Market Pricing Anomalies - Time Series and Cross-Sectional
Learning Outcome Statement:
describe market anomalies
Summary:
Market anomalies are deviations from the expected market efficiency, where asset prices do not reflect all available information. These anomalies can be identified through time-series data, cross-sectional analysis, and other methods. While some anomalies may appear to offer opportunities for excess returns, they are often difficult to exploit profitably due to factors like risk and trading costs. Over time, many anomalies tend to disappear as they are arbitraged away or as more sophisticated statistical methods fail to detect them.
Key Concepts:
Time-Series Anomalies
Time-series anomalies are patterns in asset prices over time that contradict the efficient market hypothesis. Examples include calendar effects like the January effect, where stocks show abnormal returns in January, and momentum effects, where stocks that have performed well continue to do so.
Cross-Sectional Anomalies
Cross-sectional anomalies occur when differences in returns across various securities cannot be explained by known risk factors. Examples include the size effect, where smaller companies outperform larger ones, and the value effect, where stocks with lower price-to-earnings ratios outperform those with higher ratios.
Data Mining
Data mining, or data snooping, involves extensively searching through data to find patterns that can be presented as significant anomalies, often without a prior hypothesis. This method can lead to the identification of spurious anomalies that do not hold up over time or in out-of-sample tests.
Formulas:
Fama and French Three-Factor Model
The Fama and French model extends the CAPM by including size and value factors in addition to the market risk factor, capturing additional dimensions of risk that affect stock returns.
Variables:
- :
- Expected return on stock i
- :
- Risk-free rate
- :
- Expected market return
- :
- Small Minus Big, a size premium
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- High Minus Low, a value premium
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- Sensitivity of the stock i to the market premium
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- Sensitivity of the stock i to the size premium
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- Sensitivity of the stock i to the value premium