Portfolio Management: Markowitz, CAPM, CML, APT & Returns
Key Topics
- Portfolio Management – Concept and Markowitz Model
- Portfolio Selection – Capital Market Line, Security Market Line, Capital Asset Pricing Model and Arbitrage Pricing Theory
- Portfolio Performance Evaluation – Sharpe, Treynor and Jensen Models
To provide a helpful overview, I can explain the core concepts of each section.
💰 Portfolio Management Concepts
Portfolio Management and Markowitz Model
- Portfolio Management: The art and science of making decisions about investment mix and policy, matching investments to objectives, asset allocation for individuals and institutions, and balancing risk against performance.
- Markowitz Portfolio Theory (MPT): Developed by Harry Markowitz, this model suggests that investors should focus on selecting portfolios based on their overall risk (measured by standard deviation, σ) and expected return (E[R]), rather than selecting individual assets.
- The core idea is diversification to reduce unsystematic (specific) risk.
- The model helps define the Efficient Frontier — a set of optimal portfolios that offer the highest expected return for a given level of risk, or the lowest risk for a given expected return.
📈 Portfolio Selection Models
These models explain the relationship between risk and expected return in the market, helping investors select optimal portfolios.
Capital Market Line (CML) and Security Market Line (SML)
- Capital Market Line (CML): This line represents the trade-off between risk and return for efficient portfolios that combine the risk-free asset (e.g., T-bills) with the Market Portfolio (M).
- Risk on the CML is measured by total risk (standard deviation, σ).
- CML equation: E[Rp] = Rf + ((E[RM] – Rf) / σM) σp
- Security Market Line (SML): This line represents the relationship between systematic risk (measured by beta, β) and expected return for individual securities or any portfolio.
- The SML is the graphical representation of the CAPM.
Capital Asset Pricing Model (CAPM)
- CAPM: A model used to determine a theoretically appropriate required rate of return for an asset, given its systematic risk (β). It states that the expected return on a security is equal to the risk-free rate plus a risk premium that compensates for systematic risk.
- CAPM equation: E[Ri] = Rf + βi × (E[RM] – Rf)
- E[Ri]: Expected return of the security/portfolio
- Rf: Risk-free rate
- E[RM]: Expected return of the market
- βi: Beta of the security/portfolio (systematic risk)
Arbitrage Pricing Theory (APT)
- APT: An alternative to CAPM. It suggests that an asset’s expected return can be modeled as a linear function of various macroeconomic risk factors, where the sensitivity to each factor is represented by a factor-specific beta.
- Key difference from CAPM: APT is a multi-factor model (it can use many factors, such as inflation, GNP, interest rates), while CAPM is a single-factor model (market risk is the only factor).
🔬 Portfolio Performance Evaluation
These models are used ex post (after the fact) to compare the performance of a managed portfolio against a benchmark, adjusting for the risk taken.
Sharpe, Treynor, and Jensen Measures
All three measures evaluate excess return relative to risk, but they use different measures of risk:
| Measure | Risk Metric Used | Interpretation |
|---|---|---|
| Sharpe Ratio | Total Risk (σ or Standard Deviation) | Measures the portfolio’s excess return per unit of total risk. Best for evaluating a total portfolio. |
| Treynor Ratio | Systematic Risk (β or Beta) | Measures the portfolio’s excess return per unit of systematic risk. Best for evaluating a sub-portfolio within a larger, diversified portfolio. |
| Jensen’s Alpha | Systematic Risk (β) | Measures the excess return relative to the return predicted by the CAPM. A positive α means the manager outperformed the market (after adjusting for systematic risk). |
Would you like a more detailed explanation of any specific model, such as the CAPM or the Sharpe Ratio?