Quiz Template
CAPM: Capital Asset Pricing Model

Interactive Learning Hub - Master the fundamentals of modern portfolio theory

📚 Key Notes
✅ Multiple Choice
🃏 Flashcards
🎯 Drag & Drop
🔗 Matching
🧠 Mind Map
✔️ True/False
📝 Fill in Blanks

📚 Core Concepts

What is CAPM?

The Capital Asset Pricing Model (CAPM) is a fundamental framework in modern finance that describes the relationship between systematic risk and expected return for assets, particularly stocks. It provides a method to calculate the appropriate required rate of return for an investment.

Diversification and Risk Types

Idiosyncratic Risk (Firm-Specific Risk)

  • Risk that affects only a particular company or small group of companies
  • Examples: Management changes, product recalls, patent disputes
  • Can be eliminated through diversification
  • Also called: unsystematic risk, diversifiable risk, unique risk

Systematic Risk (Market Risk)

  • Risk that affects all securities in the market
  • Examples: Economic recessions, interest rate changes, inflation
  • Cannot be eliminated through diversification
  • Also called: market risk, non-diversifiable risk
  • This is the only risk that matters for expected returns in CAPM

Beta (β): Measuring Systematic Risk

Beta measures how much a stock's return moves relative to the market portfolio's return. It quantifies the systematic risk of a security.

$$\beta_i = \frac{\text{Cov}(R_i, R_M)}{\text{Var}(R_M)}$$

Interpreting Beta:

  • β = 1: Stock moves exactly with the market (average systematic risk)
  • β > 1: Stock is more volatile than the market (aggressive stock)
  • β < 1: Stock is less volatile than the market (defensive stock)
  • β = 0: No systematic risk (e.g., risk-free asset)

Example: Microsoft vs. Gillette

Microsoft: β = 1.49 (aggressive stock)

  • If market rises 10%, Microsoft expected to rise 14.9%
  • If market falls 10%, Microsoft expected to fall 14.9%

Gillette: β = 0.81 (defensive stock)

  • If market rises 10%, Gillette expected to rise 8.1%
  • If market falls 10%, Gillette expected to fall 8.1%

🎯 CAPM Theory

The CAPM Formula

The fundamental equation that relates expected return to systematic risk:

$$E[R_i] = r_f + \beta_i(E[R_M] - r_f)$$

Where:

  • $E[R_i]$ = Expected return on asset $i$
  • $r_f$ = Risk-free rate (e.g., Treasury bill rate)
  • $\beta_i$ = Beta of asset $i$
  • $E[R_M]$ = Expected return on the market portfolio
  • $(E[R_M] - r_f)$ = Market risk premium

Security Market Line (SML)

The SML is a graphical representation of the CAPM equation. It shows the relationship between beta and expected return:

  • Y-axis: Expected Return $E[R_i]$
  • X-axis: Beta $\beta_i$
  • Intercept: Risk-free rate $r_f$
  • Slope: Market risk premium $(E[R_M] - r_f)$

Example: Using CAPM to Calculate Expected Return

Given:

  • Risk-free rate = 5%
  • Expected market return = 12%
  • Stock beta = 1.5

Calculate expected return:

$E[R] = 5\% + 1.5(12\% - 5\%) = 5\% + 1.5(7\%) = 5\% + 10.5\% = 15.5\%$

Market Portfolio

The market portfolio is a theoretical portfolio that includes all risky assets in the economy, weighted by their market values. In practice, we use broad market indices like the S&P 500 as proxies.

  • Beta of market portfolio = 1.0 by definition
  • Expected return = $E[R_M]$
  • Contains only systematic risk

💼 Applications of CAPM

1. Calculating Cost of Equity

CAPM is widely used to estimate a company's cost of equity capital for valuation and capital budgeting decisions.

Example: Cost of Equity Calculation

A company wants to determine its cost of equity:

  • Current T-bill rate: 4%
  • Historical market risk premium: 8%
  • Company's beta: 1.2

Cost of Equity: $r_e = 4\% + 1.2(8\%) = 4\% + 9.6\% = 13.6\%$

2. Alpha (α): Performance Evaluation

Alpha measures the excess return of an investment relative to what CAPM predicts. It indicates whether a portfolio manager has added value.

$$\alpha = \text{Actual Return} - \text{Expected Return (CAPM)}$$
  • α > 0: Outperformance (manager added value)
  • α = 0: Performance in line with expectations
  • α < 0: Underperformance (manager destroyed value)

Example: Mutual Fund Performance Comparison

BlindLuck Fund:

  • Beta = 0.8
  • Actual return = 12%
  • CAPM expected return = 5% + 0.8(12% - 5%) = 10.6%
  • Alpha = 12% - 10.6% = +1.4% (Outperformed!)

EasyMoney Fund:

  • Beta = 1.2
  • Actual return = 13%
  • CAPM expected return = 5% + 1.2(12% - 5%) = 13.4%
  • Alpha = 13% - 13.4% = -0.4% (Underperformed)

Conclusion: Despite EasyMoney having a higher absolute return (13% vs 12%), BlindLuck actually performed better after adjusting for risk!

3. Portfolio Beta

The beta of a portfolio is the weighted average of the betas of individual securities:

$$\beta_P = \sum_{i=1}^{n} w_i \beta_i$$

Where $w_i$ is the weight of asset $i$ in the portfolio.

Example: Portfolio Beta Calculation

Portfolio with three stocks:

  • Stock A: 40% weight, β = 1.2
  • Stock B: 30% weight, β = 0.8
  • Stock C: 30% weight, β = 1.5

$\beta_P = 0.4(1.2) + 0.3(0.8) + 0.3(1.5) = 0.48 + 0.24 + 0.45 = 1.17$

✅ Multiple Choice Questions

Test your understanding of CAPM concepts. Select the best answer for each question.

1. What does CAPM stand for?

Capital Allocation Pricing Method
Corporate Asset Portfolio Management
Capital Asset Pricing Model
Capital Appreciation Performance Measure

2. Which type of risk can be eliminated through diversification?

Systematic risk
Idiosyncratic risk
Market risk
Non-diversifiable risk

3. A stock with a beta of 1.5 is considered:

Risk-free
Defensive
Aggressive
Market-neutral

4. In the CAPM formula $E[R_i] = r_f + \beta_i(E[R_M] - r_f)$, what does $(E[R_M] - r_f)$ represent?

Total return
Risk-free rate
Expected return
Market risk premium

5. If the risk-free rate is 3%, market return is 10%, and a stock's beta is 1.2, what is the expected return?

10.0%
11.4%
12.0%
13.2%

6. What is the beta of the market portfolio?

1.0
0.0
0.5
It varies

7. A positive alpha indicates:

The stock is overpriced
Poor performance
Outperformance relative to risk
High systematic risk

8. The Security Market Line (SML) plots:

Risk vs. Volatility
Expected Return vs. Beta
Price vs. Time
Return vs. Standard Deviation

9. If a stock has a beta of 0.8 and the market falls by 10%, the stock is expected to:

Fall by 10%
Rise by 8%
Fall by 12.5%
Fall by 8%

10. Which of the following is NOT an assumption of CAPM?

Investors have different time horizons
Markets are efficient
Investors are rational
No transaction costs

11. A portfolio has 60% in Stock A (β=1.2) and 40% in Stock B (β=0.8). What is the portfolio beta?

0.96
1.00
1.04
1.10

12. Which statement about systematic risk is TRUE?

It can be eliminated through diversification
It affects all securities in the market
It is the same as idiosyncratic risk
It is not compensated in CAPM

13. If rf = 4%, E[RM] = 11%, and a stock's expected return is 13%, what is its beta?

0.78
1.00
1.18
1.29

14. CAPM is primarily used to calculate:

Cost of equity
Cost of debt
Working capital
Dividend yield

15. A stock with beta = 0 would have an expected return equal to:

Zero
The market return
The risk-free rate
Negative return

🃏 Flashcards

Click on any card to flip and reveal the answer. Master these key concepts!

CAPM
Capital Asset Pricing Model - A model that describes the relationship between systematic risk and expected return
Beta (β)
A measure of a stock's systematic risk relative to the market. β = Cov(Ri, RM) / Var(RM)
Alpha (α)
The excess return of an investment relative to the return predicted by CAPM. Measures manager skill.
Systematic Risk
Market-wide risk that cannot be eliminated through diversification. Affects all securities.
Idiosyncratic Risk
Firm-specific risk that can be eliminated through diversification. Also called unsystematic risk.
Security Market Line
A graphical representation of CAPM showing the relationship between beta and expected return
Market Risk Premium
E[RM] - rf: The additional return investors expect for taking on market risk
Risk-Free Rate
The return on an investment with zero risk, typically represented by Treasury bills
CAPM Formula
E[Ri] = rf + βi(E[RM] - rf)
β = 1
Stock moves exactly with the market. Average systematic risk.
β > 1
Aggressive stock - more volatile than the market
β < 1
Defensive stock - less volatile than the market
Market Portfolio
A theoretical portfolio containing all risky assets weighted by market value. Beta = 1.0
Diversification
The practice of spreading investments to reduce idiosyncratic risk
Cost of Equity
The return required by equity investors, calculated using CAPM
Portfolio Beta
Weighted average of individual asset betas: βP = Σ wi × βi
R-squared (R²)
Measures how much of a stock's movement is explained by market movements. Range: 0-1
Efficient Market
A market where all available information is reflected in asset prices
Expected Return
The anticipated return on an investment based on CAPM or other models
Covariance
A measure of how two variables move together. Used in calculating beta.
Variance
A measure of the dispersion of returns. Used in the denominator of beta.
Slope of SML
The market risk premium (E[RM] - rf)
Y-intercept of SML
The risk-free rate (rf)
Overvalued Stock
A stock plotting below the SML - expected return is too low for its risk
Undervalued Stock
A stock plotting above the SML - expected return is high relative to its risk

🎯 Drag & Drop Matching

Drag each term from the left to its correct definition on the right.

Systematic Risk
Idiosyncratic Risk
Beta
Alpha
Security Market Line
Market Portfolio
Risk that cannot be diversified away
Firm-specific risk that can be eliminated
Measure of systematic risk relative to market
Excess return beyond CAPM prediction
Graph showing beta vs. expected return
Portfolio containing all risky assets

🔗 Matching Exercise

Match each item on the left with its correct category on the right. Click to select pairs.

β = 1.5
β = 0.7
α > 0
α < 0
β = 1.0
β = 0
Aggressive Stock
Defensive Stock
Outperformance
Underperformance
Market Portfolio
Risk-Free Asset

🧠 CAPM Concept Mind Map

Explore the hierarchical structure of CAPM concepts. Click nodes to expand/collapse.

✔️ True or False

Determine whether each statement is true or false.

1. Systematic risk can be eliminated through diversification.
2. A stock with beta greater than 1 is more volatile than the market.
3. The slope of the Security Market Line is the risk-free rate.
4. A positive alpha indicates that a portfolio has outperformed expectations.
5. The beta of the market portfolio is 0.
6. CAPM assumes that all investors have the same expectations.
7. Idiosyncratic risk is also known as market risk.
8. Portfolio beta is the weighted average of individual stock betas.
9. A defensive stock has a beta less than 1.
10. CAPM can be used to calculate the cost of debt for a company.

📝 Fill in the Blanks

Complete each sentence by filling in the missing term or concept.

1. The measures how much a stock's return moves relative to the market.

2. The slope of the Security Market Line is the .

3. risk cannot be eliminated through diversification.

4. A stock with greater than zero has outperformed expectations.

5. The CAPM formula is E[Ri] = rf + .

6. risk is also called firm-specific risk.

7. The contains all risky assets weighted by market value.

8. A stock with beta less than 1 is called a stock.

9. CAPM is primarily used to calculate the for a company.

10. The is the return on an investment with zero risk.

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