How to Measure Portfolio Performance, In Order

Measuring portfolio performance runs in a fixed order: fix the window and the frequency, fix the return basis, name the benchmark, compute the excess, compute the risk figures on that same window, set return against risk, split the excess and say which split, measure the path separately, then write down what could not be computed at all.

An analyst is handed a portfolio return, a benchmark return and a short list of risk figures, and asked how the year went. Every instinct says to start subtracting. The instinct to subtract is worth resisting for a moment. The order in which those numbers are touched decides whether the answer produced can be checked by anyone else.

Think about how a shopkeeper answers the same question. Ask a stall owner on a busy street whether business is good and the first honest thing they say is not a number, it is a period: better than last Diwali, worse than last month. The period comes first because without it the number means nothing, and there is no way to add the period back afterwards. Performance measurement runs in a fixed order for the same reason, and every step in that order exists because a later step needs something only it can supply.

The sequence below has nine steps, each one action with a stated output. The nine steps are run end to end on the Anantara Multi-Asset Portfolio, an invented Rs 500 crore multi-asset mandate held by an invented charitable endowment, whose stated twelve month record supplies every figure in this guide. The mechanism inside each step is covered separately elsewhere in this sequence, and is pointed at here rather than rebuilt.

What has to be fixed before a single figure is computed?

Step one has no arithmetic in it at all. Two things get written down: the measurement windowThe exact start and end dates that a reported figure covers, written down before the figure is computed., meaning the exact period every figure will cover, and the data frequencyHow often the underlying observations were taken, such as daily, weekly or monthly, which is a separate question from how long the whole period is., meaning how often the observations behind those figures were taken.

The window and the frequency are two different questions, and people collapse them constantly. A twelve month window measured from daily observations and the same twelve month window measured from monthly observations produce different volatilities from the identical portfolio, so a record that states one and not the other has left half the definition out.

Every figure produced after this step belongs to the window and the frequency written down here. Change either one and all of them change. A number computed before the window was agreed cannot be repaired afterwards. It can only be recomputed, which means going back and doing all of it again.

On the Anantara Multi-Asset Portfolio, step one produces one entry and one gap. The record does give the window, one stated twelve month period. The frequency behind the recorded statistics is not stated anywhere, so it is written down as unknown at the very first step rather than quietly assumed to be monthly because monthly is common. Assuming here would be invisible five steps later.

What is the return basis, and why is it the second decision?

Step two fixes the return basisThe stated convention a return figure was built on, covering both whether costs have been taken out and which of the two standard return definitions was used.. Two questions, both answered in writing, both answered before anything is computed.

The first is whether the return is gross of feesA return figure quoted before the manager's fees and the costs of trading have been deducted from it. or net of feesA return figure quoted after the manager's fees and the costs of trading have been deducted from it.. The second is whether it is a time weighted returnThe return convention that removes the effect of when money was paid in or taken out, so that the result reflects the portfolio rather than the holder's timing. or a money weighted returnThe return convention that keeps the effect of when money was paid in or taken out, so that the result reflects the holder's actual experience..

Both of those results are called returns and both are correct. The step gets skipped for exactly that reason. A time weighted return measures the portfolio irrespective of when money arrived and a money weighted return measures what the holder actually experienced given when it arrived, they answer different questions, and a record that does not say which one it is cannot be compared with anything.

The shape is familiar from ordinary life. Two people quote the mileage of the same scooter. One rode it alone on an open road and one rode it two up through traffic. Neither is lying and neither figure is the other, and the only way to use either of them is to state which ride it came from.

On the Anantara portfolio the record does not state the basis either. Whether the 14.2 per cent return for the stated twelve month period is gross or net, and whether it is time weighted or money weighted, is simply not there. The framework marks both as unknown and continues. Recording both as unknown is the honest handling, and it is not the same as stopping. The later steps still produce figures, and those figures carry a stated caveat a reader can see rather than one they have to guess.

How is the benchmark named and checked for usability?

Step three names the comparison and then tests it. Naming is the easy half. The test is four questions asked in order: was it specified in advance of the period, is it investable as stated, is it measurable over the same window, and does it match the constraints the portfolio actually runs under.

The fourth question is the one that usually fails, and failing it is not a reason to abandon the benchmark. Where the comparison fails the fit test, the structural difference is computed here at step three and carried forward as a known offsetA difference in structure between a portfolio and its comparison that is measured and written down in advance, so that later results can be read with it already in view., rather than discovered at the end of the pack as a surprise.

A wedding gives the intuition. One family's catering bill was higher than a cousin's. Before anybody argues about the caterer, somebody writes down that the first family fed four hundred people and the cousin fed two hundred and fifty. The difference in headcount, written first, changes every later sentence in the conversation. Written last, it just sounds like an excuse.

The Anantara portfolio is measured against a composite of 60 per cent a broad equity index and 40 per cent a broad bond index. The composite was specified in advance, it is investable, and it is measurable over the same twelve months. The composite fails the fourth test. The mandate requires the portfolio to hold 10 per cent in cash, and the composite holds none. The equity share matches at 60.0 per cent, so the entire structural difference is that the portfolio carries 10.0 points of cash where the composite carries 10.0 points more fixed income. Recorded at step three, that offset sits in view for the rest of the work.

How is the excess return computed, and what must travel with it?

Step four is the subtraction everyone wanted to do first. The subtraction takes one line: the portfolio return less the benchmark return, on the window fixed at step one, on the basis fixed at step two, against the comparison named at step three. For the Anantara portfolio that is 14.2 per cent less 12.6 per cent, or plus 1.6 percentage points for the stated twelve month period.

The step is not finished when the subtraction is done. The step is finished when three things are attached to the result and stay attached to it everywhere it is printed: the benchmark it was struck against, the window it covers, and the active risk that carried it.

An excess return is quoted with its benchmark, its window and its active risk, and any one of the three missing makes the figure uninterpretable rather than merely thin. Uninterpretable is the right word. A student who says they scored eight marks more has said nothing until three things are known: more than whom, on which paper, out of what.

Which risk figures are computed, and how is it known that they tie?

Step five computes the risk figures on the identical window and then, before any of them is used, checks them against each other. Portfolio volatility, benchmark volatility, beta against the benchmark and tracking error are four numbers, and they carry only three degrees of freedomThe count of values in a set that could genuinely be chosen independently, once the arithmetic relationships between them are taken into account. between them. Fix any three and the fourth is already determined.

So step five contains a reconciliation checkA test that recomputes one figure from the others it must agree with, so that a disagreement is caught rather than carried forward., and the check is the whole point of the step. The tracking error the identity implies is computed from the other three, and confirmed to land on the tracking error measured.

If the implied figure and the measured figure do not land together, one of the four was computed on a different window or a different frequency, and every figure in the pack after that point is wrong. Any shopkeeper who has ever balanced a cash box knows this move: opening balance plus receipts less payments has to equal the closing count, and when it does not, the work stops until the reason is found, rather than the preferred number being written down.

On the Anantara portfolio the four figures for the stated twelve month period are a portfolio volatility of 11.8 per cent, a benchmark volatility of 10.4 per cent, a beta of 1.08 and a tracking error of 3.7 per cent. Run the check: 11.8 squared is 139.24, 10.4 squared is 108.16, and twice 1.08 times 108.16 is 233.6256. Adding the first two and subtracting the third leaves 13.7744, whose square root is 3.71 per cent. The implied 3.71 per cent lands on the measured figure, so the four are one sample and the work can proceed. The same three figures also give a correlation of 0.9519 with the benchmark, whose square says that 90.6 per cent of the portfolio's variance moved with it.

How is return set against risk without losing either?

Step six puts the return beside the risk that produced it. Setting one against the other is a division, and division is where information goes missing quietly, so the step has a rule attached to it.

A ratio replaces two numbers with one and therefore loses information, so it is reported with its numerator and its denominator printed beside it, along with the risk-free rate and the benchmark that defined them. The scooter shows the shape again: a mileage figure in kilometres per litre is genuinely useful and it has thrown away both the distance and the size of the tank, and nobody can get either of them back out of it.

Two of these figures come with names attached to real people, stated here rather than explained. Return over volatility is associated with William F. Sharpe, return over beta with Jack L. Treynor, and the residual return that step seven produces with Michael C. Jensen. The mechanism of each is covered separately in this sequence.

On the Anantara portfolio the risk-free rate for the stated twelve month period is 6.5 per cent, and the portfolio's return above that rate is 7.7 points. Return over volatility is therefore 7.7 over 11.8, or 0.653. The same computation on the composite benchmark is 6.1 over 10.4, or 0.587. The excess over the benchmark set against the active risk that carried it is 1.6 over 3.7, or 0.43. None of those three can be rebuilt from itself, so every one is printed with its numerator, its denominator, the 6.5 per cent rate and the composite benchmark.

How is the excess split, and how is the split that was run stated?

Step seven takes the excess return apart. Step seven is where this sequence's worst error happens, so it is written as an instruction rather than as a caution: state the question first, then run one split, then keep that split's terms together and never place a term from one split beside a term from another.

More than one honest split of the same excess return exists, none of them is the true one, and running two of them means running two separate steps with two separately stated questions. The mechanism of each split is covered separately in this sequence.

A household electricity bill went up by Rs 1,200/- this month. The rise can be split by room, or it can be split by week. Both splits are honest, both add to Rs 1,200/-, and a sentence that takes the kitchen from the first split and the second week from the second split has produced a number that means nothing at all.

Run question one on the Anantara portfolio. The expected return at a beta of 1.08 is 6.5 plus 1.08 times the benchmark's 6.1 points above the risk-free rate, or 13.088 per cent. The expected return sits 0.488 points above the benchmark's own 12.6 per cent, on the same unstated gross or net basis. About 0.49 points of the excess is simply carrying more market exposure, and the residual is 14.2 less 13.088, which is 1.112, or about 1.11 points. Now stop, state the second question, and run it separately: the recorded split of where the excess came from is an allocation effect of plus 0.35 points and a selection effect of plus 1.25 points. Both pairs total 1.60. Neither pair is the true one, and no term from either pair may be set beside a term from the other.

Why is the path measured separately from the return?

Step eight measures the path. The step states its own window and its own frequency again even though step one already fixed them. A drawdown figure printed without its window is a different kind of nonsense from a return printed without its window.

A return and a volatility describe the distribution of period results. A drawdown describes one realised ordering of those same results. No amount of further work on the first ever produces the second. They are different objects, not different amounts of the same work, which is why the path is a step of its own rather than a fifth entry inside step five.

Two things about last winter. One is the range of temperatures across the season, a spread. The other is the worst cold spell, a run of particular days in a particular order. Knowing the spread perfectly says nothing about how long the cold spell lasted, and a household deciding whether to buy another blanket cares about the second one.

On the Anantara portfolio the worst fall from a high point to a low point inside the same stated twelve months was 9.7 per cent, against 8.1 per cent for the composite benchmark. A peak to trough measurement over a different window gives a different number from the identical portfolio, so both figures carry that window every time they are printed.

What gets written down about what could not be computed?

Step nine writes the closing sheet of the pack, and the closing sheet is a list of what the data could not reach, each entry with its reason. Listing what could not be computed is a step and not an apology, and a measurement pack whose closing sheet is empty is claiming a completeness that almost never exists.

A bank statement with one sheet torn out is still useful. The danger comes from passing it on without mentioning the torn sheet. The next reader adds up what is in front of them and believes the total.

For the Anantara portfolio the list runs to six lines. Whether the return is gross or net is not recorded. Whether it is time weighted or money weighted is not recorded. The data frequency behind the statistics is not recorded. The drawdown dates are absent, so neither the duration of the fall nor the time it took to recover can be computed at all. The average actual weights across the twelve months are absent, so only the policy weights of 60.0, 30.0 and 10.0 per cent are available and those describe the design rather than the year. And no holding level comparison against the composite is possible. The list is longer than most packs would admit to, and its length is a property of the record rather than a fault in the method.

What does the sequence produce when it is run end to end?

Here is the whole thing on one table, in order, on the Anantara Multi-Asset Portfolio for its stated twelve month period. Read the right hand column and notice how many of the rows produce something that is not a number.

Run honestly, the sequence makes both lists grow, the list of what was established and the list of what could not be. Most readers do not expect the second list to grow at all. A pack that ends with a long left column and an empty right one has usually stopped looking rather than finished.