Stock Market Anomalies: Value, Size, and Momentum

Posted on Feb 14, 2025 in Finance

Cross-Section Predictability of Stock Returns

Ideally, all securities should have equal expected risk-adjusted returns, eliminating any alpha (α). However, empirical studies have identified several cross-sectional anomalies, including the value premium, size effect, and momentum. These anomalies result in the formation of groups of stocks with different average returns.

Predictability of returns?

• Yes: Behavioral finance-based explanations.
• No: The asset-pricing model used is misspecified.

Investment Strategies:

1. Value: Sort stocks according to balance sheet or income statement figures.
2. Size: Sort stocks according to their market capitalization.
3. Momentum: Sort stocks according to past performance.

Value Strategies

Value strategies compare market price with fundamental value taken from the income statement per share.

Value Strategies Performance

(A) Value strategies tend to outperform the market in the long run:

1. Buying value stocks results in superior risk-adjusted returns relative to the market.
2. Buying non-value (glamour) stocks results in inferior risk-adjusted returns relative to the market.

Value Stocks > Non-value (Glamour) Stocks

The risk factor is the difference between value and market value. Why have dimensional value strategies produced superior returns?

1. Compensation for high risk.
2. Contrarian strategies exploit mistakes and limitations of investors.

Observations:

1. There is no evidence of greater risk for value stocks; value and growth stock portfolios have similar standard deviations.
2. There is no evidence that investors tend to extrapolate past growth rates too far into the future. Future earnings growth of glamour stocks is often disappointing, while value stocks tend to surprise investors positively.

Book-to-Market Ratio (B/M)

(B) A low B/M ratio suggests past market growth, while a high B/M ratio suggests possible future growth. A positive earnings announcement often leads to a jump in stock price.

Conclusions on Value Strategies

(C) Conclusions:

• Investors often extrapolate the past too far into the future.
• Investors wrongly equate a good company with a good or safe investment, irrespective of the price.
• Investors tend to overweight firm-specific current information and underweight aggregate statistical evidence.

Why don’t investors use value strategies more extensively? Institutions and value investing often face career and reputational concerns.

Momentum Strategies

Momentum strategies capitalize on positive return persistence among high-performing stocks. On average, the worst-performing stocks over a six-month period underperform the best-performing stocks over similar horizons in the future. Going long in a portfolio of the highest-return stocks and shorting a portfolio of the lowest-return stocks, rebalancing every six months, often beats a buy-and-hold strategy.

Size Effect

The size effect demonstrates that small firms consistently experience significantly larger risk-adjusted returns than large firms.

Final Conclusion

It is not definitively clear whether rational or behavioral finance explanations are more accurate in explaining these market anomalies.

Portfolio Performance Evaluation

Key Metrics:

• Sharpe Ratio: (AR – Rf) / SD
• Treynor Ratio: (AR – Rf) / β

Where:

• AR = Average Return
• Rf = Risk-free Rate
• SD = Standard Deviation
• β = Beta

Jensen’s Alpha: AR – (Rf + β(Rm – Rf))

Where Rm = Average Return on Market

Fama-French Model

Three-Factor Model

R_it = α_i + β_im * R_mt + β_ismbSMB_t + β_ihmlHML_t + e_it

Where:

• SMB: Small Minus Big
• HML: High Minus Low

Size and book-to-market ratios explain returns on securities. Smaller firms and high book-to-market firms tend to experience higher returns. Returns are explained by size, book-to-market, and beta. Interpretation: Size and value are priced risk factors; premiums could be due to investor irrationality or behavioral biases.

Four-Factor Model

The original model, augmented with a momentum factor, is commonly used to evaluate the abnormal performance of a stock portfolio:

R_it = α_i + β_imR_mt + β_ismbSMB_t + β_ihmlHML_t + β_imomMOM_t + e_it

Problems with the Models

1. Many observations are needed for significant results.
2. Shifting parameters when portfolios are actively managed make accurate performance evaluation more elusive. For instance, the average beta is calculated through linear regression over years, raising questions about its accuracy for current data.