CAPM - Capital Asset Pricing Model

Quick links In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required 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 model takes into account the asset's sensitivity to non-diversifiable risk (also known as systemic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.
 * Eugene F. Fama
 * Kenneth R. French
 * Capital Asset Pricing Model
 * Fama and French Five-Factor Model
 * Fama and French Three-Factor Model
 * Fama and French Two-Factor Model

Market Risk (Beta)
An asset, e.g. stock, exhibits both systematic and unsystematic risk. The portion of its volatility which is considered systematic is measured by the degree to which its returns vary relative to those of the overall market.

Market risk (beta) is calculated using historical returns for both the asset and the market, with the market portfolio being represented by a broad index such as the S&P 500 or the Russell 2000.

Assumptions
The Capital Asset Pricing Model (CAPM) attempts to quantify the relationship between the beta of an asset and its corresponding expected return. Several assumptions are made:
 * 1) Investors care only about expected returns and volatility. Therefore, expected returns are maximized for any given level of expected volatility.
 * 2) All investors have homogeneous beliefs about the risk/reward trade-offs in the market.
 * 3) There is only one risk factor is common to a broad-based market portfolio, called systematic market risk. Investors are assumed to hold diversified portfolios. As a result, the CAPM model states that if an asset's beta is known, the corresponding expected return can be predicted.

Model Description
There are 3 classes of assets to consider:

- An asset that has no volatility (no risk) does not have returns that vary with the market and therefore has a beta of zero and an expected return equal to the risk-free rate.

- An asset that moves with a volatility exactly equal to the market has a beta of one. In other words, it is perfectly correlated. By definition, it's return rate is equal to the market, E(rA) = (E(rm))

- An asset that experiences greater swings in periodic returns than the market, which, by definition, has a beta greater than one. This asset is expected to earn returns superior to those of the market as compensation for this extra risk.

Making a lot of generalizations leads to the CAPM model:
 * E(rA) = r(f) + βA(E(rm)) - rf)
 * where r(f) is the risk-free rate and
 * (E(rm)) is the expected excess return of the market portfolio beyond the risk-free rate, often called the equity risk premium.

The general idea of CAPM is that investors should be compensated in two ways: time value of money and risk.
 * The time value of money is represented by the risk-free (r(f)) rate in the formula and compensates the investors for placing money in any investment over a period of time.
 * The other part of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This is done by taking an estimate of risk, (βA), and multiplying by the difference of the (returns of the asset) to the (returns of the market) over a period of time, (E(rm)) - rf).

An asset is expected to earn the risk-free rate plus a reward for bearing risk as measured by that asset’s beta. The chart below demonstrates this predicted relationship between beta and expected return – this line is called the Security Market Line.



For example, a stock with a beta of 1.5 would be expected to have an excess return of 15% in a time period where the overall market beat the risk-free asset by 10%.

The CAPM model is used for pricing an individual security or a portfolio. For individual securities, the security market line (SML) and its relation to expected return and systematic risk (beta) shows how the market must price individual securities in relation to their security risk class.

As the CAPM predicts expected returns of assets or portfolios relative to risk and market return, the CAPM can also be used to evaluate the performance of active fund managers. The difference is “excess return”, which is often referred to as “α” (or, alpha). If α is greater than zero, the portfolio lies above the Security Market Line.

Shortcomings of the CAPM Model
Several shortcomings of the CAPM model exist. Incorrectly predicting results compared to realized returns and the affect of other risk factors have put this model under criticism. The assumption of a single risk factor limits the usefulness of this model.

Eugene F. Fama and Kenneth R. French found that on average, a portfolio’s beta explains about 70% of its actual returns. For example, if a portfolio was up 10%, about 70% of the return can be explained by the advance of all stocks and the other 30% is due to other factors not related to beta. The result is a model known as the Fama and French Three-Factor Model.