The previous plate took the risk premium as the market's just and only reward, the one return that even an efficient market grants. This plate asks a question that the whole confident edifice of priced risk had somehow failed to ask of itself — whether that premium is even the right size — and returns an answer that has unsettled the field for forty years: that it is not, that the premium the market actually pays for bearing risk is many times larger than any sober reckoning of risk aversion can justify. The finding is Mehra and Prescott's, published in 1985 under a title of disarming modesty — they called it simply a puzzle — and it has resisted solution ever since. The clean account the volume has built reaches here its sharpest test, for if the premium is far too large to be the wage of rational fear, then either it compensates for dangers the clean account could not see, or it is swollen by a fear that is not rational at all. This plate will state the puzzle and show why the theory predicts so small a premium where the world pays so large a one; will measure the implausible terror that would be needed to close the gap; and will set the sober rescues that would keep the premium earned against the behavioral account that would expose part of it as the wage of a needless dread — the account toward which the bridge to another primitive points.
State the puzzle in its bare numbers. Over the long run of recorded history, in the deepest markets, the holders of shares have earned something like six in the hundred per year more than the holders of safe government bonds — the equity premium the volume has already met. The standard theory of how risk is priced, applied honestly to the actual riskiness of shares and the actual range of plausible human risk aversion, predicts a premium of a fraction of a single percent — a tenth, perhaps a half, of one per cent. The gap between the two is not a matter of fine tuning, of a model nearly right and needing adjustment; it is a chasm, the predicted premium and the observed differing not by a little but by an order of magnitude. A theory may be forgiven for missing a quantity by a tenth; it cannot be forgiven for missing it by a factor of ten or more. That so central a price, in so well-studied a market, should stand so far beyond what the reigning theory can explain is why the modest word puzzle was, if anything, an understatement, and why the equity premium puzzle became at once the most famous unsolved problem in the pricing of risk.
To see why the theory predicts so little, one must see what, in the theory, makes an asset risky enough to deserve a premium at all. It is not the mere fact that an asset's return jumps about; it is whether the asset pays off badly precisely when the holder is already badly off — when his consumption is low, his dollars scarce and dear. An asset that crashes in the bad times, deepening a hardship already felt, is genuinely fearsome and earns a premium for it; an asset whose ups and downs fall carelessly across good times and bad alike adds no particular terror and earns little. So the premium an asset deserves depends on how tightly its fortunes are bound to the ebb and flow of the holder's own consumption. And here the theory runs aground, for the consumption of a whole society is remarkably smooth — it grows year upon year with only mild tremors, the deep collapses being rare — and the returns of the stock market, wild as they are, are only loosely tied to those gentle tremors. Stocks, measured against the smooth and stately march of aggregate consumption, simply do not betray their holders, in the bad times, badly enough to have earned a premium of six per cent. By the theory's own logic, the treachery is too mild for so vast a wage.
A premium is the price of an asset's treachery in bad times; and stocks, set against the smooth march of a society's consumption, are nowhere near treacherous enough to have earned so large a one.
One might try to close the gap by supposing people simply far more risk-averse than the modest range allows — and the attempt is instructive, for it fails in a revealing way. To make the theory yield a six-per-cent premium, one must crank the coefficient of risk aversion up to thirty, fifty, or beyond, where plausible values lie between one and perhaps ten. But risk aversion that high implies behaviour no sane person displays: a man so frightened would, for instance, refuse a coin-toss between gaining a modest sum and losing a trifling one, would pay almost anything to avoid the smallest uncertainty, would order his whole life around the dread of risks the rest of us scarcely notice. Worse, the same towering risk aversion that would explain the premium brings a second disaster in its train. People that desperate for certainty would crave safe saving so intensely that they would bid the return on safe bonds far higher than the low rate we actually observe — so that the cure for the equity premium puzzle breeds a risk-free rate puzzle, the safe rate now far too low for such frightened folk. The model cannot be saved by simply making people more afraid: one parameter of fear cannot fit both the largeness of the premium and the smallness of the safe rate at once. Something other than ordinary risk aversion is at work.
A first family of answers would keep the premium honestly earned by finding, in the world, dangers the simple model overlooked. The most powerful points to what the calm historical sample leaves out: rare catastrophes. The decades over which the premium is measured happen to contain no utter ruin of the market — no confiscation, no hyperinflationary wipeout, no depression deep enough to destroy the holders of shares — but investors may rationally have feared such disasters all along, and priced shares to compensate for a calamity that, in the event, did not befall them. On this reading the six per cent is not too large at all; it is the fair price of a small chance of catastrophe, and the realized return merely reflects a lucky run in which the catastrophe stayed away — a thought the volume will meet again, in full, when it turns to the black swan. A second answer supposes that people grow accustomed to a standard of living and dread any fall below it ferociously, so that their effective fear spikes in downturns and justifies a fat premium; a third, that they fear small but lasting shifts in the economy's long-run growth. Each of these, in its way, would rescue the premium as earned — the wage not of ordinary risk but of rarer or subtler dangers the first model was too crude to register.
A second family of answers abandons the premise that the premium is rational at all, and these point through the bridge to the primitive of human bias. Combine two well-attested quirks of the mind, the behavioral economists observe, and the puzzle dissolves. The first is loss aversion: people feel the pain of a loss roughly twice as keenly as the pleasure of an equal gain, so that a holding which is as likely to fall as to rise feels, on net, unpleasant to own. The second is a kind of myopia: people evaluate their holdings far too often, glancing at their portfolios month by month or year by year rather than over the long horizon for which they truly invest. Put the two together and the result is striking. A holder who looks frequently at a volatile portfolio, and who flinches twice as hard at each frequent loss as he delights in each frequent gain, experiences the holding of shares as a steady drip of pain, even though over the decades the shares climb handsomely; and to be induced to bear that self-inflicted discomfort he demands a large premium. Reckon how often investors actually look — about once a year — and the premium their loss aversion would demand comes out close to the historical six per cent. On this account the premium is real but not earned in any deep sense: it is the wage of a discomfort that better habits of attention would dissolve, paid to those who can simply bear to look away.
On this reading the premium is not the price of a danger soberly weighed but of a discomfort needlessly suffered — the wage of looking too often and flinching too hard.
For the volume's question the puzzle is grave, whichever rescue one prefers, for it has cracked the cleanest earned account the volume found. The capital asset pricing model had seemed to settle the matter — the premium is the wage of systematic risk, weighed by beta — but it took the size of the market premium as given, and the puzzle shows that size to be a mystery the rational theory cannot, by itself, explain. If the disaster-and-habit rescues are right, the premium remains earned, but earned for dangers far subtler and rarer than the simple picture of priced volatility allowed — the wage of catastrophes feared and standards defended, not of mere market wiggle. If the behavioral account is right, then a large part of the premium is not earned at all, but is the market's payment to those who can stomach a fear that is itself a defect of attention — closer to the winnings of the steady-nerved than to the wage of a service. The volume cannot adjudicate between the two; economics has not. But it can record what the puzzle has settled: that the price of risk is emphatically not the simple, transparent wage of rationally-borne risk that the clean theory proclaimed; that sober risk aversion explains only a sliver of what the market pays; and that the remainder is either a danger we cannot quite see or a folly we cannot quite shake. Either way, the confident equation of the premium with desert has been broken.
So the puzzle stands, four decades on, a crack running through the heart of the earned account of the price of risk — the premium too large for sober fear, and salvageable only by positing hidden dangers or by confessing human folly. It leaves the volume's verdict suspended between two readings it cannot finally choose: the premium as the honest wage of catastrophes rarely seen, or the premium as the swollen wage of a dread better habits would cure. What both readings share, and what the puzzle has truly established, is that the reward for bearing risk is not what the clean theory said it was — not a quantity the market sets in cool proportion to danger soberly weighed, but a far stranger thing, shot through with what we fear and cannot price and what we feel and cannot help. The volume now turns from the priced risk of markets, where the premium could at least be measured even if it could not be explained, to a kind of uncertainty that cannot be priced at all — the genuine unforeseeable that faces the founder of an enterprise, and the profit that may, or may not, be its reward. As the table says of every price, first to last: the argument remains open.