The Basket — The Premium, Plate iv

The proverb says not to put all one's eggs in one basket, and it is the oldest piece of risk management there is. Its formalization, in the middle of the twentieth century, produced one of the very few things in economics that can fairly be called a free lunch: a way to reduce risk without surrendering a penny of expected return.

Harry Markowitz's insight, in 1952, was that the risk of a collection of assets is not the average of their individual risks, because the assets do not all move together. When one holding falls, another may rise or hold steady; the ups and downs partly cancel. The variability of a portfolio depends not only on how much each asset varies but on how the assets co-move — on their correlations — and by combining holdings whose fortunes are imperfectly correlated, an investor can assemble a portfolio less variable than any of its parts. The risk of the whole is less than the sum, and indeed less than the average, of the risks of the pieces.¹

1. Harry Markowitz, "Portfolio Selection" (1952): a portfolio's variance depends on the covariances among its holdings, not merely on their individual variances, so combining imperfectly correlated assets yields a portfolio less variable than its components. The founding result of modern portfolio theory.

Here is the remarkable part. Reducing risk ordinarily costs something — the premium of the first plate is precisely the return one gives up for safety. But diversification reduces risk at no cost to expected return: the expected return of a portfolio is simply the average of its assets' expected returns, whatever their correlations, while its variability falls as they are combined. One obtains the same average return for less risk, merely by spreading the stake. This is why diversification has been called the only free lunch in finance — every other reduction of risk is paid for in return forgone, but this one is had for nothing, by the bare arithmetic of imperfect correlation.²

2. Diversification lowers variance without lowering expected return — the portfolio's expected return is the weighted average of its parts' regardless of correlation, while its variance falls as imperfectly correlated holdings are combined. Hence the common description of diversification as the one "free lunch" in finance.

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But the free lunch has a limit, and the limit is the most important fact in the pricing of risk. As more and more imperfectly correlated assets are added, the portfolio's risk falls — but not to zero. It descends toward a floor, and there it stops. The part of each asset's risk peculiar to it — the lawsuit, the failed product, the fire at its one factory — is uncorrelated across assets and washes out as they are combined: this is idiosyncratic, or diversifiable, risk, and diversification destroys it. But the part all assets share — the risk of a recession, a war, a market-wide crash, a rise in rates — moves them together, does not cancel, and remains however many are added: this is systematic, or undiversifiable, risk, and no amount of spreading can remove it. Total risk splits cleanly in two: a part that can be shed for free, and a part that cannot be shed at all.³

3. The decomposition of risk: idiosyncratic (asset-specific, uncorrelated) risk is destroyed by diversification; systematic (market-wide, common) risk is not, since it moves all assets together. A portfolio's risk falls toward the floor of its systematic component and no further.

This division carries a consequence that the next plate makes into a theory. If idiosyncratic risk can be eliminated for free, by anyone willing to diversify, then no one need bear it — and the market will pay no one to bear it. A risk that can be costlessly avoided commands no premium; only a risk that cannot be escaped can command one. So the premium of the first plate, carried into a market of many assets and diversified investors, attaches not to the total risk of an asset but only to its undiversifiable, systematic part. The variability of a single stock, considered in isolation, is largely irrelevant to its expected return, because most of that variability is idiosyncratic and can be diversified away; what earns a premium is only the portion that moves with everything else.⁴

4. The pricing consequence: costlessly diversifiable risk earns no premium, since no one need bear it; only undiversifiable systematic risk is compensated. An asset's own variance is therefore largely irrelevant to its expected return — only its systematic part is priced. This is developed in The Systematic.

Two cautions temper the free lunch, and honesty records them. First, the cancellation depends on the correlations being less than perfect and on their staying put; in crises, correlations tend to rise toward one — everything falls together exactly when diversification is most wanted — so the protection is weakest precisely when it matters most, which is the systemic case again. Second, diversification reduces the variability of a portfolio's return but cannot defend against a fall in the whole; it is a guard against the particular misfortune, not the general one. The eggs are safer in many baskets only if the baskets are not all carried on the same cart.⁵

5. Cautions: diversification relies on imperfect, stable correlations, but in crises correlations rise toward one and assets fall together; and it reduces specific risk only, never the market-wide kind. Compare The Tail on correlated catastrophe.

Diversification does what pooling could not: it destroys a whole category of risk outright, and at no cost, leaving only the irreducible, systematic remainder. With that, the question of the premium sharpens to a fine point. If only undiversifiable risk need be borne, then only undiversifiable risk is priced — and the next plate asks exactly how. Its answer, the capital-asset-pricing model, will measure an asset's risk not by how much it varies, but by how much it varies in step with the market that no one can escape; and in doing so it will begin to turn risk from a property of the thing into a relationship between the thing and the world.