The Capital Asset Pricing Model (CAPM) is a financial model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. It describes the relationship between systematic risk and expected return for assets, particularly stocks.

The formula for the Capital Asset Pricing Model is:

\[E(R_i) = R_f + \beta_i(E(R_m) - R_f)\]Where:

- \(E(R_i)\) = Expected return of investment
- \(R_f\) = Risk-free rate
- \(\beta_i\) = Beta of the investment
- \(E(R_m)\) = Expected return of the market
- \(E(R_m) - R_f\) = Market risk premium

- Determine the risk-free rate (\(R_f\)), typically using the yield of a 10-year government bond.
- Calculate or obtain the beta (\(\beta_i\)) of the investment, which measures the investment's volatility compared to the market.
- Estimate the expected return of the market (\(E(R_m)\)), often using historical data or future projections.
- Calculate the market risk premium by subtracting the risk-free rate from the expected market return: \(E(R_m) - R_f\)
- Multiply the market risk premium by the investment's beta.
- Add the risk-free rate to the result from step 5 to get the expected return of the investment.

Let's calculate the expected return for an investment with the following parameters:

- Risk-free rate (\(R_f\)) = 2%
- Beta (\(\beta_i\)) = 1.2
- Expected market return (\(E(R_m)\)) = 8%

Plugging these values into the CAPM formula:

\[E(R_i) = 2\% + 1.2(8\% - 2\%) = 2\% + 1.2(6\%) = 2\% + 7.2\% = 9.2\%\]Therefore, the expected return of the investment is 9.2%.

This graph illustrates the CAPM. The blue line represents the Security Market Line (SML). The green point (Rf) is the risk-free rate, the red point (Rm) is the market return, and the yellow point (E(Ri)) is the expected return of the asset based on its beta.

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