The Capital Asset Pricing Model (CAPM) is a widely used financial model that helps investors and analysts understand the relationship between risk and expected returns for individual securities or portfolios of assets. It provides a framework for evaluating the required rate of return for an investment based on its risk characteristics relative to the overall market.

The CAPM is built on several key assumptions:

**Investor Rationality:**CAPM assumes that investors are rational and risk-averse, seeking to maximize their utility by making investment decisions that balance risk and return.**Efficient Diversification:**Investors can diversify their portfolios effectively, which means that they can hold a mix of assets to reduce the overall risk without sacrificing potential returns.**Single Period Investment Horizon:**CAPM focuses on a single holding period, usually one year.**Homogeneous Expectations:**All investors have the same expectations regarding the future returns, risks, and correlations of assets.**No Taxes or Transaction Costs:**CAPM assumes no taxes or transaction costs associated with buying or selling assets.**Perfect Information:**Investors have access to all relevant information about assets.

Based on these assumptions, the CAPM provides a formula to calculate the expected return of an asset or a portfolio:

*E*(*Ri*)=*Rf*+*βi*×(*E*(*Rm*)−*Rf*)

Where:

*E*(*Ri*) is the expected return of the asset or portfolio.*Rf* is the risk-free rate, representing the return on a risk-free investment like government bonds.*βi* is the asset’s beta coefficient, which measures the asset’s sensitivity to market movements. A beta of 1 indicates the asset moves in line with the market, while a beta greater than 1 implies the asset is more volatile than the market, and a beta less than 1 implies lower volatility.*E*(*Rm*) is the expected return of the market portfolio.

The formula essentially states that an asset’s expected return consists of two components:

- A risk-free rate (compensation for time and uncertainty).
- A risk premium, which is the market risk premium (
*E*(*Rm*)−*Rf*) multiplied by the asset’s beta (*βi*).

The CAPM is widely used in finance for various purposes, such as estimating the cost of equity for companies, evaluating the performance of investment portfolios, and determining whether an investment is overvalued or undervalued based on its expected return and risk. However, it’s important to note that the CAPM has been subject to criticism and limitations, such as its reliance on simplifying assumptions and its inability to fully capture the complexities of real-world markets.