## Capm – capital asset pricing model – bogleheads electricity bill

Unsystematic risk only affects an individual security or portfolio and does not affect the market as a whole. Unsystematic risk is treated as "*random noise*" in a portfolio. Consider, for example, volatility of returns. Through the use of diversification (adding many securities), the *random noise* component will eventually have a mean of zero (the definition of random noise). Standard deviation of returns is also reduced as the number of securities in the portfolio increases.

If there are enough assets in a portfolio such that diversification cannot affect the performance, the volatility of the portfolio’s returns matches that of the overall market’s returns. Risk that can not be mitigated through diversification is known as systematic risk. The portion of its volatility of returns which is considered systematic is measured by the degree to which its returns vary relative to those of the overall market.

From a fundamental perspective, Beta (β) is calculated by taking the risk-adjusted return R i (return over the risk-free rate, also known as the "Risk-adjusted" or "excess" return) over a time period of the individual asset (i) (or portfolio) divided by the risk-adjusted return (R m) of the market. Simplifying further, β is the slope of the line of the returns over this period. [1] β = Slope of the line = R i / R m.

On a more comprehensive level, the parameter beta (β) is used to describe the relationship between the returns of a security or portfolio (an asset) and the returns of the market as a whole; it combines the correlation of the asset’s returns and the market’s returns with the relative volatility of those returns:

• There is only one risk factor 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.

2. β = 1: An asset that moves with a volatility of returns exactly equal to the market’s has a beta of one. In other words, the returns are perfectly positively correlated. By definition, its expected return is equal to the market’s expected return:

3. β > 1: 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.

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, (β A), and multiplying by the MRP, (E(r M) – r f).

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.

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 alpha (α). If α is greater than zero, the portfolio lies above the Security Market Line.

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 were up 10%, about 7% of the return can be explained by the advance of all stocks and the other 3% is the result of other factors not related to beta. This observation led to the development of the Fama and French three-factor model.