In English, the expected risk premium of any investment equals its beta (βi = a measure of systematic risk) multiplied by the expected risk premium of the entire market (Rm = the expected return of the market in question minus the risk-free rate).

Beta is a measure of systematic risk, which captures the tendency of any investment to move in parallel with the market as a whole. For example, the entire stock market has a beta of one. A stock with a beta greater than one will exhibit more volatility than the market, which would be rewarded with a higher expected return in the CAPM model. A beta of less than one means that the investment is less volatile than the market, which would reduce the expected risk premium in the CAPM model.

Putting it all together, we arrive at the official CAPM equation:

E(Ri) = Rf + βi (Rm – Rf)

## Capital Asset Pricing Model Example

A quick example can help you understand the mathematical equation. First, let’s assume that the risk-free rate is 1%, the expected return of U.S. stock market is 10%, and that the risky portion of our portfolio includes exposure to the entire U.S. stock market (easily achievable using a diversified ETF like VTI).

The beta (systematic risk) of said portfolio would equal one because the portfolio includes the entire universe of publicly traded U.S. stocks (the market). If you plug that information into the CAPM equation, you get the following:

E(Ri) = 1% + 1 (10% – 1%)
E(Ri) = 1% + 1 (9%)
E(Ri) = 10%

Here you can see, our expected return equals 10%. Because the risky asset in our portfolio includes the universe of U.S. publicly traded stocks, our expected return equals the expected return of the U.S. stock market.

Hopefully, things are beginning to make sense. When a diversified portfolio has a beta of one, the expected return will always equal the market return.

## Capital Asset Pricing Model

Enough with the equations. Let’s talk about the intuition behind the CAPM model.

First, investors must choose between risky and risk-free assets. Risk-free assets provide a guaranteed return, while risky assets provide an expected risk premium above the risk-free rate. Investors who can’t stomach volatility should hold more of the risk-free asset. Investors looking to maximize growth in the portfolio should maintain a larger allocation to risky assets.

When selecting risky assets, investors should pay careful attention to diversification. Holding concentrated positions in a few companies will produce significant unsystematic risk in the portfolio, which is unrewarded by financial markets.

The better solution is to “own the market.” If you want to invest in stocks, own the entire U.S. stock market, plus developed international and emerging markets. If you want to invest in bonds, or real estate, or commodities, or any other risky asset, own the market and eliminate all unsystematic risk in the process.

The Capital Asset Pricing Model has important limitations that have been discussed at length elsewhere. For one, beta is a highly imperfect measure of risk. More recent finance research has shown that there are a variety of other risk factors that appear to influence an investments expected return – a topic that I plan on exploring in future articles.

Limitations aside, CAPM’s emphasis on diversification remains an important takeaway for all investors.