How the CAPM formula works

The capital asset pricing model, usually shortened to CAPM, writes expected or required return as

$$E(R_i)=R_f+\beta_i\left(E(R_m)-R_f\right)$$

$R_f$ is the risk-free rate. $E(R_m)-R_f$ is the market risk premium. $\beta_i$ is the asset's beta, which scales that premium. The result is the return the model associates with bearing the asset's market risk.

The formula has a clear sequence. Begin with the return available without market exposure. Find the extra return expected from the market. Multiply that premium by the asset's sensitivity to market moves. Then add the base rate back.

With a 4 percent risk-free rate and 10 percent expected market return, the market premium is 6 percentage points. A beta of 1.2 turns that into 7.2 points of risk compensation, and adding the 4 percent base gives 11.2 percent.

Beta is the slope from relating an asset's excess returns to the market's excess returns. A beta of one means the asset receives the full market premium in CAPM. A beta of 1.2 receives 1.2 times that premium. A beta of 0.8 receives 0.8 times it.

That is sensitivity, not a statement that the asset rises in every rising market or falls in every falling one. The fitted relationship has residuals, and those company-specific moves are not captured by beta. Beta can also change when the business mix, financing or estimation window changes.

Debt affects an equity beta because fixed claims make the remaining equity more sensitive to operating outcomes. How unlevered beta works separates the business sensitivity from the financing effect. The unlever beta calculator performs that conversion.

CAPM assumes investors can hold broad portfolios. In a diversified portfolio, company-specific surprises offset one another, so the model does not pay an extra expected return for bearing a risk that can be removed by spreading holdings. The risk left across a broad portfolio is systematic risk, exposure to market-wide changes.

Beta is the model's measure of that remaining exposure. The expected return line therefore rises with beta, not with total volatility. An asset can be very volatile because of company-specific events and still have a modest beta if those events have little relationship with market moves.

Risk and return places that distinction beside diversification. CAPM turns it into a pricing statement: only the covariance with the market earns the model's risk premium.

Each CAPM input is an estimate. The risk-free rate should match the currency and horizon of the cash flows being valued. A short bill rate and a long government bond yield answer different timing questions. The market premium can come from a historical average, a forward-looking valuation or a published assumption, and those methods need not agree.

Beta depends on the market benchmark, return frequency and estimation window. Thin trading can depress a measured beta, while one unusual period can pull it sharply. For a private company or a new listing, analysts often begin with comparable listed companies, remove their financing effects, average the business betas and then apply the target company's financing.

Consistency matters more than false precision. A long-horizon premium should sit beside a horizon-appropriate risk-free rate, and a beta estimated against one market should not casually multiply the premium of another.

CAPM is commonly used as a cost of equity in valuation. The output becomes the rate used to discount uncertain equity cash flows, or one component of a wider company discount rate. A higher beta raises the required rate and, with the same projected cash flows, lowers their present value.

The model result is conditional on its inputs and assumptions. It does not predict the next realised return. A stock with an 11.2 percent CAPM estimate can gain more, gain less or lose value over the period. The number is the return required by this model for the stated beta and market premium.

Read the formula as a disciplined decomposition: base rate, market premium, sensitivity. Keep the input source and date beside the result so the calculation can be reproduced. This is educational material, not financial advice.