not a triumph: the variable part landed larger than the charge and in the helpful direction, once. With the securities lending credit raised past the charge on the instrument above, the whole difference turns from behind to ahead, in the words as well as in the drawing. Whether a particular kind of income is available to a scheme at all is set by the Securities and Exchange Board of India (SEBI).

What does one year of this figure actually establish?

Less than it looks. The two parts have completely different futures. The 0.20 points of charge is a standing featureSomething built into how a thing works, so it turns up every period rather than only in the period that happened to be measured.: it is in the scheme's own terms and will show up next year and the year after for as long as those terms say so. The 0.08 points is one draw of something variable. The residual happened once, and there is no reason at all for it to be 0.08 points again.

A single year's tracking difference therefore mixes a permanent subtraction with a one off, and separating them properly needs more years than this record contains. That is not a hedge, it is the honest boundary of a one year figure. With five years of gaps, how much of each year repeated would be visible, and the repeating part would look a great deal like the charge. With one year there is one number, and the most useful thing to be said is which part of it would be expected to appear again.

Claims about the 0.08 in particular need care. The 0.08 is one observation of something that varies, not a property of the scheme. Calling it the scheme's residual, as though the scheme carries a fixed one, is exactly the wrong reading and a very easy sentence to write by accident.

What is a tracking difference not?

A tracking difference is not a measure of how much the gap moved about inside the period. A scheme could have run 0.28 points behind steadily all year, or swung about wildly and finished 0.28 points behind, and this measure reports the identical figure for both. The distinction has its own measure. Tracking error reports the spread of the gap rather than its total, and is covered separately. The last control on the instrument above spreads the identical annual gap across four quarters: as the quarters separate, the tracking error climbs from 0.00 points while the tracking difference sits unmoved at 0.28 points behind.

A tracking difference is not a comparison with any active scheme either. The record does hold one: the Girnar Large Cap Equity Fund returned 13.4 per cent net for the stated year on a charge of 1.65 per cent of assets, against the tracker's 12.12 per cent net on a charge of 0.20 per cent. The lead is 1.28 points to the active scheme, and a reader is invited to conclude the higher charge earned itself. Then notice that the charges differ by 1.45 points a year, more than the lead itself. One year, one scheme on each side, and two schemes measured against benchmarks this record does not identify with each other, is not evidence about active management in either direction.

And it is not a judgement on the manager. Of the 0.28 points, 0.20 was written into the scheme's own terms before the year began and nobody made a decision about it during the year. Anybody's judgement can have touched only 0.08 points, made of three things this record does not divide, in a single year.

Girnar Asset Management Limited, the Girnar Broad Market Index Fund, 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.