How to Construct a Diversified Portfolio in an Account
How to Construct a Diversified Portfolio in an Account
Constructing a diversified portfolio means turning a design into holdings the account can actually carry. The base is named beside every weight, the spreading is computed rather than claimed, each constraint is tested at the base it was written against, and whatever delivers the portfolio is checked against what the design asks for. Diversified is a computed result, never a description.
The kitchen behind a wedding for four hundred guests shows the shape of the work. There is a menu, agreed weeks earlier, and the menu is not the dinner. At six in the morning the head cook walks the market with that sheet of paper and starts asking a different set of questions. Is this item even available today. Will the two burners in the kitchen cook that many portions in the time available. Is this quantity so small that it is not worth the trip, and is that one so large that nothing else fits on the stove. Every one of those questions is answered in order, and each one is written on the sheet as it is settled.
Portfolio constructionThe work of turning an agreed design, such as a set of target weights, into the actual holdings an account carries, without changing the design in the process. is that walk through the market. The design arrives already agreed. The work is to turn it into positions the account can hold, and to leave behind a record that somebody else can check a year later without having to ask what was meant.
Construction is eight steps taken in order, each one producing something that can be pointed at afterwards. The weights, the holdings and the number of names were all argued out before the procedure began, so no step reopens any of them. The worked run uses the Anantara Multi-Asset Portfolio, an invented Rs 500 crore mandate run for a charitable endowment whose investment committee is chaired by Rukmini Deshpande, with Faiz Ahmad Ansari running the mandate.
Where does construction actually start, and what is fixed before it?
Step one is a refusal. Before a single holding is chosen, what is already decided is written down, and none of it is reopened while the work runs.
For the Anantara Multi-Asset Portfolio that list is short. The account is Rs 500 crore. The policy weightsThe target shares of a portfolio agreed in advance and written into the mandate, as distinct from the actual shares on any given day, which drift as prices move. are equity 60.0 per cent, fixed income 30.0 per cent and cash 10.0 per cent. On Rs 500 crore that is Rs 300 crore, Rs 150 crore and Rs 50 crore. Four constraints apply: equity 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 borrowed symbol. The comparison the portfolio is measured against is a composite of 60 per cent a broad equity index and 40 per cent a broad bond index, both left unnamed here. The asset class figures used later are assumptions the endowment itself chose, and a committee that chose differently would reach a different answer from the same procedure.
Why does the refusal need saying out loud? Because the temptation arrives immediately. The holdings go onto a list, the list looks awkward at 60 per cent equity, and 63 per cent would tidy it. A construction step that quietly changes an allocation has stopped being construction and has become allocation. Allocation was settled before the work began. The weights are an input here. If they are wrong, that is a different meeting with different people in the room.
A design lists a holding at 5 per cent. Before it is checked against the mandate's 5 per cent cap, what is needed?
Why does every weight need its base written beside it?
Step two is clerical and it is where most of the damage is prevented. Beside every percentage in the design goes the baseThe denominator a percentage is measured against. The same rupee amount produces a different percentage depending on whether it is divided by the whole portfolio or by one sleeve of it. it was struck on, in the same line, including the lines where the base looks obvious.
Here is why it is not a formality. On the Anantara Multi-Asset Portfolio the cap says 5 per cent, and the mandate writes that cap against the portfolio. Five per cent of Rs 500 crore is Rs 25 crore. Five per cent of the Rs 300 crore equity sleeve is Rs 15 crore. The largest holding is Rs 23 crore, or 4.6 per cent of the portfolio and 7.7 per cent of the sleeve. The same holding, the same rupees and the same 5 per cent produce a pass on one base and a fail on the other, so the base is doing all the work.
Think of a shopkeeper who says a supplier accounts for a fifth of the business. A fifth of what: of everything sold, or of the one counter that supplier stocks? The two readings are wildly different exposures, and the sentence hides which one is meant. A design file that lists a column of percentages with no denominator column has exactly the same problem, and nobody notices until a review.
A construction file shows one holding at 4.6 per cent on one line and the same holding at 7.7 per cent two lines later. What has gone wrong?
How is the spreading computed instead of claimed?
Step three produces a number. Step three consumes the policy weights and the holder's own stated assumptions, and it puts three figures into the file: the weighted average volatilityThe result of averaging the sleeve volatilities using the portfolio weights. The weighted average describes the case where the sleeves move in lockstep rather than the case the portfolio is actually in. of the parts, the portfolio's own volatility, and the distance between them.
On the endowment's assumptions of 18.0 per cent for equity, 5.0 per cent for fixed income and 0.5 per cent for cash, with a correlation of 0.20 between the first two and cash taken as uncorrelated, the three figures at weights of 60, 30 and 10 come out as 12.35 per cent, then 11.20 per cent, then 1.15 points. Why those figures rather than an adjective? Because 1.15 points is something a reader can recompute in a year, and the word diversified is something a reader can only agree or disagree with.
Why a correlation below one produces a gap at all is settled under correlation, and rebuilding that argument inside a construction step would spend the file on somebody else's work. The step takes the assumptions, runs the arithmetic, and writes the result down with the assumptions attached so the next reader can see what was assumed.
Step three is done. What goes into the construction file?
How is each constraint tested, and what does a test produce?
Step four runs a constraint testReading one written limit against the portfolio on the base the limit itself names, and recording the outcome as a pass, a fail, or a statement that the limit does not resolve to a number. on every line the mandate contains, one at a time, at the base that line names, and writes down a result. Not an impression. A result, with the figure and the limit both written down.
Run on the Anantara Multi-Asset Portfolio, that is four tests. Equity sits at 60.0 per cent of the portfolio against a band of 50 to 70 per cent: pass, and the recorded line carries both the 60.0 and the band. The largest holding is Rs 23 crore against a cap of Rs 25 crore, being 5 per cent of the portfolio: pass, with Rs 2 crore of headroomThe distance between where a portfolio actually sits and the limit it is being tested against, recorded so that a later reader can see how close the position was.. No unlisted holdings is a yes or a no asked once for each of the twenty eight equity names: pass as recorded. The minimum credit standing is written as a policy rather than as a symbol, so it does not reduce to a number here at all, and the honest entry in the file says so rather than inventing one.
A constraint written against the portfolio is tested against the portfolio, even when the holding it applies to sits inside a sleeve, and a test run on any other base is not a test. Read the same 5 per cent against the Rs 300 crore equity sleeve and the cap becomes Rs 15 crore, the Rs 23 crore holding fails, and the fail is meaningless because the mandate never wrote that limit.
Equity sits at 60.0 per cent with a band of 50 to 70 per cent. What is recorded?
Can the arrangement actually hold what the design asks for?
Step five is the one step that cannot be done anywhere except in the account itself. Everything up to here could be done on paper. Step five asks whether the account and whatever delivers it can carry the design at all, and the question splits into three that have to be answered separately.
Is each holding permitted under the mandate. Can the delivery arrangement actually obtain each holding. And is each position large enough to be worth the work of holding it while small enough to be traded when it needs to move. A design that fails any one of those three is still a design and is not yet a portfolio, however good the arithmetic behind it was.
On the Anantara Multi-Asset Portfolio the size question has a visible answer. The Rs 300 crore equity sleeve sits across twenty eight names. The largest is Rs 23 crore. The ten largest come to Rs 155 crore, so they average Rs 15.50 crore each, and the remaining Rs 145 crore spread across eighteen names averages Rs 8.06 crore. None of those is a rounding error inside a Rs 500 crore account and none of them dominates it. Sizes like those are what an implementableAble to be carried out in the actual account, meaning every position can be permitted, obtained, held at a sensible size and traded when it has to move. sleeve looks like when it is checked rather than assumed.
A design calls for a holding the arrangement delivering the portfolio cannot obtain. What is the result?
What does it cost to move the account to the design?
Step six asks a question construction cannot skip and this record cannot fully answer. Getting from the holdings the account has today to the holdings the design asks for takes trading, and trading has a cost that no return figure anywhere shows.
The step produces a quantity first. The Anantara Multi-Asset Portfolio recorded turnover of 34 per cent for the stated twelve month period, which on Rs 500 crore is about Rs 170 crore of trading. Turnover scales with how much has to change and not at all with how good the design is. An excellent design applied to an account already close to it costs very little to reach, and the same design applied to a very different account costs a great deal.
No dealing cost rate was ever recorded for this account, so the step stops there. Multiplying a real quantity by a made-up rate would produce a figure that looks like money and is not, and that figure would be the most quotable number in the run. So the honest output of step six here is a quantity of trading with a stated absence beside it.
The committee asks what it cost to move the account onto the design. What can step six say?
What has to be written down, and why then?
Step seven is the design fileThe written record produced by construction: the weights with their bases, the computed figures with their assumptions, every constraint result, and the date the whole thing was struck., and it is written now rather than later because later it will be written from memory.
The file holds exactly what the previous six steps produced. The date. Every weight with its base in the same line. The three figures from step three with the assumptions they were computed on. One line per constraint with the figure, the limit and the outcome. The implementation check. The quantity of trading. And step eight's answer: the residue the eight steps leave behind.
A design nobody wrote down cannot be reviewed, and what separates a later result from a later story is a record of what was intended before the result was known. Every household knows this version of it. A household can remember what it meant to spend last month, or it can look at the list actually made. Only one of those two survives an argument.
A year later the committee asks whether the diversification worked. What does the file need to contain for that question to be answerable?
What is still undiversified when all eight steps are done?
Step eight closes the procedure by naming what the previous seven did not remove. Spreading takes away what is particular to individual holdings. Spreading leaves behind whatever those holdings have in common, and the leftover does not get smaller by adding more names.
The stall outside one office gate makes the point faster than any equation. Ten stalls outside ten different gates spread the risk of one office closing. Ten stalls outside the same gate do not, however different their menus are. The gate would take all ten down at once. Residual riskWhat is left over after spreading has removed the part that was particular to individual holdings. Residual risk is the part every holding shares, and adding more of the same kind does not reduce it. is the gate, and construction does not close it.
The Anantara Multi-Asset Portfolio shows the size of that leftover plainly. Inside the stated twelve month period the portfolio fell 9.7 per cent from its highest point to its lowest before recovering. The composite comparison fell 8.1 per cent over its own peak to troughMeasured from the highest point reached inside a stated window down to the lowest point that follows it inside the same window. A different window gives a different figure, so the window is always quoted. path in the same window. Twenty eight equity names were held throughout. A design presented without its leftover has been oversold, so stating the residue is part of what construction delivers rather than an admission that construction failed. A different window would give a different fall, which is why the window is quoted every single time the figure appears.
Construction is finished and every step passed. What is still undiversified?
What does the whole procedure look like run end to end?
The Anantara Multi-Asset Portfolio's equity sleeve runs through all eight steps in order below, using only figures the record already carries. Each row is the output of one step rather than a description of a good portfolio.
| Step | What it consumed | What it produced |
|---|---|---|
| 1. Fix the inputs | The mandate and the agreed weights | Rs 500 crore at 60, 30 and 10, giving Rs 300, Rs 150 and Rs 50 crore, inside four constraints |
| 2. Name every base | Every percentage in the design | The cap is 5 per cent of the portfolio, so Rs 25 crore; the same 5 per cent on the sleeve would be Rs 15 crore |
| 3. Compute the spreading | The weights and the holder's assumptions | 12.35 per cent, then 11.20 per cent, then 1.15 points of difference |
| 4. Test each constraint | The four written limits | Equity 60.0 per cent passes the band; Rs 23 crore passes the Rs 25 crore cap with Rs 2 crore of room; no unlisted holdings passes; the credit standing has no number |
| 5. Check what it can hold | The twenty eight equity names | Largest Rs 23 crore, top ten Rs 155 crore averaging Rs 15.50 crore, the other eighteen averaging Rs 8.06 crore |
| 6. Cost the move | Turnover of 34 per cent for the stated year | About Rs 170 crore of trading, and no rate at which to price it |
| 7. Write it down | Everything above | A dated file with every base, every assumption and every test result on it |
| 8. Name the residue | The stated year's own record | A 9.7 per cent fall peak to trough inside that window against 8.1 per cent for the comparison |
| Eight steps | Nothing reopened | One file a later reader can check line by line |
Two readings of the top ten deserve their own line, and getting them the wrong way round produces a figure that cannot exist. Rs 155 crore is 31.0 per cent of the Rs 500 crore portfolio and 51.7 per cent of the Rs 300 crore equity sleeve. The next review will want both readings and would otherwise recompute them from memory, so both are recorded even though no constraint bites at either one. Ten of twenty eight names can never come to less than 35.71 per cent of the sleeve, so any figure below that floor is arithmetically impossible whatever the file says.
The ten largest equity holdings come to Rs 155 crore. Which pair of readings belongs in the file?
The error that gets made, and what it costs
A construction file records the weights, lists the holdings, and describes the equity sleeve as well diversified across twenty eight names. The file goes to the committee, nobody objects, and it passes review. Everything in it is true.
A year later the portfolio has fallen 9.7 per cent peak to trough inside the stated twelve month period and Rukmini Deshpande asks the only question a chair can ask: what was the diversification supposed to have done? The file has no answer. Nobody wrote down that the weighted average of the parts came to 12.35 per cent, that the portfolio's own figure was 11.20 per cent, or that the whole benefit was 1.15 points on assumptions the endowment itself chose. The file recorded an adjective.
The cost is a review with nothing in it to review. The design never stated what it expected to do, so nobody can say whether it behaved as designed. The meeting becomes a comparison of impressions, and the loudest impression wins. The fix is step three done properly and step seven done at the time: the computation goes into the file with its assumptions attached, and a later reader checks the claim instead of taking it.
Who actually reads a construction file, and what for
An analyst reviewing the mandate from outside runs this procedure backwards. The analyst takes the file, picks the weight that looks largest, and checks whether its base is written beside it. If it is not, everything downstream is unreadable and the review stalls there rather than at the end. Recomputing step three from the stated assumptions takes a few minutes, and the analyst compares that answer with the file's. A mismatch is not automatically a problem, but it is always a question.
A trustee on the endowment's investment committee uses the file differently and asks less of it. The trustee wants the constraint lines: which limits were tested, what the readings were, and how close anything came to an edge. The Rs 2 crore of room under the Rs 25 crore cap says how much price movement it would take before somebody has to act. Lines like that are the ones a trustee remembers.
A household running its own holdings has the same procedure at a smaller scale, and the same two failure points. The bases go unwritten, so the share of one holding gets quoted against savings on Monday and against the equity portion on Friday. And the spreading gets asserted rather than computed, so a year of falling prices arrives with no record of what the spreading was ever expected to do. The size of the account changes none of the eight steps and none of the two things that usually go wrong.
Which questions here are settled outside the room?
Two of the eight steps can run into requirements that no construction procedure sets. Step four tests the limits a mandate wrote for itself, and a particular arrangement may also carry limits written elsewhere on what it may hold, how concentrated it may be, or what has to be disclosed about it. Step five asks what the delivery arrangement can obtain, and eligibility to hold a given instrument can be settled by rule rather than by preference. The current text is published by the Securities and Exchange Board of India at sebi.gov.in, and by the Pension Fund Regulatory and Development Authority at pfrda.org.in where a retirement mandate is in view. Index construction rules and trading arrangements are published by the exchanges at nseindia.com and bseindia.com. A limit read from memory does not go stale when it moves; it simply becomes wrong. The published text governs, and not the copy sitting in a construction file.
References
| Source | What it is named for | Where |
|---|---|---|
| Securities and Exchange Board of India | Publisher of requirements on what an arrangement may hold and what must be disclosed. | sebi.gov.in |
| Pension Fund Regulatory and Development Authority | Publisher of requirements applying where a retirement mandate is in view. | pfrda.org.in |
| National Stock Exchange of India | Publisher of index construction rules and trading arrangements. | nseindia.com |
| Bombay Stock Exchange (BSE) | Publisher of index construction rules and trading arrangements. | bseindia.com |
The Anantara Multi-Asset Portfolio, Rukmini Deshpande and Faiz Ahmad Ansari are invented.
Educational material. Not advice on any investment, tax, budget or market position.