Concentrated vs Diversified Portfolio: Naming the Base

A concentrated portfolio holds few positions large; a diversified one holds many positions small. Neither word means anything until the base each weight is struck against is named and the spreading is computed rather than asserted. The Anantara Multi-Asset Portfolio's largest holding is 4.6 per cent of the portfolio and 7.7 per cent of its equity sleeve, and both figures are correct.

The working example throughout is the Anantara Multi-Asset Portfolio, an invented discretionary mandateThe written instruction under which a manager runs somebody else's money, setting out what may be held, what may not, and within what limits. of Rs 500 crore run for a charitable endowment, with Rukmini Deshpande chairing its investment committee and Faiz Ahmad Ansari running the money. Its policy weights are equity 60.0 per cent at Rs 300 crore, fixed income 30.0 per cent at Rs 150 crore and cash 10.0 per cent at Rs 50 crore, and the equity sleeveOne part of a portfolio held in a single asset class. A portfolio with equity, fixed income and cash has three of them. is held across 28 names.

Three of the figures below are settled before any of this arithmetic starts. The 28 names, the Rs 23 crore largest holding and the top ten figures come from the selection work that came before. The volatilities and the correlation are the committee's own stated assumptions, and nobody can forecast either one. Spreading removes what is particular to each holding and never what every holding shares, and that shared part is covered separately.

What exactly is a concentrated portfolio?

Start with the household version. A household running on one salary is concentrated: everything it spends, saves and borrows against depends on a single employer's decision about a single person. Nothing is wrong with that arrangement, and millions of them work well for decades. The exposure in that arrangement is narrow. One event, in one place, decides the year, and if the salary stops, nothing else in the household's income is placed to absorb it.

A concentrated portfolio is that arrangement written in securities. The concentrated portfolio holds a small number of positions, each of them large as a share of the whole, and the fortunes of any one of them show up plainly in the total. A manager running one deliberately is usually saying that the work of understanding a business is expensive, that the number of businesses anybody can understand well is small, and that spreading the money thinner than that understanding reaches buys nothing worth having. Concentration is a statement about how few things the manager is prepared to back, and it shows up in the account as a small number of large weights.

Notice what that definition does not contain: no number of holdings, no percentage, nothing saying whether ten names is concentrated or forty is diversified. Both questions have answers only once somebody says few of what, and large against what.

What exactly is a diversified portfolio?

Take the household again and change one thing: two salaries now, from two employers in two different industries, plus a small rent from a room let out. The household has not become richer. No single employer now decides the year, so the household has become harder to knock over with one event. And if the whole town's economy stops, both salaries and the rent are in trouble together. The second salary was never any protection against a shock like that.

A diversified portfolio is that arrangement in securities. The diversified portfolio holds many positions, each small as a share of the whole, and no single one of them is in a position to decide the outcome. The reasoning is the mirror image: nobody's judgement about any one business is reliable enough to bet the year on, and the spread of outcomes across the whole is what the holder actually experiences. Diversification is a statement about how much any one position is allowed to matter, and it shows up in the account as many small weights.

Both definitions are honest and both are useless on their own. Each is a claim about a fraction, and a fraction with no denominator stated beside it is not a measurement.

Why does every concentration figure have to name its base?

Because a weight is a fraction, and a fraction is two numbers. The one on top is the holding. The one underneath is the base, the total the holding is being measured against. Change the base and the percentage changes, even though not a single share moved and not one rupee was traded.

The largest Anantara holding is Rs 23 crore. Measured against the Rs 500 crore portfolio, that is 23 divided by 500, or 4.6 per cent. Measured against the Rs 300 crore equity sleeve, the same Rs 23 crore is 23 divided by 300, giving 7.666 per cent, or 7.7 per cent rounded. Both figures are correct, they answer different questions, and a report that moves between them without saying which base it is using has misled its reader about how concentrated the portfolio is.

The two questions are genuinely different. The 4.6 per cent reading answers how much of everything the endowment holds sits in this one name; the 7.7 per cent answers how much of the part that actually moves does. If Rukmini Deshpande's committee is asking whether one company failing could damage the endowment's whole position, the portfolio base is right; if it is asking how much of the equity judgement rests on one call, the sleeve base is. Answering one question with the other question's number is never acceptable.

Does the top ten line change with its base too?

The top ten line changes too, and here the difference stops being a rounding curiosity. The ten largest holdings in the equity sleeve are Rs 155 crore between them: 31.0 per cent of the Rs 500 crore portfolio, and 51.666 per cent of the Rs 300 crore equity sleeve, or 51.7 rounded. The two readings are nowhere near one another, they describe the identical Rs 155 crore, and a reader shown only the smaller one has been shown the flattering reading of an unchanged fact.

Each lands differently on a committee. Thirty one per cent sounds like roughly a third in the biggest ten and plenty of shoulders under the rest. Fifty one point seven sounds like more than half of the part that actually moves sitting in ten decisions. Nothing was misstated either time, and the base is doing at least as much work as the number.

What does the worked instance look like end to end?

Here is the whole equity sleeve with the base written into every sentence. The sleeve is Rs 300 crore across 28 names, and the largest holding of Rs 23 crore is 4.6 per cent of the portfolio and 7.7 per cent of the sleeve. The mandate's cap is 5 per cent of the portfolio, so the cap in rupees is Rs 25 crore and the holding sits Rs 2 crore inside it. The remaining Rs 2 crore of headroomThe distance left between where something stands now and the limit it is not permitted to pass. is 0.4 per cent of the portfolio. Written against the sleeve instead, a 5 per cent limit would be Rs 15 crore, and the same holding would be well outside it.

The ten largest average Rs 15.50 crore each, and the remaining 18 names hold Rs 145 crore between them, an average of Rs 8.06 crore each. Here is a check any reader can run in their head: the ten largest of twenty eight holdings can never be less than ten twenty eighths of the sleeve, which is 35.71 per cent, so any top ten figure below that against a sleeve base is impossible on its face. A second check follows from the same fact. If the ten largest averaged less than the other eighteen, the eleventh holding would be bigger than the tenth, and it would not be the eleventh.

How is diversification computed rather than claimed?

The word gets used as though saying it were the same as doing it. Diversification has a size, and the size is the difference between two numbers, both worked out from the holder's own stated assumptions: equity with a volatility of 18.0 per cent, fixed income 5.0 per cent, cash 0.5 per cent, a correlationA number between minus one and one saying how closely two things tend to move together. One means they move in lockstep, zero means they move without reference to each other. of 0.20 between equity and fixed income, and cash taken as moving with nothing at all.

The first number is the weighted average volatilityThe three sleeve volatilities averaged with each sleeve counting in proportion to its weight. It is what the portfolio would show if all three moved in perfect lockstep.: 0.60 times 18.0, plus 0.30 times 5.0, plus 0.10 times 0.5. Adding 10.80 plus 1.50 plus 0.05 comes to 12.35 per cent. If the three sleeves all moved in lockstep nothing would offset anything, and 12.35 per cent is the figure the portfolio would show. The second number is the portfolio's own volatility, computed with the correlation left where the committee put it, and it is 11.20 per cent.

The 1.15 point difference between 12.35 and 11.20 is the diversification, and a report asserting that a portfolio is diversified without computing that difference has asserted nothing at all. In rupees, on Rs 500 crore, one standard deviation of value at 12.35 per cent is Rs 61.75 crore and at 11.20 per cent it is Rs 56.00 crore. The spreading narrowed the spread of outcomes by Rs 5.75 crore on that one measure, for no reason other than that the parts do not move together.

Where do those 1.15 points actually come from?

Hold every weight and every volatility where the committee put them and change one thing: raise the correlation between equity and fixed income from 0.20 to 1.00, so those two sleeves move in perfect lockstep. Cash still moves with nothing. Recompute and the portfolio volatility rises from 11.20 to 12.30 per cent.

So 1.10 of the 1.15 points came from that correlation being 0.20 rather than 1.00, and only 0.05 points came from cash sitting apart from the other two. Cash is a tenth of the portfolio by weight and supplies about a twenty third of the spreading. A sleeve with a volatility of 0.5 per cent barely moves in the first place, so there is almost nothing in it to offset anything with.

When the mall closes for a week every shop in it closes, so ten shops in one shopping mall are ten holdings and one driver. The spreading is bought not by the number of things held but by the extent to which they move for different reasons, and the correlation is where that difference lives.

What does a cap on a single holding actually prevent?

The Anantara mandate carries a single holding capA written limit on how large any one position may be as a share of a stated total. It binds each position separately and says nothing about the positions taken together. of 5 per cent of the portfolio. A cap like that is easy to read as a statement that the portfolio is spread out. It is not.

A cap prevents something real, so start there. At the cap a position is Rs 25 crore of a Rs 500 crore portfolio, so if it were to halve, the portfolio would be down 2.5 per cent from that cause alone. Without a cap nothing in the document stands between the manager and a position several times that size. A cap is a limit on the worst case that any one position can produce, and that is a genuine thing to have.

Now the part people miss. Twenty holdings at 5 per cent each would be the entire portfolio. A mandate whose only concentration rule is that cap is therefore consistent with twenty positions, and most readers would call twenty positions concentrated. A cap describes the ceiling on one position and says nothing about how many positions there are or how the rest of the money is arranged. Anantara holding 28 names with a largest position at 4.6 per cent had to be looked up separately.

How do the two designs differ in what an account can deliver?

Set aside which design a manager believes in and ask what each one costs to run. The answer is the same whoever is running it.

A concentrated design takes fewer trades to build: ten positions is ten decisions and ten sets of instructions. One sale moves a large share of the account, so a concentrated design takes fewer trades to change as well. The same fact from the holder's chair is the flip side. One position moving moves a large share of the account, whether or not anybody wanted it to that day.

A diversified design takes more trades to build and more to change, and every one has to clear the mandate's limits first. Twenty eight positions is twenty eight things to check against the cap on every pass and twenty eight to reconcile with the custodian. A position too small to matter still costs the same to research, trade, settle and monitor as one that does, so there is a floor under how small a position can usefully be. The delivery cost of each design is different, and no return figure on any report shows any of it.

The Anantara mandate reported turnoverThe share of a portfolio replaced over a stated period. It is a measure of how much activity there was, not a measure of what the activity cost. of 34 per cent over the stated year, meaning about a third of the portfolio was replaced. Turnover counts activity and does not price it. Turnover is a signpost towards the cost of delivery rather than an answer to it.

What does neither design do anything about?

Both designs work on the same thing and neither touches what lies underneath it. Spreading removes what is idiosyncraticBelonging to one thing alone rather than shared with others. A fire at one warehouse is idiosyncratic; a nationwide slowdown is not. to each holding and cannot remove what every holding shares. Add the twenty ninth name, the fiftieth, the two hundredth, and the part they all have in common is still sitting there, unbothered by the count. Why is covered separately.

The ten shops make the point without arithmetic. Ten leases and ten sets of staff spread one shop's spoiled stock and spread nothing at all against the road outside being dug up for a month.

The shared floor is why the Anantara portfolio could hold 28 names and still fall 9.7 per cent from peak to troughMeasured from the highest point a value reached down to the lowest point that followed it, inside a stated window of time. inside the stated twelve month period. Nothing failed. Twenty eight names removed twenty eight names' worth of particular trouble and left standing what those names had in common. A different window gives a different figure. The window is quoted every time the number is.

How does a practitioner actually use this?

Faiz Ahmad Ansari uses it every time he writes a number down. The cap is written on the portfolio base, so his compliance check runs there: Rs 25 crore allowed, Rs 23 crore held, Rs 2 crore of headroom. How much of the equity judgement rests on a few calls is asked about the equity alone, so his conversation with the committee runs against the sleeve base. He names the base in the same breath as the number, and it costs him four words.

An analyst reviewing any manager uses it as a two step filter. Step one: for every concentration figure in the pack, is the base printed beside it? Step two: recompute one of them on the other base and see whether the picture changes. If the top ten look very different against the sleeve than against the total, that is not a criticism of the manager. The difference is information the pack did not volunteer.

A trustee uses it as a question rather than a calculation. When a figure is presented as evidence that a portfolio is spread, ask what it is a percentage of, then ask what the same rupees look like against the part that actually moves. The two readings answer different questions, and a committee needs to know which one it just had answered.

A household can use the same habit without any of the vocabulary. If most of what it holds sits in one place, that description is not softened by measuring it against a bigger total that includes the house it lives in and the money it cannot touch. The base chosen decides the answer produced, so it should be chosen to fit the question rather than the answer hoped for.

When does the distinction stop mattering?

Four conditions make the choice stop deciding anything. The first is a holdings count already high enough that the next name changes the portfolio by less than it costs to buy. Put a twenty ninth name of Rs 5 crore into the Anantara sleeve, funded by trimming the other 28 by one sixtieth each. The largest holding falls from Rs 23.00 crore to Rs 22.62 crore, and reads 7.54 per cent of the sleeve against 7.67 before. The gain is 0.13 points, bought with one more buy order, one more line on every cap check and one more line to reconcile, and past about there the two designs converge in effect.

The second is holdings that move together closely enough that counting them separately is bookkeeping. The size of that effect is measured above: 1.10 of the 1.15 points of benefit came from the equity to fixed income correlation sitting at 0.20 rather than 1.00, and almost none of it from the count. The same argument runs inside the equity sleeve. Twenty names driven by one thing is a concentrated portfolio wearing a diversified label, and the count on the factsheet is not the part that is wrong; the inference drawn from it is.

The third is a mandate whose position cap has already settled the matter. A 5 per cent cap on the Rs 500 crore portfolio puts a floor of twelve names under the Rs 300 crore equity sleeve. Write the same cap at 2 per cent and the limit in rupees is Rs 10 crore, so the floor rises to thirty names, above the 28 the sleeve holds. At that point the document has chosen, and nobody is choosing between the two designs. The fourth is a holding period short enough that neither effect has time to appear: the 9.7 per cent drawdown and the Rs 5.75 crore of narrowing both belong to one stated twelve month period, and a holder who will be out in three weeks was never in for the period either figure describes.

None of these four conditions announces its own expiry, and the second one usually goes first. Correlations rise in exactly the conditions where the diversification was supposed to help. The 0.20 the committee wrote down is an assumption about ordinary weather, and the week it stops holding is the week the spreading was being counted on. The count on the factsheet does not move that week. Only what the holdings move for does, and no line on the report announces it.

The Anantara Multi-Asset Portfolio, the charitable endowment that holds it, Rukmini Deshpande and Faiz Ahmad Ansari are invented.
Educational material. Not advice on any investment, tax, budget or market position.