The plate before this followed the reducible risk into the pool, where the law of large numbers dissolved it and paid its keeper the modest wage of reduction. This plate takes up what the pool leaves behind — the irreducible risk that no gathering can melt away, the risk that someone must simply hold — and the price the market sets upon the holding of it. That price is the risk premium proper: the extra return a risky asset must promise, above the rate a safe one would pay, before anyone averse to risk will consent to own it. It is the second of the two faces the first plate named — not the premium paid to be rid of risk, as the householder pays the insurer, but the premium earned for bearing it, as the market pays the investor who holds what the cautious will not. This plate will define that extra return and show why it cannot but exist — how the price of an uncertain claim is driven down until its promised yield is dear enough to overcome the dislike of holding it; will introduce its most studied instance, the long historical excess of stocks over bonds; and will bring the volume's question to the hardest form it has yet worn. For the risk premium is the wage of bearing the irreducible, earned at its root — and yet shadowed, as the insurer's tame loading was not, by the gulf between the reward expected and the reward received, between the premium reason would justify and the premium the market actually pays, and between the bearer who prospered by skill and the one who merely, this once, survived.
Set the thing out precisely. An investor may place his money in a safe asset — a short government bill, say — which returns a known and modest rate, the price of pure time that an earlier volume anatomized. Or he may place it in a risky one — a share in a company, whose return over the year might be handsomely positive or sharply negative, and is known beforehand only as a spread of possibilities around some average. The risk premium is the amount by which the average return he expects from the risky asset exceeds the certain return of the safe one. If the bill pays three in the hundred and he expects the share to pay eight, the risk premium is five: the extra yield he demands, and the market grants, for enduring the uncertainty of the share rather than resting in the safety of the bill. The total return on a risky holding thus divides cleanly in two — the risk-free rate, which is the price of time, and the risk premium heaped upon it, which is the price of risk. The first volume of this group priced the one; this plate prices the other; and the return an investor actually earns on anything uncertain is the sum of the two.
Why must the risky asset offer more — why will the market not let it pay the same as the safe one and leave the matter there? Because of the dislike of risk the volume began with. Imagine, for a moment, that it did not: that a share expected to return three, with all its lurching uncertainty, were priced to sit beside a bill that returns three for certain. No risk-averse person would hold the share, for it offers no more than the bill and asks him to bear a fear besides; all would sell the share and buy the bill. But all cannot, for the shares exist and must be held by someone. So the price of the share falls. As it falls, the return a buyer may expect from it climbs — for he now pays less to acquire the same uncertain future payoff — and it goes on falling, and the expected return goes on climbing, until at last the promised yield has risen far enough above the safe rate to coax the reluctant into holding the share after all. At that price, and not before, the market clears: the risky asset is held, but only because its price has sunk low enough, and its expected return risen high enough, to pay the holder for his fear. The risk premium is not decreed; it is the gap the market opens, by marking down the uncertain, between what the risky asset yields and what the safe one does.
A share priced to yield no more than a safe bill would find no taker; so its price must fall until the surplus return is dear enough to pay for the fear of holding it.
This reveals a relation that runs through the whole of finance, and it is worth dwelling on, for it inverts the intuition of the careless. A larger risk premium does not mean a richer asset; it means a cheaper one. The premium is exacted not by raising the future payoff but by lowering the present price, and the two are the same fact seen from opposite ends: to demand a higher return for risk is to pay a lower price for the risky thing. An earlier plate showed how any future sum is worth less today than its face, discounted by the price of time; here that discount is deepened. The worth of a risky claim is its expected future payoff discounted not merely at the safe rate, as a certain sum would be, but at the safe rate with the risk premium added on — a steeper rate, which presses the present value down further the more uncertain the payoff. The riskier the venture, the heavier the discount, the lower the price one will pay for a given expected return. So the price of risk and the price of time enter the valuation of every uncertain asset together, the one stacked upon the other, and the market's whole judgment of what an uncertain future is worth today is compressed into that single, swollen rate of discount.
The most celebrated of all risk premia, and the one on which the rest of the volume will turn, is the equity premium — the excess return that shares, taken as a whole, have paid over safe bonds across the long sweep of recorded history. The numbers are striking and, within bounds, robust. Measured over the past century and more, in the deepest markets, common stocks have returned on the order of six or seven in the hundred per year above what safe government paper returned — a premium so substantial that, compounded over a working life, it is the difference between a modest competence and a fortune. Early observers noticed the pattern; careful chroniclers later measured it across the decades and across nations, and found it nearly everywhere, though smaller than the headline American figure once the markets that failed are counted alongside those that flourished. This is the reward, in the largest and most public of all risk markets, for bearing the uncertainty of owning the productive economy rather than merely lending to it — for holding assets that crash and recover and crash again rather than the steady claim of the bond. Whether so large a reward is the just price of so much endured uncertainty, or a great deal more than any sober fear could warrant, is the question a later plate is given wholly to settle; but the premium is here, and it is real, and it is the central instance of the price this plate describes.
Now the volume's question, at the hardest pitch it has yet reached. Is the risk premium earned, or is it a windfall? At its root it is earned, and the argument is the same that vindicated the insurer's loading, transposed to a sterner key. Someone must hold the risky assets; the productive economy cannot be owned only by the safe and the certain, for it is not safe or certain. The risk-averse will not hold them save at a price that pays them for the fear; and so the premium is the wage of those who will — the bold, the wealthy, the long of horizon, those positioned to bear a spread of outcomes the cautious cannot stomach. By bearing it, they perform a genuine service: they take upon themselves the uncertainty of ownership, and in so doing free the risk-averse to hold the safe claims they prefer, and supply the venturing economy with the patient, risk-tolerant capital it could not otherwise raise. The premium is what that service commands. Where the insurer was paid for reducing risk by pooling it, the holder of the risky asset is paid for bearing the risk that pooling cannot reach — and that, too, is a service, and its reward, too, is at root a wage. The price of risk, received, is the honest payment for standing where the fearful will not.
Someone must own the productive economy, and it is not safe; the premium is what the willing are paid for standing where the cautious will not.
And yet the risk premium is a harder thing to vindicate than the insurer's loading, in three ways the rest of the volume will pursue, and honesty requires they be named here at the outset. The first is that the premium is a reward expected, not a reward received. The insurer's loading was nearly sure, smoothed by the law of large numbers; the risk premium is anything but — it is the average of a spread, and the spread is the whole point. The investor who earns it is the investor whose risk did not, this time, destroy him; and the comfortable average conceals the many who bore the identical risk and were ruined, who do not survive to be counted in the figure. The second shadow is that the premium the market actually pays may exceed the premium that reason could justify. The equity premium, measured, is so large that the standard reckoning of risk aversion cannot account for it without supposing people far more frightened of loss than any sane weighing of the odds would make them — a discrepancy so stubborn it has earned its own name and its own plate to come. If part of the premium is paid for a fear beyond reason, then that part is not the price of a service but the wage of a panic. The third shadow is that the premium rewards the mere bearing of risk, and cannot by itself tell the holder who bore risk and triumphed by judgment from the one who bore it and triumphed by luck — and the sorting of skill from fortune is the labour the volume keeps for its end. Expected against realized, justified against paid, skill against luck: three gulfs lie beneath the clean surface of the earned premium.
So the risk premium is the price of risk in its central and most consequential form — the extra return demanded, and granted, for holding the uncertain that no pool can dissolve. It is earned at its root, as the insurer's loading was, but in a sterner sense: the wage of bearing the irreducible, the payment that coaxes the willing to hold what the productive economy must have held and the cautious will not touch. In the equity premium it stands plainly visible, large and persistent, the reward for owning the venturing economy rather than lending to it. But beneath that clean surface run the three gulfs this plate has marked — between the reward expected and the reward the survivor alone receives, between the premium reason would justify and the larger premium the market exacts, and between the courage that earns and the luck that merely collects — and the volume's remaining plates are the patient sounding of them. The next turns to a discovery that complicates the premium before it can be judged: that not all of an asset's risk earns a reward at all, for some of it the holder need never have borne. There is a risk one is paid to carry and a risk one carries for nothing, and the telling of them apart is where the volume goes next. As the table says of every price, first to last: the argument remains open.