Active and Passive Management: What Each One Costs

Active management is the deliberate holding of a portfolio that differs from a stated benchmark, with the intention of returning more than it. Passive management is the opposite intention: hold the benchmark's constituents in its weights and accept its return less costs. The choice is not skill against no skill. What separates them is which costs are accepted and which outcomes are ruled out.

Almost every disagreement about these two approaches is really a disagreement about a number nobody has computed. The numbers below are computed on one portfolio, and volatility and the simple ratios are applied rather than taught.

The running example is the Anantara Multi-Asset Portfolio, an invented discretionary mandate of Rs 500 crore run by Faiz Ahmad Ansari for an invented charitable endowment whose committee is chaired by Rukmini Deshpande. The mandate holds equity at 60.0 per cent or Rs 300 crore, fixed income at 30.0 per cent or Rs 150 crore and cash at 10.0 per cent or Rs 50 crore, Rs 500 crore exactly. Its benchmarkThe stated thing a portfolio is measured against, named in advance so the difference can be added up. is a composite holding a broad equity index at 60 per cent alongside a broad bond index at 40, called the composite benchmark here. Every figure below belongs to that portfolio and to one stated twelve month period.

What is active management, exactly?

Active managementRunning a portfolio deliberately different from a stated benchmark, hoping the difference adds to the return rather than subtracting. is the deliberate holding of a portfolio that differs from a stated benchmark, with the intention of returning more than it. Two words in that sentence carry the whole definition. The first is deliberate and the second is stated: without a stated benchmark there is nothing to deviate from, and the word active stops meaning anything measurable.

Take the everyday version first. A vegetable seller sets out the same eight items every morning because that is what the street sells. Another leaves out two of them and adds coriander and a stack of lemons instead. The second seller is running an active stall, not because he works harder but because his tray is measurably different from the street's, and at week's end it can be said by how much and in which direction it paid. If nobody wrote down what the street's tray contains, the coriander can be admired but nothing can be said about whether the deviation earned anything.

The finance version needs no extra machinery. The composite benchmark is 60 per cent equity and 40 per cent bonds and carries no cash line at all, so set beside the mandate's 60, 30 and 10 the deviation is arithmetic rather than opinion: equity matches at 60 against 60, fixed income sits ten points light at 30 against 40, and cash sits ten points heavy at 10 against zero. The sizes of those three differences add to 20 points.

The subtraction needed two lists of weights and no opinion of anybody. The definition insists on a stated benchmark for exactly that reason. Stating the benchmark turns a preference into a quantity. A manager who says he prefers to hold cash has said something about himself. A manager whose stated benchmark holds no cash and whose portfolio holds ten points of it has said something that can be added up.

A formal single number compresses a full holding by holding version of that subtraction. The measure is called active share, it belongs to K. J. Martijn Cremers and Antti Petajisto, and it is set out separately in the sequence on risk monitoring and performance evaluation. Only its shape matters for the comparison: differences in weights, added up, against a stated list.

What is Passive Management, and is it really a choice free of decisions?

Passive managementHolding what a stated benchmark holds, in its weights, and taking the return that produces after the cost of keeping the match. is holding the benchmark's constituents in the benchmark's weights and accepting its return less costs. Written like that, passive management sounds like the absence of a decision. The sound is wrong.

Passive management is not the absence of decisions: it contains one very large decision, taken once, made early, and revisited less often than almost anything else in the arrangement, and that single choice determines more of the outcome than anything an active manager does afterwards. The decision is which benchmark to hold. Everything after it is execution.

The Anantara mandate is measured against a composite of 60 per cent equity and 40 per cent bonds. Choosing that composite decides the mix, the rough shape of the swings, and the kind of year that will feel bad. None of that is revisited on a Tuesday. The benchmark is settled at the start and then inherited, sometimes for a decade, sometimes by people who were not in the room when it was chosen.

The everyday version is a household kitchen where one person decides, once, that everyone eats what is in season and cheap at the local market. After that there are no menu decisions, only shopping. The kitchen looks decision free from the inside and is not. The single rule settles the nutrition of every meal for years, and nobody revisits it, so nobody examines it either. Calling something a default is how it stops being examined.

Two consequences follow. A passive portfolio is not risk free in any sense: it carries exactly the risk of the thing it tracks, deliberately taken. And the passive decision is the one nobody audits. A manager who deviates gets a review meeting. The choice that decided what the deviation is measured against rarely gets one.

So the honest statement of the pair is not decisions against no decisions. The pair is many small revisable decisions against one large unrevised one. A portfolio held passively still has to be right about the thing it decided to hold, and being wrong about that is not cheaper for having been decided only once.

How Active Management Differs From Passive Management, and how is that difference measured?

Most writing on this pair reaches for temperament: the active manager is restless, the passive holder is patient. Temperament is a story about people, and a story about people cannot be checked. The difference between the two approaches is measurable, and it has three measures.

The first is how much the holdings differ. The subtraction performed above came to 20.0 points. The second is how much the returns differ, measured as tracking errorHow far a portfolio's return tends to sit away from its benchmark's over a stated period., here 3.7 per cent. The third is how much the portfolio is traded, measured as turnoverHow much of a portfolio was sold and re-bought inside a stated period., here 34 per cent. All three readings cover the same twelve months.

All three of those are continuous rather than binary, so the answerable question is how active a portfolio is, not whether it is active at all. A portfolio tracking a broad index with a tracking error near zero sits at one end, a portfolio ignoring the benchmark entirely sits far along, and everything real sits between. Where a mandate sits is the interesting part of any conversation about it.

Now the part almost always skipped: the risk figures constrain each other. The record carries a portfolio volatility of 11.8 per cent, a benchmark volatility of 10.4 per cent, a betaHow much a portfolio tends to move for a given move in its benchmark, in either direction. of 1.08 and a tracking error of 3.7 per cent, all for the same twelve months. Only three of the four can be chosen: given the two volatilities and the beta, the tracking error follows.

The record carries 3.7 per cent and the identity produces 3.7114 per cent, the same figure to one decimal place. The point is not the fourth decimal. Those four figures are arithmetically tied together and only three of them are free, so a mandate cannot advertise a low tracking error and a high beta and a portfolio volatility well above its benchmark's all at once.

Active vs Passive Management: how do the two compare, criterion by criterion?

The only fair way to run this comparison is to put both approaches against the same five questions in the same order: what the holder pays for, what determines the result, what can go wrong, what the record measures, and how long before that record says anything at all.

Read the rows and a pattern shows up that most summaries flatten. The passive column is not the safe column. Its failure runs slower and quieter, and it runs that way because the one decision was wrong for this holder and nobody revisits it for years. The active column fails faster and more visibly. Failing visibly is not the same as failing more often.

The asymmetry that matters is this: passive management rules out one outcome, doing better than the benchmark, and in exchange it rules out another, doing worse than the benchmark by more than the cost of matching it. That is a trade, not a saving: one tail is given up to be spared the other. Whether it suits any holder is a question about that holder's own obligations.

The Anantara record allows the mandate to be placed rather than described. Over the stated twelve months the portfolio returned 14.2 per cent at a volatility of 11.8 per cent. The composite benchmark returned 12.6 per cent at 10.4 per cent, and the risk-free rate was 6.5 per cent for the same period. Both coordinates are needed: a point that is higher and also further right has not been placed until both things have been said about it.

Because the portfolio sits further right as well as higher, the plain return comparison is not enough on its own. Divide each excess over the 6.5 per cent risk-free rate by its own volatility. For the portfolio, 14.2 less 6.5 over 11.8 is 0.653. For the benchmark, 12.6 less 6.5 over 10.4 is 0.587. On plain returns the portfolio stands 12.7 per cent above the benchmark; on the adjusted readings, 11.3 per cent above. Both carry the same risk-free rate and the same benchmark, without which neither compares with anything. There is also the information ratioThe excess return earned for each unit of tracking error, so return per unit of distance from the benchmark., the gross excess of 1.6 points over the 3.7 per cent tracking error, or 0.43.

What does active management cost, and where does the cost hide?

Two costs arrive with active management and only one is ever quoted: the charge for the management itself, and the cost of the trading that the management does. A holder who has read the first has read about half the bill.

A gross returnA return figure stated before charges and trading costs have been taken out of it. figure shows neither cost. A portfolio's turnover is itself a cost, and the return figure printed above it has already been printed without that cost. That is not an accusation of bad faith but a fact about the order in which figures are produced: the gross number is available first and reaches a committee pack first, while the costs arrive later and separately, if at all.

The second cost is the one people wave at rather than compute, so size it properly. Turnover of 34 per cent on a Rs 500 crore portfolio means Rs 170 crore was replaced over the stated twelve months, leaving Rs 330 crore that was not. In whole rupees that is Rs 1,70,00,00,000/- of buying and selling, whatever it cost.

The trading can be priced without inventing a number. Suppose the round trip of selling one thing and buying another costs c per cent of the value moved. The value moved was 34 per cent of the portfolio, so the whole of it bears 0.34 times c percentage points. The letter stays in because c is not one number: it moves with what is being traded, how much of it moves at once and who is on the other side. Any value of c substituted in produces the answer.

Why does beating a benchmark not prove that active management worked?

The argument here is arithmetic rather than scepticism. Over the stated twelve months the Anantara portfolio returned 14.2 per cent gross against the composite benchmark's 12.6 per cent, a gross excess of 1.6 points. Most reporting stops at that sentence. The 1.6 points have not been split yet, so stopping there is the mistake.

The portfolio carried a beta of 1.08 against that benchmark. The benchmark itself returned 6.1 points above the 6.5 per cent risk-free rate, being 12.6 less 6.5. Carrying a beta of 1.08 rather than 1.00 means carrying eight per cent more of that same benchmark exposure, and eight per cent of 6.1 points is 0.488 points. So a portfolio that simply held more of the same market, with no other decision in it, would have been expected to return 6.5 plus 1.08 times 6.1, or 13.088 per cent. The portfolio returned 14.2 per cent, and 14.2 less 13.088 is 1.112 points.

Of the 1.6 points of gross excess, 0.488 points could have been obtained by carrying more of the same market and required no active decision at all, so the only quantity active management is being judged on here is the 1.112 points left after that is removed. Compute the share rather than reading it off: 0.488 divided by 1.6 is 0.305, so 30.5 per cent of the celebrated figure was exposure.

The beta-adjusted residual has a name, and the name is part of the term: Jensen's alphaWhat is left of a return once the part explained by benchmark exposure is removed., after Michael C. Jensen, set out in the sequence on risk monitoring and performance evaluation. The shape is the part that carries everywhere: a headline gap is not a result until the exposure has been taken out. Taking it out has to be done on purpose, because nothing in the reporting does it by itself.

One warning attaches to carrying this arithmetic anywhere. The same 1.6 points splits two entirely different ways. The split set out above asks how much of the gross excess was market exposure, and gives 0.488 and 1.112. A separate split, run in the monitoring sequence, asks where it came from as between allocation and selection, and gives 0.35 and 1.25. Both sum to 1.6 and neither is the true one. Taking a term off one side and a term off the other produces a sentence that computes correctly while saying nothing.

What does the arithmetic of active management actually claim?

One argument about the two approaches needs no data at all, and it is misquoted in both directions. The argument belongs to William Sharpe, who set it out in The Arithmetic of Active Management in the Financial Analysts Journal in 1991, and the name is part of the term.

Divide every rupee invested in a market into two parts. The passive part tracks a stated list and the active part is everything else. The two together are the whole market, so together they earn what the market earns. The passive part earns the market return less the cost of matching it, so what is left for the active part in aggregate must be the market return before costs and less than it after them.

The arithmetic is a statement about an average, and it says nothing whatsoever about any individual portfolio. The distance between an average and one portfolio is precisely where the misuse happens, in both directions. One side quotes it to prove that no manager can do better, which it does not claim. The other points at a manager who did better and calls the argument refuted. One manager ahead of the market leaves the average exactly where it was.

The argument needs no assumption about how well prices reflect information, no assumption about how clever anybody is, and no data. The argument follows from the parts adding up to the whole. Resting on nothing but that addition is why it outlasts arguments that sink almost everything else about the pair.

How long a record does it take before the comparison settles?

Longer than one year, and saying so is the answer rather than a way of avoiding one. The Anantara record is one portfolio, one benchmark and one stated twelve month period, producing 1.112 points of residual. The question is whether a figure of that size, over that length of record, can tell a decision that worked apart from a year that happened to go well.

Put the residual beside the movement it must be read against. The portfolio's own volatility over the same twelve months was 11.8 per cent, and 11.8 over 1.112 is 10.6. The quantity being judged is roughly a tenth of the size of the ordinary movement it is sitting inside, so a single year cannot tell the two apart, and no amount of confidence in the manager changes that arithmetic.

Two consequences follow. A committee reviewing after one strong year is not reviewing skill, whatever the agenda says. And the record needed grows longer as the residual shrinks and as the volatility rises, so the more subtle the manager, the longer the wait. The apparatus for judging a record, including the appraisal ratio and attribution, is covered separately.

Where does the efficient market argument sit, and why does the arithmetic not depend on it?

Behind this comparison sits an argument about whether prices already reflect what is known. If they do, deviating from a stated list is expensive and pointless; if they do not, deviating is where the return lives. The argument belongs to Eugene Fama, who set it out in Efficient Capital Markets in the Journal of Finance in 1970.

The efficient market argument is settled somewhere else, and none of the arithmetic above waits on it. The split of a gross excess into an exposure part and a residual is arithmetic whatever anybody believes about prices, the three measures of how active a portfolio is are measurements, and the arithmetic of active management follows from the parts adding to the whole.

How does an investment committee actually read this in a meeting?

In five lines, prepared before anybody sits down. The five lines apply as much to a household reading a statement as to an endowment like the one Rukmini Deshpande chairs.

A return without a period and a benchmark is not a measurement, so an analyst states both before quoting any figure. Then whether the figure is gross or a net returnA return after charges and trading costs, which is what a holder receives., and of what. Gross and net can point opposite ways inside one year. Then splits the gross excess, prices the trading from the mandate's own turnover, and says the record length out loud.

A lender assessing a borrower whose wealth sits in a managed portfolio runs the same five lines for a different reason: the volatility and the turnover tell it how fast the collateral can change size and how much of the return survives the costs. A household runs them over a statement with a pen. Compared with what, over what period, before or after charges, and how long has this record been running. The five lines cost about two minutes and are the difference between reading a portfolio and being read to.

When does the choice between them stop mattering?

Four conditions make the choice not worth arguing about, and each is about the holder's situation rather than either approach being wrong. Where one of them holds, something else is already moving the result by more than the difference between the two approaches, so the choice does not decide the outcome.

The first is a mandate constrained so tightly that its permitted deviations cannot carry it past the index. Anantara took 20.0 points of weight difference for 1.112 points of residual. Allow it 2.0 points and, if the decisions scale with the room given, the residual falls to about 0.111. The year still moves 11.8 points, so a record already too short would have to run ten times longer.

The second is a holding period too short for either thesis to express itself. Eighteen months cannot separate a residual from the year's own movement, and the single passive choice is meant to suit a holder across the years it is inherited. Over that horizon the entry and exit dates decide the result.

The third is a charge gap smaller than the tracking difference. The mandate sat 3.7 per cent of tracking error away, and any route that tracks a list drifts from it too. Where the gap in charges between two routes to the same benchmark is smaller than the amount by which either drifts in a year, the cheaper route is not reliably the closer one. The Anantara record holds neither level. The condition is about which of the two is larger.

The fourth is a holder whose result is dominated by when the money went in. The residual is 1.112 points on a 14.2 per cent return, and 1.112 over 14.2 is 0.078. A contribution pattern that shifts the average amount at work by about eight per cent therefore moves the rupees earned by as much as the whole residual. On Rs 500 crore that is Rs 5,56,00,000/-.

None of the four announces its own expiry. Constraints get widened at a review nobody minutes as a change of approach, an eighteen month horizon becomes eleven years because the money was never needed, and contributions stop the day someone retires. The condition lapses quietly and the choice starts deciding again, so the four are worth re-asking on a date rather than on a feeling.