Capital Market Theory and CAPM: Complete Study Notes for AIF Managers

Capital Market Theory (CMT) is a natural extension of Modern Portfolio Theory (MPT). While MPT focuses on the construction of efficient portfolios of risky assets, Capital Market Theory introduces the concept of a risk-free asset. The introduction of this asset fundamentally changes how investors approach portfolio selection and how risky assets are priced in a competitive market.

The most dominant model emerging from this theory is the Capital Asset Pricing Model (CAPM), which provides a coherent framework for determining the required rate of return for any risky asset based on its systematic risk.

1. Fundamental Assumptions of Capital Market Theory

Capital Market Theory relies on several assumptions to create a standardized model of market behavior. While many of these are theoretical, the model effectively predicts market movements and helps in the valuation of securities.

• Homogeneous Expectations: All investors estimate the same probability distributions for future rates of return.
• One-Period Time Horizon: Investors make decisions based on a single, identical hypothetical period (e.g., one year).
• Risk-Free Borrowing and Lending: Investors can lend money at the risk-free rate (by buying T-bills) or borrow money at that same rate.
• Infinite Divisibility: All investments can be bought or sold in fractional shares.
• Perfect Markets: There are no taxes, transaction costs, or inflation.
• Market Equilibrium: All investments are correctly priced relative to their risk levels at the start of the period.

2. The Capital Market Line (CML)

The Capital Market Line represents the new "Efficient Frontier" when a risk-free asset is introduced to a universe of risky assets.

Characteristics of a Risk-Free Asset

A risk-free asset is defined by its certainty of return.

• The standard deviation of return is zero.
• It has zero correlation with all other risky assets.
• It provides the risk-free rate of return (rf).
• On a risk-return graph, it lies exactly on the vertical (Y) axis.

The CML Equation

When an investor combines a risk-free asset with a portfolio of risky assets, the expected return is a linear weighted average.

Formula for Expected Portfolio Return:

E(Rport) = WRF(RFR) + (1 - WRF)E(Ri)

Where:

• WRF = Proportion of wealth in the risk-free asset.
• RFR = Risk-Free Rate.
• E(Ri) = Expected return on the risky portfolio.

The Market Portfolio (M)

The Market Portfolio is the point of tangency between the risk-free rate and the efficient frontier of risky assets. In theory, Portfolio 'M' contains every risky asset in the world (stocks, bonds, real estate, etc.) in proportion to its market value. Because it is perfectly diversified, all unsystematic risk is eliminated.

3. Diversification and Types of Risk

The total risk of an investment consists of two distinct components:

Unsystematic (Non-Market) Risk

This is the risk unique to a specific company or industry (e.g., a strike, a management change, or a product failure).

• Key Point: This risk can be eliminated through diversification.
• CMT Insight: Because it can be diversified away, investors are not compensated for bearing unsystematic risk.

Systematic (Market) Risk

This is the risk that affects the entire market simultaneously (e.g., changes in interest rates, GDP growth, or political instability).

• Key Point: This risk cannot be diversified away.
• CMT Insight: Investors demand a risk premium only for bearing systematic risk.

The Diversification Threshold: Research suggests that the marginal benefit of risk reduction dies down after adding 20 to 30 securities to a portfolio. Beyond this point, only systematic risk remains.

4. The Capital Asset Pricing Model (CAPM)

CAPM defines the relationship between the systematic risk of a security and its expected return. It uses Beta as the primary measure of systematic risk.

Understanding Beta

• Beta = 1.0: The security moves exactly in line with the market.
• Beta > 1.0: The security is more volatile than the market (Aggressive).
• Beta < 1.0: The security is less volatile than the market (Defensive).

The CAPM Formula

The required rate of return for any asset is calculated as follows:

E(Ri) = RFR + Beta * (E(Rm) - RFR))

Where:

• E(Ri) = Expected return on the individual security.
• RFR = Risk-free rate.
• Beta = Systematic risk of the security.
• E(Rm) = Expected return on the market portfolio.
• (E(Rm) - RFR) = Market Risk Premium.

5. The Security Market Line (SML)

The SML is the graphical representation of the CAPM. It plots the relationship between systematic risk (Beta) on the X-axis and the expected rate of return on the Y-axis.

Identifying Valuation Anomalies

The SML is a powerful tool for fund managers to identify mispriced securities:

1. Undervalued Securities: If a security’s estimated return plots above the SML, it provides a higher return than its risk warrants. Investors should BUY.
2. Overvalued Securities: If a security’s estimated return plots below the SML, its return is too low for its risk level. Investors should SELL.
3. Fairly Valued Securities: If the return plots on the SML, it is correctly priced for its risk.

Example Calculation: If the RFR is 8%, the Market Return is 22% (Premium = 14%), and a stock has a Beta of 1.2:

Expected Return = 8% + (1.2 * 14%) = 24.8%

If that stock is currently expected to return 26%, it is undervalued (plotting above the SML).

6. Multi-Factor Models: Arbitrage Pricing Theory (APT)

While CAPM uses a single factor (Market Risk), researchers recognized that multiple factors influence returns. Arbitrage Pricing Theory (APT), developed by Stephen Ross, is the primary alternative.

APT vs. CAPM

• Factors: APT assumes returns are a function of multiple factors (inflation, GNP growth, interest rates) rather than just market movement.
• Betas: Unlike CAPM's single beta, APT uses multiple betas to measure sensitivity to each specific factor.
• Flexibility: APT does not require the assumption of a "Market Portfolio" or normally distributed returns.

The APT Formula:

E(Ri) = L0 + L1 * bi1 + L2 * bi2 + ... + Lk * bik

Where:

• L0 = Return on an asset with zero systematic risk.
• Ln = Risk premium for factor n.
• bin = Sensitivity (Beta) of the asset to factor n.

Key Takeaways for Exam Preparation

• CML vs. SML: The Capital Market Line (CML) uses standard deviation (total risk) and is for efficient portfolios. The Security Market Line (SML) uses Beta (systematic risk) and is for individual securities or any portfolio.
• The Zero-Beta Concept: A risk-free asset has a beta of zero and a standard deviation of zero.
• Market Portfolio Beta: By definition, the Beta of the Market Portfolio is always 1.0.
• Leverage on the CML: Investors can achieve returns higher than the market portfolio by borrowing at the risk-free rate and investing more than 100% of their wealth in Portfolio 'M'.
• Stability of Beta: Empirical tests show that Beta is more stable for portfolios (especially those with 50+ stocks) than for individual securities.