CAPM Calculator

1. What is the CAPM Calculator?

Definition: The CAPM (Capital Asset Pricing Model) Calculator computes the expected return of an asset based on its systematic risk (beta) relative to the market. It also calculates the risk premium of the asset, which is the additional return over the risk-free rate due to market risk exposure. CAPM quantifies the risk-return relationship, aiding in investment evaluation.

Purpose: Used by investors and financial analysts to estimate an asset’s expected return and risk premium, evaluate investment opportunities, and determine the cost of equity for corporate finance decisions, such as capital budgeting or stock valuation.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\( \text{Risk Premium} = \beta \times (E(R_m) - R_f) \)

\( E(R_i) = R_f + \text{Risk Premium} \)

Where:

\( E(R_i) \): Expected return of the investment (%);
\( R_f \): Risk-free rate (e.g., yield on Treasury bills) (%);
\( \beta \): Beta, measuring the asset’s sensitivity to market movements;
\( E(R_m) \): Expected market return (e.g., S&P 500 return) (%);
\( E(R_m) - R_f \): Market risk premium;
\( \text{Risk Premium} \): Asset’s risk premium due to market risk (%).

Steps:

Enter the risk-free rate as a percentage (e.g., 2.4 for 3-month Treasury bills).
Enter the beta of the asset (e.g., 0.47 for a low-volatility stock like Walmart).
Enter the expected market return as a percentage (e.g., 8 for S&P 500).
Calculate the market risk premium: \( E(R_m) - R_f \).
Compute the asset’s risk premium: \( \beta \times (E(R_m) - R_f) \).
Compute the expected return: \( R_f + \text{Risk Premium} \).
Display both results, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 4 decimal places.

3. Importance of CAPM Calculation

Calculating the CAPM and risk premium is essential for:

Investment Decisions: The expected return and risk premium help investors assess if an asset’s return justifies its risk, aiding in portfolio construction.
Cost of Equity: The expected return is used to estimate the cost of equity, a key component in calculating the weighted average cost of capital (WACC).
Risk Assessment: The risk premium quantifies the additional return for taking on market risk, helping investors understand an asset’s risk exposure.

4. Using the Calculator

Example 1: Calculate the risk premium and expected return for a stock with a risk-free rate of 3%, a beta of 4, and an expected market return of 9%:

\( R_f \): 3%;
\( \beta \): 4;
\( E(R_m) \): 9%;
\( \text{Risk Premium} \): \( 4 \times (9 - 3) = 4 \times 6 = 24\% \);
\( E(R_i) \): \( 3 + 24 = 27\% \).

Result: Risk Premium = 24.0000%, Expected Return = 27.0000%.

Example 2: Calculate the risk premium and expected return for Walmart stock with a risk-free rate of 2.4%, a beta of 0.47, and an expected market return of 8%:

\( R_f \): 2.4%;
\( \beta \): 0.47;
\( E(R_m) \): 8%;
\( \text{Risk Premium} \): \( 0.47 \times (8 - 2.4) = 0.47 \times 5.6 = 2.632\% \);
\( E(R_i) \): \( 2.4 + 2.632 = 5.032\% \).

Result: Risk Premium = 2.6320%, Expected Return = 5.0320%.

5. Frequently Asked Questions (FAQ)

Q: What is the risk premium of the asset?
A: The risk premium of the asset is the additional return over the risk-free rate due to the asset’s exposure to market risk, calculated as \( \beta \times (E(R_m) - R_f) \).

Q: How does CAPM differ from the Sharpe Ratio?
A: CAPM estimates the expected return and risk premium based on systematic risk (beta) and market risk premium, focusing on market risk. The Sharpe Ratio measures excess return per unit of total risk (standard deviation), evaluating overall risk-adjusted performance.

Q: What is a good expected return or risk premium?
A: A good expected return or risk premium depends on the investor’s risk tolerance. High-beta assets (e.g., >1) should have higher risk premiums and expected returns to compensate for risk, while low-beta assets (e.g., <1) offer lower but more stable returns.