# Capital Asset Pricing Model (CAPM) Calculator

## CAPM Definition

The Capital Asset Pricing Model (CAPM) is a financial model that helps estimate the return on an investment relative to its risk. This model is widely used in finance for pricing risky securities and calculating expected returns on assets, considering both the risk of those assets and the cost of capital. CAPM is based on the idea that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free rate in the formula, ensuring investors are compensated for the time their money is invested. The risk is represented by the beta (Î²), which measures the tendency of a stock's return to respond to swings in the market.

## CAPM Formula

The CAPM formula is expressed as follows:

Re = Rf + Î²*(Rm - Rf)

where:

• ReÂ = Cost of Equity
• RfÂ = Risk-Free Rate
• Î² = Beta
• RmÂ = Expected Market Return

### Explanation of the Formula Components

• Cost of Equity (Reâ€‹): This is the return that a company is expected to offer to its equity investors to compensate for the risk of investing in the company's stock. It represents the expected return on investment.
• Risk-Free Rate (Rfâ€‹): This is the return on a risk-free investment, typically government bonds. It serves as a benchmark for the minimum return an investor should expect, as it assumes no risk.
• Beta (Î²): Beta measures the volatility or systematic risk of a security in comparison to the broader market. A beta greater than 1 indicates that the security is more volatile than the market, while a beta less than 1 means it is less volatile.
• Expected Market Return (Rmâ€‹): This is the return that is anticipated from the market as a whole. It reflects the average return an investor expects to earn from the market.

The CAPM formula links these components to assess the relationship between the expected return of an investment and its risk. It helps in making informed decisions about whether a stock provides a reasonable expected return for the level of risk taken.

## CAPM Example

Let's consider an example to illustrate the CAPM. Suppose the risk-free rate is 3%, the expected market return is 10%, and a stock has a beta of 1.5. According to the CAPM formula:

ReÂ = 3% + 1.5*(10%Â - 3%) --> 13.5%

This means, given its risk profile (beta of 1.5), investors would expect a 13.5% return on the stock to compensate for the risk they are taking compared to a risk-free investment.