The Capital Asset Pricing Model (CAPM) is a fundamental concept in finance that provides a framework for evaluating the expected return of an asset based on its risk relative to the overall market. Developed by William Sharpe, John Lintner, and Jack Treynor in the 1960s, CAPM builds on the premise that investors are rational and risk-averse, aiming to optimize the trade-off between risk and return. The model assumes a single-period investment horizon, frictionless markets, and that all investors have homogeneous expectations regarding returns, variances, and covariances of assets. The primary objective of CAPM is to estimate the expected return of an individual security or a portfolio as a function of its systematic risk, measured by beta, in relation to the market as a whole. Mathematically, CAPM expresses the expected return of an asset as: [ E(R_i) = R_f + \beta_i [E(R_m) - R_f] ] Where (E(R_i)) is the expected return on asset (i), (R_f) is the risk-free rate, (\beta_i) is the beta of the asset, and (E(R_m)) is the expected return of the market portfolio. The term ([E(R_m) - R_f]) represents the market risk premium, which is the additional return investors demand for taking on market risk over a risk-free investment. Beta ((\beta_i)) measures the sensitivity of the asset’s returns to the overall market returns and captures the systematic risk that cannot be diversified. A beta of 1 indicates that the asset’s return moves in line with the market, while a beta greater than 1 indicates higher volatility, and less than 1 indicates lower volatility than the market. The application of CAPM in portfolio selection is significant because it provides investors with a method to determine whether a security offers a fair expected return for its level of risk. In portfolio construction, CAPM helps in identifying efficient portfolios, which are those that provide the maximum expected return for a given level of risk. By combining assets with different betas, investors can achieve diversification, thereby reducing unsystematic risk while remaining exposed only to systematic risk, which is rewarded in the market. CAPM is also used in calculating the cost of equity for firms, which is essential in capital budgeting decisions, asset valuation, and performance evaluation of portfolio managers. CAPM forms the foundation for two important graphical representations in portfolio theory: the Security Market Line (SML) and the Capital Market Line (CML). The Security Market Line represents the relationship between the expected return of individual securities and their systematic risk (beta). It is a straight line that originates at the risk-free rate and has a slope equal to the market risk premium.