How to Build a Strategic Asset Allocation, Step by Step

Building a long term policy mix runs in seven steps: state the objective and the constraints, choose the classes, state the assumptions and label them, compute what each candidate mix produces, test each candidate against the constraints, measure the diversification actually obtained, and write down in advance how the result will be judged. The last step is the one usually missing.

Everything this procedure uses has already been taught. The assumption set, the expected return and variance arithmetic, the optimiser, the way a constraint bites, the risk contributions and the diversification computation are all covered elsewhere. The order they run in has never been laid out.

So each step below says only what it takes in, what it hands on and what it leaves unresolved, then names where its machinery is covered. A procedure that stops to re-derive a variance has stopped being a procedure.

The procedure is worked once, end to end, on the Anantara Multi-Asset Portfolio, an invented Rs 500 crore mandate for an invented charitable endowment whose committee is chaired by Rukmini Deshpande and whose manager is Faiz Ahmad Ansari. A strategic asset allocationThe long term split of a portfolio across broad classes, set as policy and meant to hold through ordinary market movement. built this way is a document, and by the seventh step nothing has been bought.

Each step also carries an address. Instead of re-deriving, it names the subject where its machinery already sits, and moves on.

Where does the sequence start, and why not with the assumptions?

The sequence starts with the objectiveThe written statement of what the money is being asked to achieve, naming a return and a level of movement in value together. and the constraints, before any number is computed. Some mix always reaches a return named alone, so a return named alone is not an objective. The objective names a return and a risk together, and it settles whether the holder can live inside the mix that reaches the return.

The order matters because assumptions are soft and targets are sticky. Picture a household saving for a wedding three years out. Fix the number first at the expected cost of the wedding, then ask what savings might earn, and the answer has a way of being exactly the rate that closes the gap. Nobody lied; the question was asked in the order that produces one answer.

Fixing a target before the assumptions are written produces assumptions engineered to reach the target, and no arithmetic later can undo that. Step one therefore closes the objective and the constraints before step three writes a single expected return.

The mandate sequence settled the constraintA written limit on what the portfolio may hold or do, as distinct from an objective, which states what it is trying to achieve. lines, not this step. Step one collects them, converts each into the form a later step can test, and writes them at the top of the working paper without arguing with any of them.

A committee suspecting its target is out of reach would naturally say so at the start, but step one may not decide whether the objective can be reached. The answer is arithmetic nobody has done yet, so the procedure forbids the guess. A committee that guesses here tends to quietly soften the objective or the band before step three, and that is the same failure in a different coat.

Here the output is one line naming a long term return and the movement in value the endowment has agreed it can sit through, plus the four constraints above. Everything after this is arithmetic or a test, working on fixed inputs.

How are the classes chosen, and how many is enough?

Step two picks the classes, and three conditions decide, applied in order. Each class has to be driven by something different from the others. Each has to be available to this mandate, and availability rules out anything unlisted before the arithmetic begins. And each has to be something the holder will put an expected return and a volatility against in writing, with their name on it.

The third condition decides the count; no rule says three classes or six or eleven. A class with no stated expected return and no stated volatility cannot enter step four at all, so the number of classes is set by how many the holder will actually put numbers on. A committee that adds a fourth class it cannot describe numerically has added a row the arithmetic will skip, not diversification.

The first condition works the way a shopkeeper thinks about suppliers. A second supplier helps only if it fails on different days from the first, and two suppliers in one street, hit by the same road closure, are one supplier written twice. The test for what counts as different is set out under asset classes and the allocation decision.

How are the assumptions stated, and what must be written beside them?

Step three writes the assumption set down: an expected return and a volatility for each class, and a correlation for each pair. Those numbers are the whole numerical content, and every earlier stage has already used them. Step three adds the label, and the label is not a formality.

Beside the numbers goes the date they were agreed and the words saying whose they are: here, the committee's own assumptions, agreed on a stated date, for the purpose of designing a policy mix. Not a forecast, not a market expectation, not anybody's published estimate.

A set of assumptions with no owner and no date will be read as a forecast by the next person who picks it up, whatever the drafters intended. Two years later the numbers survive in a spreadsheet and the room they were agreed in does not, and a number with nobody's name against it acquires an authority nobody granted it. The label costs one line.

With the label on, the set can be read as a shape: one class carries most of the return and most of the movement, one far less of both, and one is close to still.

How are the candidate portfolios computed?

Step four takes a candidate portfolioA set of weights across the chosen classes, summing to the whole portfolio, proposed but not yet tested against the mandate. and turns it into two numbers, an expected return and a volatility. Describing a mix by that pair rather than by the return alone is Harry Markowitz's idea, set out in his 1952 paper Portfolio Selection.

Step four computes and does not re-derive. A procedure that pauses to rebuild a variance is redoing work an earlier step has already finished. Where the rules for those two numbers come from is the risk and return sequence; how a frontier is drawn out of repeated candidates, and how the optimiser searches among them, is portfolio optimisation; what jittering the assumptions does to the answer is resampled efficiency.

Run it once on the candidate at 60, 30 and 10. The expected return builds as 0.60 times 12.0, plus 0.30 times 7.5, plus 0.10 times 6.0. The three products are 7.20, 2.25 and 0.60, and they sum to 10.05 per cent.

The volatility is the half that cannot be averaged. Four terms, 116.64 for equity, 2.25 for fixed income, 0.0025 for cash and 6.48 for the equity to fixed income cross term, sum to a variance of 125.3725. Cash contributes no cross term because step three took it as uncorrelated.

The square root of 125.3725 is 11.196986, and the document records it as 11.20 per cent. Wherever a subtraction is shown in full below, the longer value is the one subtracted.

Why does the constraint test come after the computation?

Step five asks each computed candidate one question: does it sit inside every constraint written down in step one. Here the binding one is the equity band, and equity at 60 per cent sits inside 50 to 70, so the candidate is admissible at Rs 3,00,00,00,000/- of equity, Rs 1,50,00,00,000/- of fixed income and Rs 50,00,00,000/- of cash.

Now the ordering. Filtering first, by refusing to compute anything outside 50 to 70, is faster, returns the same admissible mixes, and throws away the most useful thing this step produces. A mix that reaches the objective from outside the band is a finding about the objective rather than a dead end, so a candidate that fails the test is informative. Filter first and the failing mix is never computed, so nobody sees how far outside it fell.

Here is that finding made concrete. Suppose the committee had assumed equity at 11.0 per cent rather than 12.0. With cash set aside so every point of the shortfall lands on the equity weight, what split of equity and fixed income reaches the same 10.05 per cent? The gap to close is 2.55 points and each point of equity weight buys 3.5, so 2.55 divided by 3.5 is 0.7285714, or 72.9 per cent equity.

Equity at 72.9 per cent sits outside the ceiling of 70 the mandate wrote down, so the candidate is not admissible and fails step five. At the ceiling of 70 the same probe returns 7.70 plus 2.25, or 9.95 per cent, so the mandate as written cannot reach 10.05 per cent under an 11.0 per cent equity assumption. The objective is short by 0.10 points.

As a step, admissibilityWhether a computed candidate sits inside every constraint the mandate wrote down, tested after the numbers exist. is worth exactly that. It turns a disagreement between the objective and the mandate into a number the committee can act on. Rukmini Deshpande can now ask the endowment whether 9.95 per cent is acceptable or whether the objective should move.

Run the same probe across a range of equity assumptions and the band draws a window: 12.60 per cent needs exactly the floor of 50, and 11.142857 per cent needs exactly the ceiling of 70. The objective of 10.05 per cent is reachable inside this mandate only while the equity return assumption sits between 11.14 and 12.60 per cent, and the committee's own 12.0 sits inside that window at 56.7 per cent equity.

Walk off the far edge too. The failure there looks nothing like the first. At an assumed 13.5 per cent each point of equity weight buys 6.0, so the probe needs 2.55 divided by 6.0, or 42.5 per cent equity. A weight of 42.5 per cent is below the floor of 50, and it fails step five as surely as the 72.9 candidate did.

Look at what the floor forces instead. At 50 per cent equity the probe returns 6.75 plus 3.75, or 10.50 per cent. The floor does not leave the objective short; it overshoots by 0.45 points, and by requiring more equity than the objective needed it pushes the probe volatility from 8.69 per cent up to 9.81 per cent. The ceiling case alone suggests a band constrains ambition; the floor case shows one can equally force 1.12 points more assumed movement in value than the objective asked for.

One line of housekeeping. The probe is not the mix. The Anantara policy mix holds cash at 10 per cent, and the candidate at 60, 30 and 10 is what goes into the document. The probe is a diagnostic on the objective and never a candidate.

How is the diversification actually obtained measured?

Step six is a measurement. Take the weighted average of the class volatilities at the candidate weights, the amount the portfolio would move by if the three classes moved together, and subtract the portfolio volatility from step four. The difference is the diversification obtainedThe number of points by which a portfolio's volatility falls short of the weighted average of its parts., and it goes into the document as a number.

Here the weighted average is 10.80 plus 1.50 plus 0.05, or 12.35 per cent. Against the portfolio volatility of 11.196986 the diversification obtained is 1.153014, and against the recorded 11.20 the document carries 1.15 points.

Step six exists because the word diversified is otherwise applied by inspection, and a portfolio called diversified with no number behind the word has been described rather than measured. Anyone can look at three classes and call the mix diversified. Only the subtraction says how much, and 1.15 points is small enough to be worth knowing.

The 1.15 comes entirely from the correlation assumption written in step three. Had every pair been taken as uncorrelated the volatility would have been 10.90 per cent and the benefit 1.45 points; had every pair been taken as moving together the benefit would have been exactly zero. Why correlation does that to a variance is the risk and return sequence, and this step only reads the number off.

What is written down before any year has happened?

Step seven writes the test: not the result, not a review process, not a promise to monitor, but a written statement put in the same document at the same meeting as step four, recording what would make this mix wrong, over what horizon it is assessed, and what size of gap between the design figureThe expected return the procedure computed for the chosen mix, a property of the assumptions rather than a prediction. and a realised year means nothing at all.

The third is arithmetic the committee has already done. With a design figure of 10.05 per cent and an assumed volatility of 11.20, one standard deviation of ordinary variation runs from minus 1.15 per cent to 21.25 per cent. Step three agreed to that spread, and the spread is very wide.

A realised year 4.15 points away from a design figure of 10.05 per cent is 0.37 of one standard deviation, and 0.37 of one standard deviation is not evidence about anything at all on the assumptions this mandate wrote down. The arithmetic is 4.15 divided by 11.196986, or 0.3706. Write that line in before any year has arrived. The stated twelve month period in the record delivered 14.2 per cent, and that period is the case the line was written for.

Two of those three cannot be computed from what this mandate's record holds, and saying so precisely is part of the step. The record locks an assumed volatility, so the size of an ordinary gap follows. The record locks no distribution, no range around any assumption and no horizon, so how often such a gap should occur, how wrong the 12.0 might be, and over how many years the mix runs all remain undetermined.

The timing, and only the timing, makes this a test written in advanceA statement of what a result would have to look like to count as evidence, agreed before that result exists. rather than a rationalisation. The identical sentence written after 14.2 per cent had arrived would be an excuse. A test written after a result is known is not a test. Step seven therefore belongs in the same meeting as step four.

What has actually been produced when the seventh step is finished?

A document, and nothing else: equity, fixed income and cash at 60, 30 and 10 on Rs 5,00,00,00,000/-, against an assumption set the committee has signed and dated, with 1.15 points of diversification measured and a line saying that a gap of 4.15 points is 0.37 of one standard deviation.

Nothing has been bought, no security has been named, and not one rupee has moved. The procedure produced a design and a way of judging it, and what to hold inside each class belongs to the sequence after this one. How the mix is kept at those weights as prices drift, and what happens when somebody moves away from them for a while, are covered under rebalancing and tactical allocation.

Three steps write things down, three compute, and the seventh commits to how the result will be read, each leaving open exactly what a later step settles.

What must never be a step in this procedure?

Five things get proposed in real design meetings and none is a step. None is barred for being difficult; each is barred because it destroys the evidence a later step depends on.

Choosing the classes after seeing which mix reaches the objective is not a step. Choosing that way runs step two on the output of step four, and the class list that comes back is the one that closes the gap, exactly as the wedding savings rate did.

Widening the band because a candidate did not fit is not a step. The band came from step one, before any arithmetic existed, and a limit that moves whenever a computation is inconvenient has stopped being a limit. Step five produces the 0.10 points instead, and 0.10 points is a question for the endowment rather than a repair to the mandate.

Calling the mix diversified is not a step. Step six is the subtraction, and 1.15 points is all the word is allowed to mean here.

Writing the test after a result has arrived is not a step. A line that could have been shaped by the number it is applied to settles nothing, so the same sentence written late carries none of its value.

And naming a security is not a step, for a different reason: it is not in this procedure at all. Seven steps produce a document, and what to hold inside each class starts from it.