The Investment Objective: Return and Risk Together

Either half alone can be satisfied trivially, so an investment objective states a return and a risk together. The return half names what the portfolio must earn, over what period, and against what benchmark. The risk half names how much variation the holder will accept while it tries. Stated apart, the return figure becomes a figure that more market exposure always reaches.

Read the last sentence twice. Most written objectives fail quietly at exactly that point. A committee agrees a number, the number sounds ambitious, everybody signs, and nobody notices that the number can be reached by a route the document never discussed. A year later the number has been met and the room has no way of asking how. The document gave them nothing to ask with.

The running example throughout is the Anantara Multi-Asset Portfolio, an invented discretionary mandate of Rs 500 crore run by Faiz Ahmad Ansari for a charitable endowment whose investment committee is chaired by Rukmini Deshpande. Its policy shape is 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. Every return, variability and ratio below belongs to one stated twelve month period on that mandate. One twelve month window cannot be annualised into a longer record, extended, or laid beside a figure measured over some other window.

The record for the Anantara Multi-Asset Portfolio does not contain the wording the committee actually adopted. The record holds what the mandate permits and what the stated year produced. Missing from it are the return figure Rukmini Deshpande's committee wrote down and the level of variation they agreed to accept. Where the record is silent the field stays empty, marked NOT SUPPLIED, and an objective written out below to demonstrate the arithmetic is a constructed illustration rather than a record of what was agreed.

What is an investment objective, and what makes one usable?

An investment objectiveThe pair of written statements at the top of a policy document saying what the money is trying to earn and how much variation the holder will accept while it tries. is not one sentence. An objective is two sentences that have to be read together, and its whole usefulness comes from their disagreement. One pushes towards more. The other pushes towards steadier. A manager works in the space where both are satisfied at once, and that space is narrower than either sentence on its own would suggest.

There is a simple test for whether a committee has written an objective at all, and it takes about four seconds. Ask whether satisfying the first half makes satisfying the second half harder. If one easy action satisfies both halves, nothing about the pair can ever be failed, and what has been written is a description of intent rather than an objective. Hold everything in cash for a year and a risk sentence of "large swings are not acceptable" is satisfied perfectly. If the return sentence is also satisfied by that, the pair governs nothing.

The same test runs outside finance. Suppose a household says it wants to spend less and eat better. Spending less and eating better pull against each other, and every week the household discovers exactly where. Now suppose it says it wants to spend less and cook at home more. Spending less and cooking at home do not pull; one action satisfies both, so the sentence records a mood rather than a standard. The finance version behaves identically, only with more decimal places attached.

Run the test on the household sentences and the difference is immediate. One pair produces a decision every week. The other produces a feeling and never a decision. A single action clears both halves at once, and nothing is ever left to weigh.

What is a Return Objective, and what are its three parts?

A return objectiveThe half of the objective naming what the portfolio is trying to earn, over a stated window, measured against a stated comparison. has three parts, and it drops out of use the moment any one of them goes missing. The figure. The period the figure applies to. And the benchmarkThe comparison a portfolio's result is read against. Here it is an unnamed composite of 60 per cent a broad equity index and 40 per cent a broad bond index. it is read against. A figure with no period attached is not a rate at all, and a rate with no benchmark beside it cannot be assessed against anything, so a return objective missing either part cannot be checked even in principle.

Take the parts one at a time. Each one fails differently. "Earn 12 per cent" is a number, not a rate: twelve per cent over what, a quarter, a year, a decade? Adding the period produces a rate. Whether earning that rate was an achievement still cannot be said, and nothing yet sits beside it to read it against. Adding the benchmark makes the sentence checkable by anyone who can read the record. Checkability is the entire point of writing an objective down.

For the Anantara Multi-Asset Portfolio the second and third parts sit in the record. The period is one stated twelve month window and the benchmark is a composite of 60 per cent a broad equity index and 40 per cent a broad bond index, both unnamed here, with index methodology being the publishing exchange's own. The first part, the figure the committee adopted, is not in the record and is therefore left empty.

What is a Risk Objective, and in what unit is it written?

A risk objectiveThe half of the objective naming how much variation the holder is willing to live with, written in a unit the portfolio's own record produces. names how much variation the holder is prepared to live with while the return half is being pursued. The part that decides whether it works is the unit. Nothing in the year end record can be laid beside a risk objective written in feelings, so a sentence like that governs nothing. The only sentence that can be checked is one written in a unit the record already produces.

Three ordinary units do the job, and all three come straight out of a portfolio record. The first is volatilityHow widely a return has moved around its own average over a stated window, in the same units as the return itself., the variability of the return itself. The second is the worst fall inside a stated window, measured from the highest point to the lowest before any recovery. The third is a distance from the benchmark. The distance unit asks not how much the portfolio moved but how far it was allowed to sit away from the comparison.

Two of these have readings in the Anantara Multi-Asset Portfolio's record for the stated twelve months. Variability of the return came in at 11.8 per cent, against 10.4 per cent for the composite benchmark. The worst fall was a drawdownThe largest fall from a high point to a subsequent low point inside a stated window, before any recovery. A different window gives a different figure. of 9.7 per cent from the highest point to the lowest, against 8.1 per cent for the composite. The third unit belongs to the monitoring material and is covered separately, so nothing is done with it here.

Because the levels are not in the record, the useful thing to show is the shape of a sentence that could be checked in each unit, with the level left as an empty field rather than filled in with a figure nobody wrote.

Now the part that trips people, and it is worth a picture. A return of 14.2 per cent and a fall of 9.7 per cent describe the same twelve months and do not contradict each other in the slightest. The return compares the two ends of the window. The drawdown measures the worst distance travelled inside it. A window is not a straight line between its endpoints, so the return and the worst fall are two different measurements of one period and neither can stand in for the other. Change the window and the drawdown changes. The window is therefore quoted every time the figure appears.

A different window gives a different answer, and that is the practical reason the window travels with the figure. Measure the same path from month zero to month six and the worst fall is 122.0 down to 118.0, or 3.28 per cent rather than 9.7 per cent. Same path, same holdings, different question asked.

How Return Objectives and Risk Objectives Work Together, and why does either alone fail?

The two halves work together because they pull against each other, and the pull is the mechanism. Any return figure can be reached by carrying more market exposure, so the risk half is what stops the return half from being trivially satisfiable, and the return half is what stops the risk half from being satisfied by sitting in cash. Remove either one and the pair stops being a constraint and becomes a wish.

Watch the arithmetic when both halves are written in units that touch the same record. Suppose, purely as a constructed illustration, that a return half asked for 14.2 per cent over the stated twelve months and a risk half said the variability of the return may not exceed 11.8 per cent. The composite benchmark returned 12.6 per cent, sitting 6.1 percentage points above the risk-free rateThe return available without taking market exposure, stated here as 6.5 per cent for the same twelve months. Every risk-adjusted figure needs it printed beside it. of 6.5 per cent, and it moved with a variability of 10.4 per cent.

On market exposure alone, the return half needs a betaHow much of the benchmark's movement a portfolio carries. A beta of 1.08 moves about 1.08 times as far as the benchmark, up and down alike. of at least 7.7 divided by 6.1, or 1.2623. The risk half allows a beta of at most 11.8 divided by 10.4, or 1.1346. The two ranges do not overlap. No amount of market exposure satisfies both halves at once. The pair as drafted forces the manager to find return that is not exposure, and forcing exactly that is the job of the pair.

There is an exchange rate hiding in those two lines, and it is worth naming. Each 0.01 of beta buys 0.061 points of return and costs 0.104 points of variability. Dividing 10.4 by 6.1 gives 1.705. Every point of return bought with market exposure costs about 1.70 points of variability, and a document holding only the return half never shows the reader that price.

What could a return figure alone have permitted in the stated year?

The argument for the pair only lands in numbers. Stated as a principle it sounds like ordinary caution. Stated as arithmetic it becomes a fact about what a manager could have done inside a document that would have raised no objection. So take the constructed return half of 14.2 per cent again, and strip the risk half away entirely.

Reaching 14.2 per cent on market exposure alone needs 6.5 plus b times 6.1 to equal 14.2. Solving for b gives 7.7 over 6.1, or 1.2623. Carry that beta against a benchmark whose variability was 10.4 per cent and the portfolio's own variability comes out at 1.2623 times 10.4, or about 13.13 per cent. The Anantara Multi-Asset Portfolio actually ran at 11.8 per cent. The same return figure was therefore reachable by a route carrying about 1.33 percentage points more variability than the mandate actually carried, and a document holding only the return half would not have contained a single word about it.

Two assumptions sit inside that arithmetic and both belong in the main text rather than in a footnote. The comparison assumes no alpha, meaning the second route earns nothing beyond what its exposure delivers. And it assumes every extra point of variability is market variability rather than something else. Neither assumption is a claim about how a portfolio behaves; they are the conditions under which this particular comparison is clean.

The 14.2 per cent came from somewhere, and splitting it is what a risk half makes visible. At the beta the mandate ran, 1.08, market exposure alone accounts for 6.5 plus 1.08 times 6.1, or 13.088 per cent. The portfolio produced 14.2 per cent gross of fees. The leftover of 1.112 points gross is the part that carrying more of the market does not explain, and no return figure standing on its own can tell a committee whether that leftover exists at all. Fees are then taken out of a gross figure to give a net one, and the arithmetic of that is covered separately. Every return quoted above is gross.

What do the risk-adjusted readings say, and what has to be printed beside them?

Once both halves exist, the natural next step is to read them as one number: how much return arrived per unit of variability. Return over volatilityReturn above the risk-free rate divided by the variability of that return. It says how much return arrived for each unit of movement endured. does that. For the Anantara Multi-Asset Portfolio over the stated twelve months the sum is 14.2 less 6.5, or 7.7, divided by 11.8, giving 0.653. For the composite benchmark the sum is 12.6 less 6.5, or 6.1, divided by 10.4, giving 0.587.

Both readings were computed net of a particular risk-free rate, against a particular benchmark, over one particular window. Change any of the three and the number changes without anything about the portfolio changing at all, so neither reading means anything on its own. The 6.5 per cent, the composite and the twelve month window therefore travel with the ratio everywhere it is quoted, including on the axis of a drawing.

Is the mandate's own return assumption an objective?

No, and the distinction is the one people collapse fastest. The Anantara Multi-Asset Portfolio's committee wrote down its own assumptions for the three asset classes: equity at 12.0 per cent, fixed income at 7.5 per cent and cash at 6.0 per cent. At the policy weights of 60, 30 and 10 those give 0.60 times 12.0, plus 0.30 times 7.5, plus 0.10 times 6.0. Adding 7.20, 2.25 and 0.60 gives 10.05 per cent. The 10.05 per cent is what the holder's own assumptions imply, and an implication is a different kind of statement from an instruction to the portfolio.

Now lay that beside what happened. The stated year delivered 14.2 per cent gross against the 10.05 per cent the assumptions implied, and ran a variability of 11.8 per cent against the 11.20 per cent those same assumptions produce for the policy portfolio, a figure derived in the allocation material covered separately along with the weighted average of 12.35 per cent and the 1.15 point difference between the two. One year is one draw, and an assumption was never a forecast, so neither gap is evidence of skill or of error. Saying exactly that is the finding rather than a way of avoiding one.

How Time Horizon Changes Portfolio Construction, and what does it leave alone?

The time horizonThe length of time the money is expected to stay invested before the holder needs it. It is written into the objective rather than left to be inferred. is the third thing the objective carries, and it does something more radical than most treatments admit. A horizon does not change what a return is, and it does not change how variability is computed. A figure measured over a window longer than the holder's horizon is irrelevant to that holder rather than merely uncertain, so the horizon decides which figures on a record matter at all.

The distinction between uncertain and irrelevant is worth slowing down on. Uncertain means the measurement is the right one and its value is not certain. Irrelevant means the measurement is the wrong one entirely. A holder who needs the money in eleven months will never experience a nine year window, so a nine year average tells that holder almost nothing useful. The holder will experience eleven months, and eleven month windows behave differently from nine year ones even when the underlying holdings are identical.

None of this depends on who the holder is. The Anantara Multi-Asset Portfolio is run for a charitable endowment, and an endowment usually carries a long horizon because the purpose it funds does not end. A private holder saving towards one event runs exactly the same arithmetic with a different number in it, and nothing in the mechanism changes when the holder changes, only the horizon itself does. A household saving for a wedding eighteen months away and an endowment funding scholarships indefinitely are doing identical mathematics with different windows.

Why does a longer horizon narrow the average and widen the total at once?

Here is the part almost every treatment gets exactly half right. Lengthen the horizon and the variability of the average annual return falls. Lengthen the same horizon and the variability of the total outcome rises. Both statements are true, both follow from the same single figure, and quoting only the first is the commonest way a long horizon gets presented as safety. One assumption underpins both: the years are independent of each other. Real years are not, so the arithmetic below illustrates a relationship rather than projecting anything.

Start from the 11.8 per cent the Anantara Multi-Asset Portfolio recorded over its one stated twelve month period. Over four such years the variability of the average annual return is 11.8 divided by the square root of four, that is 11.8 divided by two, giving 5.90 per cent. Over nine years it is 11.8 divided by three, giving 3.93 per cent. The average really does settle. Now the other column: over four years the variability of the cumulative outcome is 11.8 times two, giving 23.6 per cent, and over nine years 11.8 times three, giving 35.4 per cent. On a Rs 500 crore starting value that last figure is Rs 177 crore of the value the holder began with.

Say what the right hand column means in money, because percentages hide it. On a Rs 500 crore starting value, the one year figure is about Rs 59 crore of movement in the cumulative outcome, the four year figure about Rs 118 crore and the nine year figure about Rs 177 crore. The holder who was told that a longer horizon makes things safer was told about the left hand column and never shown the right hand one, and the right hand one is the column their actual money sits in.

How does a committee actually use the pair on a Tuesday?

Three questions, asked in order, before anybody opens the holdings list. Three answerable questions are what the pair buys a room, and they are the practical reason the two halves are written adjacent rather than in different sections of the document. An investment committee like Rukmini Deshpande's works down the list and each question has one figure that answers it.

Was the return figure met, over the window it was written for? Answering that is a comparison, not a judgement, and it takes ten seconds. How was it met? Answering the second question needs the return split at the beta actually carried. For the Anantara Multi-Asset Portfolio's stated year that means reading 13.088 per cent of exposure against 14.2 per cent gross delivered. Did the variation stay inside what was accepted? Answering the third needs the year's variability of 11.8 per cent and its worst fall of 9.7 per cent laid against the accepted level. Only the first of those three questions can be answered by a document holding a return figure alone. A room working from such a document runs out of questions after ten seconds.

A lender does the same work in a different vocabulary when it looks at a borrower: not just whether the borrower earned enough this year, but how much of that earning came from taking on more of whatever the borrower was already exposed to. A household running one salary and a rising share of savings in one employer's own stock is asking the identical question without the notation. Did the position improve, or was it simply more of the same bet?

What does the investment objective not decide?

An investment objective does not decide the allocation. The objective does not decide the holdings, and it does not decide who runs the money or through what arrangement. The objective constrains the answer without containing it, and a document whose objective already implies one allocation has written the allocation and labelled it an objective. The failure is real, and it is quiet. The document looks complete.

See it on the Anantara Multi-Asset Portfolio's own numbers. The mandate permits equity between 50 and 70 per cent. On Rs 500 crore that is a corridor from Rs 250 crore to Rs 350 crore. The policy weight of 60.0 per cent sits at Rs 300 crore, inside that corridor. The objective and the constraints between them narrowed a Rs 500 crore decision down to a Rs 100 crore corridor, and then a separate decision put the number at Rs 300 crore. Two decisions, taken by different means, and confusing them is how a committee ends up thinking it never chose the allocation at all.