The Model Portfolio: One Design Across Many Accounts

A model portfolio is one written design, a list of holdings with a target weight against each, applied across many separate accounts instead of being held as a single pool. The design is settled once and every account is then traded toward it. Because accounts begin from different holdings and trade at different moments, none reproduces the design exactly.

Almost every argument about performance eventually turns on the distinction that answer hides. A design was written, and a result was delivered. The design and the result carry the same name in conversation, they are reported with the same digits, and they are not the same object. One of them holds securities. The other holds nothing at all.

The Anantara Multi-Asset Portfolio is a discretionary mandate of Rs 500 crore run by Faiz Ahmad Ansari for a charitable endowment whose investment committee is chaired by Rukmini Deshpande. Every figure that follows belongs to that mandate and to one stated twelve month period.

One thing about the arrangement has to be said now and then left alone. Under a discretionary mandateAn arrangement in which the manager takes each decision without going back to the holder for approval, inside limits the holder wrote down in advance. the securities sit in the holder's own name at a custodian, and somebody else decides what those securities are. Ownership at the custodian and delegation of the decisions are the whole of what a model portfolio needs from the arrangement. The arrangement is covered separately under the name separately managed account, and everything else about it waits there.

What is a model portfolio, and what does it actually hold?

A model portfolio holds nothing. Holding nothing is not a trick answer, it is the definition. A model portfolioA written design listing the holdings, the weight each one should carry and the rule for bringing an account back to those weights. The design is an instruction, not a holding. is a document: a list of holdings, a weight written against each one, a permitted band around some of those weights, and a rule saying when an account that has drifted gets brought back. Printed out, it is the entire object. The design has no bank account, no custodian and no tax position.

Think of a recipe pinned to a kitchen wall. The recipe does not feed anyone. Twenty households cook from the same recipe on the same evening, and twenty different dinners appear. One household ran out of salt, one started an hour late, and one has a smaller pan. Nobody blames the recipe for the differences, and nobody would say the recipe ate anything. The design carries no return, no cash and no tax position of its own, so everything a holder actually experiences happens inside an account rather than inside the design.

Two words get used loosely here and they are worth separating before anything else is built on them. A policy weightThe share of a portfolio the holder has decided an asset class should carry over the long run. A policy weight is a decision taken in advance, not an observation of where the portfolio sits today. is the share of the whole that an asset class is meant to carry, decided by the holder in advance. A target weightThe share written against one named holding inside the design. Accounts are traded toward it, and it is the number a drifted account is brought back to. is the share written against one named holding inside the design. The Anantara mandate carries policy weights of 60.0 per cent equity, 30.0 per cent fixed income and 10.0 per cent cash. On Rs 500 crore that is Rs 300 crore, Rs 150 crore and Rs 50 crore, and the three sum to Rs 500 crore exactly.

Notice what the design has done and what it has not. The design has fixed the shape of the whole before a single holding was chosen. The design has not put one rupee anywhere. Between one rebalancing and the next, the actual weights in every account drift away from those numbers as prices move, and nobody has done anything wrong when they do. Drift is what happens to a design that is left alone in a moving market.

One more thing was settled before the design was written, and the design sits inside it rather than above it. The Anantara mandate carries four constraints: equity anywhere between 50 and 70 per cent, no single holding above 5 per cent of the portfolio, no unlisted holdings, and a minimum credit standing on the fixed income sleeve stated as a policy rather than as a rating symbol. The four constraints were agreed when the mandate was written and are applied rather than argued again. Five per cent of Rs 500 crore is Rs 25 crore, so the cap is a rupee amount before it is a percentage, and the largest holding at Rs 23 crore sits inside it with Rs 2 crore to spare.

What makes a Diversified Portfolio diversified rather than merely spread?

Spreading and diversifying are not the same thing, and the difference is arithmetic rather than vocabulary. Money can be spread across twenty things that all rise and fall together. The result is twenty holdings and one position. A portfolio is diversified to the extent that its parts do not move together, and how much they fail to move together is a quantity that can be computed. Until somebody computes it, the word diversified is a description of intent rather than a statement about the portfolio.

The everyday version is a household with three earners. If all three work at the same plant, the household has three salaries and one exposure: the plant closes and every rupee of income stops on the same day. If one works at the plant, one teaches and one runs a stall, the same three salaries carry far less shared fate. The count of income sources did not change. The change is in how tightly the three incomes move together.

The Anantara mandate carries its own stated assumptions for this, chosen by the holder rather than forecast by anyone: equity at 18.0 per cent volatility, fixed income at 5.0 per cent, cash at 0.5 per cent, an equity to fixed income correlation of 0.20, and cash treated as moving with nothing. A different set of assumptions gives a different answer. The assumptions are therefore written down where they can be checked.

Start with the wrong answer. Being wrong in one specific way is instructive here. If the three sleeves moved in perfect lockstep, the portfolio's volatility would simply be the weighted average of the three, and the weighted average is 12.35 per cent.

Now the right answer. The parts do not move in lockstep, so the arithmetic runs through variance rather than through a simple average. Each sleeve contributes the square of its own weighted volatility, and each pair that moves together contributes a cross term scaled by its correlation. With equity and fixed income at 0.20 and cash moving with nothing, the four ingredients come to 125.3725, and the square root of that is 11.20 per cent.

The whole of the diversification is the difference between those two numbers. Twelve point three five against eleven point two zero is a gap of 1.15 percentage points, and that gap exists for exactly one reason: the correlation between equity and fixed income is 0.20 rather than 1.00. Push the correlation up to one and the cross term grows from 6.48 to 32.40, the variance climbs, and the gap closes. The 1.15 points is the diversification, and a design that calls itself diversified without producing a number like it has asserted precisely nothing.

Two cautions come with that number, and both matter more than the number does. The 1.15 points is computed from assumptions the holder chose, so it describes the design rather than the world. And it is a statement about spread, not about loss: a lower volatility does not promise a smaller fall in any particular period. The arithmetic supports something narrow, and worth having anyway. On these assumptions, spreading this way carried 1.15 points less spread than not spreading would have.

How does one design reach many separate accounts?

By instruction, and then by trading. The design is written once and reviewed on a stated cycle. Each account is then traded from wherever it happens to be toward wherever the design says it should be. The trading step is the one people skip when they imagine a model being applied, and the trading step is where every difference between accounts is born.

Four things differ at every account and no design can equalise any of them. The account already holds something on the day it joins. Money arrives when the holder has it rather than when the market is convenient. A holder may carry restrictions of their own on top of the mandate, narrowing what that account is permitted to hold. And trading costs whatever it costs on the day it happens. The four differences are structural rather than sloppy, so two accounts running one design correctly will still end a period apart.

How much room does the written design actually leave?

More than most readers expect, and the room is itself part of the design. The Anantara mandate does not fix equity at a point. The mandate states a band of 50 to 70 per cent and then records 60.0 per cent as the chosen setting inside that band. A band is not a target and the midpoint is not neutral: choosing 60.0 per cent was a decision, taken in the same way that choosing 68 per cent would have been a decision.

The reason to feel this rather than read it is that the same percentages produce completely different rupee amounts, and rupees are what get traded. At the 50 per cent floor the equity sleeve is Rs 250 crore. At the 70 per cent ceiling it is Rs 350 crore. Rs 100 crore of difference sits inside a design that is correct at every point along the way. A design expressed in percentages is only half a design until somebody multiplies it by the size of the account.

What is Portfolio Turnover, and what is 34 per cent in rupees?

Portfolio turnoverThe share of a portfolio that was replaced over a stated period. Turnover is a rate rather than an amount, and it means nothing until the period and the size of the portfolio are both named. is the share of a portfolio replaced over a stated period. For the Anantara Multi-Asset Portfolio that figure is 34 per cent over the stated twelve month period. Roughly a third of what the mandate held at the start was not what it held at the end. The period matters as much as the number: the same trading measured over six months and over two years produces two different figures, so the window is quoted every single time.

Here is the move that turns the number into information. Thirty four per cent of a Rs 500 crore mandate is Rs 170 crore of trading. Rs 170 crore is an amount somebody had to deal, settle and pay for. An investment committee can respond to that sentence in a way it cannot respond to thirty four per cent. A percentage is not an amount, and a turnover figure only starts to mean something once it has been multiplied by the size of the portfolio it describes.

The turnover rate leaves something out, and the omission matters as much as the number itself. Rs 170 crore of replacement could be four large positions sold and four bought, or it could be sixty small adjustments spread across the year. The rate is identical in both cases and the two situations are not alike: they involve different numbers of orders, different sizes of order, and quite possibly different costs. The record for this mandate does not say which pattern produced the 34 per cent.

What is a Transaction Cost, and why is this one missing?

A transaction costWhat it costs to carry out a trade, taken together: the charges levied on dealing, the difference between the buying and selling sides of a quote, and the movement a large order causes in the price it is chasing. is what it costs to do the trading that turnover measures. A transaction cost has three parts and only one of them appears on any bill. The charges levied on dealing are visible. The two sides of a quote sit apart. Buying and selling at the same instant loses the width between them. A large order also moves the price it is trying to reach, and that movement is the largest of the three for a big order and the hardest to see.

A round tripOne complete sale and the matching purchase that replaces it. Replacing a holding involves two trades, so the cost of replacing is the cost of both sides together. is one complete sale and the matching purchase that replaces it. Turnover measures replacement, and replacing something takes two trades rather than one. The round trip is therefore the natural unit. If replacing costs a certain amount per round trip, then turnover of 34 per cent drags the portfolio by 0.34 of that amount over the period. The relationship is straightforward and the arithmetic is trivial.

The calculation stops here. The second number was never recorded. The record for the Anantara Multi-Asset Portfolio carries the 34 per cent turnover and carries no dealing cost rate of any kind, so the drag is 0.34 of an unknown quantity. Writing a plausible one in would be worse than the gap: a reader would carry it away as a figure, it would be indistinguishable from a real one, and it would be an invention dressed as a measurement.

Something useful can still be done with an unknown. The shape is worth writing down even when the number is not available. The drag scales with turnover in a straight line: at 34 per cent it is roughly a third of one round trip, at 68 per cent it would be roughly two thirds, and at 10 per cent it would be a tenth. The slope of that line is the missing rate. Anyone holding the missing rate can finish the calculation in one multiplication, and anyone who does not hold it should say so.

Model Portfolio vs Managed Portfolio: which one produced the return?

Both terms are in daily use and they are routinely swapped for one another. A great deal of confusion about performance begins there. The model is the intention. The model is weights on paper, identical for every account, and it is the same object whether one account follows it or four hundred do. A managed portfolioThe actual set of securities and cash sitting in one account at one moment, after the account's own constraints, its cash timing and its trading have all had their turn. is what is actually sitting in one account at one moment, after the constraints, the timing of money and the trading have all had their turn.

Four criteria carry every practical consequence, and the model and the managed portfolio are worth comparing on those four and no others. What does each one hold? Whose is it? What varies between accounts? And which of the two produced the return a holder actually received?

The fourth row is the one to keep. A return has to be produced by something that was actually held, and the design held nothing, so every rupee a holder received came out of the managed portfolio rather than out of the model. That is not a technicality. The number a holder is shown is usually the design's number, and the number sitting in the holder's account is usually smaller.

Why does the delivered result never match the designed one?

Because delivery costs money, and the cost is charged against the account rather than against the design. The Anantara mandate carries its own commercial terms, private to that mandate and nothing more: a management fee of 1.25 per cent of assets, and a performance fee of 15 per cent of whatever the return exceeds a 10 per cent hurdle. Neither figure is a market rate, an industry level or anything any regulator sets.

Work them through on the stated period. Management first: 1.25 per cent of Rs 500 crore is Rs 6.25 crore. Performance next: the return was 14.2 per cent, the hurdle is 10 per cent, so 4.2 points cleared the hurdle. On Rs 500 crore that is Rs 21 crore, and 15 per cent of Rs 21 crore is Rs 3.15 crore. Add the two and the delivery bill is Rs 9.40 crore. Against Rs 500 crore of assets that bill is 1.88 per cent.

Now put that against the result. The design returned 14.2 per cent gross of feesA return measured before the cost of running and delivering the portfolio has been taken out. A gross figure describes the portfolio rather than the holder's outcome. for the stated period, and the benchmark returned 12.6 per cent, so the gross excess was plus 1.6 points. Take out 1.88 points of delivery cost and the return net of feesA return measured after the cost of running and delivering the portfolio has been taken out. A net figure corresponds to what reached the holder. is 12.32 per cent, against the same 12.6 per cent benchmark. The net excess is minus 0.28 points.

The same result in rupees is blunter still, and rupees are what an investment committee argues about. A gross excess of 1.6 points on Rs 500 crore is Rs 8.00 crore. The delivery bill was Rs 9.40 crore. The design beat its benchmark by Rs 8.00 crore gross and the delivery cost Rs 9.40 crore, so the holder finished Rs 1.40 crore behind. The Rs 1.40 crore shortfall is the same minus 0.28 points expressed as money.

Both of those statements about the period are true, and neither of them is the excess return. Plus 1.6 points describes the portfolio before the cost of delivering it. Minus 0.28 points describes the holder after that cost. Both figures cover the same portfolio, the same period and the same benchmark, differing only in whether the delivery bill has been taken out. An excess return figure carries no meaning unless the word gross or the word net stands in the same sentence.

How does a committee or a household use this on a Tuesday?

An investment committee like the one Rukmini Deshpande chairs opens a review with three numbers rather than with the holdings list, and all three are prepared before the meeting starts. The first is what the design returned for the period, stated gross. The second is what the delivery cost, in rupees and as a share of assets. And the third is what the account returned net, against the same benchmark on the same period. The three numbers take a single sheet and they settle what would otherwise be an hour of anecdote.

The order matters more than it looks. The last number read is the one people leave the room with. Reading net last is what stops a committee celebrating a gross number. Faiz Ahmad Ansari, running the mandate, has the same interest in the order: a manager who reports gross and stops has produced a number that does not describe anybody's outcome, and a holder who eventually works that out will trust nothing else in the report either.

A lender or an analyst looking at the same arrangement from outside asks a fourth question the committee sometimes forgets. Which of the two objects am I being shown? A track record built from a model is a record of a design, applied to no account, with no cash timing and no trading in it. A track record built from a real account carries all three. Both can be honest and they are not comparable, so the first job on any record is to find out which one it is.

A household does exactly this work with a pen and no arithmetic beyond subtraction. Write down what the savings arrangement earned. Write down what was charged to run it, in rupees rather than as a percentage. Rupees are what left the account. Subtract. The gap between the designed result and the delivered one exists at every size, and the only reason it goes unnoticed in a household is that nobody produces a report that separates the two.

What does the design never decide?

The model states what to hold and in what proportion, the band around each weight, and the rule for bringing a drifted account back. The model gives a complete answer to one question and silence on six others, and the six are exactly the questions a holder ends up caring about.

Who holds the securities, and where do they sit. Whose money sits beside the holder's, if anybody's does. What can the holder see, and how often. What does the arrangement cost, and on what basis is the cost struck. How does the holder get out, and how quickly. And who writes the rules that the whole arrangement has to satisfy. Not one of those six is a design question, so a reader who has understood the model perfectly still knows nothing about how the arrangement is delivered.