The **Capital Asset Pricing Model (CAPM)** is a theory of asset pricing that is based on an asset’s *systematic risk*. The basic elements of the theory are the **time value of money** and risk. The idea of the** time value of money** is captured in the idea of the risk-free rate that we’ve already discussed. The other half of the CAPM equation represents risk and calculates the amount of compensation the investor needs for taking on additional risk.

This is computed by taking a risk measure (beta) that compares the returns of the asset to the market over a period and to the market premium: the return of the market that is leftover after you subtract risk-free rate. **Beta** reflects how risky an asset is compared to overall market risk (a benchmark) and is a function of the volatility of the security and the market as well as the correlation between the two. For stocks, the market is usually represented as the S&P 500 but can be represented by other indices.

The CAPM was the work of economist William Sharpe and was first fully defined in his 1970 book *Portfolio Theory and Capital Markets*. Sharpe’s model starts with the idea that individual investment contains two discrete types of risk. **Systematic Risks** are market risks that cannot be diversified away (e.g., interest rates, recessions, and inflation). Unsystematic Risk (also known as **specific risk**) is risk unique to individual stocks and can be diversified away as the investor increases the number of stocks in a portfolio. In other words, it represents the component of a stock’s return that is not correlated with overall market moves.

Modern portfolio theory shows that specific risk can be counteracted through diversification. The trouble is that diversification still doesn’t solve the problem of systematic risk; even a portfolio of all the stocks traded in the market can’t eliminate that risk. This points out why we need to diversify across several asset classes, and informs us about how to diversify within the equity class. In essence, CAPM evolved as a tool to measure this systematic risk.

The idea that stocks have a true value that can be different from the market value is an old one. The **fundamental value** of an asset has to be distinguished from its price that we can observe in the market. The fundamental value can be identified with the *natural price* as defined by Adam Smith. He defines the natural price to be such that it gives the owner a sufficient profit. The price that can be observed can be interpreted as the **market price** (again, in the sense of Adam Smith). The market price is determined by demand and supply of the asset and can, therefore, deviate from the fundamental value, but in the end, will converge to the fundamental value.

### Beta

According to CAPM, **beta** is the only relevant measure of a stock’s risk. It measures a stock’s relative volatility (covariance). In simple terms, it shows how much the price of a particular stock jumps up and down compared with the degree that the market as a whole jumps up and down. If a share price moves exactly in line with the market, then the stock’s beta is 1.0. A security with a beta of 1.5 would rise by 15% if the market rose by 10% and fall by 15% if the market fell by 10%.

### Sharpe Ratio

The ratio describes how much excess return you are receiving for the extra volatility that you endure for holding a riskier asset. Remember that, according to CAPM, you always need to be properly compensated for the additional risk you take for not holding a risk-free asset. The larger the value of the Sharpe ratio, the more attractive the risk-adjusted return.

The Sharpe ratio is a good measure of risk for large, diversified, liquid investments, but for others, such as hedge funds, it can only be used as one of a number of risk/return measures. One inconvenient fact about the ratio is that it requires a normal distribution of returns to be accurate. This means that clever fund manager can “trick” the Sharpe ratio to suggest that a fund has very low risk compared to its returns until it explodes.

Long-Term Capital Management (LTCM) had a very high Sharpe ratio of 4.4 before it imploded in 1998. Just as in nature, the investment world is not immune to long-term disaster earthquakes, and floods happen in places where they were not expected. If it weren’t for these kinds of rare and dangerous events, no one would invest in anything but stocks. The takeaway is that we can use the Sharpe ratio as an indication of risk-adjusted reward, at least under certain circumstances.

The Sharpe ratio is an excellent way to compare “what if” analyses when you are designing portfolios. If you can get the same nominal rate of return from two different portfolio configurations, then you will obviously want to choose the one with the best Sharpe ratio. This idea is so prevalent in fact that you can enter a list of funds into many software packages and have your allocation percentages calculated to maximize the Sharpe ratio.

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