Asset allocation: how the mix drives risk

Asset allocation is the split of a portfolio across broad asset classes. Stocks, bonds, cash and real assets are the usual four, and the allocation is nothing more than what share of the money sits in each.

That is a different decision from security selection, which is which particular holdings fill each class. Both affect the outcome. They do not affect it in the same way, because holdings inside one class are driven by the same forces.

Two things the table leaves implicit. Cash is steady in nominal terms only, so a balance that never falls still loses purchasing power to inflation year after year, which is why steady is not the same as safe over a long horizon. And a bond bought in another currency adds the exchange rate to whatever else moves it, which can dominate both of the other two.

A class earns the name when a different engine drives it, not when it gets a different label. That is what gives one class a chance of having a good year while another has a bad one. Choosing between two stocks is a choice inside one engine; choosing between stocks and bonds is a choice of engine.

A portfolio's expected return over a single period is the weighted average of what its parts are expected to return:

$$E(r_p) = \sum_i w_i \, E(r_i)$$

Its risk is not a weighted average of the parts' risks. It depends on how the parts move together:

$$\sigma_p^2 = \sum_i \sum_j w_i w_j \, \text{cov}(r_i, r_j)$$

Every weight $w_i$ in both lines is an allocation decision. Which classes are in scope, and how much money is being paid in at all, come before them; after that, the weights are what the rest of the portfolio is built on.

The claim that asset allocation explains about 90 percent of performance traces to a specific pair of results, and it is quoted far more often than it is stated correctly.

Brinson, Hood and Beebower, writing in 1986, took 91 large pension plans in the United States and compared each plan's quarterly returns from 1974 to 1983 with the returns of its own stated policy mix. On average, the policy mix accounted for about 93.6 percent of the variance of a plan's quarterly returns. An update published in 1991, covering 82 plans from 1977 to 1987, gave about 91.5 percent. The two windows overlap heavily, so those are two readings of a similar era rather than two independent decades.

Ibbotson and Kaplan, in 2000, separated the questions that figure had been collapsing together. Their answers came from 94 United States balanced mutual funds measured monthly and 58 United States pension funds measured quarterly:

Read the first row carefully. It is a statement about the wobble of one portfolio through time, not about how much money it made and not about why one investor beat another.

Most of even that 90 percent is simply that every diversified portfolio moves with the general market. Knowing the allocation tells you how much market exposure is present, and market exposure drives most of what happens in most periods. Later work by Ibbotson and co-authors split the figure apart and found that once the general market's movement is taken out, what is left divides roughly evenly between the allocation policy and the active decisions layered on top of it. So the 90 percent is closer to a statement about being invested at all than about the particular mix chosen.

The 40 percent row is the one to carry into a comparison of two portfolios. Allocation is the largest single explanation of why they differ, and it is not the only one. Costs, selection and timing hold the rest.

Three separate questions get compressed into the phrase "how much risk should I take", and they have different answers.

Risk capacity is structural and can be worked out on paper. How long until the money is spent, how much of the goal is already funded, what other income exists, how much can still be paid in, and whether a fall would force a sale. A pot that funds essential spending in three years has almost none. A pot that will not be touched for thirty years, alongside a salary, has a great deal.

Risk tolerance is behavioural. It is how far a portfolio can fall before the holder abandons the plan. It is hard to measure by asking, because the question is usually put after good years and answered by someone who has not recently watched the number drop. A questionnaire records an intention; a bad quarter is what tests it.

Required return is what the plan needs to earn to reach the goal on the money being paid in. It is the one people quietly let override the other two, and it is the wrong one to let win. If a goal needs 9 percent a year while the most risk the plan can carry supports an expected 4, what has to move is the plan, the contributions or the goal. What will not move to meet it is the market.

The binding constraint is the smaller of capacity and tolerance. High capacity with low tolerance ends in a sale at the bottom, which turns a paper fall into a realised one and gives up whatever recovery follows. Low capacity with high tolerance ends in a forced sale, which does the same thing without any decision being made at all. Neither case is rescued by assuming markets always come back on the schedule a plan needs, and testing that assumption is most of what capacity is for. This is also why the ordering matters more than the precision: an allocation held through a bad year usually finishes ahead of a better one abandoned in the middle of it.

Horizon is the input that does most of the work in setting an allocation, and it is routinely mis-measured as an age or a retirement date.

The horizon of a pot is when the money leaves it. Money that will be spent in two years has no room to recover from a bad draw, whatever the age of the person holding it. A retirement pot is spent gradually across decades, so on the day the salary stops the money in it has not reached a horizon of zero. The first year of spending has, and the last year of spending is thirty or more years away. That is one pot with a range of horizons inside it, which is a different problem from one deadline.

Two features of a goal change how much risk the same horizon can carry.

• Fixed against flexible. A tuition bill on a known date for a known amount can absorb almost nothing. Discretionary spending that can be delayed or trimmed can absorb a lot, because a bad year moves the plan rather than breaking it.
• Paying in against drawing out. A fall is not the same event for a saver as for a spender. Money not yet invested buys in cheaper afterwards, so a saver whose remaining contributions are large next to the balance can finish ahead because of one. A saver with a large pot and few payments left gets almost none of that, because the fall lands on the balance rather than on the payments. A balance being drawn from is hurt outright, since units sold into a decline are gone before any recovery arrives.

The same set of annual returns can support or exhaust a withdrawal plan depending on when the bad years land. Order matters during accumulation too, in the opposite direction, and it is largest for anyone holding a big balance with few contributions left to make. Sequence of returns risk works through both sides.

What this rules out is treating a whole portfolio as though it had a single date attached. Different money inside it has different jobs.

The best known shorthand is to hold a percentage of stocks equal to 100 minus your age, with the rest in bonds. Variants using 110 or 120 spread through the decades when lives were lengthening and bond yields were falling.

At every age the columns sit 10 percentage points apart, 20 from end to end, which already says the rule is a family of opinions rather than a calculation. Bond yields have since risen again, which is worth noticing: the case for one variant over another rests on conditions that move while the rule itself looks fixed. Target date funds run the same idea more carefully, gliding from mostly stocks toward a mixed portfolio on a published path, though two funds carrying the same target year can hold quite different amounts of stock on the date they are named for.

What the rules do well is prevent the two errors that cost the most: holding decades of long-horizon money in cash, and holding next year's rent in stocks. That is worth having, and it takes no analysis to apply.

What they leave out is everything except age.

• Funded status. Two people of the same age, one whose pot already covers essential spending and one whose does not, have different capacity, and the direction is not obvious in either case.
• Other income. Guaranteed income that covers the basics acts like a large bond holding you do not see on the statement.
• Human capital. Future earnings behave like an asset. Stable earnings behave like a bond, which leaves room for more stock risk. Earnings tied to markets, or to an employer whose stock you also hold, behave like more stock, which leaves less.
• Tolerance. No rule based on a birth date knows what its holder will do in a bad quarter.

An allocation is a target, and a portfolio does not stay on it. Each class compounds at its own rate, so the weights move on their own.

Take a 60 percent stock, 40 percent bond portfolio through a decade in which stocks compound at 10 percent a year and bonds at 3 percent. Those two rates are picked to make the arithmetic visible rather than as a forecast, and both are nominal. Nobody buys or sells anything. It ends at about 74 percent stocks. Run the same portfolio through a single year in which stocks fall 40 percent and bonds gain 5 percent instead, and it ends at about 46 percent stocks. Left alone, a portfolio carries the most risk right after the largest rise and the least right after the largest fall, which is not a schedule anyone would write down on purpose.

Rebalancing is selling what has grown past its weight and buying what has fallen below it. It is what keeps the allocation you chose the allocation you hold. Two usual approaches are on a calendar, or when a weight drifts past a band such as five percentage points. Adding new contributions to the underweight class does part of the job with no selling at all.

What rebalancing reliably buys is control of risk rather than extra return. Trimming the faster grower to top up the slower one lowers ending wealth over any stretch in which one asset out-compounds the others the whole way through, and it adds return only when the leaders take turns. Portfolio rebalancing sets out that trade-off and the costs that come with it.

The allocation dial is what a stock fall runs through:

Bonds rising while stocks fall is a tendency, not a rule: an inflation shock can push both down together. Costs matter too. In the United States, selling inside a taxable account to rebalance can realise a gain, so where each asset sits across account types is a separate decision from the allocation. The friction exists in most places; its size and its rules are local. This page is education rather than advice about your own money.