If diversification destroys all risk but the systematic, then the price of risk should compensate only the systematic part — and an asset should be judged risky not by how much it varies on its own, but by how much it adds to the undiversifiable risk of a portfolio already spread as widely as it can be. This is the idea the capital-asset-pricing model made precise, and it remains the workhorse of the field.
The model, built in the 1960s by Sharpe, Lintner, and others on Markowitz's foundation, imagines every investor holding the same widely diversified market portfolio, from which all idiosyncratic risk has been washed away. The only risk left to bear is the market's own, and the relevant risk of any single asset is therefore its contribution to that market risk — how much it moves when the market moves. This is the asset's beta: the sensitivity of its return to the return of the market as a whole. An asset with a beta of one moves, on average, with the market; a beta of two amplifies its swings; a beta near zero is, in market terms, very nearly riskless, however much the asset may jump about on its own.1
From this the premium falls out as a clean straight line. An asset's expected return, the model says, equals the risk-free rate — the rate of the volume on the rate, the reward for mere waiting — plus its beta times the market's risk premium. Risk that does not move with the market, however violent, earns no premium at all; risk that moves with the market earns a premium in exact proportion to its beta. The premium per unit of systematic risk — the market's own excess return over the risk-free rate — is the market price of risk, the single rate at which the market compensates the one risk that no one can escape. Two assets equally wild in isolation can carry utterly different premia, if the variability of the one is idiosyncratic and the other's systematic.2
In this result the nature of risk quietly changes beneath one's feet. Through the first plates, risk was a quantity — the variance of a gamble, the amount by which an outcome might swing. The capital-asset-pricing model prices something else entirely: not variance but covariance — not how much an asset moves, but how much it moves with the market. An asset's priced risk is a relationship, between its fortunes and the fortunes of everything else, and an asset considered in isolation has no determinate risk at all until that relationship is fixed. The volatile gold-mine that rises when the market falls may actually reduce a portfolio's risk, and so command a negative premium — investors paying for the privilege of holding it, accepting a lower return — because it pays off in bad times, when a payoff is most wanted. Risk has ceased to be a property of the thing and become a property of the thing's place in the whole.3
Honesty requires the model's empirical record stated plainly, for it is mixed. The capital-asset-pricing model is theoretically beautiful and practically indispensable, taught and used everywhere; but when economists test whether beta actually explains the returns of stocks, the fit is poor. Returns turn out to depend on things the model says should not matter — the size of the firm, the ratio of its book value to its market price, its recent momentum — the famous anomalies, which beta cannot account for. Whether these reflect further, missed dimensions of systematic risk, as some hold, adding factors to the model, or the mispricing born of investor psychology, as others hold, remains unsettled. The model's logic — that only undiversifiable risk is paid for — survives; its simplest empirical claim — that a single market beta measures that risk — does not.4
What survives the empirical trouble is the part that matters for this volume: the principle that the price of risk attaches only to what cannot be diversified away, and that what cannot be diversified away is an asset's covariance with the common fate — with the states of the world that strike everyone at once. The deepest form of the idea, the consumption-based version, holds that an asset is risky in exact measure as it pays off badly when people are already badly off, when goods are scarce and a dollar most precious — and safe, even worth more than its expectation, when it pays off in such times. The premium prices not uncertainty as such, but the dread of particular states: the states in which we can least afford to lose.5
The premium, then, is paid only for systematic risk, and systematic risk is not a quantity an asset possesses but a relationship it bears to the common fate — its tendency to fail just when failure is least affordable. This is the theory of the price of risk at its most refined, and looking forward, in expectation, it is a theory of real elegance and force. But a premium is a promise about averages, and the great fortunes and great ruins of the actual world are single draws, run once and never repeated. The flagship plate turns from the expected to the realized, and asks what the price of risk looks like after the dice have stopped — when we survey the fortunes that risk-bearing produced, and find that we can see only the winners.