Untitled Notes

Using CAPM to Identify Mispricing
- Explore how CAPM can be applied to identify mispriced stocks.
Multi-Factor Models of Stock Returns
- Fundamental (value) and size strategies
- Long-only and long-short portfolios
- Multi-factor modeling:
  - Fama-French 3-factor model
  - Technical (momentum) strategies
  - Fama-French-Carhart 4-factor model
- Critical assessment of the models and their implications.
- Provide examples and case studies related to the content.

CAPM predicts that the market portfolio should have the highest Sharpe ratio. All securities should lie on the Security Market Line (SML):
- Equation: \mui - Rf = \betai(\mum - R_f)
- Rearranging gives: \mui = Rf + \betai(\mum - R_f)

Market beta ((\beta)) is positively related to expected return ((\mu)).
Beta is the only determinant of expected return; other factors like size, growth, etc., are irrelevant.
- Asserted Equation: \mui - Rf = \alphai + \betai(\mum - Rf)
Stocks with a non-zero CAPM alpha can help improve the market's Sharpe ratio.
Anomalies are identified as stocks that deviate from model predictions. Specifically, CAPM anomalies are stocks that exhibit non-zero alphas.

Alpha vs. Anomalies: Both alpha and anomalies represent portfolio strategies yielding returns that differ systematically from CAPM predictions.
- Testing CAPM traditionally involves running regressions to check for significant alpha, which can be problematic due to statistical errors and regression assumptions.
- A more robust testing method involves identifying additional variables or portfolios beyond the market that predict stock returns.

Fama-French Model (1992) identifies characteristics beyond beta predicting stock returns:
- Size: Market Capitalization (ME)
- Definition: ME = Market\,Equity = Number\,of\,Shares \times Share\,Price
- Value: Book-to-Market Ratio (BM)
- Definition: BM = \frac{BE}{ME} where BE = Book Equity.
- MV should ALWAYS be greater than MV
- if BV is MUCH less than MV we call it a “growth” company
- if BV is a little less than MV we call it a “value” company
- Value firms are much easier to value
Findings:
- Small firms and value firms consistently outperform larger and growth firms when controlling for CAPM beta.
- Value is a particularly strong indicator of performance.

Value Stocks: Stocks undervalued by the market, usually sell at low prices relative to earnings or book value and provide above-average dividends.
Growth Stocks: Shares of companies with high growth prospects, typically trading at high prices relative to earnings or book value and paying little to no dividends.

Fama and French build portfolios on size and book-to-market in their 1992-1993 studies.
Portfolios are formed each July and held until June the following year.
Analysis is based on performance of these portfolios (5x5 methodology).

The cumulative gains from investments between 1926 to 2022 demonstrate significant differences in returns across portfolio strategies.
Examples:
- Market (9.9% annual return) vs Small Value (16.0% annual return).
- These statistics underscore the importance of incorporating value and size in investment strategies.

Long-Only Portfolios: Invest entirely in assets, weighted to sum to one. Example calculation of return:
- Given investments in shares yielding specific profits, calculate gross and net returns.
Long-Short Portfolios: Involves both long positions and shorts, where weights can sum to zero. Formulas include:
- R{LS} = R{Long} - R_{Short}
- Calculate alphas and betas for both long and short positions:
- \alpha{LS} = \alpha{Long} - \alpha_{Short}
- \beta{LS} = \beta{Long} - \beta_{Short}

Given risk-free rate at 1% and expected betas and returns for companies:
- Calculation of expected return for a long-short portfolio consists of using excess returns and individual stock calculations, ultimately leading to an overall expected return based on both stocks' performances including alphas.

Construction involves strategic positioning across various assets based on historical performance.
Implement a diversified strategy, including high book-to-price ratio stocks long and low book-to-price ratio stocks short.
Portfolio returns take into account market exposure and specific investment strategies (value vs. growth).

The inclusion of momentum (UMD) is important in extending the Fama-French model, leading to a four-factor approach:
- UMD targets the potential upward and downward movement of assets based on prior performances.
Jegadeesh and Titman (1993) developed momentum investment strategies through systematic ranking and shorting practices based on stock performance.

Chart data indicating cumulative returns from different strategic portfolios from July 1926 to September 2022 highlights the substantial returns from multi-factor models including momentum elements.
Momentum (UMD) demonstrated a clear positive impact on Sharpe ratio improvements, raising it from 0.525 to 0.955.

Future efficacy of these strategies remains in question due to potential crowding effects diminishing returns as more investors enter these trades.
Recent analyses suggest that while fundamental strategies are well-known, their performance has decreased post-2008.
Continued evolution and adaptation of models remain essential to stay ahead in investment strategy effectiveness and maximizing portfolio returns.