Portfolio theory and capm - CAPM and sml applications

Learning Outcomes

This article explains the application of portfolio theory, the capital asset pricing model (CAPM), and the security market line (SML) for CFA Level 1 candidates, including:

• Understanding the role of diversification in reducing nonsystematic risk and why only systematic risk is priced in equilibrium.
• Distinguishing between systematic and nonsystematic risk within the CAPM framework and relating these to total portfolio risk.
• Describing the CAPM expected return equation, identifying each input, and explaining the economic intuition behind beta and the market risk premium.
• Calculating and interpreting beta for individual securities and portfolios, using portfolio weights to obtain portfolio beta as a weighted average.
• Applying the SML to judge whether individual assets or portfolios are fairly valued, underpriced, or overpriced relative to required return.
• Using CAPM and the SML to inform portfolio selection, compare alternative investments, and assess risk-adjusted performance for exam-style problems.
• Recognizing key assumptions, limitations, and common exam pitfalls associated with CAPM and SML applications, including estimation issues and practical deviations from the model.

CFA Level 1 Syllabus

For the CFA Level 1 exam, you are expected to understand the application of CAPM and the security market line (SML) within portfolio theory, with a focus on the following syllabus points:

• Describe the assumptions and mechanics of the CAPM.
• Explain systematic vs. nonsystematic risk and their implications for portfolio return.
• Calculate and interpret portfolio expected return, variance, and beta.
• Illustrate the use of the security market line (SML) for evaluating individual assets and portfolios.
• Apply CAPM/SML to portfolio selection, risk assessment, and performance appraisal.
• Identify limitations and potential pitfalls when applying CAPM to real investments.

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. Why is only systematic risk relevant for expected return under the CAPM?
2. What does a security plotted above the security market line (SML) indicate?
3. Give the formula for portfolio beta and describe its meaning.
4. How does a change in a portfolio's beta affect its expected return, according to CAPM?

Introduction

Portfolio theory and CAPM are central to modern finance. They provide a framework for understanding risk, diversification, and the required return on individual assets or portfolios. By modeling the risk-return trade-off, the CAPM enables you to evaluate investments, set expected returns, and optimize portfolios using the concept of the security market line (SML).

Key Term: systematic risk
The risk affecting the entire market or economy that cannot be eliminated through diversification. Also called market risk.

Key Term: nonsystematic risk
The risk specific to an individual asset or sector, which can be diversified away in a portfolio.

Key Term: capital asset pricing model (CAPM)
A model that predicts the expected return on an asset based on its sensitivity (beta) to systematic risk, given risk-free rate and expected market return.

Key Term: security market line (SML)
The graphical depiction of the expected return–beta relationship under the CAPM, showing the minimum required return for any level of systematic risk.

Key Term: beta (β)
A measure of an asset’s systematic risk relative to the market; β = 1 indicates market-level risk, β < 1 indicates less, and β > 1 more than market risk.

CAPM Fundamentals

The CAPM proposes that the expected return on an asset depends only on its sensitivity to market (systematic) risk. In equilibrium, investors will not earn additional return for holding diversifiable (nonsystematic) risk, since it can be eliminated through portfolio construction.

The CAPM expected return formula is:

Where:

• $E(R_i)$ = expected return on asset i
• $R_f$ = risk-free rate
• $\beta_i$ = beta of asset i
• $E(R_m)$ = expected return of the market portfolio

Interpretation: Investors can earn the risk-free rate, but must take on systematic risk (as captured by β) to expect a higher return. Assets with higher beta command higher expected returns.

Portfolio Beta and the SML

The CAPM can be visualized using the Security Market Line (SML). It plots expected return against beta, providing a benchmark for asset pricing:

• Securities on the SML are correctly priced.
• Securities above the SML offer higher-than-required returns and may be considered underpriced.
• Securities below the SML are overpriced.

Key Term: portfolio beta
The weighted average of the betas of the securities comprising a portfolio, representing its overall systematic risk.

Worked Example 1.1

A portfolio consists of 30% in Stock A (β=1.2), 50% in Stock B (β=0.8), and 20% in Stock C (β=1.5). What is the portfolio beta?

Answer:
Portfolio beta = (0.3 × 1.2) + (0.5 × 0.8) + (0.2 × 1.5) = 0.36 + 0.4 + 0.3 = 1.06.

This portfolio has slightly more systematic risk than the market average.

Applying the CAPM for Asset Selection

The CAPM is used for:

• Setting a required or expected return for assets given their beta.
• Evaluating if a security or portfolio is under- or over-priced (by comparing its expected return to the SML).
• Informing portfolio construction by combining securities for a target risk (β).

Worked Example 1.2

Suppose the risk-free rate is 3% and the expected return on the market is 9%. If Security Y has β = 1.4, what is its required return according to CAPM?

Answer:
Required return = 3% + 1.4 × (9% – 3%) = 3% + 1.4 × 6% = 3% + 8.4% = 11.4%

Worked Example 1.3

A stock with β = 0.5 has an expected return of 6%, risk-free rate is 2%, and expected market return is 8%. Should the stock be bought or sold?

Answer:
CAPM required return = 2% + 0.5 × (8% – 2%) = 2% + 3% = 5%
Actual return (6%) > required (5%), so the stock is underpriced – it plots above the SML and may be attractive.

Exam Warning

Be careful: The CAPM calculates expected return based on beta. You do not receive extra return for bearing diversifiable risk. Only systematic risk (quantified by beta) is priced, regardless of the asset's total volatility.

Portfolio Construction: The CAPM in Practice

Most investors hold diversified portfolios. According to CAPM:

• Only systematic risk is priced.
• The expected return for any well-diversified portfolio can be found using its beta.
• Combining a risk-free asset with the market portfolio (beta=1) results in the capital market line, while combining the risk-free asset with any risky portfolio uses the capital allocation line.
• Leveraging or deleveraging the market portfolio changes the portfolio’s risk and expected return.

Revision Tip

Always calculate portfolio beta as the weighted average beta of all holdings based on their portfolio weights. Use this to plot the portfolio on the SML.

Limitations and Practical Considerations

While foundational, CAPM has limitations:

• Real-world returns often deviate from the SML, especially over short horizons.
• Estimating beta and market returns relies on historical data.
• CAPM assumes frictionless markets and homogeneous investor expectations.
• Multi-factor models (like Fama-French) may explain returns better in practice.

Despite these drawbacks, CAPM remains a fundamental tool in risk-return analysis, portfolio selection, and performance appraisal at CFA Level 1.

Summary

The CAPM and SML provide a framework to determine the required return on any asset or portfolio based on systematic risk (beta). Only systematic risk is priced; diversifiable risk is not compensated in equilibrium. The SML sets the benchmark for assessing if securities are over- or under-priced. While the CAPM rests on simplifying assumptions and has empirical weaknesses, it is essential knowledge for CFA candidates.

Key Point Checklist

This article has covered the following key knowledge points:

• Only systematic risk (β) is priced in the CAPM; diversifiable risk is not compensated.
• The SML plots the expected return–beta relationship for all assets.
• The CAPM formula sets expected/required return based on beta.
• Portfolio beta is the weighted average of security betas.
• Assets above the SML are underpriced; below, overpriced.
• Limitations of CAPM: estimation, assumptions, empirical fit.

Key Terms and Concepts

• systematic risk
• nonsystematic risk
• capital asset pricing model (CAPM)
• security market line (SML)
• beta (β)
• portfolio beta