20 Chapter 9 – Systematic Risk and Equity Risk Premium

Conceptual Questions

1. Understanding Systematic Risk

Systematic risk is the inherent risk that affects the entire market or economy, such as interest rate changes, inflation, or recessions. It cannot be eliminated through diversification because it impacts all securities to some extent. Unsystematic risk, on the other hand, is specific to a company or industry and can be reduced by holding a diversified portfolio.

2. Market Portfolio

The market portfolio represents a theoretical portfolio that includes all assets in the market, weighted by their market value. It serves as a benchmark for systematic risk because it reflects the average risk level of the entire market. Beta measures how much an individual security or portfolio moves in relation to this market portfolio.

3. Beta Interpretation

• • • Beta > 1: The asset is more volatile than the market. Example: Tesla (beta ~2.0).
    • Beta < 1: The asset is less volatile than the market. Example: Procter & Gamble (beta ~0.6).
    • Beta = 1: The asset moves in line with the market. Example: S&P 500 ETF.

4. Equity Risk Premium

The equity risk premium is the additional return investors demand for taking on the higher risk of investing in stocks over risk-free assets. It reflects investors’ expectations of compensation for market risk and is a critical component of the CAPM.

5. Limitations of CAPM

Limitations include:

• • • Relies on historical data for beta, which may not predict future volatility accurately.
    • •Assumes markets are efficient and all investors have the same expectations.
    • •Ignores other factors that can influence returns, such as company size or momentum.

Scenario-Based Problems

1. Portfolio Beta Calculation

Portfolio Beta = (0.4 × 1.2) + (0.35 × 0.8) + (0.25 × 1.5)

= 0.48 + 0.28 + 0.375 = 1.135

Interpretation: The portfolio is slightly more volatile than the market, as its beta is just above 1.

2. Estimating Cost of Equity with CAPM

Cost of Equity = 2.5% + 1.3 × (8% – 2.5%)

= 2.5% + 1.3 × 5.5%

= 2.5% + 7.15%

= 9.65%

Interpretation: The stock’s required return is 9.65%, reflecting its higher risk relative to the market.

3. Comparing Betas

Stock X: Beta = 0.7 → Expected movement: 10% × 0.7 = 7%

Stock Y: Beta = 1.6 → Expected movement: 10% × 1.6 = 16%

Riskiness: Stock Y is riskier as it reacts more strongly to market changes.

4. Impact of Equity Risk Premium on Cost of Equity

Original Cost of Equity = 2.5% + 1.4 × 5% = 9.5%

New Cost of Equity = 2.5% + 1.4 × 6% = 11.9%

Impact: The cost of equity increases by 2.4 percentage points, reflecting higher compensation for market risk.

5. Risk-Free Rate Adjustment

Original Cost of Equity = 2% + 1.2 × 7% = 10.4%

New Cost of Equity = 3% + 1.2 × 7% = 11.4%

Impact: A 1% increase in the risk-free rate raises the cost of equity by 1%.

Case Study Application

1. Beta and Investment Decisions

•Project A: Expected Return = 3% + 1.5 × 6% = 12%

•Project B: Expected Return = 3% + 0.8 × 6% = 7.8%

Fairly Priced?

•Project A: Expected return matches the required return (fairly priced).

•Project B: Expected return is slightly above the required return (attractive option).

Recommendation: Prioritize Project A for its higher potential return if the company can handle its higher risk.

2. Real-World Application: Amazon’s Beta

Expected Return = 2% + 1.3 × 5% = 8.5%

Interpretation: Amazon’s beta of 1.3 reflects higher volatility than the market, consistent with its position in the tech and e-commerce sectors.

3. Impact of Beta on Portfolio Construction

Suggested Allocation:

• • • • 40% low-beta stock (utility) for stability.
      • 40% medium-beta stock (consumer staples) for balanced risk.
      • 20% high-beta stock (tech) for growth potential.

Justification: This allocation minimizes risk while retaining exposure to potential high returns.

Interactive Challenge

1. Beta Puzzle

• • • Tesla → Beta = 2.1 (high growth and volatility).
    • Procter & Gamble → Beta = 0.6 (stable, defensive sector).
    • S&P 500 ETF → Beta = 1.0 (tracks market average).

2. Dynamic Equity Risk Premium

• • • Recession Impact: Equity risk premium increases as investors demand more compensation for heightened market uncertainty, leading to higher required returns.
    • Booming Economy Impact: Equity risk premium decreases as market confidence rises, leading to lower required returns.