No matter how much you diversify your investments, some level of risk will always exist. Investors therefore naturally seek a rate of return that compensates for this risk. The Capital Asset Pricing Model (CAPM) helps calculate the investment risk and return on investment that an investor should expect.

## Systematic risk vs. unsystematic risk

The financial asset pricing model was developed by financial economist (and later Nobel laureate in economics) William Sharpe, set out in his 1970 book *Portfolio theory and capital markets*. His model is based on the idea that individual investment contains two types of risk:

*Systematic risk*– These are market risks, ie the general perils of investing, which cannot be diversified. Interest rates, recessions and wars are examples of systematic risks.*Unsystematic risk*– Also known as “specific risk”, this risk relates to individual stocks. In more technical terms, it represents the component of a stock’s return that is uncorrelated to general market movements.

Modern portfolio theory shows that specific risk can be removed or at least mitigated through portfolio diversification. The problem is that diversification still does not solve the problem of systematic risk; even a portfolio holding all stocks in the stock market cannot eliminate this risk. Therefore, when calculating an earned return, systematic risk is what afflicts investors the most.

## The CAPM formula

CAPM evolved as a way to measure this systematic risk. Sharpe found that the return on an individual stock, or portfolio of stocks, should equal its cost of capital. The standard formula remains the CAPM, which describes the relationship between risk and expected return.

Here is the formula:

$$

R

a

=

R

r

F

+

β

a

∗

(

R

m

−

R

r

F

)

or:

R

a

=

Expected return of a security

R

r

F

=

Risk-free rate

R

m

=

Expected market return

β

a

=

The Security Beta

begin{aligned} &R_a = R_{rf} + beta_a *left(R_m – R_{rf} right) &textbf{where:} &R_a = text{Expected return of a security} &R_{rf} = text{Risk-free rate} &R_m = text{Expected market return} &beta_a = text{The beta of the security} &left(R_m – R_{ rf} right) = text{Stock market premium} end{aligned}

Ra=RrF+βa∗(Rm−RrF)or:Ra=Expected return of a securityRrF=Risk-free rateRm=Expected market returnβa=The Security Beta

The starting point for CAPM is the risk-free rate, usually a yield on 10-year government bonds. A premium is added, which equity investors demand in compensation for the additional risk they run. This stock market premium is the expected return of the market as a whole minus the risk-free rate of return. The equity risk premium is multiplied by a coefficient that Sharpe called “beta”.

## Role of Beta in CAPM

According to CAPM, beta is the only relevant measure of a stock’s risk. It measures the relative volatility of a stock, i.e. it shows how much the price of a particular stock rises and falls compared to how much the whole stock market rises and falls. If a stock’s price moves exactly in line with the market, the stock’s beta is 1. A stock with a beta of 1.5 would rise 15% if the market rose 10% and fall 15% if the market fell by 10%.

Beta is determined by a statistical analysis of daily individual stock price returns relative to daily market returns over the exact same time period. In their classic 1972 study “The Capital Asset Pricing Model: Some Empirical Tests,” financial economists Fischer Black, Michael C. Jensen, and Myron Scholes confirmed a linear relationship between the financial returns of equity portfolios and their betas. They studied stock price movements on the New York Stock Exchange between 1931 and 1965.

Beta, compared to the risk premium of stocks, indicates the amount of compensation that stock investors need to take on additional risk. If the stock’s beta is 2.0, the risk-free rate is 3% and the market rate of return is 7%, the market excess return is 4% (7% – 3%). As a result, the stock’s excess return is 8% (2 x 4%, multiplying the market return by the beta), and the stock’s required total return is 11% (8% + 3%, the excess return of the stock plus the risk-free rate) .

What the beta calculation shows is that a riskier investment should earn a premium over the risk-free rate. The amount above the risk-free rate is calculated by the equity market premium multiplied by its beta. In other words, it is possible, by knowing the different parts of the CAPM, to assess whether the current price of a stock is compatible or not with its probable return.

## What CAPM means for investors

This model presents a simple theory that provides a simple result. The theory says that the only reason an investor should earn more, on average, by investing in one stock than another is that a stock is riskier. Not surprisingly, the model has come to dominate modern financial theory. But does it really work?

It’s not entirely clear. The big sticking point is the beta version. When professors Eugene Fama and Kenneth French examined stock returns on the New York Stock Exchange, the US Stock Exchange and the Nasdaq, they found that differences in beta over a long period did not explain the performance of different stocks. . The linear relationship between beta and individual stock returns also breaks down over shorter time periods. These results seem to suggest that CAPM may be in error.

Although some studies raise doubts about the validity of the CAPM, the model is still widely used in the investment community. While it is difficult to predict from beta how individual stocks might react to particular moves, investors can probably safely infer that a portfolio of high beta stocks will move more than the market in either direction. , and that a portfolio of low-beta stocks will move less than the market.

This is important for investors, especially fund managers, as they may be reluctant or prevented from holding cash if they believe the market is likely to fall. If so, they may hold low-beta stocks instead. Investors can tailor a portfolio to their specific risk-return requirements, aiming to hold securities with betas greater than 1 when the market is up, and securities with betas less than 1 when the market is down. decrease.

Not surprisingly, CAPM has contributed to the rise in the use of indexing — assembling a portfolio of stocks to mimic a particular market or asset class — by risk-averse investors. This is largely due to CAPM’s message that higher returns than the market as a whole can only be achieved by taking on higher risk (beta).

## The essential

The financial asset pricing model is by no means a perfect theory. But the spirit of the CAPM is correct. It provides a useful metric that helps investors determine the return they deserve on an investment, in exchange for putting their money at risk.