A Quick Review on Different Asset Pricing Models

Intro

Talking about any history is like talking about investment ( or trading, whatever), people used to prove that they are correct by simply saying ” look, if you bought xxx in year yyy, you could have zzz money by now”.

Talking about the history of the Asset pricing also the same, we feel some models are quite interesting, because of their simplicity and assumptions, one might feel like how come they even did not thought about xxx that ‘obviously’ affects the return of yyyy ? Of course, it is obvious today, you are like a time traveler, you have all the future knowledge so you can critique with comfort the things in the history, while it happened, at that time, you might would not do that.

CAPM (Capital Asset Pricing Model)

• Introduction: The CAPM, developed by Sharpe and Lintner (Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk” (1964)), is a model that describes the relationship between systematic risk and expected return for assets, particularly stocks. It’s used to determine a theoretically appropriate required rate of return of an asset.
• Problem Addressed: To understand how risk (specifically, systematic market risk) affects the expected return of an asset.
• Formula:
  •  E(R_i) = R_f + \beta_i \times (E(R_m) - R_f) 
  • E(R_i) : Expected return of investment
  • R_f : Risk-free rate
  • \beta_i : Beta of the investment
  • E(R_m) : Expected return of market
• Data Requirements: Historical returns of the asset, the market, and the risk-free rate.
• Performance and Use: Useful for pricing assets and understanding their risk-return profile, but assumes a single-period, which might not always be practical.
• Pros and Cons:
  • Pros: Simplifies the risk-return relationship, widely used for asset pricing.
  • Cons: Relies on historical data for beta, assumes market efficiency, and all investors have the same expectations.

Fama-French 3-Factor Model

• Introduction: Expanded the CAPM by Fama and French to include size and value factors.
• Problem Addressed: To explain differences in returns across diversified portfolios that CAPM couldn’t explain.
• Formula:
  • Expected Return = R_f + \beta_{market} \times (E(R_m) - R_f) + \beta_{size} \times SMB + \beta_{value} \times HML
  • SMB (Small Minus Big): Size premium
  • HML (High Minus Low): Value premium
• Data Requirements: Market returns, risk-free rate, returns on diversified portfolios, size, and book-to-market values.
• Performance and Use: Provides a better understanding of the determinants of stock returns, widely used in academic research and practical portfolio management.
• Pros and Cons:
  • Pros: Accounts for anomalies in market returns, more comprehensive.
  • Cons: More complex, requires more data, and assumes factors remain constant over time.

Momentum and Contrarian Effects

• Introduction: Examines the tendency of stocks to continue their recent performance trends.
• Problem Addressed: To understand and capitalize on the observed phenomenon of stocks continuing to rise or fall.
• Formula: Not a single formula, but involves ranking stocks based on past returns and analyzing performance.
• Data Requirements: Historical stock prices and returns.
• Performance and Use: Used in quantitative trading strategies, though subject to high volatility.
• Pros and Cons:
  • Pros: Empirical evidence supports these effects, can be profitable.
  • Cons: Requires active management, can be risky, and is subject to reversal.

4. Fama-French-Carhart 4-Factor Model

• Introduction: An extension of the Fama-French model by Carhart, including a momentum factor.
• Problem Addressed: To further refine the explanation of stock returns by adding a momentum factor.
• Formula: Same as Fama-French 3-Factor Model, with an additional term for momentum (MOM).
• Data Requirements: Same as the 3-factor model, plus momentum data.
• Performance and Use: Provides a more detailed analysis of portfolio returns, especially for explaining short-term trends.
• Pros and Cons:
  • Pros: More comprehensive, captures short-term trends.
  • Cons: Increased complexity and data requirement, assumes that past performance predicts future performance.