Does the Stock Market Rationally Reflect Fundamental Values?

Summers tests the hypothesis that a security’s price equals the present value of its expected future cash flows discounted at a constant, known required rate of return r, which he writes as P_t = E_t[Σ D_{t+s}/(1+r)^s | Ω_t] (eq. 1), equivalent to the statement that excess returns R_t - r equal a serially uncorrelated error e_t orthogonal to information Ω_t (eqs. 3-4). He deliberately assumes the expected-return model is known with certainty – acknowledging “recent theoretical work suggests that the particular model of ex-ante returns considered here cannot be derived rigorously” – because doing so isolates the test of efficiency itself from the usual joint-hypothesis problem, and because it can only overstate, not understate, the power of the tests he goes on to examine.

The paper’s alternative hypothesis is that log price deviates from log fundamental value by a term u_t that follows a first-order autoregressive process, p_t = pt + u_t, u_t = αu{t-1} + v_t with 0 ≤ α ≤ 1 – so that valuation errors tend to persist, but not to grow without bound.* Summers notes this specification “clearly captures Keynes’s notion that markets are sometimes driven by animal spirits unrelated to economic realities,” is “consistent with the experimental evidence of Tversky and Kahneman that subjects overreact to new information,” and “captures Robert Shiller’s suggestion that financial markets display excess volatility and overreact to new information” – though it does not capture Blanchard and Watson’s distinct notion of intermittent rational speculative bubbles, in which valuations diverge arbitrarily rather than mean-revert.

Summers frames the core methodological point as a basic principle of hypothesis testing: “the inability of a body of data to reject a scientific theory does not mean that the tests prove, demonstrate or even support its validity,” and the usefulness of any test depends on its power to discriminate the null from specific, plausible alternatives – which is why “findings that excess returns cannot be predicted using past data on sunspots” provide weaker support for efficiency than a demonstration that returns are not serially correlated. The paper’s project is accordingly to show that the standard serial-correlation and announcement-based tests have essentially no power against the fads alternative in Q2, so their repeated failure to reject efficiency says little about whether fads-type mispricing is actually absent.

Combining the model and the alternative hypothesis implies excess returns follow an ARMA(1,1) process with negative serial correlation (eq. 6-8); calibrating the fads process to σ²_u = 0.08 (so valuation errors have a standard deviation close to 30 percent of price) and α = 0.98 (so the market takes about three years to eliminate half of any valuation error), Summers finds the theoretical first-order autocorrelation of monthly excess returns is only -0.008 – far smaller than the roughly 0.042 standard error implied by 600 monthly observations (fifty years) under the null. “In order to have a 50 percent chance of rejecting the null hypothesis it would be necessary to have data for just over 5000 years,” and even in the extreme case where all of the variance in returns is spurious (σ²_e = 0, so a²_u = 0.10), the theoretical first-order autocorrelation is only -0.01 – still undetectable. Summers notes this calculation “overstates the power of tests actually performed” by assuming constant variance and normal residuals, so real-world power is if anything lower.

No: “under the alternative hypothesis considered here, the market responds immediately to news about fundamentals…and no abnormal patterns in returns are generated subsequent to major news announcements” – the fads hypothesis and market efficiency “make exactly the same prediction about true news,” so the extensive evidence that prices respond promptly to announcements, often cited as support for efficiency, has no power to distinguish between the two hypotheses.

Even granting these tests more power than could actually be achieved in practice (by assuming the unobservable fundamental value p is known), Summers shows the implied expected excess return from a one-standard-deviation valuation error is small relative to typical monthly return volatility: in his calibrated example (α = 0.98, σ_u ≈ 0.28), a one-standard-deviation undervaluation implies an expected monthly excess return of only about 0.56 percent, against a monthly return standard deviation of about 6 percent.* Regressing excess returns on the (hypothetically observed) mispricing, the implied coefficient has a standard error large enough that the null of efficiency would fail to be rejected at the 5 percent level with probability one-half when α = 0.98, and with probability greater than five-sixths when α = 0.99 – so, Summers concludes, “tests of semi-strong efficiency do not have much more power against the type of inefficiency considered here than do tests on serial correlation.”

Summers argues the same identification problem that limits economists’ tests also limits speculators: “if the large persistent valuations errors considered here leave no statistically discernible trace in the historical patterns of returns, it is hard to see how speculators could become aware of them,” and separately, even a speculator who did somehow identify a mispricing would face expected excess returns that are “small and uncertain,” so risk-averse arbitrageurs “will only be willing to take limited positions when they perceive valuation errors,” leaving errors uneliminated unless widely recognized. He illustrates the broader point – those that fundamentals can diverge from price without a statistically detectable trace – with Schaefer’s finding that some British government bonds (gilts) were dominated securities “with probability one” in an economic sense, yet period-by-period returns on the dominated bond and its dominating portfolio were too imperfectly correlated to achieve statistical significance; and with the case of stock index futures, which have been priced to yield returns several percentage points above the perfectly-correlated underlying market portfolio without arbitrage eliminating the gap.

The paper points to the persistent discount of closed-end mutual funds relative to the easily-measured market value of their underlying portfolios, to Schaefer’s gilt-pricing anomaly, to takeover premiums “frequently paid even in cases where there are no obvious economic advantages to combination,” and to French and Roll’s finding that stock prices move markedly more during exchange trading hours than during otherwise-similar non-trading intervals – evidence Summers reads as suggesting that “much of the volatility in the market is in some sense self-generating” rather than driven by news about fundamentals. He also cites his own work with Shleifer (Shleifer and Summers) arguing there is no reason to expect market forces to eliminate irrational traders, since risk-bearing can even let them come to dominate the market.

Summers is explicit that he is not disputing “the central message of the huge literature on market efficiency,” namely the difficulty of earning abnormal returns using only public information, and so the paper does not call into question standard portfolio-management prescriptions derived from market efficiency. What it does call into question is the further, commonly drawn inference that observed prices are therefore rational assessments of fundamental value – a distinction he says matters for corporate financial policy, for event-study research, and “even more” for macroeconomic theories such as the q theory of investment that treat asset prices as faithfully revealing the present value of the cash flows an asset will generate. He closes by suggesting that a “more catholic approach” to modeling how errors enter asset prices, potentially drawing on the literature on individual choice under uncertainty, is preferable to “insisting on the basis of very weak available evidence that market valuations are always rational.”