Trading Costs: Spread, Impact and Shortfall Compared

Trading costs come in four separable parts: the spread paid to transact, the impact the order itself has on the price, the drift between deciding and dealing, and the cost of the part that never got filled. Implementation shortfall adds them up by comparing a paper portfolio with the real one. The Anantara portfolio replaced Rs 170 crore over the stated year, so every rate was paid twice.

Security selection finished with a holding chosen. The next step begins one moment later, at the awkward moment nobody writes a memo about: the holding has been chosen and it is not yet held. Something has to happen in between, and that something has a price. The decision is free and getting there is not, and no return figure shows the difference unless somebody states which side of it the figure sits on.

Everything here is worked on the Anantara Multi-Asset Portfolio, an invented discretionary mandate of Rs 500 crore run by Faiz Ahmad Ansari for a charitable endowment whose investment committee is chaired by Rukmini Deshpande. The equity sleeve is Rs 300 crore, the fixed income sleeve Rs 150 crore and the cash sleeve Rs 50 crore, all fixed before any of the arithmetic below begins.

One warning before the arithmetic, and it shapes everything below. A trading costEverything that separates the price a decision was taken at from the price finally achieved, including charges visible on a note and price movement that is not. has a rate, and no rate is stated below. Spreads, brokerage, transaction taxes and impact estimates differ by market, by broker and by month, so any single stated level would be wrong somewhere within a week of being written. A multiplier is what turns a rate into a portfolio figure, and the rate itself stays a supplied input. The multiplier is fixed by the portfolio's own turnover; the level is an input, and a stated level would be read as a market fact.

Why is a chosen holding not yet a held holding?

Think about buying vegetables at a Saturday market for a wedding. A buyer decides at eight in the morning on fifty kilos of onions at the price shown on the board. By the time the buyer has walked to the stall, the first ten kilos go at the board price, the stallholder sees how much is wanted and the next twenty go higher, and the last twenty are not there at all because the stall has been cleared of everything it held at any sensible price. One decision was made. Four different things were paid: the gap between what the stall buys at and sells at, the price move the buyer's own size caused, the drift during the walk, and the twenty kilos that never arrived.

A portfolio does the same thing at a different scale and with better paperwork. Faiz Ahmad Ansari decides that a name should be held at a certain size. Between that decision and the position sitting in the account there is a transaction, and a transaction is not a neutral pipe. A transaction is a negotiation with whoever is on the other side, and the other side is not obliged to be there at the price the decision assumed.

What is the spread, and who actually pays it?

At any moment there are two prices for the same thing, not one. There is the price at which somebody will sell it and the price at which somebody will buy it, and the second is always the lower of the two. The spreadThe gap at one moment between the price a buyer has to pay and the price a seller would receive for the same thing. is that gap. Whoever wants to transact immediately crosses it, and crossing it is a real cost even though nobody sends a bill for it.

The street version is a currency counter at an airport. The board shows two numbers side by side, one for buying and one for selling, and the counter makes its living on the distance between them. No invoice is issued for that distance. The traveller simply receives fewer rupees than the mid price would have given, and the difference has moved from the traveller to the counter.

The spread is paid on the way in and again on the way out, so it is driven by how much trading happens rather than by how many holdings are kept. This is the single most useful thing to understand about it. A portfolio of twenty eight names that never changes pays the spread once, at the beginning, and then never again. A portfolio of twenty eight names that replaces a third of itself every year pays it over and over, on money that is not new. The number of holdings says almost nothing about this cost. The trading does.

Why does the order itself move the price against the buyer?

Market impactThe part of a price move that the order itself caused, because the size wanted had to be absorbed by whoever was willing to take the other side. is the part of the price move that the order itself caused. Impact exists because the other side of a trade is not infinite. There is a queue of people willing to sell at one price, a shorter queue willing to sell at a slightly worse price, and so on. A small order takes the first queue and nobody notices. A large order eats through the first queue, then the second, then the third, and the average price paid ends up worse than the one that was showing when the order started.

The wedding onions again. Fifty kilos at one stall clears the good stock and pushes the buyer into the poor stock at a higher price. Fifty kilos spread across ten stalls over three hours does not. Nothing about the onions changed. The relationship that changed was between the size wanted and the size the place could absorb without noticing.

Impact is not paid to anybody, it is caused, and that makes it the one component nobody can shop for a better rate on. A brokerage charge is a price somebody quotes, and it can be negotiated. Impact is a consequence of the order's own size arriving in a place that has a finite amount of willing counterparty behind it. Changing how the trading is done changes the impact. No amount of ringing anybody up produces a discount on it.

How is slippage different from market impact?

SlippageThe distance between the price at the moment a decision was taken and the price actually achieved, counted whatever the reason for the move. is the distance between the price at the moment of the decision and the price actually achieved. The silence in that definition matters. Slippage does not say the move was anybody's fault. Slippage counts the whole distance, including the part the order caused and the part that was going to happen anyway while the order sat there.

The width of that definition is why slippage and impact are not synonyms, even though people use them as though they were. Impact is a subset. Slippage is the container. If Faiz Ahmad Ansari decides at ten in the morning and the order is worked until three in the afternoon, everything that moved the price across those five hours lands inside slippage, including an item of news that had nothing to do with the Anantara portfolio at all.

Slippage contains impact but is wider than it. A serious cost report therefore shows the two separately rather than folding one into the other. Folding them together hides the only actionable half. Impact responds to how the trading is done. The rest of slippage responds to how long the order takes. Elapsed time is a different lever, and a report that will not separate the two cannot say which lever to reach for.

What does an order that never filled cost?

Here is the component most treatments leave out, and it is the interesting one. Suppose a decision is taken to buy Rs 10 crore of something. An equal share across the twenty eight names in the Rs 300 crore equity sleeve works out at Rs 10.71 crore, and Rs 10 crore is a round number close enough to it for an illustration. The order goes to the market. Half of it fills. The other half does not, and at some point the order is cancelled because the price has run away.

Ask what the unfilled half cost, and nothing appears anywhere. There is no contract note for a trade that did not happen, no charge, no line in any report. But the portfolio now holds half of a decision that somebody took at full conviction, and whatever that decision was worth, the portfolio is getting half of it. If the idea was good, half the good is missing. If the idea was bad, that was luck, and luck is not a process.

The cost of what never filled never appears on a contract note, so any cost report built from contract notes is structurally incapable of finding it. That is not a criticism of the report. The absence is a statement about where the report gets its raw material. Reaching this component requires a comparison against something that is not a trade record, and that is precisely what the next idea does.

What two portfolios does implementation shortfall compare?

Implementation shortfallA way of measuring what getting into a position cost, by comparing the return of a portfolio built at the decision prices with the return of the portfolio that actually exists. is the idea that ties the other four together, and it belongs to Andre Perold, who set it out in 1988. The move is simple and slightly annoying. Simple and slightly annoying is usually the sign of a right answer. Two portfolios are built. The first is a paper portfolioAn imaginary holding built exactly as decided, at the prices that were on the screen when the decision was taken, with no trading and no costs., struck at the prices that were showing when each decision was taken, holding exactly what was decided, costing nothing to build because it was never built. The second is the portfolio that actually exists. Their returns are then compared over the same window.

The gap is the shortfall. The gap swallows all four components at once without separating them, and every one of the four is a reason the real portfolio differs from the paper one. The spread is in there. The impact is in there. The drift while the order was worked is in there. And crucially the unfilled part is in there too. The paper portfolio holds the whole position and the real one holds half.

The usefulness of implementation shortfall is not the number it produces but the discipline it forces: somebody has to write down what was decided, and at what price, and when. Most organisations cannot compute it, and the reason is never the arithmetic. The reason is that nobody recorded the decision price. The trade record exists because a machine created it. The decision record exists only if a human chose to create it, and that choice is the whole measurement.

How Transaction Costs Affect Portfolio Returns: what does the multiplier do?

Now the part that converts all of this into a portfolio figure. Start with what the record holds. TurnoverA measure of how much of a portfolio was replaced over a period, stated as a share of the portfolio rather than as a count of trades. for the Anantara portfolio over the stated twelve month period was 34 per cent. The record reads that as about a third of the portfolio being replaced.

Turnover is defined differently in different places, and the definition changes the answer, so say the convention out loud. Here it means replaced value as a share of the portfolio. So 34 per cent of Rs 500 crore is Rs 170 crore of value replaced. Now the step people skip: a replacement is not one trade. A replacement is a sale and a purchase. The traded valueThe total value that actually went through the market over a period, counting a sale and a purchase separately rather than netting them off. is therefore twice Rs 170 crore, or Rs 340 crore.

The Rs 340 crore of traded value is the base every cost rate gets applied to. Expressed against the portfolio it gives the number that does all the work here: Rs 340 crore divided by Rs 500 crore is 0.68. The general form is that portfolio drag equals twice the turnover times the cost rate per side, and for the Anantara portfolio that multiplier is 0.68.

What does a cost rate do at a multiplier of 0.68?

Now supply a rate and watch the machine run. A basis pointOne hundredth of one per cent. A hundred basis points make one percentage point, and cost rates are usually quoted this way because they are small. is one hundredth of one per cent, and cost rates are quoted this way because they are small. The dragHow much a cost reduces the return of the whole portfolio, expressed against the portfolio rather than against the amount that was traded. on the portfolio is 0.68 times whatever the rate per side happens to be.

Three rates make the point, and their origin matters. Each is supplied by the reader, and each is round because a round number is easy to scale, not because anybody observed it. At 10 basis points a side, Rs 340 crore of trading costs Rs 34,00,000 and the drag is 6.8 basis points of the portfolio. At 25 basis points a side the cost is Rs 85,00,000 and the drag is 17.0 basis points. At 50 basis points a side the cost is Rs 1,70,00,000 and the drag is 34.0 basis points.

How big is the deduction next to the year that was reported?

The record splits the stated year's excess return two ways, and one of them is used here. Of the 1.6 points of gross excess return over the composite benchmark, the attribution split records an allocation effect of plus 0.35 points and a selection effect of plus 1.25 points. On a Rs 500 crore portfolio, 1.25 points is Rs 6,25,00,000. Rs 6,25,00,000 is what the year of selection work was worth in rupees, gross.

Set the trading cost beside it. At 25 basis points a side, Rs 340 crore of trading costs Rs 85,00,000, and Rs 85,00,000 against Rs 6,25,00,000 is 13.6 per cent. A seventh of what the selection work was worth went on getting there, at a rate nobody would call extreme.

The record carries two different decompositions of the same year, and mixing them is a known trap, so a second comparison is worth running. The beta split asks how much of the excess was simply carrying more market, and it leaves 1.11 points as the part that was something else. On Rs 500 crore that is Rs 5,55,00,000. A drag of 17.0 basis points against 111 basis points is 15.3 per cent of it. Two questions, two bases, two answers, and neither one is the true split.

And now the sentence that keeps the arithmetic honest. The record does not state whether the 14.2 per cent return for the stated year, or the selection effect inside it, is measured before or after trading costs, so nothing computed above is subtracted from either. The size of the deduction is shown and not applied. Subtracting a cost that might already be inside a figure counts it twice. Double counting looks like diligence, and that appearance makes it a worse error than not counting at all.

What does the record actually label as gross and as net?

Two figures in the record describe the same twelve month period and point in opposite directions, so both carry a label wherever they appear. The gross excess return over the composite benchmark is plus 1.6 points. The net figure for the same year is a shortfall of 0.28 points, and the distance between them is the mandate's own fee drag. Rs 6.25 crore of management fee plus Rs 3.15 crore of performance fee is Rs 9.40 crore, or 1.88 per cent of the Rs 500 crore portfolio. The fee drag itself is set out under mandate fees.

The labelling habit itself is what matters. An excess figure stated without the word gross or the word net is ambiguous between two opposite conclusions about the same year, and the repair is writing the label every time rather than remembering which one was meant.

What rate would it take to level with the recorded figures?

Since the record holds no rate, the only honest way to put a number on one is to turn the arithmetic around. Instead of asking what trading cost, ask what a rate would have to be for the drag to reach a figure the record does hold. Dividing the recorded figure in basis points by the multiplier of 0.68 gives the rate per side that levels with it.

Against the 1.11 points the beta split leaves, that rate is 163.2 basis points a side. Against the 1.25 point selection effect, 183.8 basis points a side. Against the whole 1.6 points of gross excess return, 235.3 basis points a side. Every one of those is an inversion of a recorded figure, not a measurement of anything, and reading it as a market cost would be an error.

What does the whole build look like on the Anantara portfolio?

Put every step in one place, from the portfolio down to the drag, so the chain can be checked line by line rather than believed.

A reader who has met the base law is already asking the sleeve question, so close on it. Turnover here is struck against the portfolio. The record does not split it by sleeve. So the honest statement is a bound rather than a figure. If every one of the year's replacements had happened inside the Rs 300 crore equity sleeve, that sleeve turned over Rs 170 crore of Rs 300 crore, or 56.7 per cent. If none of them had, it turned over nothing. The record fixes the total and bounds the parts, and saying so is a finding rather than an evasion.

What makes one cost figure comparable with another?

Four labels, and a cost figure carrying fewer than four cannot be laid beside anything. The period it was struck over. A cost for eighteen months and a cost for twelve are different animals. The traded value it was computed on, here Rs 340 crore and not the Rs 500 crore portfolio. The base it is expressed against. A cost of 17.0 basis points of the portfolio and a cost of 25 basis points of the traded value are the same money wearing different clothes. And whether the unfilled part is inside it, almost always no.

A cost quoted without those four labels is not comparable with anything. The base law imposes the same discipline on a weight, and for the same reason. Two managers reporting 25 basis points can mean completely different things by it, and neither is lying. One means 25 basis points of traded value on each side, coming to 17.0 basis points of the portfolio for the year. The other means 25 basis points of the portfolio for the year outright. Same phrase, and the second is nearly half as much again as the first.

How does anybody use this in a room, on a Tuesday?

An investment committee like Rukmini Deshpande's does not need a precise cost estimate to use any of this. The committee needs three lines on one sheet, prepared before the meeting. The turnover for the period and the traded value it implies. The drag at two or three rates that the committee itself picks and writes down as its own assumption. And whether the return figure in front of them is stated before or after those costs, with the answer written as unstated where it is unstated.

An analyst comparing two mandates does the same work for a different reason. Two managers with identical net results and very different turnover look identical on a selection effect and are not the same at all. The one that traded twice as much reached the same place by a more expensive road, and if the process never measures the road it will keep choosing the more expensive of two equal options without ever knowing it did.

A household does this with a bank passbook and no arithmetic at all. Every time a savings product is switched, something is paid: an exit charge, a spread on a currency, a stamp somewhere, a few days out of the market. Nobody itemises it. The count of switches is the multiplier and everything else is the rate, so the way to see it is to count the switches rather than compute a rate. Counting the round trips is the whole discipline in miniature, and it takes a pencil.