Capital Asset Pricing Model

Beta is the ratio of an asset's covariance with the market portfolio to the variance of the market portfolio. Equivalently, it is the correlation between asset and market returns multiplied by the asset's standard deviation and divided by the market's standard deviation. That construction is the heart of the model: total volatility enters only through the part that co-moves with the market, because in a world where every investor holds the same well-diversified market portfolio, asset-specific noise cancels and no investor demands payment for bearing it.

The pricing statement follows directly. Required return equals the risk-free rate plus beta times the difference between the expected market return and the risk-free rate. A beta of one earns the full market premium, a beta of zero earns only the risk-free rate, and a negative beta asset (one that pays off when the market falls) commands a required return below the risk-free rate because it functions as insurance.

The Security Market Line plots required return against beta and applies to every asset and portfolio, efficient or not. The Capital Market Line plots expected return against total standard deviation and applies only to efficient combinations of the risk-free asset and the market portfolio. Confusing the two is a persistent source of error: an individual stock with substantial idiosyncratic risk sits well below the CML but, if fairly priced, lies exactly on the SML.

Deviation from the SML is the model's practical output. An asset whose forecast return exceeds its CAPM-required return plots above the line and is judged undervalued; the vertical distance is Jensen's alpha. Portfolio beta is simply the market-value-weighted average of component betas, so the SML relation aggregates cleanly from securities to portfolios.

CAPM's dominant application is the cost of equity input to weighted average cost of capital, which in turn discounts free cash flows in valuation, sets hurdle rates for capital budgeting, and is used by regulators to set allowed returns for utilities and network operators. Practitioners adjust the raw regression beta toward one (a common convention weights the historical estimate about two-thirds and unity about one-third) because betas mean-revert over time. For private firms or divisions, an industry beta is unlevered using a comparable's debt-to-equity ratio and tax rate, then relevered at the subject firm's capital structure.

In performance evaluation, CAPM underpins the Treynor ratio, which divides excess return by beta rather than by standard deviation, and Jensen's alpha, which measures return earned beyond the beta-implied benchmark. Both are appropriate when the portfolio is one sleeve of a diversified whole.

Expect to move fluently in every direction through the SML equation: solve for required return given beta, back out an implied beta from a required return, and infer the market premium from two points on the line. You should compute beta from covariance and variance data, or from correlation and the two standard deviations, and combine security betas into a portfolio beta by market-value weights.

Be equally ready to reason about the assumptions (homogeneous expectations, frictionless markets with unlimited borrowing and lending at the risk-free rate, a single period, and full diversification) and to explain which conclusion collapses when a given assumption fails. Finally, distinguish required return from forecast return: the gap between them, not the level of either, drives the buy or sell conclusion.