Pooled Vehicles: How One Portfolio Serves Many Owners

One portfolio can serve thousands of people because each of them holds units, and units are identical claims on the whole pool. Divide the net assets of the pool by the number of units in existence and the answer is the worth of one. Holders can then join and leave on separate days without disturbing each other, but only while every transaction is struck at that computed figure.

The arrangement begins from an awkwardness. A portfolio is one set of holdings. A saver is one person, with one amount of money, who happens to have it on one particular Tuesday. Everybody arrived on a different day with a different sum, and everybody will leave on a different day too. Put a few thousand savers and one portfolio in the same room and the result is a bookkeeping problem rather than an investing problem. A pooled vehicleOne set of holdings run as a single portfolio, with many people holding proportional claims on the whole of it rather than on any item inside it. answers that problem with a single device, and the device is the unit.

Girnar Asset Management Limited, an invented house, runs the Girnar Large Cap Equity Fund, an open ended equity scheme holding net assetsEverything the pool holds, minus everything it owes, measured at the moment of the count. of Rs 4,200 crore against 120.00 crore units in issue, spread across 3,80,000 folios. Kalyani Bhagat manages the portfolio and Sohail Merchant heads operations. The trustee company, the custodian, the registrar and transfer agent, the auditor and the distributor each hold a defined role in the arrangement, and the role does the work rather than the name of whichever organisation fills it.

Two things are settled elsewhere and neither is rebuilt here. Why savers pool at all, what the arrangement makes possible and what it costs a person in control, is worked separately. So is the legal shape of the thing: which party stands where, which of them is answerable to whom, and how the law describes each of their positions. The arrangement is taken as given, and one narrower question follows: how does one portfolio serve many people at the same time, how is each person's share measured and kept distinct, and what does the record have to do to keep that straight?

What is a unit actually a claim on?

A unit is an equal proportional claim on a pool. Three quiet negatives hide inside that sentence. Read it slowly. A unit is not a share in Girnar Asset Management Limited, the company that runs the scheme; the manager's own profits and losses are its own affair and never reach the pool. A unit is not a debt owed by anybody, so nobody has promised to hand back what was put in. And a unit is not a claim on any named security the pool happens to hold. A unit is a claim on the pool, whole and undivided, and its size is expressed as a fraction of the total number of units rather than as a list of things.

Three things follow, and all three are worth saying flatly rather than implying. First, every holder's share is measured in units and moves with the same figure per unit as everybody else's, so no holder is on a separate meter and no holder has a different starting mark. Second, nobody's share is walled off from what happens to the pool: if the holdings fall, every unit falls together, in the same proportion, and there is no arrangement sitting inside the pool that shelters one holder while exposing another. Third, a holder cannot reach into the pool and take one particular security out. The claim is on the pool as a whole and it is settled in money at the computed figure per unit, never by handing across a named holding.

The everyday version is an apartment block that buys one water tanker between all its flats. Nobody's water is stored in a personal drum. There is one tank, each flat holds a stated number of shares in it, and the amount each flat may draw is worked out from its shares against the total shares rather than from what it paid on the day. No flat can point at a specific litre and call it theirs. The shared tank is the whole idea, and everything that follows is arithmetic laid on top of it.

How is the worth of one unit worked out?

By division, and the division is short enough to do in the head once the two inputs are to hand. Net assets on the Girnar Large Cap Equity Fund come to Rs 42,00,00,00,000/-. Units in issue come to 1,20,00,00,000. The first divided by the second is Rs 35.00, exactly, with nothing left over. Rs 35.00 is a result rather than a price, and the difference between those two words is the most useful distinction in this section. A price is something a person or a market arrives at. The division is arithmetic: two disclosed numbers go in, one number comes out, and no human judgement sits between them.

A division that reverses cleanly is a division worth trusting. Run this one backwards. 1,20,00,00,000 units at Rs 35.00 each comes back to Rs 42,00,00,00,000/-, the figure the first line started from. The two routes are the same identity written in opposite directions rather than two independent confirmations, so this is a check on the arithmetic rather than fresh evidence about the scheme, and which of the two it is matters.

Both inputs carry a timestamp, and the value per unitThe result of dividing net assets by units outstanding, worked out at one stated moment rather than continuously. inherits it. Net assets change whenever the prices of the holdings change. Units outstandingHow many units are in existence at the moment of the count, a figure that rises as people join and falls as people leave. change whenever somebody joins or leaves. So the figure is struck at a stated moment and belongs to that moment, in the way a photograph belongs to the second it was taken. The figure is not a running quote and not a promise about tomorrow.

The everyday version makes the arithmetic feel inevitable. A wedding kitchen sets down one enormous vessel of curd and ladles it into identical cups. Nobody decided in advance how full a cup would be. The size of one cup is simply whatever the vessel held, divided by the number of cups filled from it. If the cook adds more curd and fills proportionately more cups, the cup size does not change. If the cook adds more curd and fills too few cups, every cup gets bigger, and somebody has quietly gained at somebody else's expense. Somebody quietly gaining at somebody else's expense is the entire second half of what follows.

One more division puts a human scale on the pool. Spread Rs 42,00,00,00,000/- across 3,80,000 foliosThe account on which one holder's units are recorded and maintained by the registrar and transfer agent. and the average folio holds about Rs 1,10,526/-, rounded down from a figure that runs on without ending. The rounding has a visible cost: 3,80,000 folios at Rs 1,10,526/- each is Rs 41,99,98,80,000/-, or Rs 1,20,000/- short of the pool. The residue is the rounding and nothing else. In units, the same average folio holds about 3,157.895 units, and 3,157.895 units at Rs 35.00 comes back to about Rs 1,10,526/- again.

Why can the claims not come in different sizes?

Most treatments slide past this as though equality were a courtesy, and it is not. Suppose the claims came in different sizes. One holder's unit would then entitle them to a shade more of the pool than another holder's unit did. Somebody would then have to record, for every single account, what that particular account is separately entitled to, and keep that record accurate through every day the holdings moved. Follow the consequence one step further. A set of individual entitlements against a shared set of investments is a set of individual accounts wearing a costume. Equality here is not a gesture towards fairness; it is the one thing that lets a single portfolio serve many people without quietly turning into many portfolios.

The same logic appears in a mall. Ten shops share one generator. If every shop negotiated its own share of the diesel, there would have to be a meter on every shutter and a separate bill each month, at which point the shared generator has bought nobody anything: ten arrangements stand where one was supposed to stand. The shared generator is worth having only because everybody draws on the same terms. One meter and one division then settle the whole thing. A pooled scheme with 3,80,000 accounts is that mall with a very large number of shutters. Equality there is not decorative but load bearing.

Equality is also why the arithmetic above could be so short. One numerator, one denominator, one answer, and that answer serves every account on the register. The registrar and transfer agent does not need to know anything about a holder in order to value their holding: it needs the number of units on the folio, and the one figure per unit that the whole scheme shares. Take equality away and that single figure has to become 3,80,000 figures.

What breaks when somebody joins at the wrong price?

Everything established so far has one weak joint, and it fits in a single sentence. Issue fresh units to an arriving holder at anything other than the computed figure, and what a unit is worth shifts for every holder already there. Not their unit count, which is untouched, and not the total size of the pool, which is exactly what it would have been anyway. The pool is being cut into a different number of pieces than the money justified, so the figure each of those units is worth moves.

The equal treatmentThe requirement that a transaction by one holder should leave the remaining holders standing exactly where they stood before it. problem is the idea the whole sequence has been walking towards. State the test plainly: after somebody joins or leaves, is every remaining holder in the position they would have been in had that person never appeared? If yes, the arrangement treated them equally. If no, something moved between them, and the only place it can have moved from is each other.

The mechanism is not intuitive. Notice how it works. AllotmentThe act of creating fresh units and recording them against a holder's account, which raises the number of units in issue. raises two things at once: the money in the pool and the number of units in issue. If those two rise in the same proportion, the division comes back to where it was and nobody has moved. If they rise in different proportions, the division lands somewhere else, and everybody's unit lands there with it. The size of the arriving cheque decides how much can move. The figure the units were struck at decides whether anything moves at all.

Two consequences follow, and they explain a lot of how these arrangements are supervised. The first is that somebody is always joining and somebody is always leaving, so the pressure never goes away. The second is that the operator sits on both sides of the transaction, issuing the units and also serving the holders whose units are about to move. Whoever operates the scheme therefore cannot be the one who decides the answer. The requirement fixing which computed figure applies to a transaction is therefore written by a regulator and not by the party doing the issuing, a point taken up again below.

What do three entry prices do to the same Rs 350 crore?

Take the scheme at rest. Net assets of Rs 4,200 crore, 120.00 crore units, and therefore Rs 35.00 a unit. Now let Rs 350 crore of new money arrive. Hold everything else still and vary exactly one thing: the figure the fresh units are issued at. The pool receives Rs 350 crore under every version, so net assets afterwards are Rs 4,550 crore under every version too. All that changes is how many units that Rs 4,550 crore has to be shared among.

Version one, issued at the computed figure of Rs 35.00. Rs 350 crore divided by Rs 35.00 creates 10.00 crore units. Units in issue become 120.00 plus 10.00, or 130.00 crore. Now do the division again: Rs 4,550 crore over 130.00 crore units is Rs 35.00. Not approximately Rs 35.00 but exactly Rs 35.00. The money and the units both rose by one twelfth, and a fraction is unmoved when the top and the bottom are multiplied by the same thing. Nobody gained, nobody lost, and the arriving holder's 10.00 crore units are worth Rs 350 crore, which is what they paid.

Version two, issued at Rs 40.00. Rs 350 crore divided by Rs 40.00 creates only 8.75 crore units, so units in issue become 128.75 crore. The division now reads Rs 4,550 crore over 128.75 crore units, or Rs 35.3398 a unit. Every unit already in issue has risen by Rs 0.3398, and there are 120.00 crore of them, so the holders already there are up by Rs 40,77,66,990.29. Look at the other side of it. The arriving holder's 8.75 crore units at Rs 35.3398 are worth Rs 309.2233 crore, against Rs 350 crore handed over, so they are down Rs 40,77,66,990.29. The same figure, to the paisa, in the opposite direction.

That arithmetic contains an equals sign that is really an approximation, and it deserves one honest note. Rs 0.3398 a unit across 120.00 crore units comes to Rs 40,77,60,000/-, or Rs 6,990.29 short of the figure printed above. Nothing went missing from the pool. The shortfall is purely what rounding the per unit change to four decimal places costs. The true change is thirty five one hundred and third parts of a rupee and runs on without ending. The two sides of the transfer agree at that unrounded value, not at Rs 0.3398, and it is worth saying which of the two the agreement holds at.

Version three, issued at Rs 30.00, and it runs the other way. Rs 350 crore divided by Rs 30.00 creates 11.6667 crore units, so units in issue become 131.6667 crore. Rs 4,550 crore over 131.6667 crore units is Rs 34.5570 a unit. Every existing unit has fallen by Rs 0.4430, and across 120.00 crore units that is Rs 53,16,45,569.62 gone from the holders already there. The arriving holder's 11.6667 crore units at Rs 34.5570 are worth Rs 403.1646 crore against Rs 350 crore paid, so they are up by Rs 53,16,45,569.62. Equal and opposite again.

A careful reader will spot a small point of convention on that third version. Rs 350 crore at Rs 30.00 does not land on a whole thousandth of a unit, and this scheme records units to three decimal places. Rounding the allotment to the nearest thousandth moves the resulting figure per unit by less than one ten thousandth of a rupee. The division above is therefore carried through at its exact value rather than at the rounded unit count.

The two shaded rows carry the closing point. Read them as a pair before moving on. In every column they add to Rs 4,550 crore. Not roughly, but exactly. The two rows are the only two claims on the pool and the pool is the only thing they are claims on, so the arithmetic could not have produced anything else. Rs 350 crore reached the pool under every one of the three versions, so the pricing created nothing and destroyed nothing; the whole difference between the columns is a transfer between the people inside the arrangement.

The picture makes one thing plain that the table can only imply. At true scale the boundary between the two claims moves about six pixels, on a bar six hundred and forty pixels long. Nothing on that image looks like a scandal. And yet those six pixels are Rs 40,77,66,990.29. The mechanism is genuinely small to the eye and genuinely large in rupees, and the magnified panel underneath holds both of those truths at once, since showing only one would teach the wrong instinct.

Two features of that curve are worth a sentence each. The curve crosses nil at one point only, and that point is the computed figure itself. Exactly one issue price leaves nobody moved. The curve is also not a straight line. Issuing cheap creates more units to divide the pool among and issuing dear creates fewer, so the drop below Rs 35.00 is steeper than the climb above it. Underpricing does more damage per rupee of error than overpricing does good.

Where does the value go as the entry price moves?

Three prices are three points. The control below sweeps the whole range between them, in steps of twenty five paise, and recomputes the division at every step. The control opens at Rs 35.00, the case where nothing happens: the marker sits on the computed figure and both slots underneath are empty. Neutrality comes first and the transfer second. Reverse the order and a transfer starts to look like the normal state of affairs rather than a departure from one.

Two things move together. The marker on the upper rail is the figure per unit belonging to the holders already there, and it walks away from Rs 35.00 in whichever direction the issue price is pushed. The two bars underneath are the same movement counted in rupees, one bar for the 120.00 crore units already in issue and one for the units created for the arriving money. The two bars are always the same length and always point in opposite directions. A transfer with only one side would require money to appear from outside the pool, so the equal lengths are the arithmetic itself rather than a coincidence in the drawing.

The ends of the range are instructive. At Rs 40.00 the marker settles at Rs 35.3398, with Rs 40,77,66,990.29 in the upper bar and the same amount in the lower one. At Rs 30.00 the marker drops to Rs 34.5570, with Rs 53,16,45,569.62 running the other way. The pool being divided has not changed size by a single rupee at any setting, so the marker never leaves the rail.

Is a pricing transfer the same thing as a trading cost?

No, and these two get run together so often that they deserve their own block. A pricing transferWorth shifting from one set of holders to another because units changed hands at something other than the computed figure. happens at the instant of the transaction. The transfer moves worth between the people in the arrangement and leaves the total exactly where it was: Rs 4,550 crore under every price, with only the line inside it moving. A trading costWorth that actually departs the pool when it buys or sells, so that what remains is smaller for everybody still in it. happens afterwards, when the pool has to go into the market and actually buy something with the money that arrived, or actually sell something to pay somebody out. The trade takes money out of the pool, and the pool is smaller for everyone who stayed.

One of the two redistributes and the other leaks, and a single question tells them apart: is the pool the same size afterwards? If yes, it is a transfer, and somebody inside the arrangement is up by precisely what somebody else is down. If no, it is a cost, and the money has gone to somebody outside it. The everyday version is a household dividing a bag of rice. Weighing the shares badly is a transfer: one person gets more, another gets less, and the bag is the same bag. Spilling some on the floor during the dividing is a cost: everybody's share is smaller and nobody picked up what fell.

Running them together misdiagnoses both, in opposite directions. Treating a genuine cost as a transfer sends the reader looking for the holder who gained, and there is nobody there, so the conclusion is that nothing happened. Treating a genuine transfer as a cost gives the conclusion that the pool leaks, when in fact the pool is intact and a particular set of holders has quietly funded a particular arriving one. The first mistake makes a real drag invisible. The second sends a reader hunting for a leak that was never there. The mechanism that did the work is a rule about pricing, and it goes unexamined.

What must already exist before anybody can transact?

Three conditions, and they have to arrive in this order because each one leans on the one before it. The first is a valuation of the pool: somebody has to establish what the holdings are worth and what the arrangement owes, or there is no numerator. The second is a stated moment that the valuation belongs to. A valuation without a timestamp cannot be attached to anything. The third is a rule connecting one holder's application to one of those stated moments. Without the third condition the first two are ornaments. A scheme could hold a shelf of perfectly correct valuations and still settle every application at whichever one suited it.

The third condition is the one everything so far has been circling. The Securities and Exchange Board of India (SEBI) writes it, publishes it at sebi.gov.in, and revises it from time to time, and it is precise and detailed in the original. Its timing, its period, its amount and its method are read there on the day they are needed.

Ask why the last one cannot be left to the operator and the answer is uncomfortable rather than complicated. Whoever runs the scheme stands on both sides of the transaction at once. The operator creates the fresh units for the arriving holder, and it is also the party answering to the 3,80,000 folios whose units are about to move. Any discretion over the figure is discretion over which of those two sides gets the better of it. The trustee company exists partly to sit on that seam, and the requirement itself exists so that there is no discretion there to sit on.

What can this record not show about the pool?

The gaps in a record are the other half of the habit. The record behind this scheme carries no holdings for the Girnar Large Cap Equity Fund: no securities, no weights, no sector split and no list of trades. Flow data is absent too, so how often money of this size actually arrives stays an open question. One figure for net assets and one for units is the whole of it, with no series behind either. Everything above was built from that, and what the shortage did and did not cost is worth being exact about.

The shortage cost the transfer arithmetic nothing at all. Look back at what the worked instance actually consumed: net assets, units in issue, the money arriving, and the figure the fresh units were struck at. Four inputs, none of them a holding. The effect of a mispriced entry on everybody in a pool can be worked out to the paisa without knowing a single thing the pool is invested in. The demonstration above is therefore complete rather than gestured at.

The cost falls on the second half of the story, and it is worth naming rather than papering over. When Rs 350 crore lands, somebody has to buy something with it, and that purchase has its own price and its own cost. Which security, at what price, and what the buying itself took out of the pool, is not in this record and cannot be reconstructed from anything that is. A number invented to fill that gap would look like the rest of the arithmetic and would be worth nothing. A blank clearly marked as one is the better outcome by far.

Girnar Asset Management Limited, the Girnar Large Cap Equity Fund, the Girnar Broad Market Index Fund, Kalyani Bhagat and Sohail Merchant are invented.
Educational material. Not advice on any investment, tax, budget or market position.