Does the Stock Market Rationally Reflect Fundamental Values?

Summers argues that the standard statistical tests used to support the Efficient Markets Hypothesis – tests for serial correlation in excess returns, and for predictable excess returns conditional on an estimated mispricing – have very low statistical power against a specific, economically interesting alternative: that market valuations differ from the rational present value of fundamentals by a large, slowly-decaying (but not exploding) multiplicative error that behaves like “fads.” In a numerical example calibrated to match the observed variance of monthly U.S. stock returns, a valuation error with a standard deviation of about 30 percent of price, and a half-life of around three years, generates a theoretical first-order autocorrelation in excess returns of only about -0.008 – smaller than the roughly 0.04 standard error one would get from fifty years of monthly data, so this large, persistent mispricing would be statistically undetectable; achieving a 50 percent chance of rejecting market efficiency in this example would require just over 5,000 years of data. Because “the same problems of identification which plague financial economists also plague would-be speculators,” the paper argues the inability of statistical tests to detect such errors also implies that speculative arbitrage is unlikely to eliminate them, so that failures to reject market efficiency should not be read as evidence that market prices are, in fact, rational reflections of fundamental value – a distinction Summers says matters most for macroeconomic theories, such as Tobin’s q theory of investment, that treat asset prices as if they faithfully reveal the present value of future cash flows.

The Limits of Arbitrage

Shleifer and Vishny argue that textbook arbitrage – “simultaneous purchase and sale of the same…security in two different markets,” requiring no capital and entailing no risk – does not describe how real-world arbitrage works, because professional arbitrage is typically conducted by a small number of specialized investors managing other people’s capital rather than their own. This “separation of brains and resources” matters because the investors supplying that capital generally cannot evaluate the arbitrageur’s strategy directly, so they allocate and withdraw funds based on the arbitrageur’s recent performance – a mechanism the authors call “performance-based arbitrage” (PBA). In their formal model, this breaks the standard result that arbitrageurs become more aggressive the further prices move from fundamental value: because an arbitrageur’s measured returns are worst exactly when a mispricing he has bet against has deepened, PBA investors may rationally withdraw capital at precisely that moment, forcing the arbitrageur to cut his position (or liquidate entirely) when the trade’s expected return is highest. The model formally shows that in “extreme circumstances” – when arbitrageurs are already fully invested and the mispricing worsens further – prices fall more than one-for-one with the underlying noise-trader shock, and this loss of market “resiliency” gets worse as performance sensitivity rises, even though on average arbitrageurs still make money and move prices toward fundamentals, consistent with Friedman’s observation that destabilizing arbitrage is “equivalent to saying that arbitrageurs lose money on average” – just not always. The paper uses this logic to predict which markets will attract concentrated arbitrage capital (those, like bonds and foreign exchange, where mispricing can be identified and realized quickly, with little fundamental risk) and to offer an alternative, idiosyncratic-risk-based explanation for why some well-known return anomalies, such as the value/glamour spread, persist despite looking exploitable on paper.

Journal of Finance | Macro Paper Warehouse

Does the Stock Market Rationally Reflect Fundamental Values?

The Limits of Arbitrage