Intro to Finance: Risk and Return Capital Asset Pricing Model CAPM ERi Rf βi ERm Rf

What This Is

The Capital Asset Pricing Model (CAPM) is a fundamental concept in finance that explains the relationship between risk and expected return on investments. It helps investors and analysts understand how much return they can expect from an investment based on its level of risk. For example, consider Apple Inc. (AAPL) with a beta of 1.2, the risk-free rate of 2%, and the market return of 8%. Using the CAPM, we can estimate Apple's expected return as follows: E(Ri) = Rf + βi × (E(Rm) – Rf) = 0.02 + 1.2 × (0.08 – 0.02) = 0.12 or 12%.

Key Formulas & Symbols

• E(Ri) = Rf + βi × (E(Rm) – Rf) where E(Ri) = expected return on investment i, Rf = risk-free rate, βi = beta of investment i, E(Rm) = expected market return.
• βi = beta of investment i, a measure of systematic risk.
• Rf = risk-free rate, the return on a risk-free asset (e.g., U.S. Treasury bond).
• E(Rm) = expected market return, the average return on the market portfolio.
• σm = standard deviation of the market return.
• σi = standard deviation of the return on investment i.
• Cov(Rm, Ri) = covariance between the market return and the return on investment i.
• Var(Rm) = variance of the market return.

Step-by-Step Calculation

1. Estimate the risk-free rate (Rf): Use the yield on a U.S. Treasury bond or the current interest rate on a short-term government bond.
2. Estimate the expected market return (E(Rm)): Use historical data or a market index (e.g., S&P 500).
3. Estimate the beta (βi): Use historical data or a beta estimate from a reliable source (e.g., Bloomberg).
4. Calculate the expected return on investment i (E(Ri)): Plug in the values into the CAPM formula: E(Ri) = Rf + βi × (E(Rm) – Rf).

Common Mistakes

• Mistake: Using the wrong beta estimate or assuming a beta of 1 for all investments.
• Correction: Use a reliable beta estimate from a reputable source, and consider the specific characteristics of the investment.
• Mistake: Failing to account for the risk-free rate in the CAPM formula.
• Correction: Include the risk-free rate in the calculation to ensure accurate expected returns.
• Mistake: Assuming the CAPM applies to all investments, including those with high idiosyncratic risk.
• Correction: Recognize that the CAPM only applies to investments with systematic risk, and use other models (e.g., Arbitrage Pricing Theory) for investments with high idiosyncratic risk.

Exam / CFA Tips

• Tip: Be prepared to estimate the risk-free rate and expected market return using historical data or market indices.
• Tip: Understand the difference between systematic and idiosyncratic risk, and how they affect the CAPM.
• Tip: Be cautious of question wording that implies the CAPM applies to all investments, and adjust your approach accordingly.

Quick Practice Problem

Scenario: Tesla Inc. (TSLA) has a beta of 2.5, and the market return is expected to be 10%. What is Tesla's expected return using the CAPM?

Answer: E(Ri) = 0.02 + 2.5 × (0.10 – 0.02) = 0.22 or 22%.

Explanation: Tesla's expected return is higher than the market return due to its higher beta.

Last-Minute Cram Sheet

1. E(Ri) = Rf + βi × (E(Rm) – Rf): The CAPM formula.
2. βi = beta of investment i, a measure of systematic risk.
3. ⚠️ The CAPM only applies to investments with systematic risk.
4. Rf = risk-free rate, the return on a risk-free asset.
5. E(Rm) = expected market return, the average return on the market portfolio.
6. σm = standard deviation of the market return.
7. σi = standard deviation of the return on investment i.
8. Cov(Rm, Ri) = covariance between the market return and the return on investment i.
9. Var(Rm) = variance of the market return.
10. ⚠️ The CAPM assumes investors are rational and risk-averse.