Asset Classes and How the Allocation Decision Uses Them

An asset class is a group of holdings whose returns are driven by the same underlying condition and which behaves differently from the other groups a portfolio holds. Asset allocation is the decision about how much of the portfolio each class receives. The test that separates one class from another is their correlation, not their label, their legal form or the market they trade in.

Whether two things are separate classes is not settled by what they are called, by who issues them, by what law governs them or by which screen they appear on. The separation is settled by a number, and a thing settled by a number can be got wrong quietly, by a room full of careful people who never wrote the number down.

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 investment committee is chaired by Rukmini Deshpande. Its stated shape is equity at Rs 300 crore, fixed income at Rs 150 crore and cash at Rs 50 crore. In per cent that is 60.0, 30.0 and 10.0, and the three sum to Rs 500 crore exactly. The three figures are the policy weights, the shape the holder decided in advance. Every return, volatility and correlation below is an assumption the holder itself wrote down rather than anybody's published estimate, and a different set of assumptions produces a different portfolio.

What makes a group of holdings an asset class?

Ask around a table what an asset class is and the answer comes back as a list: equity, bonds, cash, property, gold, maybe a few more. A list of names says what the categories have historically been called, not why they are the categories, and not whether the four things on the table today are four classes or two.

The useful definition has two halves and both have to hold. First, a class is a group of holdings that share a return driverThe underlying condition whose movement explains most of what a group of holdings does. Two things with the same driver rise and fall together., meaning one underlying condition whose movement explains most of the group's behaviour. Second, that group behaves differently from the other groups the portfolio already holds. A group that shares a driver with something already held is not a new class however different its name, its paperwork or its trading venue happens to be.

The everyday version. A household has bought a flat, put savings into a deposit at a local bank, and kept the shares its only earner receives from the company where that earner works. Now ask the driver question. The flat is in the town built around that one company. The bank lends mostly to that company and to the businesses that supply it. The shares are the company. One condition moves all three. On the labels this household holds three asset classes; on the drivers it holds one, three times over, and every review that reads the labels will pronounce it well spread.

The intent was right. The household wanted its savings not to fall over all at once, and that is the whole reason anybody thinks about classes. The method was wrong. The check ran on the labels rather than on the driver. One question comes before any other for anything that arrives described as a new class, and the question is what moves it. The answer has to be something other than what already moves the portfolio.

Why is correlation the test rather than the name on the box?

Because the portfolio does not read names. The portfolio adds up money, and the arithmetic that governs how the parts add up has exactly one input for the relationship between two groups. The single input is correlationA number between minus one and one saying how closely two things move together. One means lockstep; nought means their movements say nothing about each other., a number between minus one and one. Every other difference between the two groups, of description, custody, listing or jurisdiction, reaches the portfolio only through that number.

Using correlation as the separator is the move Harry Markowitz made in Portfolio Selection in 1952. People already believed that spreading holdings is wise. The point was that the benefit of spreading them is a computable quantity depending on how the parts move together rather than on how many parts there are.

Take the limiting case. Suppose two groups have a correlation of exactly 1.00. Then the volatility of the pair, in any proportion, is the plain weighted average volatilityEach part's volatility multiplied by its weight, added up. It is what a portfolio would carry if every part moved in lockstep with every other. of the two. There is no leftover and nothing gained. At a correlation of 1.00 the diversification is not small but zero, by arithmetic rather than by observation. Two perfectly correlated groups are therefore one class whatever the paperwork says.

Run it on the mandate. The Anantara portfolio assumes volatilities of 18.0 per cent for equity, 5.0 for fixed income and 0.5 for cash. At weights of 60.0, 30.0 and 10.0 the weighted average of those three is 0.60 times 18.0 plus 0.30 times 5.0 plus 0.10 times 0.5. The three terms come to 10.80 plus 1.50 plus 0.05, or 12.35 per cent. The weighted average is what the portfolio would carry if everything in it moved together. At the assumed correlation of 0.20 between equity and fixed income, and with cash taken as uncorrelated, the portfolio actually carries 11.20 per cent. The 1.15 point difference is the entire benefit, and it exists only because one assumed number is 0.20 rather than 1.00.

The four bars differ by less than a point and a half across the whole range, so the benefit of holding separate classes is real, computable, and smaller than the word diversification suggests. Nobody has to earn the 1.15 points, nobody has to be right about anything to collect them, and they are available purely because two assumed numbers were not the same.

What is Asset Allocation, and what has actually been decided when it is done?

Asset allocation is the decision about how much of the portfolio each class receives. The output is a set of weights that sum to a hundred per cent, and the decision is finished when they are written down and agreed. For the Anantara mandate that was three numbers: 60.0, 30.0 and 10.0.

The allocation decision is worth a section for what it excludes. Asset allocationDeciding how much of a portfolio each class receives, as weights adding to a hundred per cent. It fixes proportions, not names. is a decision about exposureHow much of a portfolio depends on one particular thing moving, be it a market, an interest rate, a currency or a local condition. to drivers, and it is not a list of what to buy: when it is finished, nothing has been bought. The committee has said how much of the whole should depend on equity conditions, how much on fixed income conditions and how much should sit in something that barely moves, and nothing at all about which instruments, issuers, maturities or names.

The domestic version is a wedding budget. A household decides that of the total, roughly half goes to the venue and food, a quarter to clothing and jewellery, a fifth to travel and lodging, and the rest is held back for whatever gets forgotten. The budget is settled in one sitting, before a single caterer is called. Yet what kind of wedding this will be is already decided. Everything chosen later has to fit inside a share that is now fixed.

A person picking holdings inside the fixed income sleeve is working inside Rs 150 crore that was never theirs to enlarge, fixed by somebody else at an earlier meeting. The allocation decision sets the size of every subsequent decision. For that reason it is taken first, and the committee takes it rather than the person doing the picking.

Which three classes does this mandate use, and what is each one doing?

Three, and the holder wrote its own numbers for each. Equity is assumed to return 12.0 per cent a year at a volatility of 18.0 per cent, fixed income 7.5 at a volatility of 5.0, and cash 6.0 at a volatility of 0.5. The correlation between equity and fixed income is assumed to be 0.20, and cash is treated as uncorrelated with either. The endowment wrote each of those numbers for itself rather than reading any of them off a published estimate.

Each class is doing a different job. Equity supplies the return and the risk, both by a wide margin. Fixed income supplies a lower return at a volatility a little over a quarter of equity's, and cash returns 1.5 points less than fixed income at a volatility of half a point. Cash is not in the portfolio to earn; it is there because it does not move, and a class whose job is not to move is doing something the return column cannot show.

Put the weights on those assumptions and the expected return is the plain weighted average: 0.60 times 12.0 is 7.20 points, 0.30 times 7.5 is 2.25 points, and 0.10 times 6.0 is 0.60 points. Add them and the policy portfolio expects 10.05 per cent a year. On Rs 500 crore that is Rs 50,25,00,000/-, of which Rs 36,00,00,000/- comes from the equity sleeve, Rs 11,25,00,000/- from fixed income and Rs 3,00,00,000/- from cash.

There is no interaction term, no adjustment, no place where two classes together produce something neither produces alone, and correlation does not appear in the calculation at all. Expected return is the one quantity where the portfolio really is the sum of its holdings, and every later difficulty below comes from the fact that risk is not.

What happens to expected return as the weights move?

To keep this to one moving part, pin the cash sleeve at 10.0 per cent throughout and let equity and fixed income share the remaining 90.0 points. Walk equity from nought up to 90.0 per cent in steps of 30 points and compute the expected return at each stop.

At nought per cent equity the portfolio is 90.0 per cent fixed income and 10.0 per cent cash, expecting 6.75 plus 0.60, or 7.35 per cent. At 30.0 per cent equity, 3.60 plus 4.50 plus 0.60, or 8.70 per cent. At 60.0 per cent, the policy weight, 10.05 per cent. At 90.0 per cent equity, with no fixed income at all, 10.80 plus 0.60, or 11.40 per cent. Each 30 point step adds exactly 1.35 points of expected return, and the step is the same size at the bottom of the range as at the top.

The assumed gap between equity at 12.0 and fixed income at 7.5 is 4.5 points, so every 10 points of weight moved from one to the other carries 0.45 points of expected return with it, and 30 points carries 1.35. The starting point does not matter: moving from 10 to 20 per cent equity buys the same 0.45 points as moving from 80 to 90.

Read down the two right hand columns rather than across the rows. The return column adds 0.675 at every step without exception. The volatility column adds 0.54, then 1.64, then 2.15, then 2.37, then 2.47, then 2.53. Same steps of weight. Utterly different behaviour.

Why does volatility refuse to move in a straight line?

Because the quantity that adds up is not volatility. The quantity that does add up is portfolio varianceVolatility squared. It is the quantity that actually adds across the parts of a portfolio, which is why volatility itself does not.. Variance is volatility squared, and volatility is recovered by taking the square root at the end. Squaring on the way in and rooting on the way out is exactly the operation that turns equal steps into unequal ones.

The everyday version. A cyclist adds sacks of rice to a carrier. The first is heavy but manageable. The second makes the bicycle wobble. The third does not merely add its own weight. The machine is now closer to the point where it goes over, so the third sack makes the wobble from the first two matter more. Volatility behaves the same way, and nobody decides it: the trade between return and risk gets worse as equity rises whether or not anybody at the table intends it to.

The first 30 points of equity cost 2.18 points of volatility for 1.35 points of return, the middle 30 cost 4.52 for the same 1.35, and the last 30 cost 5.00 for the same 1.35 again.

Opening the variance at the policy weights shows where the bending comes from. Four terms go in. Equity's own term is 0.60 squared times 18.0 squared, and 0.36 times 324 is 116.64. Fixed income's own term is 0.09 times 25, or 2.25. Cash's own term is 0.01 times 0.25, or 0.0025. And then the cross termThe part of a portfolio's variance that comes from two classes moving together rather than from either one alone. between equity and fixed income is twice 0.60 times 0.30 times 18.0 times 5.0 times 0.20, or 6.48. Add the four and the variance is 125.3725, whose square root is 11.20 per cent.

The cross term exists at all only because the correlation is not nought. Change 0.20 to 0.00 and 6.48 disappears, taking the variance to 118.8925 and the volatility to 10.90 per cent. The cross term is the only place in the whole calculation where two classes meet. Every point of volatility a portfolio carries beyond the parts it holds separately arrives through it.

The crossing point in that figure is a coincidence of these particular assumptions, so do not build anything on it. Below 50.0 per cent equity this portfolio expects more return than the volatility it carries; above it, the reverse, and the gap widens every step. At 90.0 per cent equity it expects 11.40 per cent at a volatility of 16.20, a spread of 4.80 points that did not exist at the left hand edge.

What would it cost if the two risky classes turned out to be one?

Keep the weights still, at 60.0, 30.0 and 10.0, and leave cash uncorrelated. Change one thing. The holder assumed equity and fixed income move together only weakly at 0.20. Suppose they in fact move in lockstep at 1.00.

Nothing at all happens to the expected return. Correlation appears nowhere in that calculation, so the expected return stays at 10.05 per cent. Everything happens in the variance. The cross term of 6.48 becomes twice 0.60 times 0.30 times 18.0 times 5.0 times 1.00, or 32.40. The variance rises from 125.3725 to 151.2925 and the volatility rises from 11.20 to 12.30 per cent. The portfolio would carry 1.10 more points of volatility, about Rs 5,50,00,000/- of one standard deviation on Rs 500 crore, in exchange for exactly the same expected return it had before.

The weighted average of the three volatilities is 12.35 per cent, and the perfectly correlated portfolio reaches 12.30, stopping 0.05 short. The 0.05 point gap is the whole contribution of the cash sleeve staying uncorrelated with everything else. Very little of the diversification came from the smallest class.

Nobody at the table observed 0.20. Somebody chose it, and every claim this portfolio makes about its own risk rests on that choice being roughly right. The correlation a holder assumes between its two largest classes decides more about what the portfolio actually is than almost any other single number in the document, and it is the number least likely to be argued about.

What does a proposed class have to earn before it can be admitted?

Somebody will eventually walk into Rukmini Deshpande's committee with a fourth group and the word class attached to it. Three things have to be true before the arithmetic can take it, and that class admission testThe set of conditions a proposed group must meet before a portfolio calculation can take it in as a separate class. is not to refuse things but to know what refusing looks like.

First, the group is not already inside something held. If its return driver is the same driver that moves the equity sleeve, then whatever it is called it is equity under a new name, and the portfolio has simply increased its equity weight. Second, its correlation with the classes already held is below 1.00, the earlier test read in the direction of admission. Third, somebody will state an expected return, a volatility and a correlation against every class already held.

Most proposed classes stop at the third condition. A group nobody will put three numbers on cannot enter the calculation at all, however persuasive the case sounds in the room. That is not a judgement about the group but a fact about arithmetic: a variance needs every pairwise correlationA correlation stated for each possible pair of classes. Every one has to exist before a variance can be computed., and a missing one is a hole where a number has to be.

Count what a fourth class demands. Three classes need three pairwise correlations, four need six, five need ten. The count grows as the number of pairs, not as the number of classes, so each admission asks for more than the last one did.

Which settings does the mandate actually admit?

The arithmetic runs happily from nought to 90.0 per cent equity. The mandate does not. The Anantara constraints allow equity between 50 and 70 per cent, and that band was written before any class question was asked, so most of the range just walked was never available to anybody.

Compute the edges. At 50.0 per cent equity the portfolio expects 9.60 per cent at a volatility of 9.60 per cent, the same coincidence noted above. At 70.0 per cent equity it expects 10.50 per cent at a volatility of 12.84 per cent. So the mandate admits 0.90 points of expected return and 3.24 points of volatility. The band is written in weights, but what it actually fixes is a narrow range of return against a range of risk more than three times as wide, and nobody chose that ratio because it falls out of the arithmetic.

Return is linear in the weight, so the weight scale and the return scale are one scale wearing different numbers, and the shaded slice sits in the same place on both. On the volatility scale it has moved left and narrowed.

How does a committee use any of this in a room on a Tuesday?

Three questions, prepared before the meeting, answered in numbers rather than in adjectives. Each is meaningless until the one before it is settled, so Faiz Ahmad Ansari brings them to Rukmini Deshpande's committee in that order.

The first is what drives each class, and whether any two are driven by the same thing. The second sets the weighted average volatility, what the portfolio would carry if everything moved together, against the portfolio volatility at the assumed correlations. The difference between the two is the entire benefit being claimed. Here those are 12.35 and 11.20 per cent, so the claim is worth 1.15 points, about Rs 5,75,00,000/- of one standard deviation on Rs 500 crore. The third is which single assumed number, if wrong, would change the answer most, and here that is the 0.20.

A portfolio described as diversified without those two volatility figures beside each other has been described rather than measured, and the word on its own asserts nothing at all. The pair of figures costs one line in a paper to compute and converts a comfortable adjective into a number anybody at the table can argue with.

The household version needs no spreadsheet and takes ten minutes: each place the savings sit, what would have to go wrong for it to fall, and whether the same answer appears twice. If the flat, the deposit and the shares all say the same employer, the household holds one thing three times, and it will find that out either now on one sheet of paper or later all at once. The test is the same test the endowment runs, and the only difference between the two is the size of the numbers.