How to Size a Portfolio Position Against the Right Base

Sizing a portfolio position means turning a decision to hold something into an amount, and the base the limit is written against settles the test before any arithmetic does. The Anantara Multi-Asset Portfolio caps one holding at 5 per cent of the portfolio, and 5 per cent of the Rs 500 crore portfolio is Rs 25 crore. Written against the Rs 300 crore equity sleeve instead, those same words would mean Rs 15 crore.

Start with a wedding. The shape of the problem is the same there, and nobody has to know any finance to see it. A household sets a budget and says that no more than 10 per cent goes on flowers. Two weeks later the decorator sends a quotation and somebody has to say yes or no. Ten per cent of what? Of the whole wedding, catering and venue and clothes included, or of the decoration line alone? The two readings are not close together. On a Rs 40,00,000/- wedding with a Rs 6,00,000/- decoration line, one reading permits Rs 4,00,000/- of flowers and the other permits Rs 60,000/-. Nothing about the flowers changed between those two sentences. The number sitting underneath the percentage changed, and nothing else did.

The number sitting underneath a percentage has a name in a portfolio, and finding that number is the first step of the procedure rather than a detail inside it. A percentage limit is not a limit until the base it is measured against is known, and the same six words can permit one amount or refuse it depending on nothing but that. Everything below is the order the work runs in, one step at a time, worked on the Anantara Multi-Asset Portfolio, an invented Rs 500 crore mandate run for an invented charitable endowment whose investment committee is chaired by Rukmini Deshpande and whose mandate is run by Faiz Ahmad Ansari.

What does sizing a position actually decide?

Position sizingThe step that converts a decision to hold a particular thing into a stated amount of money, tested against whatever written limit applies to it. decides one thing: how many rupees of one holding the portfolio carries. Position sizing is a narrow step. A great deal gets attributed to it that belongs to the steps on either side, so the narrowness is worth being clear about.

Somebody else has already decided that this holding belongs in the portfolio at all. Somebody else has already written the limit that the size has to respect. Sizing sits between those two decisions and produces an amount. Sizing does not endorse the holding, does not judge the limit, and does not settle how concentrated the portfolio ought to be. Sizing converts a decision into a number, and the number is only meaningful alongside the base it was struck on.

The Anantara mandate carries four written constraints and sizing engages exactly one of them. Seeing which one, and seeing what the other three convert into, is the quickest way to keep the step inside its own boundaries.

The seven steps below are the order the work runs in. Each one states what it takes in, what it hands to the next step, and what it deliberately leaves open. None of them explains how any measure works. Every measure the steps use was settled elsewhere and is applied here rather than rebuilt.

1. Find what the limit is written againstTakes in the mandate as it is written. Hands on one word: the baseThe total that a percentage is struck against. Change the base and the same percentage becomes a different amount of money.. Leaves every quantity open. Nothing has been measured yet.
   The base is a fact about the document, not a reading of it.
2. Convert the limit into rupees on that baseTakes in the base and the percentage. Hands on a single rupee figure. Leaves open where the position stands. The holding has not been read yet.
   5 per cent of Rs 500 crore is Rs 25 crore.
3. Strike the position in rupees on the same baseTakes in the holding. Hands on a second rupee figure standing on the same base as the first. Leaves open whether anything passes, until the two are put beside each other.
   Both sides on one base, or the comparison is not a comparison.
4. Compute the headroomTakes in the two rupee figures. Hands on the gap between them, in rupees and in points of the stated base. Leaves open what anybody ought to do about the gap.
   Rs 25 crore less Rs 23 crore is Rs 2 crore.
5. Strike the same position on the other baseTakes in the same holding once more. Hands on a second reading carrying its own base. Leaves open which of the two readings a later question will want.
   4.6 per cent of the portfolio, 7.7 per cent of the sleeve.
6. Count what the trade adds to turnoverTakes in whatever was bought or sold to reach the size. Hands on a quantity added to the turnover count for the year. Leaves the cost open. The Anantara record carries no rate at which to price a trade.
   A quantity, and not a cost.
7. Write the line down with both basesTakes in everything above. Hands on one line in the file carrying the amount, both weights, both bases, the limit, the limit's base and the date. Leaves nothing open, and leaving nothing open is the whole point of it.
   A weight with no base beside it is not a weight.

Which base is the limit written against?

Step one asks a question that looks like paperwork and is the entire test in disguise. The Anantara Multi-Asset Portfolio carries a mandate constraint reading that no single holding may exceed 5 per cent of the portfolio. The line says the portfolio, so the base is the portfolio. There is no interpretation involved and no house convention to fall back on. The document either names a base or it does not, and if it does not, the resolution is a correction to the document rather than a decision at the desk.

Naming the base matters here because the Anantara portfolio has at least two totals a reader might reach for. There is the Rs 500 crore portfolio, and there is the Rs 300 crore equity sleeve inside it. Both are real quantities in the record and both are used constantly. A capA written ceiling on a single holding, expressed as a percentage of some named total or as a rupee amount. that names neither is an argument waiting to happen, and it is an argument that only surfaces on the day somebody wants a different answer.

Neither reading is a mistake in the abstract. A mandate could perfectly well write its single holding limit against the equity sleeve, and some do. A reader cannot choose between the two after the fact. The Anantara mandate names the portfolio, so the portfolio is the base, and the Rs 15 crore figure in the second row shows only what a different document would have meant.

How does a percentage limit become a rupee figure?

Step two converts, and it converts before anything is compared. Converting first is not a preference about presentation. A limit written as a percentage and a holding written in rupees are two different kinds of thing, and putting them side by side without converting one of them is how a review talks past itself for an hour.

On the Anantara portfolio the conversion is short. Five per cent of Rs 500 crore is Rs 25 crore, or Rs 25,00,00,000/- written out. The Rs 25 crore figure now sits in the file as the amount a holding is actually tested against, and nobody reading the file next has to recompute it. The conversion is also where the base stops being an abstraction: the moment the rupee figure appears, it is obvious which total produced it.

The ladder above is worth keeping in view for a reason that has nothing to do with the 5 per cent line. Once a committee can see that one point of the Anantara portfolio is Rs 5 crore, the conversation about how tightly to write any limit becomes a conversation in rupees rather than in points. A percentage is a compact way of writing a rupee figure, and the compactness is exactly what hides the base.

How is the position itself struck on that base?

Step three reads the holding and expresses it in rupees on the same base as the limit. On the Anantara portfolio the largest holding in the equity sleeve is Rs 23 crore, or Rs 23,00,00,000/-. Against the Rs 500 crore portfolio that is a portfolio weightA holding expressed as a share of the whole portfolio, which on this mandate is the Rs 500 crore total. of 4.6 per cent. Against the Rs 300 crore equity sleeve the same rupees are a sleeve weightThe same holding expressed as a share of one asset class sleeve rather than of the whole portfolio. of 7.7 per cent.

Both of those are correct arithmetic. The mandate's line is written on the portfolio, so only the first of the two is the figure the mandate test uses. The second figure is not discarded, and step five is where it goes, but it does not enter this comparison. The rule that keeps step three honest is simple: both sides of the test stand on the same base, or there is no test.

The relationship between the two readings is fixed rather than incidental, and knowing that is a useful defence. The Rs 300 crore sleeve is 60 per cent of the Rs 500 crore portfolio, so a sleeve reading is always the portfolio reading multiplied by Rs 500 crore over Rs 300 crore. The multiplier is about 1.667. The two never converge and never cross.

The fixed ratio also means the mandate's cap can be honestly restated on the other base without changing what it permits. Rs 25 crore is 8.33 per cent of the Rs 300 crore sleeve, so a cap of 5 per cent of the portfolio is exactly a cap of 8.33 per cent of the sleeve. Translating a limit onto another base preserves the verdict. Swapping the base without translating the limit destroys the verdict, and the two operations look almost identical in writing.

How much headroom is there, and in what terms?

Step four subtracts. Rs 25 crore less Rs 23 crore is Rs 2 crore, or Rs 2,00,00,000/-. The gap between the cap and the holding is the headroomThe distance between where a position stands and the limit it is tested against, stated in rupees and in points of the base the limit uses., and stating it in rupees alone is only half the job. Rs 2 crore is 0.4 per cent of the Rs 500 crore portfolio. The cap uses that same base, so the two figures can be read together without further conversion.

There is a third way to read the same gap, and it answers a different question again. Rs 2 crore is about 8.7 per cent of the Rs 23 crore holding itself. A reader wants that third reading when the question is how far the holding could move before a decision is forced. The 8.7 per cent carries a condition: it holds only while the rest of the portfolio stays still. A rising holding lifts the Rs 500 crore total it is being measured against, so the cap is actually reached at a rise of about 9.15 per cent rather than 8.7. The comparison of concentrated and diversified construction works that case through. The derivation belongs there. The discipline that belongs here is stating which of the three readings has been quoted.

Headroom is the figure that turns a compliance answer into something forward looking. A position that passes with Rs 2 crore to spare and a position that passes with Rs 20 crore to spare are both compliant and are not in the same situation at all. A holding with almost no headroom is a rebalancing trade waiting for a price move to trigger it, and the file that records only the pass has not said so.

Why record the position on the other base as well?

Step five strikes the same Rs 23 crore against the Rs 300 crore equity sleeve, gets 7.7 per cent, and writes it down beside the 4.6 per cent. The second reading looks like duplication and is not. The two figures answer two different questions. Both questions get asked about this portfolio, usually by different people in different meetings.

The cap is written on the portfolio, so the mandate test wants the portfolio reading. A concentration review wants the sleeve reading. The question in that review is how much of the risk bearing part of the portfolio is riding on one name. The record already contains the sleeve level version of that question. The equity sleeve holds 28 names, the top ten come to Rs 155 crore, and the remaining 18 average about Rs 8.06 crore each. Rs 155 crore is 31.0 per cent of the Rs 500 crore portfolio and 51.7 per cent of the Rs 300 crore sleeve.

Recording one reading and deriving the other later is where files go wrong. The derivation gets done under time pressure by somebody who does not know which total was used. Two columns cost nothing to write and they remove the entire class of argument.

Steps one to five together produce a short ledger, and the ledger is worth seeing whole. Every line of it is either taken from the document or computed from a figure above it.

What does the 5 per cent cap actually prevent?

A single holding cap is routinely described as though it settled concentration. Whether the cap really does settle concentration is the question readers ask most, and the arithmetic showing that it does not is two lines long.

A cap of 5 per cent of the Rs 500 crore portfolio is Rs 25 crore a name. Ten names each sitting at that ceiling would come to Rs 250 crore. Rs 250 crore is 50.0 per cent of the portfolio and 83.3 per cent of the Rs 300 crore equity sleeve. The Anantara sleeve's recorded top ten are Rs 155 crore, so they sit Rs 95 crore below what the cap alone would permit. The cap did not produce that gap. Something else did, and the record does not say what.

The cap does bite in one direction that is easy to miss, and it bites on the number of names rather than on the concentration. Rs 300 crore of equity divided by a Rs 25 crore ceiling is exactly twelve, so a sleeve of that size cannot be assembled from fewer than twelve holdings while the cap stands. A single holding cap sets a floor under the count of names, and says almost nothing about how the money is spread across them. The recorded sleeve holds 28.

The distribution of room across the sleeve is nothing like even, so headroom is worth looking at beyond the largest name. The largest holding has Rs 2 crore under the cap. A holding at the top ten average of Rs 15.50 crore has Rs 9.50 crore. A holding at the other eighteen average of about Rs 8.06 crore has close to Rs 16.94 crore. Only the first of those three is anywhere near the line.

Change the base the cap is written on and that floor moves with it. A cap of 5 per cent of the Rs 300 crore sleeve would be Rs 15 crore a name, and the same sleeve could then not be assembled from fewer than twenty holdings. The base under a single holding cap sets how many names the sleeve must carry at minimum. A floor under the count of names is a construction consequence rather than a compliance one.

What does the trade do to everything else being measured?

Step six is a counting step. Reaching a size means buying or selling, and a rebalancing tradeA purchase or sale made to move a holding or a sleeve back to an intended size, as distinct from a trade made because a view changed. is not free even when it is small. A rebalancing trade adds to the turnover count for the year, and the Anantara record measures turnover separately from return.

The record carries 34 per cent of turnover for the stated twelve month period. On Rs 500 crore that is about Rs 170 crore of the portfolio replaced across the year. A move of Rs 2 crore in one holding is 0.4 per cent of the portfolio, so it is a small contribution to that count and it is not nothing. The record carries no rate at which to price a trade, so this step produces a quantity and stops. The turnover comparison is where that missing rate is worked through.

Scaling the trade against the year makes the size of the omission clear. Thirty four per cent of Rs 500 crore is about Rs 170 crore of the portfolio replaced across the stated period, and a single Rs 2 crore adjustment is 0.4 per cent of the portfolio beside it.

What gets written down, and in what form?

Step seven writes the line. A holdings fileThe record listing what the portfolio holds, in what amount, with the weights and limits each holding is tested against. that carries an amount and a weight and nothing else has recorded a number that cannot be checked six months later. Nobody reading that file can tell what the percentage was struck on.

Six fields make the line self contained: the amount in rupees, the weight, the base that weight was struck on, the limit, the base the limit is written against, and the date. Drop the two base fields and the other four stop being readable together. The amount survives. Rupees carry their own meaning. The weight and the limit do not.

A weight recorded without its base is not a weight but a number that resembles one, and the difference only shows up under pressure. A missing base is the most common defect in a holdings file and also the cheapest to fix. The fix costs two columns and no additional work: both readings were already produced in steps three and five.

Nothing in that line has to be produced specially at the moment of writing. Every field was handed forward by one of the earlier steps. Step seven transcribes rather than computes.

What happens when the base is lost?

The failure has two directions and only one of them is comfortable to talk about. Both are worth working. A treatment that shows only the flattering direction has taught half the lesson.

What does position sizing not decide?

Step eight is not a step but the boundary of the sequence, and stating the boundary is what keeps the seven steps honest. Sizing takes a decision to hold something and turns it into an amount. Everything on either side of that belongs to somebody else.

The narrowness is a feature. A step that quietly answered the wider questions would be doing so without any of the evidence those questions need, and the answers would then be carried forward as though they had been decided properly. The seven steps produce an amount and a record of how it was struck, and refusing to produce anything else is what makes the amount trustworthy.