Questions: Market Anomalies and Asset Pricing Puzzles

Question 1

A researcher finds that stocks with high short interest consistently earn negative abnormal returns over the following month, even after adjusting for beta. She concludes this proves financial markets are inefficient. A colleague challenges this conclusion. What is the strongest challenge?

• A. One month is too short a measurement window to draw reliable conclusions about market efficiency
• B. High short interest might proxy for a priced risk factor that CAPM fails to capture — anomaly tests always simultaneously test market efficiency and the assumed pricing model
• C. Short sellers are sophisticated insiders and their positions are not exploitable by ordinary investors
• D. Abnormal returns disappear once the transaction costs of establishing short positions are factored in

Answer: (B)

This is the joint hypothesis problem in action. Any test of market efficiency must specify what 'normal' returns are, which requires an asset pricing model. If short-interest stocks earn excess returns relative to CAPM predictions, there are two interpretations: (1) markets are inefficient and these stocks are mispriced, or (2) CAPM is misspecified and high short interest proxies for a genuine risk factor that commands a premium. Return data alone cannot distinguish these. The colleague's challenge is correct: the finding is anomalous relative to CAPM, but that could reflect model failure rather than market failure.

Question 2

The equity premium puzzle is best described as:

• A. The empirical finding that stocks have underperformed bonds over most 30-year horizons, contradicting the prediction that risk-bearing earns a premium
• B. The difficulty of explaining why the historical equity-bond return gap is so large that it requires implausibly extreme levels of risk aversion within standard expected utility models
• C. The paradox that small-cap stocks earn higher returns than large-cap stocks despite being easier to diversify
• D. The observation that investors hold too many equities relative to what portfolio theory prescribes, suggesting they are risk-seeking rather than risk-averse

Answer: (B)

The puzzle is not that equities outperform bonds — that's expected as compensation for bearing systematic risk. The puzzle is the *magnitude* of the premium (~5–8% annually in U.S. data). Under standard consumption-based asset pricing with plausible risk aversion (coefficient 1–10), the model predicts a premium of less than 1%. Matching the observed premium requires a risk aversion coefficient above 30, implying investors would refuse coin flips for trivially small losses — behavior inconsistent with observed economic decisions. The puzzle reveals a deep failure of standard utility models to match asset market data, not a simple question about whether stocks beat bonds.

Question 3

The momentum anomaly — past 3-12 month winners outperforming past losers — constitutes definitive evidence that financial markets are informationally inefficient, since no rational risk story can explain it.

• T. True
• F. False

Answer: False

Momentum is among the most persistent and puzzling anomalies, and rational risk-based explanations are strained — but 'strained' is not the same as 'impossible.' The joint hypothesis problem means any anomaly is simultaneously evidence against EMH and against the pricing model. Researchers have proposed risk stories involving time-varying expected returns and momentum crash risk (momentum strategies suffer severe losses during market reversals). The behavioral explanations (underreaction, overconfidence) fit the data better, but behavioral biases should be arbitraged away by rational investors — which is itself a puzzle. 'Definitive evidence' is too strong; the debate remains live.

Question 4

Market anomalies typically weaken or disappear after being published in academic journals, because publication allows more capital to exploit the strategy and arbitrage away the mispricing.

• T. True
• F. False

Answer: True

This 'anomaly decay' is well-documented. After a strategy is published, institutional investors incorporate it into their trading, increasing demand for the pattern's winners and selling its losers, which compresses the return differential. This is actually consistent with the EMH — the market becomes more efficient once information about the pattern is publicly available. However, not all anomalies fully disappear; some (like momentum) remain partially intact, suggesting either genuine risk compensation or limits to arbitrage that prevent complete elimination.

Question 5

What is the joint hypothesis problem, and why does it make anomalies fundamentally ambiguous evidence about whether financial markets are efficient?

Model answer: Every test of market efficiency requires a model of what 'fair' returns are. When we test whether an anomaly represents a mispricing, we are simultaneously testing two things: (1) the EMH, and (2) the asset pricing model used to compute expected returns. If small stocks earn 'excess' returns, it could mean markets are inefficient and small stocks are underpriced, or it could mean CAPM is wrong and small stocks bear a real risk factor that commands a premium. Return data alone cannot separate these explanations. This is why Fama and French responded to the size and value effects by adding risk factors to CAPM rather than declaring markets inefficient — both responses are consistent with the same data.

The joint hypothesis problem is one of the deepest methodological challenges in empirical finance. It implies that any anomaly finding is only as strong as the asset pricing model it uses as a benchmark. This is why anomaly research has driven the development of multi-factor models (Fama-French 3-factor, Carhart 4-factor, Fama-French 5-factor) — as the benchmark model improves, some anomalies 'disappear' by being reinterpreted as risk factors, while others survive even the more sophisticated models and remain genuine puzzles.