Equal, Market Cap and Fundamental Weighting Compared

A weighting scheme decides how much of a portfolio each holding gets, once the list of holdings is already settled. Equal weighting gives every name the same share. Market capitalisation weighting gives each name a share proportional to its market value. Fundamental weighting keys the share to an accounting quantity rather than to a price. The same list of names produces three different portfolios.

A committee spends nine meetings deciding which twenty eight names deserve to be held, agrees the list, and then somebody asks the flat question: how much of each? The room usually answers that in about four minutes, on instinct. The four minutes spent on sizing decide more of the portfolio's behaviour over the next five years than several of the nine meetings did.

One invented mandate carries every figure below. The mandate is the Anantara Multi-Asset Portfolio, a discretionary multi-asset holding of Rs 500 crore run by Faiz Ahmad Ansari for an invented charitable endowment whose investment committee is chaired by Rukmini Deshpande. Its policy mix is 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 three sum to Rs 500 crore exactly. Everything below works on the equity sleeve of Rs 300 crore, held across 28 names.

One habit has to be fixed before a single weight is quoted. The same holding is 4.6 per cent of the Anantara portfolio and 7.67 per cent of the Anantara portfolio's equity sleeve, and both figures are correct. Every weight below therefore names the total it was divided by. Skip it and the figure is wrong by a factor of 0.60 without anybody noticing.

What does a weighting scheme actually decide?

A weighting schemeA stated rule that turns an already settled list of holdings into a size for each one. takes a list of holdings as given and decides the size of each one. The scheme cannot add a name, it cannot drop a name, and it has nothing to say about whether the names were worth choosing. Given twenty eight businesses nobody has any confidence in, it produces twenty eight weights with the same calm efficiency it applies to a list that took a year to assemble.

Think about a household filling a shopping bag for the week. The first decision is what goes in the bag: rice, oil, lentils, vegetables, a little fruit. The second decision gets almost no attention: how much of each. The same six items in different quantities produce two very different weeks of eating, and nobody in the household would confuse the two decisions.

Choosing the names and choosing the sizes are two separate decisions, taken on two separate arguments, and a scheme cannot rescue a list. Most arguments that look like arguments about weighting are really arguments about exposure. Two people arguing about whether to weight equally or by market value are not disagreeing about the arithmetic. The arithmetic is not in dispute. The disagreement is about how much of the portfolio should depend on the largest names moving, and that argument is far more useful had out loud.

What are the three schemes keyed to?

All three schemes answer the same question and differ in exactly one respect: the quantity the weight is keyed to. Equal weighting keys it to the number of names. Market capitalisation weighting keys it to market value. Fundamental weighting keys it to an accounting quantity. Every other difference between the three, including which of them has to trade, how a cap meets them and how much money each can carry, follows from that single choice.

What does equal weighting commit a portfolio to?

Equal weightingA rule under which each of n holdings receives one divided by n of the total. gives every name one divided by the number of names. On the Anantara equity sleeve that is one divided by 28. The share is 3.5714 per cent of the sleeve, reported as 3.57 per cent, and in money Rs 10,71,42,857/- a name, with Rs 4/- left over that has to land somewhere. On the portfolio base the identical position is 3.5714 times 0.60, or 2.14 per cent. Both numbers describe the same rupee amount.

The word equal sounds like the description of a state. Equal weighting is not one. The prices of 28 businesses do not move together. One rises 4 per cent in a fortnight while another falls 2 per cent, and the two positions are no longer the same size. An equally weighted portfolio stops being equally weighted on the first day prices move. Equal weighting is not a state a portfolio sits in but a rule that has to be reapplied to hold.

The everyday version is a wedding kitchen with eight pots on eight flames, each started with the same quantity. The flames are not identical, so twenty minutes later the pots are not the same. Eight equal pots at serving time require somebody to come back and even them out, and that evening out is work. The evening out is not a failure of the plan. It is the plan.

The spreading apart of the positions has its own name. Weight driftThe gap that opens between a holding's target weight and its actual weight because prices moved, with nobody trading. is the gap between what a rule says a position should be and what it actually is, purely because prices moved. Drift is not a mistake and nobody caused it. Drift is the ordinary consequence of holding things whose prices are not synchronised.

Why does market capitalisation weighting need no maintenance?

Market capitalisation weightingA rule under which each holding's share is its own market value over the market value of all of them. gives each name a share equal to its market value divided by the total of all the market values. The cleverness there is arithmetic rather than insight. Because the target weight is itself a share of total value, a price move changes the numerator and the denominator together, so the actual weight and the target weight land on the same new number. The portfolio is already where the rule says it should be.

Work it on three invented names, A, B and C, holding Rs 30 crore each. A rises 50 per cent, B does not move, C falls 20 per cent. The figure below computes each name's share of the new total. Because the target is defined the same way, from the same values, the target weights are those same three numbers. Market capitalisation weighting is the only one of the three schemes whose weights update themselves when prices move, so it requires no trade at all to stay on target.

Needing no trade is why market capitalisation weighting is the default almost everywhere it appears, and the reason is arithmetic rather than merit. A rule that never requires a trade is cheap to run at any size, on any day, in any market. Nothing there says it produces better outcomes.

What does fundamental weighting key the weight to instead?

Fundamental weightingA rule that keys each holding's share to a published accounting quantity rather than to its market price. sets the target share from an accounting quantity: revenue, book value, cash flow, dividends, or a blend of them. Whatever is chosen, the one thing it is never keyed to is the price. Breaking the link between what a holding costs and how much of it is held is the whole point of the scheme.

Breaking that link carries the same cost equal weighting carries. Prices move every day. Revenue and book value do not; they are restated when a set of accounts is published, and then they sit still, so the actual weights walk away from targets that are standing still. The quantity fundamental weighting keys to updates on a reporting calendar while the prices update every session, so fundamental weighting buys its independence from price with a permanent maintenance obligation.

Take the same three names and give them invented revenue of Rs 500 crore, Rs 300 crore and Rs 200 crore, a total of Rs 1,000 crore. The three revenues set targets of 50, 30 and 20 per cent. Build a Rs 90 crore portfolio to those targets and apply the identical price moves. The total becomes Rs 108.90 crore, and the actual weights land where the figure below draws them, against targets that have not moved at all.

Notice the direction of the three trades the figure above names. The rule sells the name whose price rose and buys the two that did not, and the three amounts net to zero because nothing has been added or withdrawn. Nobody in the room decided that and nobody had a view about A. The direction fell out of the arithmetic.

Keying the target to a published number has one more consequence. The accounting quantity does eventually change. Suppose name A restates its revenue to Rs 550 crore while B and C stand still, as the table below sets out. A share of a total moves whenever any part of the total moves, so two of the three targets moved without the underlying business changing by a rupee. So fundamental weighting trades on two clocks at once: the price clock that opens the gap daily, and the reporting clock that moves the target the gap is measured against.

Which of the three schemes has to trade when prices move?

Run the equal weighting rule over the same three names and the same price moves. After the moves the portfolio holds Rs 99 crore, so one third of it is Rs 33 crore exactly, and the figure below draws what each name has to be traded to reach that.

Put the two side by side. The market capitalisation weighted version of that portfolio traded nothing at all; the equally weighted version moved Rs 24 crore gross to get back on target. Trading is not an overhead sitting on top of equal weighting and fundamental weighting. Trading is part of what those two schemes are, and a description of either that leaves it out has described something else.

Lined up on the identical instance, the cost of the rule becomes a number rather than an adjective. Two of the three schemes turned over roughly a quarter of themselves in a single reapplication, at 24.24 per cent and 23.97 per cent counted both ways, and neither of those two had a view about anything.

Both schemes that trade, equal and fundamental, trade in the same direction: they sell what has risen and buy what has fallen. Nobody chose that as a view. Selling the riser is what happens when the target does not move with the price and the actual weight does. Equal weighting and fundamental weighting are net sellers of what has risen. The exposure is real whether or not anybody intended it. Market capitalisation weighting lets the risers grow, so it has the opposite property by default.

How far is the Anantara sleeve from equal, and against what base?

The invented sleeve is not equally weighted and never claimed to be. Equal weighting across 28 names would give every holding 3.57 per cent of the sleeve. The largest holding in the record is 4.6 per cent of the portfolio, or Rs 23,00,00,000/-, and dividing 4.6 by 0.60 puts it at 7.67 per cent of the sleeve. Divide 7.67 by 3.57 and the largest name sits at 2.15 times its equal weight. The multiple is the entire visible effect of letting prices rather than a rule decide the sizes.

Bring in the mandate's limit. The Anantara mandate carries a holding capA stated ceiling on how large any one holding may be, written against a named base. of 5 per cent of the portfolio on any single holding. Divide 5 by 0.60 and the same cap is 8.33 per cent of the equity sleeve. On the sleeve base the cap sits 0.67 points above the largest holding and on the portfolio base 0.40 points above it, and both describe the identical Rs 2 crore between Rs 23 crore and Rs 25 crore.

The base of a percentageThe total a percentage is divided by. Change it and the same rupee amount reads as a different number. stops being a pedantic point here and becomes the whole argument. The figures 4.6 and 7.67 describe the same holding, the caps of 5 and 8.33 describe the same cap, and any account that moves between the two without saying which base it is standing on has misled its reader about concentration. Naming the base is the discipline a shopkeeper uses in quoting a margin on cost or on selling price: two different numbers for one unchanged rupee of profit.

The question has an arithmetic answer, and the answer points at something the cap does that people rarely notice. A cap of 5 per cent per name means no name can carry more than one twentieth, so a fully invested portfolio needs at least 20 names, and a sleeve that is 60 per cent of the portfolio needs at least 12. The Anantara sleeve holds 28, so the cap is not what produced the number of names. Move the control below and watch the equal weight bar climb toward the cap line as names are removed.

How does a holding cap meet each scheme?

A cap looks like one instrument and behaves like three, depending on what it is sitting on top of. Under market capitalisation weighting the weight follows the value and the value follows the price, so a large name can simply grow past the cap. So the cap binds and the portfolio has to trade after all: the scheme whose whole attraction is that it never needs a trade acquires a trading obligation the moment a limit is written over it.

Under equal weighting at 28 names every position sits at 3.57 per cent of the sleeve, less than half the cap on the same base. A cap set that far above every position costs nothing to obey and therefore reveals nothing about the portfolio. A cap is a different instrument on every scheme it sits over, binding often on one, almost never on another, and that difference is a property of the scheme rather than of the cap.

A cap does one more thing that gets missed entirely. A cap sets a floor under the number of names as well as a ceiling on each one. Nobody writes a cap intending to legislate a count, and yet that is exactly what a cap does the moment the portfolio is meant to be fully invested.

How much money can each scheme actually carry?

CapacityHow much money a rule can be run with before its own dealing moves the prices it is dealing at. is how much money a scheme can be run with before the dealing it requires starts moving the prices of the things being dealt. Capacity settles the argument in practice and has nothing to do with returns. Market capitalisation weighting puts the most money into the names that can absorb the most money. The two quantities are the same quantity. Market capitalisation weighting therefore scales almost without effort.

Equal weighting does the opposite by construction. At 28 names it puts precisely the same Rs 10,71,42,857/- into the smallest name as into the largest. The smallest name has to swallow an amount sized by the total rather than by its own ability to absorb it, and it has to do so again at every reapplication of the rule. Capacity is an operational constraint about what can be dealt without moving prices, not a view about which scheme produces better returns, and the two get confused constantly.

The street version is a vegetable seller who buys the same quantity of every item because it keeps the stall tidy: the same crate of onions and the same crate of a rare herb the whole market only produces two crates of. The onion order costs nothing to place. The herb order moves the price against the seller every week. The ordering rule does that, not anything about the herb.

How does a committee use any of this on a Tuesday?

Not by choosing a scheme. By asking four questions in a fixed order before any weight in a monitoring pack is believed. A committee like Rukmini Deshpande's opens a monitoring pack quoting concentration figures. The first thing worth establishing is which total each percentage was divided by. The pack will move between the portfolio and the sleeve without warning, and the two totals differ by a factor of 0.60.

The second question is whether the scheme requires a trade to stay on target. The answer settles whether a dealing line appears every quarter forever or not at all. The third is where the cap actually bites, and the fourth is how much the smallest position is being asked to absorb. The figure below pairs each of the four with its answer from this mandate. A committee that can answer those four has understood the weighting decision better than one that has debated which scheme is superior for an hour.

A household does a smaller version of this without calling it anything. Someone putting the same amount into six savings decisions every month, whatever those six have done, is running an equal weighting rule and will quietly sell whichever one grew the moment they rebalance. Someone who lets the six run is running a value weighted rule and will find one of them has become half of everything. Most people are running one without having chosen it.

Which scheme is right?

None of them, and the question is the wrong shape. Each of the three is a different exposure: equal weighting leans away from the largest names, market capitalisation weighting leans into them, and fundamental weighting leans toward whatever the chosen accounting quantity favours. The choice between them is a choice between exposures, not between a correct answer and an incorrect one.

Anybody who calls one scheme better without first saying better at what has skipped the question rather than answered it. Better at carrying a large amount of money has an operational answer, and it is given above. Better at requiring no maintenance has an arithmetic answer, and that is given above too. Better at producing returns has no honest answer. The answer would depend on a period nobody chose in advance and on evidence nobody has.

A method survives that argument and a preference does not. Name the quantity the weight is keyed to, work out from that whether the scheme has to trade and in which direction, state the base of every percentage before comparing it, ask where the cap bites on the scheme under consideration, and ask what the smallest position must absorb. None of that needs anybody to declare a favourite. In a room where two people already have one, that is exactly what makes the method useful.

When does the choice between the schemes stop mattering?

Under any of four conditions the whole weighting argument is not worth the meeting. The first is a cap that binds before the scheme's own logic does. With the control above set to 12 names, every equally weighted position lands on 8.33 per cent of the sleeve, the cap exactly, and twelve holdings of Rs 25,00,00,000/- fill the Rs 300 crore sleeve with nothing left over. At that count, fully invested, no scheme can put a name anywhere else. The cap has chosen the weights and the scheme has chosen nothing.

The second is a list whose names are close in size. On this sleeve the largest holding sits at 2.15 times its equal weight, so an equally weighted book and a market capitalisation weighted one are visibly different portfolios. On a list where the largest sits at 4.00 per cent of the sleeve against an equal weight of 3.57, that multiple is 1.12 and the two rules are arguing over four tenths of a point. The third is a count low enough that every scheme concentrates anyway. At eight names even equal weighting, the least concentrated of the three, puts 12.50 per cent of the sleeve into every name. The fourth is a rebalancing interval so long that the book has drifted into something else before anybody looks.

None of those four conditions announces its own expiry. Names grow apart, a cap is loosened at a meeting nobody minuted carefully, a holding is added, an interval lengthens because one quarter was busy. The scheme was deciding nothing for years and then it was deciding everything, and no notice went round on the day that changed.