💲Intro to Investments Unit 11 – Capital Asset Pricing and Factor Models

Key Concepts and Definitions

• Capital Asset Pricing Model (CAPM) framework for determining the expected return of an asset based on its systematic risk
• Beta measure of an asset's sensitivity to market movements, calculated as the covariance between the asset's returns and the market's returns divided by the variance of the market's returns
• Systematic risk non-diversifiable risk that affects the entire market (interest rates, inflation)
• Unsystematic risk company-specific risk that can be diversified away through portfolio diversification
• Risk-free rate theoretical rate of return on an investment with zero risk, typically based on government bond yields
• Market risk premium additional return investors expect to receive for taking on the risk of investing in the market
  • Calculated as the difference between the expected return of the market and the risk-free rate
• Factor models attempt to explain the returns of assets by identifying common factors that drive their performance (macroeconomic variables, firm characteristics)

Historical Context and Development

• Modern Portfolio Theory (MPT) developed by Harry Markowitz in the 1950s, laid the foundation for the CAPM
  • MPT introduced the concept of portfolio diversification and the efficient frontier
• CAPM introduced by William Sharpe, John Lintner, and Jan Mossin in the 1960s
  • Extended MPT by introducing the concept of systematic risk and the relationship between risk and expected return
• Efficient Market Hypothesis (EMH) proposed by Eugene Fama in the 1970s, suggests that asset prices reflect all available information
  • EMH is closely related to the CAPM, as both assume that investors are rational and have homogeneous expectations
• Arbitrage Pricing Theory (APT) developed by Stephen Ross in 1976 as an alternative to the CAPM
  • APT allows for multiple risk factors to explain asset returns, rather than just systematic risk
• Fama-French Three-Factor Model introduced in 1992, extending the CAPM by adding size and value factors
• Carhart Four-Factor Model (1997) further extended the Fama-French model by adding a momentum factor

The Capital Asset Pricing Model (CAPM)

• CAPM equation: $E(R_i) = R_f + \beta_i[E(R_m) - R_f]$
  • $E(R_i)$ expected return of asset $i$
  • $R_f$ risk-free rate
  • $\beta_i$ beta of asset $i$
  • $E(R_m)$ expected return of the market
• Security Market Line (SML) graphical representation of the CAPM, showing the relationship between an asset's beta and its expected return
• Assumptions of the CAPM:
  • Investors are risk-averse and aim to maximize their expected utility
  • Investors have homogeneous expectations and access to the same information
  • There are no transaction costs or taxes
  • Investors can borrow and lend at the risk-free rate
• Implications of the CAPM:
  • Higher systematic risk (beta) leads to higher expected returns
  • Diversification can eliminate unsystematic risk, but not systematic risk
• Empirical tests of the CAPM have shown mixed results, with some studies supporting the model and others finding inconsistencies

Factor Models: Types and Applications

• Arbitrage Pricing Theory (APT) multi-factor model that allows for multiple risk factors to explain asset returns
  • Factors can include macroeconomic variables (GDP growth, inflation) or firm characteristics (size, value)
• Fama-French Three-Factor Model extends the CAPM by adding size (SMB) and value (HML) factors
  • SMB (Small Minus Big) represents the return difference between small-cap and large-cap stocks
  • HML (High Minus Low) represents the return difference between high book-to-market and low book-to-market stocks
• Carhart Four-Factor Model adds a momentum factor (WML) to the Fama-French model
  • WML (Winners Minus Losers) represents the return difference between past winners and past losers
• Other factor models include the Pastor-Stambaugh Liquidity Factor Model and the Fama-French Five-Factor Model
• Applications of factor models:
  • Portfolio construction and risk management
  • Performance attribution and benchmarking
  • Asset pricing and valuation

Risk and Return Relationships

• Risk-return tradeoff principle that higher expected returns come with higher levels of risk
• Systematic risk and beta:
  • Systematic risk cannot be diversified away and is measured by beta
  • Assets with higher betas are more sensitive to market movements and have higher expected returns
• Unsystematic risk and diversification:
  • Unsystematic risk is company-specific and can be reduced through portfolio diversification
  • Well-diversified portfolios are primarily exposed to systematic risk
• Total risk sum of systematic and unsystematic risk
  • $Total\ Risk = Systematic\ Risk + Unsystematic\ Risk$
• Risk measures:
  • Standard deviation measures the dispersion of returns around the mean
  • Sharpe ratio measures risk-adjusted performance by dividing excess returns by standard deviation
  • Treynor ratio measures risk-adjusted performance by dividing excess returns by beta

Practical Applications in Portfolio Management

• Asset allocation process of determining the optimal mix of asset classes (stocks, bonds, cash) based on an investor's risk tolerance and investment objectives
  • CAPM and factor models can help estimate expected returns and risk for different asset classes
• Portfolio optimization process of constructing a portfolio that maximizes expected return for a given level of risk or minimizes risk for a given level of expected return
  • Mean-variance optimization, based on MPT, is a common approach
• Performance evaluation process of assessing the risk-adjusted performance of a portfolio or investment strategy
  • CAPM and factor models can be used to calculate risk-adjusted performance measures (Sharpe ratio, Treynor ratio)
• Risk management process of identifying, measuring, and mitigating risks in a portfolio
  • CAPM and factor models can help identify sources of risk and measure portfolio sensitivity to different risk factors
• Style analysis process of determining the investment style of a portfolio manager (value, growth, small-cap, large-cap)
  • Factor models can be used to decompose portfolio returns and identify the manager's style exposures

Limitations and Criticisms

• Assumptions of the CAPM:
  • Unrealistic assumptions (perfect market, no transaction costs, homogeneous expectations) limit the model's practical applicability
  • Investors may not be fully rational or have homogeneous expectations
• Single-factor limitation:
  • CAPM relies on a single risk factor (market risk), which may not fully capture the complexity of asset returns
  • Other factors (size, value, momentum) have been shown to explain returns beyond market risk
• Estimation challenges:
  • Difficulty in accurately estimating input parameters (risk-free rate, beta, market risk premium)
  • Estimation errors can lead to incorrect conclusions and investment decisions
• Empirical inconsistencies:
  • Some studies have found that the CAPM does not fully explain observed asset returns
  • Low-beta stocks have been shown to outperform high-beta stocks, contrary to CAPM predictions
• Time-varying risk and return:
  • CAPM assumes that risk and return are constant over time, which may not hold in practice
  • Risk and return characteristics can change due to market conditions, economic cycles, and other factors

Recent Developments and Future Trends

• Behavioral finance incorporation of psychological and behavioral factors into asset pricing models
  • Investors may exhibit biases (overconfidence, loss aversion) that affect their investment decisions and market prices
• Machine learning and big data:
  • Application of machine learning techniques (neural networks, decision trees) to identify new risk factors and improve factor models
  • Use of alternative data sources (satellite imagery, social media sentiment) to enhance factor models
• Sustainable investing and ESG factors:
  • Increasing focus on environmental, social, and governance (ESG) factors in investment decision-making
  • Integration of ESG factors into factor models to capture non-financial risks and opportunities
• Dynamic factor models:
  • Development of factor models that allow for time-varying risk and return characteristics
  • Incorporation of macroeconomic variables and regime-switching models to capture changing market conditions
• Advancements in portfolio optimization:
  • Use of robust optimization techniques to account for estimation errors and model uncertainty
  • Incorporation of transaction costs, liquidity constraints, and other practical considerations into optimization models