Harry Markowitz established **Modern Portfolio Theory (MPT)** and the investment concept of diversification in 1952. One of Markowitz’ doctoral students, William Sharpe, streamlined his work and developed a more accessible approach to diversification known as the Capital Asset Pricing Model (CAPM). For their work, both individuals were awarded the Nobel Prize in Economic Sciences in 1990.

The Capital Asset Pricing Model expands Modern Portfolio Theory in two ways. First, it considers both risky and risk-free assets. Second, it breaks down investment risk into two distinct components – systematic and unsystematic risk.

## Understanding the Capital Asset Pricing Model

In the CAPM, an investment portfolio is divided between risky and risk-free assets, where “risk-free” means that the investment return is known with certainty. Traditionally, the risk-free investment is represented by short-term Treasury bills or an FDIC-insured savings account.

The idea is that investors can always invest in a risk-free asset and have a guaranteed return. For example, if you invest your money in a **reputable savings account**, you will earn the stated interest rate. There are no additional risk factors to consider, and everyone earns the same “risk-free” return on investment.

**Different Types of Investment Risk**

Most investments are not risk-free. For example, **stocks** are inherently risky. Although an investor always expects to earn a positive return when purchasing a stock, she might be disappointed or pleasantly surprised by the performance over time, because fluctuations in stock prices will determine the investor’s actual return on investment.

The future value and expected rate of return depend on a number of risk factors that are unknown when the investment is made. CAPM suggests that these potential risk factors can be broken down into two different categories.

The first type of risk, called **systematic risk**, is common to all risky assets. Systematic risk examples include:

- Tax code or economic interest rate changes
- Expectations of other market participants (investors)
- Currency fluctuations, inflation, and economic cycles (including recessions).

Systematic risks cannot be diversified away. Whether you own one stock or several thousand stocks, the value of your investment partially depends on risk factors that are inherent in our modern economy.

The second type of risk, called **unsystematic risk **(or idiosyncratic risk), captures the unique risk factors associated with an individual company or sector.

For example, Exxon Mobil (the oil giant) is subject to several unique risks:

- New energy alternatives could reduce or replace worldwide demand for fossil fuels (oil and gas)
- New energy regulations could increase the cost of production, reducing shareholder profits, and therefore, the value of Exxon stock.

These unsystematic risks can be diversified away. Concerns about alternative energies and worldwide demand can be eliminated by owning the entire energy sector, not just companies that produce oil and gas. Concerns about energy regulations can be eliminated by further diversifying the portfolio to include non-energy related sectors.

Because these risks are diversifiable, CAPM suggests that investors should not be rewarded for bearing the risk. In other words, any type of unsystematic risk should not produce an increased return on investment within competitive financial markets and should be eliminated by rational investors through diversification.

## The CAPM Equation

The Capital Asset Pricing Model combines all of the information discussed thus far into a simple equation:

- E(R
_{i}) = R_{f}+ risk premium

In English, the expected return of any risky asset E(R_{i}) equals the risk-free rate (R_{f}) plus an expected risk premium for investing in the risky asset.

The risk premium component of the equation does not consider unsystematic risk, which can be eliminated through proper diversification. The risk premium captures only systematic risk, which can further be broken down into the following equation:

- risk premium = β
_{i}(R_{m}– R_{f})

In English, the expected risk premium of any investment equals its beta (β_{i} = a measure of systematic risk) multiplied by the expected risk premium of the entire market (R_{m} = 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(R
_{i}) = R_{f}+ β_{i}(R_{m}– R_{f})

### Capital Asset Pricing Model Example

A quick example can help you better understand the mathematical equation. First, let’s assume that the risk-free rate is 1%, the expected return of the U.S. stock market is 10% (roughly the historical average), 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(R
_{i}) = 1% + 1 (10% – 1%) - E(R
_{i}) = 1% + 1 (9%) - E(R
_{i}) = 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.

## The Intuition Behind CAPM

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 largely 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.