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**What is and How to Calculate the Capital Asset Pricing Model (CAPM)**

Investors calculate the capital asset pricing model (CAPM) to analyze the relationship between risk and return when pricing securities. CAPM provides a valuable data point to the investor based on the idea that a certain level of compensation is to be expected given an element of risk. In calculating CAPM, the formula incorporates the time value of money along with the level of risk to arrive at a discount rate for factoring into stock valuation.

**How to Calculate CAPM**

Simply put, the formula for CAPM can be described as:

**Expected Return = Risk Free Rate + Risk Premium**

Where the risk-free rate of return accounts for the time value of money and the other component, the risk premium, builds in the level of risk the investor is willing to take on in this investment. The idea behind building in a risk premium is that, even with a well-diversified portfolio, an investor assumes a certain level of risk and rational investors expect to be compensated in a way that is commensurate to that risk level. In other words, unless rational investors believe they are being fairly compensated given the investment risk, they will forego the investment.

### Factoring Stock Beta into the CAPM Calculation

Stock beta is the measure of how volatile a stock is compared to the overall market. When determining beta, the beta of the market as a whole is set to 1.0 and individual stock beta will vary according to their deviation from the movements of the market. Any stock that proves to be more volatile than the market is assigned a beta that is greater than 1.0 and those stocks are assumed to be riskier. Stocks that demonstrate less of a swing than the overall market would carry a beta that is less than 1.0. Those stocks are generally seen as less risky.

### Guidelines for Using the CAPM Calculator

The rate available from U.S. Treasury bills is often used as the baseline for an available risk-free rate of return.

To find a stock’s beta, go to Yahoo! Finance, enter the stock symbol in the Get Quotes window and click on the Key Statistics on the left-hand side. You will find the stock beta on the right under the Stock Price History.

The expected return from a broad market index, like the S&P 500 often serves as the expected market return for the CAPM calculation

## The Capital Asset Pricing Model (CAPM) Explained

In order to compensate themselves for holding a risky asset, rational investors demand to be paid a ‘risk premium’. The greater the risk, the greater the risk premium should be. The expected return that an investor can expect to achieve can be calculated by using the Capital Asset Pricing Model formula, which expresses the expected return in terms of the return an investor would expect to achieve for holding a risk-free asset plus the risk premium.

The Capital Asset Pricing Model formula is:

E = F + ß* (M – F)

Where:

- E is the Expect return that an investor could make on the investment.
- F is the risk-free rate of return that can be achieved.
- ß is the Beta of a security.
- M is the anticipated Market Return of a portfolio.

The risk premium, mentioned above, is given by the part of the formula: ß * (M – F).

** CAPM Worked Example**

Where the return on risk-free Treasury bills is 2%, there is an expect Market Return of 6% and the beta of our example security ‘XYZ Inc.’ is 1.5, then according to the CAPM formula, the Expected Return is:

E = 2 + 1.5 * (6 – 2)

E = 2 + 1.5 * 4

E = 2 + 6

So, the expected return is 8% in this example.

** CAPM Assumptions**

Various assumptions underlie the capital asset pricing model. These are:

- Investors are rational and risk-averse and seek to maximize their risk-adjusted returns.
- All trading can be done free from tax and without any transaction costs.
- The market is highly liquid and dealing will not affect market prices.
- Information is free and made available to all investors simultaneously.
- All investors can lend and borrow money at the risk-free rate of return.
- The time-horizon over which investments are made is identical for all investors in the market.

These assumptions are not all equally valid, you may recognize some as being more credible than others. However, the purpose of the model is to help understand and provide a prediction for the return that may be achieved on a security, which it does.

A wise investor would not rely on the CAPM alone when making investment decisions, but do much more research before investing.

** CAPM Limitations**

The risk-free rate of return is normally taken to be that available on treasury bills, doing so is common practice, but is does highlight the need to choose a correct risk-free asset.

The market portfolio should in theory contain all available global investments. In practice, it is normally limited to just one market, e.g. the S&P500 in the United States.

The beta coefficient is derived from historical data and can change over time, so it’s ability to predict future price changes can be limited.

Securities are not in practice distributed according to a standard (or Gaussian) bell-shaped curve. Whilst the standard distribution is a very good working model, security price distribution exhibits kurtosis, i.e. ‘fat tails’ with large price movements occurring more often than would be expected if a standard bell-shaped curve was strictly accurate.

**Capital Asset Pricing Model – Alpha Definition**

On the Capital Asset Pricing Model page, the return that an investor could expect to make was defined. It is important to note that this is the return that an investor could expect to make in the future. When calculating alpha however, the alpha is ‘backward looking’ and refers to past performance of a security or investment fund, as it is calculated using actual performance data.

The difference between the return that would have been reasonably expected, using the historic data for its beta, and the return that was actually produced is known as alpha, represented by the symbol ‘α’.

Very simply, alpha is defined in the following formula:

α = actual portfolio return – expected portfolio return.

We can substitute the ‘expected portfolio return’ with the formula from the Capital Asset Pricing Model (CAPM), to give the full formula for calculating alpha as:

**α = actual portfolio return – (F + β* (M – F))**

where:

- F is the risk-free rate of return.
- β is the Beta of the security.
- M is the Market Return of a portfolio.

Calculated from historic data.

This formula can be used to calculate the alpha both of an individual security or an investment fund.

Alpha is also known as ‘Jensen’s Alpha’, after it was developed for the purpose of measuring mutual fund performance by American economist Professor Michael Cole Jensen. It is therefore most typically used in evaluating how much value a portfolio or fund manager add by actively managing a portfolio. A positive figure for the alpha would indicate that the fund manager has outperformed the market, whilst a negative figure indicates that they underperformed.

**Alpha in practice**

In practice, many actively managed mutual funds do not manage to return a positive alpha in the long run. This much is predicted by the efficient market hypothesis, which states that it won’t be possible for an investor, or fund manager, to achieve returns that are in excess of average market returns on a consistent basis.

Additionally, there is the cost of actively managed funds to take into account, the costs act as a drag on fund performance.

One alternative to active management of a mutual fund would be for an investor to opt for a passive index tracking fund instead. However, even here the alpha would be slightly below zero, due to the management expense of running the index fund which would not be present in performance of the underlying index that is being tracked, although the cost involved for an index tracking fund are usually very much less than for an actively managed fund.