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# Capital Asset Pricing Model (CAPM)

The capital asset pricing model (CAPM) is used in finance to determine a theoretically appropriate rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk.

CAPITAL ASSET PRICING MODEL (CAPM)

The capital asset pricing model (CAPM) is used in finance to determine a theoretically appropriate rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The CAPM formula takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), referred to as beta (â) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. The model was introduced by Jack Treynor, William Sharpe, John Lintner and Jan Mossin independently, building on the earlier work of Harry Markowitz on diversification and modern portfolio theory.

Formula

The CAPM is a model for pricing an individual security or a portfolio. The security market line (SML) and its relation to expected return and systematic risk (beta) show how the market must price individual securities in relation to their security risk class. It enables to calculate the reward-to-risk ratio for any security in relation to the overall market s. Therefore, when the expected rate of return for any security is deflated by its beta coefficient, the reward-to-risk ratio for any individual security in the market is equal to the market reward-to-risk

ratio, thus:

Individual security s = Market s securities (portfolio) Reward-to-risk ratio Reward-to-risk ratio

,

The market reward-to-risk ratio is effectively the market risk premium and by rearranging the above equation and solving for E(Ri), the Capital Asset Pricing Model (CAPM) is obtained.

Where:

is the expected return on the capital asset is the risk-free rate of interest

(the beta coefficient) the sensitivity of the asset returns to market returns, or also ,

is the expected return of the market

is sometimes known as the market premium or risk

premium (the difference between the expected market rate of return and the risk-free rate of return).

Asset pricing

Once the expected return, E(Ri)-, is calculated using CAPM, the future

cash flows of the asset can be discounted to their present value using this rate (E(Ri)-), to establish the correct price for the asset.

In theory, therefore, an asset is correctly priced when its observed price

is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then the asset is overvalued

Asset-specific required return

The CAPM returns the asset-appropriate required return or discount rate - i.e. the rate at which future cash flows produced by the asset should be discounted given that asset's relative risk. Betas exceeding one signify more than average "risk"; betas below one indicate lower than average. Thus a more risky stock will have a higher beta and will be discounted at a higher rate; less sensitive stocks will have lower betas and be discounted at a lower rate.

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