Capital Market Expectations and Why They Fail Together

A capital market expectation is a forward view somebody records about an asset class: the return assumed over a stated horizon, the spread assumed around it, and the co-movement assumed against every other class. The three assumptions are the whole input set for the allocation methods that follow. The conditions that pull returns below the assumption usually push co-movement above it, so the three degrade together.

Most readers meet the three inputs one at a time and assume that a bad year for one is unrelated to a bad year for another. The arithmetic below shows what that assumption costs on one invented record where every figure is fixed.

The running example is the Anantara Multi-Asset Portfolio, an invented discretionary mandate of Rs 500 crore run by Faiz Ahmad Ansari for an invented charitable endowment whose 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, summing to Rs 500 crore exactly. Every performance figure here belongs to one stated twelve month period and to that record alone.

How a portfolio return and a portfolio volatility are built from weights, volatilities and a correlation is covered under portfolio return and risk. The open question is where those numbers come from and who decided them. The inputs are fixed before the machine that consumes them ever runs, and no machine repairs an input.

What is a capital market expectation, and what is it not?

A capital market expectationA forward view of what an asset class is assumed to return, how widely that return is assumed to move, and how it moves alongside other classes, over one named period ahead. is a forward assumption about a distribution, not about a path, a particular year, or a level reached on a date. Saying an asset class is expected to return 12.0 per cent means writing down the centre of an assumed distribution and, separately, how wide it is assumed to be.

A vegetable seller who has run the same stall for nine years can say what a normal Tuesday takes. She is not predicting Tuesday; she is describing the middle of a spread she has learned, and how far a bad Tuesday falls below it. Asked about next Tuesday, she gives the middle and the spread and refuses the rest.

Three things an expectation is not, each confused with it constantly. A path is a sequence of dated points, so an expectation is not a forecast of a path. A year is one draw and a distribution says nothing about which draw arrives, so an expectation is not a prediction of a single year. And it is not a promise of any kind.

Take the equity assumption the record carries: a return of 12.0 per cent with a volatility of 18.0 per cent. The assumption is a spread centred at 12.0. The band of one standard deviation runs from 12.0 less 18.0, or minus 6.0 per cent, up to 12.0 plus 18.0, or 30.0 per cent.

Every one of those numbers is stated over a horizonThe length of the period ahead an assumption is stated over. One year and ten years are different questions, and a number answering one does not answer the other.. The horizon is part of the definition rather than a caption on it, so a figure with no horizon attached is not a weak expectation, it is not an expectation at all. A return of 12.0 per cent assumed for the coming year and the same figure assumed as a decade average are different claims spelled with the same digits.

The invented record carries an equity assumption of 12.0 per cent, a fixed income assumption of 7.5 per cent and a cash assumption of 6.0 per cent, and no horizon for any of them. The committee holds three numbers and a missing field, and the missing field stays missing.

Every assumption belongs to somebody. The three figures are what the endowment's investment committee recorded, and a committee's record of what it will plan on is not a forecast of a market.

What is an expected return, and over what horizon is it stated?

An expected returnThe centre of the spread an asset class is assumed to produce over a stated period ahead, not the outcome of any particular year. is the centre of the assumed distribution over the stated horizon. The definition is that short. Setting the number is the hard part, and nobody else settles it.

The expected return is the least reliable of the three inputs and simultaneously the one every later method leans on hardest. A centre estimated from history is a mean, and a mean of a noisy series is itself noisy. A household budget shows it. The average monthly grocery bill over three months says almost nothing. The range those months sat inside says a great deal.

The work on the optimiser puts a number on how far its answer moves when a return assumption moves a little. The sensitivity belongs with the optimiser, and where an assumption came from belongs with the assumption.

The record carries three expected returns, one for each class, and the policy weights are given. Equity is 0.60 times 12.0, or 7.20. Fixed income is 0.30 times 7.5, or 2.25. Cash is 0.10 times 6.0, or 0.60. The three sum to 10.05 per cent. The answer is a weighted average and nothing more. The return side of an allocation is the easy side for exactly that reason.

A weighted average of returns is exact. The average needs no correlation and does not change if every relationship in the set is rewritten. The volatility side behaves completely differently, and treating the two as symmetric is how a reader goes wrong on the risk arithmetic.

What is an expected volatility, and what can it not say?

An expected volatilityThe assumed width of the spread around the expected return, over the same stated horizon. Volatility says how far from the centre a year lands, not in which direction. is the assumed width of that same distribution over that same horizon. The interesting part is what an expected volatility refuses to answer.

The width of a spread moves more slowly and more visibly than its centre, so expected volatility is the most stable of the three inputs and the one history supports best. The comparison is about relative difficulty, not a claim that anybody gets it right. Expected volatility is the input a committee argues about least.

The deviations are squared before they are averaged, so volatility is symmetric. A rise of 6.0 points above the centre and a fall of 6.0 points below it both enter as 36.00 and count as identical events. So an expected volatility cannot say how much might be lost. Loss is taken up separately, with a measure built for it.

What is an expected correlation, and why is it the hardest of the three?

An expected correlationThe assumed extent to which two asset classes move together over the stated horizon, on a scale where 1.00 means in step and 0.00 means no relation. is the assumed co-movement of each pair over the horizon. Nothing elsewhere settles why this input is the one that quietly breaks.

Expected correlation is the hardest of the three because the pairs multiply far faster than the classes do, and because correlation is the least stable of the three across changing conditions. Take the counting first. Three classes need three returns, three volatilities and three pairwise correlations, for nine numbers. Eight classes need eight and eight, but twenty eight correlations, for forty four. Twelve need twelve and twelve, and sixty six correlations, for ninety.

Three friends sharing a flat have three relationships to keep straight. Twelve people in a wedding party have sixty six. The seating chart takes longer than the guest list did for that reason. Nobody is surprised by that at a wedding, and everybody is surprised by it in an expectation set.

The record has the same problem one level down. Since 28 times 27, halved, is 378, the equity sleeve of 28 names carries 378 pairwise relationships. Nobody writes 378 correlations down, so relationships between holdings get handled by assumption rather than by estimate.

Three classes make three pairs, so the record's own correlation set is three numbers: equity against fixed income at 0.20, and cash taken as uncorrelated with both, at 0.00 twice.

The second reason is the instability, and it accounts for most of what follows. A return or a volatility assumption is wrong by degrees. A correlation assumption can be roughly right for years and then, in the conditions where it matters most, be wrong by a margin that changes the answer rather than nudging it.

How to build capital market expectations: which three routes are there?

Three routes, and a set almost always uses more than one. Each produces a number by a different path, and the path has to travel with the number. A figure that arrives without its route cannot be argued with, improved or checked.

The first route is adjusted history: take what was observed over a long period, then adjust it for what is known to have changed since. The adjustment is the whole of the work. A shopkeeper does it untaught, starting from last year's festival week takings and adjusting because a second shop opened across the road.

The second route is the building block methodAssembling an expected return from its stated components, so that each part can be argued with on its own.: a return is assembled from named components rather than observed whole in a single figure. The point is not accuracy but argument: a committee can say which component it doubts instead of saying only that the total feels high.

The third route is open judgement: somebody states a view, says it is a judgement, and says what it rests on. Open judgement is honest and reviewable. The dangerous version is a judgement dressed as an estimate, with two decimal places and no route. The decimals do the persuading the reasoning could not.

An expectation with no falsifying conditionA stated circumstance that, if it came about, would show an assumption to have been wrong. attached is a preference wearing a number, so whichever route is used, the set must record its horizon, its inputs and what would falsify it. A preference is fine to hold, but it should be labelled, because one mistaken for an estimate stops being examined.

Watch this against the record. The committee's equity assumption is 12.0 per cent. Had it come from the building block route, the record would carry the components that add to it, each one arguable separately. The record carries the total and nothing else.

Why correlation matters in portfolio construction: where does the relationship enter?

In exactly one place. The return of a combination is a weighted average of the returns, with no relationship between the holdings in it. The variance is not a weighted average of anything: it carries a squared term for each holding plus a cross term for each pair, and the covarianceThe paired term in a portfolio variance that carries how two holdings move alongside each other. The covariance is the correlation multiplied by both volatilities. is the only place a relationship can enter.

At the policy weights the variance is the equity term of 116.6400, plus the cross term of 6.4800, plus the fixed income term of 2.2500, plus the cash term of 0.0025, for a total of 125.3725, and the square root of that total is 11.20 per cent. The cash term is real rather than missing, and far too small to draw at any honest scale.

Harry Markowitz set this out in Portfolio Selection in 1952: the case for spreading a portfolio rests on the covariance between holdings rather than on their number. A set of holdings can therefore be long and still behave like one position.

Here is what the cross term is worth. The weighted average of the three volatilities is 0.60 times 18.0, plus 0.30 times 5.0, plus 0.10 times 0.5, giving 10.80 plus 1.50 plus 0.05, or 12.35 per cent. The weighted average is what the volatility would be if the three parts moved together perfectly. Computed with the correlations it is 11.20 per cent. The 1.15 point difference is the spreading benefit itself, and it exists only because the equity to fixed income correlation is assumed at 0.20 rather than 1.00.

Correlation, not the count of holdings, is what decides whether combining anything helps at all. Put twenty eight holdings together and assume they move in step, and the combination has the volatility of one of them. Put four together and assume no relationship, and the combination has half.

How capital market expectations inform asset allocation: what exactly gets passed on?

The complete input set, and nothing else. Every method that follows takes the same three kinds of number and produces a shape from them. The nine numbers are produced once and consumed many times, so an error in any one of them reappears in every method downstream.

Two numbers come out the other side, and both fall out of the nine rather than being chosen. At the policy weights the expected return is 10.05 per cent and the expected volatility is 11.20 per cent.

Now a distinction the invented record forces. Its stated figures for equity, fixed income and cash are what the committee chaired by Rukmini Deshpande decided to plan on. An expectation is a forward view of what a market is assumed to do. The holder's set is a record of what one committee chose to assume. The two answer different questions even when they carry identical digits, and the committee's three figures are therefore not capital market expectations.

Only one of the two can be found wrong later. A forward view has something outside itself to be checked against, provided its horizon and its falsifying condition were recorded. A decision to plan on a number can be judged prudent or imprudent, but no measurement contradicts it.

The record's three figures are not a forward view of anything, so the arithmetic below works from realised figures instead.

What does one correlation assumption do to a blend?

Every figure here is either locked in the invented record or computed from figures that are. The two things combined are the Anantara Multi-Asset Portfolio and its composite benchmark, an unnamed blend of a broad equity index and a broad bond index. Over the stated twelve month period the portfolio returned 14.2 per cent with a volatility of 11.8 per cent, the benchmark 12.6 per cent with a volatility of 10.4 per cent, and the portfolio's beta was 1.08.

The four figures above are realised for one stated year and are not expectations. The effect of a correlation can be shown without pretending to know one. Beta is the covariance divided by the benchmark's variance. The correlation is therefore the beta times the benchmark volatility divided by the portfolio volatility: 1.08 times 10.4, or 11.232, divided by 11.8, giving 0.9519. Three locked figures determine the fourth, so the correlation here is derived rather than assumed.

The same lock works in the other direction. The tracking error is the square root of 11.8 squared plus 10.4 squared less twice 1.08 times 10.4 squared: 139.24 plus 108.16 less 233.6256, or 13.7744, and the square root of 13.7744 is 3.7114 per cent. Any three of these four fix the fourth, so a set of four that does not reconcile is not four opinions, it is one arithmetic error.

Combining the two half and half, the return of the blend is 0.50 times 14.2 plus 0.50 times 12.6, or 13.4 per cent exactly, and the return stays 13.4 per cent at every possible correlation. The volatility is where everything happens: at the derived 0.9519 the blend's volatility is 10.97 per cent against a weighted average of 11.10 per cent.

Rerun the identical blend with a correlation assumption of 0.50 and the volatility is 9.62 per cent. The gap is 1.35 percentage points of volatility on identical returns, identical volatilities and identical weights, produced by nothing except the correlation assumption.

Read the right hand column downward. Between a correlation of 1.00 and one of 0.9519 the benefit is 0.13 points, a difference that rounds to nothing anybody would notice. Between 1.00 and 0.00 it is 3.24 points on a base of about eleven. Across its plausible span the correlation input is most of the risk answer.

Run that miss through as a plan. A committee that had written 0.50 into its set was planning a blend at 9.62 per cent of volatility, and what arrived behaved like 10.97, or 14 per cent more spread. The conditions that pushed the co-movement up are the same conditions that would have been pulling the return assumption down.

Moving the correlation alone moved the risk answer by 1.35 points while nothing else changed, so the correlation input dominates the risk side of a combination answer. Every figure used belongs to one invented record and one stated twelve month period, and no correlation among them describes a real market.

Why do the three fail together rather than one at a time?

Because they are not three separate descriptions of three separate things. The three are descriptions of one thing, how a set of markets behaves, and one set of conditions acts on all of it at once. Returns come in below what was assumed, and the things meant to be moving separately start moving together.

The everyday version is a street of shops outside one factory gate. The tailor, the tea stall and the phone repair counter serve different customers, and on any ordinary week they move separately. A landlord holding rent from all three would call the row well spread. Then the factory shuts for a month, all three have a bad month in the same month, and the reason they had been moving separately was never a property of the businesses.

The failure is joint and not three independent ones, so treating the three inputs as separately uncertain understates the problem badly rather than slightly. If the three were independent, a bad draw on one would meet ordinary draws on the others and the errors would partly cancel. The three inputs are not independent, so the bad draws arrive together.

The record has its own instance of the humility this demands. The policy portfolio was designed around an expected return of 10.05 per cent and the stated year delivered 14.2 per cent; it was designed around a volatility of 11.20 per cent and realised 11.8 per cent. Reading the first gap as skill and the second as a modest overshoot is tempting. Resist both: one year is one draw.

What must an expectation set carry alongside its numbers?

Four things, cheap to write and expensive to omit. The horizon the figures are stated over. The route that produced each one. The date the set was fixed. And the conditions that would trigger a revision. A set missing those four can never be found to have been wrong, and so can never be improved.

The four missing fields explain why sets get carried forward for years. Review needs something to check against. If nobody wrote down what the figures were meant to describe, over what period, or what would have counted as evidence against them, a bad year produces an argument rather than a finding.

Inventing a horizon in order to have something to draw is exactly the failure under discussion.

Who reads an expectation set in a room, and on which day?

An investment committee like Rukmini Deshpande's meets, and somebody has circulated a paper with a table of assumptions in it. The useful version of that meeting runs four steps, and the order matters more than the content of any one step.

An analyst reading somebody else's set does a shorter version. Find the horizon. If there is none, stop and say so. Everything downstream is then uninterpretable rather than merely uncertain. Then find the correlation table, usually the last exhibit, and check whether its figures differ from last year's. Identical figures are evidence of copying, not of checking.

A household does the same work without any of the vocabulary. The questions are what the savings depend on, what the income depends on, and whether the two would have a bad year together. A deposit at the bank where a person works, an equity plan run by that same employer and a home in the town the employer built are three decisions with one condition underneath them.