The plate before this priced the bearing of risk as though all risk were of one kind, to be borne or shed entire. This plate shows that it is not — that an asset's risk is of two kinds, and that one of them may be got rid of for nothing. The discovery is the work of Harry Markowitz, who in 1952 set down in a few pages the mathematics of holding more than one thing at once, and found in it the single closest approach to a free lunch that the dismal study of finance affords. The lunch is this: that by holding many assets whose fortunes do not rise and fall in step, an investor may shrink the unsteadiness of his whole holding below the average unsteadiness of its parts — and may do so without giving up a penny of the return he expects. Risk falls; reward does not; and the difference is had for nothing but the trouble of spreading. This plate will set out that free lunch and the cancelling of fortunes that produces it; will draw the great distinction it opens — between the risk peculiar to a single asset, which spreading dissolves, and the risk shared by all, which no spreading can touch; and will follow the hard corollary that has governed finance ever since: that one is paid only for the risk that cannot be diversified away, and that the bold gambler's winnings, won on a risk he need never have borne, are not the wage of courage but the luck of a bet.
State the thing with care, for its plainness hides its depth. Take the return one expects from a portfolio of several assets: it is simply the average of the returns one expects from each, weighted by how much is held in each — nothing is gained or lost, in expectation, by combining them. But the risk of the portfolio — the degree to which its return will swing, year to year, away from that average — is not the average of the risks of its parts. It is less. For the parts do not all swing the same way at the same time: when one asset is having a poor year, another may be having a fair one, and the two deviations, pointing opposite ways, partly cancel in the sum. The combined holding is therefore steadier than the typical holding within it. And here is the marvel — the steadiness is bought at no cost in expected return, for the average return was preserved untouched while the risk was pared down. To diversify is to lower one's risk for free. It is, in the only phrase the field has ever quite agreed upon, the one free lunch in all of investing; and the old merchant who split his cargo among several ships rather than trust it all to one hull had grasped its essence centuries before the mathematics arrived to prove him wise.
Dwell on the cancelling, for everything rests upon it. Two assets are said to move together, or apart, by how their returns are correlated — whether a good year for the one tends to fall in the same year as a good year for the other, or not. If two assets moved in perfect step, rising and falling exactly together, combining them would buy nothing: their swings would reinforce rather than cancel, and the blend would be exactly as unsteady as its parts. But few assets move in perfect step, and some move oppositely; and wherever they are less than perfectly aligned, their fortunes partly offset, and the blend is steadier than the average part. The less aligned the assets — the more independent their fates — the more thoroughly the offsetting works, and the more risk is pared away. Gather enough assets whose troubles are unrelated, and their separate misfortunes, striking at random and in no concert, very nearly wash one another out, leaving an aggregate that scarcely trembles where each part lurches. This is the same deep fact that ran the pool of the third plate — the law of large numbers, by which many independent wild things make one calm sum — turned now from the claims of the insured to the returns of assets. What the insurer did with a thousand separate dreads of fire, the investor does with a hundred separate and unrelated business risks.
When one holding sinks as another rises, their opposed misfortunes cancel in the sum; and the steadier whole is bought at no cost in return.
But the cancelling has a limit, and the limit is the most important thing in this plate, for it cleaves the risk of every asset into two parts of wholly different character. Some of what makes an asset's return swing is peculiar to that asset alone: its chief executive falters, its factory burns, its new product fails, a rival outflanks it. Such misfortunes are particular and unconnected — one firm's calamity is unrelated to the next's — and so, gathered into a large portfolio, they strike at random and cancel, as the fires did in the pool. This is the diversifiable risk, the idiosyncratic risk, the risk specific to the single name; and in a well-spread holding it very nearly vanishes. But some of what makes an asset's return swing is not peculiar to it at all: it is shared with every other asset, because it springs from forces that move the whole economy together — a recession, a war, a sharp turn in interest rates, a financial panic. When these strike, they strike everything at once; all assets fall together; and no spreading can help, for there is nothing for the fall of one to be offset against when all are falling alike. This is the undiversifiable risk, the systematic risk, the market risk — the risk an asset shares with the world. Total risk is the sum of the two: the idiosyncratic, which diversification dissolves, and the systematic, which it cannot touch.
It follows that diversification, for all its magic, is a magic with a floor. As an investor adds more and more imperfectly-related assets to his holding, the idiosyncratic risk falls away — quickly at first, then more slowly, most of it gone by the time a few dozen well-chosen names are held — but the systematic risk does not fall at all, for it is common to every name he might add. His total risk descends toward that systematic floor and there it stops; no further spreading can lower it, because what remains is the risk of the whole market, which he holds in every asset and cannot diversify against without quitting the market altogether. The fully diversified investor has shed everything that can be shed, and is left holding the market's own risk, naked and irreducible. And this is precisely the risk the earlier plates named as the residue of the pool and the home of the real reward — the correlated risk that no gathering dissolves, the risk that someone, in the end, must simply bear. Diversification disposes of the avoidable; it delivers its practitioner, stripped of every needless fear, to the foot of the one fear that cannot be avoided.
From this cleaving of risk follows the single most consequential idea in the pricing of uncertain things, and it sharpens the reward of the previous plate to a fine point. If the idiosyncratic risk of an asset can be shed for nothing — if any investor may make it vanish merely by holding the asset among enough others — then no investor needs to bear it, and the market, peopled by investors who have all diversified, will pay no premium for bearing it. Why should it? A reward offered for enduring a risk that costs nothing to escape would be a reward no one need claim, competed away in an instant by the diversified crowd. The premium, therefore, attaches only to the systematic risk — the risk that cannot be shed, that every diversified holder must carry whether he will or no. An asset is rewarded not for how much its return swings in total, but only for how much of that swing is of the inescapable, market-wide kind; an asset that lurches wildly but idiosyncratically, its troubles all its own, earns scarcely any premium at all, for its wildness can be diversified into nothing. The reward of the previous plate is thus revealed to be narrower than it first seemed: not the wage of bearing risk, but the wage of bearing the one risk that bearing cannot avoid.
The market pays nothing for the risk one could have shed for free; the premium is the wage of the risk that no prudence can escape.
This carries a verdict the volume has been working toward, and it falls hard on a figure the world is fond of celebrating. Consider the man who staked his whole fortune on a single venture — one company, one technology, one roll of the dice — and emerged immensely rich. The world calls him bold, and reckons his fortune the reward of his courage in bearing risk. But the risk he bore was, in the main, the idiosyncratic risk of that single bet, the very risk he could have shed for nothing by spreading his stake across a hundred ventures instead of pouring it into one. He was not paid by the market for bearing that risk; the market pays nothing for it. He simply bore it, needlessly, and the dice fell his way. His fortune is therefore not the wage of a service rendered — the market rendered him no wage for an avoidable risk — but the upside of a gamble that came good, a draw from the lucky tail of a distribution most of whose draws were ruin. And the others who bore the identical concentrated risk and lost are not on hand to temper our admiration, for the ruined do not write memoirs. The earned premium, the volume now begins to see clearly, is the sober wage of bearing the systematic risk that cannot be escaped; the great concentrated fortune is something else — not courage rewarded but a bet that happened to win, and a confusion of luck with desert that the volume's last plates are given to dispelling.
So diversification, the one free lunch, does more than lower the prudent investor's risk; it reorders the volume's whole understanding of what the price of risk rewards. It shows that an asset's risk is of two kinds — the idiosyncratic, peculiar to itself, which any holder may dissolve for nothing by spreading; and the systematic, shared with the world, which no holder can escape. And it draws from this the line that runs through all that follows: that the market pays a premium only for the second, the inescapable risk, and nothing for the first, the avoidable one. By this the reward of risk is at once vindicated and narrowed — vindicated, because the wage for bearing the systematic risk that someone must bear is genuinely earned; narrowed, because the celebrated winnings of the bold and concentrated gambler are not that wage at all, but the luck of a bet he need never have placed. There is a risk one is paid to carry and a risk one carries for nothing; the great fortunes raised upon the second are monuments not to courage but to chance. It remains only to name and to measure the inescapable risk — the systematic risk for which alone the market pays — and that measure is the subject of the next plate. As the table says of every price, first to last: the argument remains open.