# Capital asset pricing model

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Valuation and cost of capital.

(CAPM).

The capital asset pricing model links the expected rates of return on traded assets with their relative levels of market risk (beta).

The model’s uses include estimating a firm’s market cost of equity from its beta and the market risk-free rate of return.

The CAPM assumes a straight-line relationship between the beta of a traded asset and its expected rate of return.

The model assumes that investors expect a return equal to the theoretically risk-free rate of return, plus a premium for the degree of risk accepted.

## CAPM calculation

Expressed as a formula:

Re = Rf + beta x (Rm - Rf)

Rj = Rf + beta x (Rm - Rf)

Where:

Re = return on equity.

Rj = return on any traded risky asset

Rf = theoretical risk-free rate of return.

Beta = relative market risk.

Rm = average expected rate of return on the market.

Example

Rf = theoretical risk free rate of return = 4%.

Beta = relative market risk = 1.2.

Rm = average expected rate of return on the market = 9%.

Return on equity (Re):

= 4 + 1.2 x (9 - 4)

= 10%.

This equity investment requires an expected rate of return of 10%, higher than average rate of return on the market as a whole of only 9%, because its market risk (measured by beta = 1.2) is greater than the average market risk (of only 1.0).

Under the capital asset pricing model only the (undiversifiable) market risk of securities is rewarded with additional returns, because the model assumes that rational market participants have all fully diversified away all specific risk within their investment portfolios.

## Use of the CAPM to quantify cost of equity

When the CAPM is used to calculate an estimate of the cost of equity, it is conventionally expressed as:

Ke = Rf + beta x (Rm - Rf)

Where:

Ke = cost of equity

(& other terms are defined as above)