Dynamic Asset Allocation: Rules That Change the Mix

Dynamic asset allocation changes the mix by a rule written in advance, so nothing is decided at the moment the weights move. The rule is keyed to a stated quantity, such as a fall from a peak or a volatility reading, and it acts whenever that quantity crosses a stated level. Where it stops is settled by the mandate rather than by the rule.

A rule can be written to do anything its author can express in arithmetic. The rule can do to a portfolio only what the mandate already permits, and no more.

Dynamic asset allocationChanging the mix by a rule written in advance, keyed to a stated quantity, so the weights move without anybody taking a decision at the moment they move. changes the mix by arithmetic alone. A rule simple enough to check by hand shows the mechanism most plainly, and the arithmetic works the same way whatever the rule.

The running example is the Anantara Multi-Asset Portfolio, an invented Rs 500 crore discretionary mandate run by Faiz Ahmad Ansari for a charitable endowment whose investment committee is chaired by Rukmini Deshpande. Its policy weights are equity 60.0 per cent at Rs 300 crore, fixed income 30.0 per cent at Rs 150 crore and cash 10.0 per cent at Rs 50 crore. The mandate permits equity between 50 and 70 per cent, a corridor from Rs 250 crore to Rs 350 crore. It caps any single holding at 5 per cent, or Rs 25 crore.

Strategic allocation sets the long term policy mix, and tactical allocation deals with a deviation taken on a view inside the permitted band; the contrasts between the two are covered separately. The remaining case is a weight change with no view behind it and no decision behind it either. The band binds a rule exactly as tightly as it binds a person.

What is dynamic asset allocation?

Dynamic asset allocation is a mix that changes by a rule, and the rule was written before the circumstances that make it act. A committee sits down on a quiet morning and writes a sentence of the form: if this measured quantity reaches this level, move this much from this class into that class. The sentence is signed and everybody goes away. Months later the quantity reaches the level and the weights move, with nobody in the room that day forming a view. The trade happens because a sentence written earlier says it does.

When a person takes a position instead, the judgement is formed at the moment of action, in the middle of whatever is going on, with the noise of the day in the room. The information is fresher and the state of mind is worse. The single difference that defines dynamic allocation is that the judgement has been moved from the moment of action to the moment of drafting, where it can be argued about calmly, tested against the mandate, and written down in words somebody else can read.

The everyday version is a household rule about the monthly salary. A household that decides in January that the first Rs 20,000/- of each month goes to the deposit before anything else is spent has done exactly this. The decision is taken once, in January, when nobody is standing in a shop; in July the money moves and no decision is taken in July. The discipline comes from having been thoughtful in January and having written it down, not from being strong in July.

Two things follow. A rule is inspectable: anybody can read it and say in advance what it will do. A judgement nobody has formed yet cannot be read at all. A rule can also be checked against the mandate line by line on the day it is written, while nothing is happening. A person forming a view in a falling market has to remember the constraints instead.

What is the rule keyed to, and why does that decide everything?

Every rule has a trigger quantityThe measured quantity a rule watches, and does nothing about until it crosses a stated level., the thing it watches. Everything a rule feels like in practice, whether it acts early or late, often or rarely, on movement or on level, comes from this one choice. The size of the move it makes is a detail by comparison.

Three kinds of trigger cover most of what gets written. A rule keyed to a drawdownThe fall from the highest point reached to the lowest point that follows, measured inside a stated window. cannot act until a fall has already happened. A fall from a peak is not measurable before then. A rule keyed to a volatility reading acts when dispersion rises. The rise may come before a fall, during one or after one. A rule keyed to a valuation acts on a level rather than a movement, so it can wait years and then act on a quiet day.

Two rules with an identical response size and different triggers are not variations of one rule, they are different rules that happen to move the same amount, and the trigger is where their whole character lives. A committee that spends its meeting arguing about how much to move and accepts the trigger without discussion has argued about the wrong half of the sentence.

A second choice hides inside the first. A trigger quantity is not a fact waiting to be read; it is a measurement, and a measurement needs a stated window, a stated starting point and a stated reading frequency before it produces a number at all. Those three choices are the most common way a rule that looks fully written turns out not to be, and they have a section of their own below.

How does a rule differ from a person taking a position?

In both directions. The usual account is a sales pitch with the costs left out. A rule has three properties a person does not, and the third is a real loss.

A rule cannot hesitate: when the level is crossed the trade happens, so a committee cannot agree in principle and then find reasons to act next month. A rule cannot be talked out of acting, so the most confident voice in the room does not prevail over the written policy. The inability to hesitate and the inability to be argued with are the whole reason anybody writes a rule.

And it cannot notice that the circumstances are unusual. A person reading a screen can see that the fall is being driven by something the rule was never written with in mind, and can say so; a rule reads its quantity, finds the level crossed and acts, as readily on the day it should not as on any other. Blindness to circumstance is a real cost, and the honest case for a rule is not that the cost is absent but that the first two properties are bought deliberately and the third is paid for knowingly.

One more asymmetry. A person who acts badly can be asked to explain, and the explanation improves the next decision. A rule that acts badly explains nothing. The improvement has to come from somebody reopening the document and rewriting the sentence, and that needs an owner and a date. A rule with nobody scheduled to review it keeps doing the same thing long after the room has stopped agreeing with it.

What does the rule do to the portfolio while it acts?

The rule below has a simple shape: reduce the equity weight by one percentage point for every percentage point of portfolio drawdown beyond 5 per cent, put the proceeds into cash, and leave fixed income at 30.0 per cent throughout. The whole rule is that one sentence, written plainly enough that every step it produces can be checked by hand.

Apply it to the record. In the Anantara portfolio's one stated twelve month period the worst fall from its highest point to its lowest was 9.7 per cent, against 8.1 per cent for the composite benchmark over the same window. The rule fires on the excess beyond 5 per cent, an excess of 4.7 points. Equity moves from 60.0 per cent to 55.3 per cent, cash from 10.0 per cent to 14.7 per cent, and fixed income not at all. On Rs 500 crore that leaves Rs 276.50 crore of equity against Rs 300 crore before, with Rs 23.50 crore moved into cash.

The holder's own assumptions, chosen rather than forecast, are these: equity is assumed to return 12.0 per cent with a volatility of 18.0 per cent, fixed income 7.5 per cent with 5.0 per cent, and cash 6.0 per cent with 0.5 per cent, with a correlation of 0.20 between equity and fixed income and cash uncorrelated. A different set gives a different answer at every step below.

At the policy weights the expected return is 0.60 times 12.0 plus 0.30 times 7.5 plus 0.10 times 6.0, or 10.05 per cent, and the volatility from the same assumptions is 11.20 per cent. At 0.553 and 0.300 and 0.147 the same sum gives 6.636 plus 2.250 plus 0.882, or 9.768 per cent, and the volatility becomes 10.36 per cent. So the rule took 0.84 points off the volatility and 0.28 points off the expected return, in one action, from the same trade.

A rule that reduces risk gives up expected return, and the amount can be computed before the rule is ever signed. A description that mentions the volatility coming off and not the return going with it has described half the rule. Neither half is an opinion; each falls out of the holder's own assumptions in one line of arithmetic.

The two do not come off at the same kind of rate. A weighted average of fixed assumptions is a straight line, so every equity point given up costs exactly 0.0600 points of expected return, first point or tenth. Volatility comes off at about 0.178 points per equity point, and that rate drifts as the mix changes.

A reader watching one number move tends to assume everything moved. Fixed income holds Rs 150 crore in every row of that table, and the corridor, the Rs 25 crore single holding cap and the equity names held are all exactly what they were. Only the equity weight and the cash weight move, by equal and opposite amounts.

Where does the rule stop, and who decides that?

A rule reads like a complete instruction, and the appearance is exactly what misleads people. A rule is a proposal that the mandate either can or cannot execute. The Anantara mandate permits equity between 50 and 70 per cent, so the mandate floorThe lowest weight a mandate permits for a class, written into the investment policy. for equity is 50.0 per cent, or Rs 250 crore of the Rs 500 crore. The illustrative rule starts cutting at a drawdown of 5 per cent and cuts one point per point after that, and the arithmetic is 5 plus 10, so it arrives at 50.0 per cent equity when the drawdown reaches 15 per cent.

Past that point the formula keeps producing numbers and the mandate keeps refusing them. At a drawdown of 18 per cent the formula asks for 47.0 per cent equity, or Rs 235 crore. The mandate permits Rs 250 crore, so the instruction is 3.0 points larger than anything anybody is allowed to carry out. The stopping point belongs to the mandate rather than to the rule. A rule drafted without the constraints open beside it is not a conservative rule or an aggressive one, it is an unexecutable one.

In rupees: the corridor runs from Rs 250 crore to Rs 350 crore of equity, and the rule at the stated year's worst drawdown moves Rs 23.50 crore across to leave Rs 276.50 crore. The rule can walk that marker to the left wall and no further. Whatever it says after that is a matter for whoever can change the corridor, and the corridor belongs to the committee rather than to the author of the rule.

Take two readings from that control by hand. At its default of 9.7 per cent, equity is 55.3 per cent and the mix is expected to return 9.77 per cent with a volatility of 10.36 per cent, against the policy point of 10.05 and 11.20. At a drawdown of 15 per cent equity reaches 50.0 per cent, return 9.45 and volatility 9.42, and from there the readings stop changing however far the control is pushed. The flat stretch on the right of that control is the mandate, drawn.

What happens on the way back up?

Whatever the rule says, and this one says nothing at all. The silence is the point. Every rule of this shape needs a restoring conditionThe written half of a rule that says when a reduction is undone and the weight goes back up.: a stated condition under which the reduction is reversed and the weight goes back up. The restoring condition is the element most often left unwritten. The reducing half feels urgent at drafting time, and nobody wants to be the person who wrote down when to buy back.

Leave it out and the arithmetic is unforgiving. A drawdown is a temporary event by construction: a fall from a peak either recovers or the peak is redefined. A reduction with no restoring condition is permanent. So a rule missing that element makes a permanent change to the portfolio on the strength of a temporary event, every time it fires. A permanent change made on a temporary event is a ratchetA mechanism that moves in one direction only and never back., a mechanism that can move one way and not the other, and a rule with no way back walks steadily toward the bottom of the permitted band and stays there.

One episode understates it. Suppose the same kind of episode happens three times, with the peak redefined in between, and the rule is written as a reduction rather than as a level: each time, cut 4.7 points into cash. The equity weight goes 60.0, then 55.3, then 50.6, and on the third occasion the formula asks for 45.9 while the mandate permits 50.0, so only 0.6 of the 4.7 points asked for is traded. Three ordinary looking episodes and the portfolio sits on its floor, with nothing in the document that would move it back up.

The cost is not the first reduction. The cost is the shape of the mandate several years later, with the portfolio at the bottom of a band it was given ten points of room inside and no meeting anybody can point to where that was decided. The restoring condition is written at the same time as the reducing condition, in the same document, or it never gets written at all. A committee that adopts one half in March and thinks about the other in June has adopted a ratchet for three months, and three months is long enough for an episode.

The rule fires on a drawdown, but which drawdown?

A drawdown is not a property of a portfolio the way its total is. A drawdown is a measurement taken from the highest point reached to the lowest point that follows, inside a measurement windowThe stretch of time inside which a peak and a trough are located. that somebody chose. Change the window and both can move, so the same portfolio produces a different number. Every drawdown figure in this record is quoted with its window attached for that reason.

The record gives the portfolio's worst fall as 9.7 per cent within one stated twelve month period, against 8.1 per cent for the composite benchmark in the same window. The two depths are all the record locks. The record carries no price path, no dates for the peak or the trough and no series of any kind. A depth answers how far and never when, so without a path no rule can be said to have fired on a particular day, at any frequency, or with any result.

Had the rule read a one month window instead, the number would have been a different number and this record cannot say what. A rule keyed to a drawdown is keyed to a measurement choice, and that choice decides how often it fires, how deep the fall must be before it acts and how quickly it notices a recovery.

The same discipline applies to any rule anybody proposes against any record. The rule is arithmetic and the policy weights and the mandate limits are all stated, so the weights are computable. The outcome is not, and an outcome would need a path.

What has to be specified before a rule can be run at all?

Seven things, and the list is short enough to check in a meeting. The trigger quantity. The measurement window it is read over. The level at which it fires. The response sizeHow much the rule moves when it fires, stated as a weight, a rupee amount or a formula., or how much moves. The class that funds the move. Every reduction has to go somewhere, and the destination changes the arithmetic. The restoring condition. And the limits the rule has to respect, set by the mandate and not by the rule.

Run the illustrative rule against that list and it fails on two of the seven. The rule never says over what window the fall is measured, and it never says what happens on the way back up. A rule perfectly adequate for showing the arithmetic could not be run by anybody on Monday morning without two decisions being taken that nobody wrote down.

A blank element does not stay blank. The rule fires on a Tuesday, somebody has to decide what window to read, and they decide it on the Tuesday, mid fall, alone, usually without recording that a decision was taken at all. Every blank is a decision moved from the calm room back into the noisy one, exactly the journey the rule was written to prevent.

How does anybody use this in a room, on a Tuesday?

By reading a proposed rule out loud against the seven elements. An investment committee like Rukmini Deshpande's is handed a paragraph by somebody who has thought hard about it, and the first useful contribution in the room is not agreement or disagreement, it is naming which of the seven elements the paragraph actually contains.

Then two arithmetic checks, both of which fit on the back of the agenda. Where does the rule meet the mandate, and at what value of the trigger: here a drawdown of 15 per cent, and knowing it before adoption is different from discovering it during an episode. And what does each step give up on the holder's own assumptions, so the reduction in expected return sits on the paper beside the reduction in volatility rather than being mentioned by nobody.

An analyst reviewing somebody else's mandate does the same reading in reverse. Given a document, find the rules, list their elements and mark the blanks. A rule with a blank in it is not a smaller rule, it is a discretionary arrangement wearing the clothes of a rule, and saying so is the single most useful thing a reviewer can put in a report.

The household version is exact rather than analogous. A household that writes "if the salary is late, stop the monthly investment" has written a trigger, a level and a response, and almost certainly not the restoring condition. The investment stops in the month the salary is late. What starts it again, and when? If nobody wrote that down, the household has a ratchet in its savings plan and will find out in about two years, when it notices that the monthly investment stopped in a difficult March and never resumed.