Strategic Asset Allocation: The Long-Term Policy Mix

Strategic asset allocation is the long term policy mix a holder commits to before any market view is formed. The Anantara Multi-Asset Portfolio's policy mix of 60 per cent equity, 30 per cent fixed income and 10 per cent cash falls out of the holder's own stated return and volatility assumptions, and it produces an expected return of 10.05 per cent at a volatility of 11.20 per cent.

One word in the answer above does all the work, and the word is falls. Nobody picked 60, 30 and 10 off a shelf. The three numbers are the output of a short calculation run on a set of assumptions somebody wrote down and signed. Change the assumptions and the arithmetic hands back a different mix. So the honest way to read any policy mix is backwards: not "why did they choose this", but "what did they have to believe for this to come out".

The Anantara Multi-Asset Portfolio is an invented discretionary mandateAn arrangement in which the holder hands over the day to day decisions, inside written limits, rather than approving each one. The limits are agreed first and stay fixed. of Rs 500 crore run by Faiz Ahmad Ansari for an invented charitable endowment whose investment committee is chaired by Rukmini Deshpande. Means, variances and correlations are covered separately.

A share of a portfolio is easy to nod along to and a rupee figure is not, so here are the same three lines with the money written out in full rupees.

What is strategic asset allocation, and what is the word strategic doing?

Strategic is doing three jobs at once, and it is worth separating them. First, the mix is fixed in advance and in writing, so there is a document somebody signed and can be shown later. Second, it is fixed for a period measured in years rather than in quarters, so it is not something the next set of numbers is expected to move. Third, and this is the part that gets lost, it is fixed before anybody has a view about what markets are going to do next. The policy mix is settled at the moment the holder knows least, and that is not a flaw in the method, it is the method.

Most households already run something like this. A household that decides at the start of the month what share of the salary goes to rent, to the school fee and to the jar on the shelf has written a policy mix. The household writes the split before the month happens. An expensive week two does not rewrite it. And the reason it works is precisely that it was decided in a calm moment rather than in the middle of the month, when every claim on the money is shouting at once.

The consequence people skip is structural rather than empirical. Every decision taken later sits inside the mix. Choosing what to hold inside the equity sleeve cannot change the fact that 60 per cent of the money is exposed to equity at all. Trading on any given morning cannot change it either. So the mix does not merely contribute to the outcome, it sets the range inside which every later decision moves the result. Nothing decided after the mix can undo what the mix already decided. The least informed decision in the whole sequence is therefore the one with the widest reach.

The same idea draws as a set of frames rather than as a line. The mandate is written first and is the outermost frame. The policy mix is chosen inside it. The holdings inside each class are chosen inside the mix, and the morning's trades are chosen inside the holdings. Each ring is settled before anything inside it is known.

What is a policy mix actually built from?

Three things, and nothing else. The objective and the constraints already written into the mandate. A stated expected returnThe single number a holder writes down as the average yearly return it is assuming for a class. The number is an input to a calculation, not a prediction of any particular year. and a stated volatilityThe standard deviation of a return series, used here as the width of the spread around the average. The spread is symmetric and is not by itself a measure of the chance of loss. for each class. And a stated correlationA number between minus one and one saying how closely two return series move together. Zero means their movements carry no information about each other. between each pair of classes. Take any one of the three away and there is nothing to compute.

The third is the one readers forget, and forgetting it is not a small omission. A weighted average needs nothing but the weights and the class returns. Without the correlations, therefore, the expected return of the mix can still be worked out. The spread of the mix cannot be worked out at all. A combination's spread depends on how its parts move against each other, and that dependence is exactly what a correlation states. A holder who has written down returns and volatilities but no correlations has written down half a calculation and cannot finish it.

Where do the assumptions come from?

The assumptions come from the holder. Somebody sat in a room, argued about it, and wrote numbers on a sheet. For the Anantara Multi-Asset Portfolio that sheet says equity 12.0 per cent expected return at 18.0 per cent volatility, fixed income 7.5 per cent at 5.0 per cent, cash 6.0 per cent at 0.5 per cent, a correlation of 0.20 between equity and fixed income, and cash taken as uncorrelated with either. Rukmini Deshpande's committee chose and signed every one of those numbers, and a chosen number is not a forecast, not a market expectation and not anybody's published estimate.

There is no source anywhere from which a true expected return for a class can be drawn. Choices exist instead, each defensible, each arguable, and each producing a different portfolio when the arithmetic is run. The claim that a mix falls out of the assumptions therefore carries a warning inside it: a mix is only as settled as the numbers it fell out of.

So the right question to ask of any policy mix is not whether 60 per cent equity is right. Nobody can answer that one. The question is what return and what spread were assumed for each class, and what was assumed about how the classes move together. If those three answers are not written down, the mix was not computed. The mix was preferred.

How Strategic Asset Allocation Works

Run as a sequence rather than described, the whole thing is six steps. State the objective and the constraints. Choose the classes that will be held. State the assumptions. Compute what each candidate mix produces. Check the winner against the constraints. Write it down. The output of all six steps is a document, and at the end of it nothing whatsoever has been bought.

Most descriptions of allocation slide quietly past that last point into something else. A signed policy mix names classes, weights and a horizonThe length of time a decision is meant to hold for before it is reopened. A policy mix carries a horizon measured in years, and that horizon is what stops the next quarter from reopening the mix.. The document does not name a security, a counterparty or a morning on which anything is to be done. Every one of those questions is still open when the ink dries, and each is answered by a different decision.

What return does the policy mix produce?

The expected return is the easy half. The expected return of a combination is the weighted average of the expected returns of its parts and nothing else. The line runs: 0.60 times 12.0 is 7.20, 0.30 times 7.5 is 2.25, and 0.10 times 6.0 is 0.60. Adding them gives 10.05 per cent. Averaging does not care how the parts move against each other, so no correlation appears anywhere in that line.

Which has a consequence that works without a calculator. Because the calculation is exactly linear in the weights, moving ten points from fixed income into equity always adds the same amount, whatever the starting mix. The assumed gap between the two classes is 12.0 less 7.5, or 4.5 points. A tenth of 4.5 points is 0.45. Move ten points from fixed income to equity at any starting mix and the assumed expected return rises by 0.45 points, every single time.

Why is the volatility the harder half?

Because it is not a weighted average, and there is no way to make it one. The varianceThe square of the volatility. Variance adds up neatly across the parts of a combination. The arithmetic is therefore done in variance and the answer converted back at the end. of the mix is built from four terms: one for each class on its own, plus one cross term for the pair that is assumed to move together at all. Written out with the Anantara numbers it is 0.36 times 324, plus 0.09 times 25, plus 0.01 times 0.25, plus twice 0.18 times 90 times 0.20.

Work the four: 116.64, then 2.25, then 0.0025, then 6.48. The four sum to a variance of 125.3725, and the square root of 125.3725 is 11.20 per cent. Notice what the first three terms are. Each one is a class squared against itself, and each would be sitting there unchanged if all three classes were secretly the same thing wearing different labels. Only the fourth term carries a correlation, so only the fourth term knows that equity and fixed income are different things, and everything the word diversification means lives inside it.

The two halves of the calculation therefore behave completely differently as the equity weight moves, and it is worth seeing them side by side. On the left, expected return walks up in equal steps because averaging is linear. On the right, volatility curves, gently at first and then steeply. The squared term on the largest and most volatile class grows faster than the weight does.

The diversification, computed rather than asserted

The three assumed volatilities, averaged at the same weights: 0.60 times 18.0 is 10.80, 0.30 times 5.0 is 1.50, 0.10 times 0.5 is 0.05, and those add to 12.35 per cent. The 12.35 per cent is not a made up reference point. When things move in lockstep their spreads simply add up in proportion, so 12.35 per cent is exactly what the portfolio would carry if every part moved with every other. The Anantara Multi-Asset Portfolio comes out at 11.20 per cent instead.

The 1.15 point difference between 12.35 and 11.20 is the diversification, and it is not a description of the portfolio, it is a subtraction anybody can check. This is the argument Harry Markowitz set out in Portfolio Selection in 1952: what a combination does is governed by how its parts covary, so spreading across things that do not move together is a different act from simply holding more things. The diversification benefitThe amount by which a combination's volatility falls below the weighted average of its parts' volatilities. The benefit is a difference between two computed numbers, not a property that can be seen by looking. exists here only because the correlation was assumed at 0.20 rather than 1.00.

Push the assumed correlation from 0.20 to 1.00 and the volatility rises from 11.20 to 12.30 per cent. So 1.10 of the 1.15 points came from that one number, and the remaining 0.05 points is the small effect of holding cash that is assumed to be uncorrelated with anything. The entire diversification of this three class portfolio rests on one number a committee wrote down, and no part of that number was observed.

So move the number and watch. Below, one control slides the assumed correlation between equity and fixed income from 0.00 to 1.00, holding the weights at 60, 30 and 10, the volatilities at 18.0, 5.0 and 0.5, and cash uncorrelated throughout. The bar is the portfolio volatility. The dashed rule above it is the 12.35 per cent weighted average, fixed. The shaded strip between them is the diversification, and watching it close is more useful than reading any number in a box. At the default of 0.20 the bar stands at 11.20 per cent and the strip is 1.15 points deep.

What is the difference between a policy weight and an actual weight?

The 60, 30 and 10 are the weights the document commits to. The three numbers are a decision. The weights the portfolio is actually carrying on any particular morning are something else entirely: they are whatever prices left behind overnight. If equity rose and fixed income did not, the equity share is above 60 this morning and nobody chose that. A policy weightThe share of a portfolio the holder has decided each class should carry. A policy weight is written down in advance and stays put until the document is reopened. is a commitment and an actual weightThe share each class happens to occupy on a given day, worked out from what the holdings are currently worth. An actual weight moves whenever prices move, with or without any trading. is an observation, and confusing the two is the most common mistake in this whole area.

Every household knows this one too. A household decides that a fifth of the salary goes to the savings jar. Then the electricity bill arrives larger than usual, and at the end of the month the jar holds a seventh rather than a fifth. Nobody changed the plan. The plan is still a fifth. The world changed instead, and the gap between the plan and the month is exactly the gap between a policy weight and an actual weight. Trading back towards the plan is rebalancingTrading back towards the written weights after prices have moved them. How and when it is done is a separate decision with its own rules, and it is not settled by the policy mix., and rebalancing is a separate decision with its own arithmetic, covered separately.

Does the mix sit inside the mandate the holder wrote?

The mix has to, and checking is step five for a reason. The Anantara mandate states equity between 50 and 70 per cent. The chosen mix carries 60, and 60 sits inside the band with ten points of room on each side, so the mix is admissible. But notice that admissible is not the same as determined: the mandate bandA stated range a weight must stay inside, written into the governing document. A band rules positions out. A band does not choose the one that is taken. ruled out everything below 50 and above 70 and left every point in between, so where inside the band the mix sits was itself a decision somebody took.

The gap between the designed portfolio and one realised year

The mix was built to produce 10.05 per cent at a volatility of 11.20 per cent. Over one stated twelve month period the Anantara Multi-Asset Portfolio returned 14.2 per cent at a realised volatility of 11.8 per cent. Two gaps, then: 4.15 points of return and 0.60 points of spread. The temptation is to read the first as skill and the second as a small modelling error, and both readings are wrong for the same reason.

The arithmetic comes before the opinion. The assumption said the yearly outcome would be spread around 10.05 with a standard deviation of 11.20 points. The year came in 4.15 points above the centre. Dividing 4.15 by 11.20 gives 0.37. A single year landing four tenths of one standard deviation from the assumed centre is the least surprising thing that could possibly have happened, and calling it evidence of anything is calling the middle of a distribution a signal.

The volatility gap is smaller still once it is put in proportion. Realised 11.8 against an assumed 11.20 is 0.60 points, or about 5.4 per cent above the assumption. A volatility estimated from twelve months of data is a loose estimate under any of the usual approximations, and how loose it is falls under the statistics of return series. Neither gap is evidence of skill and neither is evidence of error, and saying so precisely is the finding rather than a hedge.

What does the policy mix commit the holder to?

Three things, and it is a short list. The classes that will be held. The weight each class carries. The horizon the whole arrangement is meant to hold for. The commitment contains nothing else.

The list of what the mix leaves open is longer. The mix names no security. The mix names nobody who will hold or administer the money. The mix says nothing about what is bought on any given morning, or when anything is traded, or through what arrangement the holdings are carried. The separation is exactly why the mix can be written and signed while every one of those questions is still open, and the separation is what makes the sequence work in the order it does.

How a committee actually uses the document through the year

Rukmini Deshpande's committee meets through the year and the policy mix is on the table at every meeting, but what it is being used for is not what most people assume. The mix is not a target the last quarter is measured against. The mix is the written answer to a question that only gets reopened when the question itself changes: what does this endowment need the money to do, over what period, inside what limits.

So the useful meeting asks whether anything about the holder has changed. Has the spending the endowment must fund moved. Has the horizon shortened. Have the constraints in the mandate been rewritten. Have the assumptions themselves come to look indefensible for reasons that are not simply last year's numbers. A question about the holder can reopen the mix, and a question about last year's return, on its own, cannot. An analyst reading somebody else's policy mix from the outside runs the same test in reverse: find the assumption sheet, check the arithmetic reproduces the stated mix, and treat any mix whose assumptions are not written down as a preference rather than a calculation.