The plate before this proved that the market rewards only the risk that cannot be shed — the systematic risk an asset shares with the whole market — and pays nothing for the idiosyncratic risk a holder may diversify away. But it left that priced risk unnamed and unmeasured, a quantity known only by what it was not. This plate supplies the name and the measure, and they are the work of William Sharpe, whose capital asset pricing model, set out in 1964, gave the price of risk the cleanest expression it has ever had. The name is beta; the measure is how much an asset's return moves with the market as a whole — how much of the market's own rise and fall it carries on its back. And the model's claim is as bold as it is elegant: that an asset's entire reward for risk is fixed by this one number, rising in exact proportion to its beta, and that an asset's private wildness, however violent, earns it nothing at all. This plate will define beta and lay out the model; will show why, by the logic of the previous plate, beta and beta alone commands a premium; will mark the elegance that made the model the cornerstone of all modern finance; and will weigh, with the honesty the volume owes, the awkward and abundant evidence that the world prices risk a good deal less tidily than the model's beautiful straight line would have it.
Recall precisely what the previous plate left undone. It had split an asset's risk into the diversifiable part, peculiar to the asset and washed away in any broad holding, and the systematic part, shared with the market and ineradicable; and it had shown that only the second earns a premium. But how much of the second does a given asset carry? Two assets may both be systematically risky, yet not equally so — one swinging twice as hard as the market when the market moves, another only half as hard. Beta is the number that captures this. It measures the sensitivity of an asset's return to the market's: a beta of one means the asset tends to move point for point with the market, rising four when the market rises four; a beta of two means it amplifies the market, rising eight when the market rises four, and falling as hard when the market falls; a beta of one-half means it moves but gently, half as far as the market each way; a beta of zero means its fortunes are unrelated to the market's, all its risk idiosyncratic; and a beta below zero — rare and precious — means it moves against the market, rising when the market sinks, a natural hedge. Beta, in short, is the dose of market risk an asset carries: the measure, at last, of the one risk the previous plate proved is priced.
With beta in hand, the model states the price of risk in a single line. The expected return on any asset, it says, is the safe rate of return plus its beta multiplied by the premium the market as a whole commands over that safe rate. Set the safe rate at three and the market's premium at five — so that the whole market, with a beta of one by definition, is expected to return eight — and then every asset's expected return is read straight off its beta: an asset of beta two is expected to return three plus two times five, or thirteen; an asset of beta one-half, three plus half of five, or five and a half; an asset of beta zero, merely the safe three, for it adds no market risk and earns no premium; and an asset of negative beta, less even than the safe rate, for it reduces a portfolio's risk and one will pay, in forgone return, for the comfort it brings. The premium an asset earns, in other words, is exactly its beta times the market's premium — proportional to beta, and to nothing else. All the rest of an asset's risk, the great idiosyncratic remainder, earns precisely zero, for it can be diversified into nothing and the market will not pay a man for bearing what he need not bear. The whole reward for risk is compressed into a single coefficient.
An asset is paid for the market's risk it carries, and for nothing else; its own private wildness, however violent, earns it not a penny.
Pause to see why this must be so, for the reason is the previous plate's logic carried to its end. Picture the market as peopled entirely by sensible investors, every one of whom has diversified, so that each holds some slice of the whole market and none holds any single asset's idiosyncratic risk undiluted. To such an investor, the only thing a new asset adds to his already-diversified holding is its systematic part — the degree to which it will sink when the whole market sinks, deepening the one loss he cannot escape. Its idiosyncratic part he will diversify away to nothing, as he has all the others; it costs him nothing, and he will pay nothing to avoid it. So what he demands to be paid for, in holding the asset, is precisely the market risk it adds — and that is exactly what beta measures: the asset's contribution to the undiversifiable risk of the whole. An asset that lurches wildly but on its own account, its beta near zero, adds almost nothing to the diversified investor's real risk, and so earns almost nothing, for all its private violence; an asset that moves faithfully and forcefully with the market, its beta high, piles onto the one risk no one can shed, and must pay for the privilege. The market prices the contribution to inescapable risk, and beta is its name.
The beauty of this was, and remains, immense. At a stroke the model reduced the whole tangled question of what an uncertain asset should return to a single observable number, and drew the relation as a straight line — the security market line, as it came to be called — rising evenly from the safe rate as beta climbs. It gave the corporation a way to reckon the return its investors required, and so the rate at which to discount its projects; it gave the steward of a portfolio a way to judge whether a manager's gains were skill or merely the reward of a high beta cheaply bought; it gave the theorist a complete and closed account of risk's price, and the ordinary saver a reason to hold the whole market and trouble himself no further. For this Sharpe shared a Nobel prize, alongside the author of the previous plate. The capital asset pricing model is the high-water mark of the rational theory of the price of risk — the moment at which the premium seemed fully tamed, reduced to arithmetic, every asset's reward for risk made legible in a single coefficient that the market itself supplied. Had the world only obeyed it, the volume's question would be three-quarters answered: the earned premium exactly weighed, and the rest shown to be diversifiable folly that earns nothing.
But the world has not quite obeyed it, and honesty requires the discrepancies be set down plainly, for they are large and they have not gone away. The first is that the line is too steep on paper. When the model's prediction is tested against decades of returns, the actual relation between beta and reward proves flatter than the theory demands: assets of low beta have tended to return more than their betas warrant, and assets of high beta less, as though the market underpays for safety and overpays for daring — a discrepancy now systematically harvested under the banner of betting against beta. The second, and graver, is that beta is not the whole story. Careful study has found that other traits of an asset foretell its return as well as beta or better — that small companies have tended to outreturn large ones, and cheap shares to outreturn dear ones, by margins beta cannot explain — so that the single coefficient, far from capturing all of risk's price, captures only part of it, and the clean one-factor line has had to be propped up by models of three factors and five. The straight line the theory drew so confidently, the world has bent and smudged; beta is rewarded, but so are things that beta cannot see.
The line the theory drew so cleanly, the world has smudged: beta is rewarded, but so are things that beta cannot see.
What these discrepancies mean for the volume's question is itself disputed, and the dispute is among the deepest in all of finance. Grant first what the model gets right, for it is a great deal: in giving the premium as the wage of systematic risk, exactly proportional to beta, it states the earned account of the price of risk in its most precise and defensible form — each asset rewarded for the inescapable risk it carries, and nothing for the escapable risk it does not, the wage of the unavoidable weighed to a number. So far the premium is earned, and beautifully accounted. But the extra rewards the model cannot explain — the premium to smallness, to cheapness, to recent strength — pose a question it cannot answer. Either they are compensation for further kinds of systematic risk that the single beta was too crude to capture, in which case they too are earned, the wage of dangers the first model overlooked; or they are the footprints of the market's own mistakes, mispricings a sharper arbitrage should have erased and somehow did not, in which case they are not earned at all but won by those alert enough to exploit the errors of others. The first reading keeps the price of risk wholly a wage; the second admits into it a strand of something else — reward not for bearing risk but for catching the market out. Finance has argued the point for half a century without settling it, and the volume will not settle it here. And beneath even the part the model captures cleanly lies the question the next plates press: that the market's premium itself — the very price of systematic risk that beta merely apportions — may be larger than any sober fear can justify.
So beta gives the price of risk its cleanest and most-cited measure — the wage of the inescapable, weighed asset by asset in a single coefficient — and stands as at once the triumph of the earned account and the place its cracks first show. It vindicates the premium as the reward for systematic risk, and tells us, where it holds, exactly how much each asset has earned. But it holds only roughly: the line is flatter than it should be, and rewards accrue to qualities beta cannot see, which may be other risks honestly priced or the market's errors quietly harvested. And it leaves untouched the question of whether the market's whole appetite for risk is rightly sized at all. The volume turns next to a claim that grows directly from the model's world of diversified investors and priced systematic risk: that if risk is the only thing the market pays for, and the market has already priced it, then no skill in the picking of assets can reliably beat the price — that the market, in a word, is efficient. Whether that is so, and what it would mean for the rewards that skill appears to earn, is the subject of the plate to come. As the table says of every price, first to last: the argument remains open.