# How to calculate a beta factor

Written by steve johnson
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The beta factor, also known as coefficient of beta, or simply "beta," is considered an accurate method of assessing risk used by investors and others in the financial sector. The concept of beta was developed with the Capital Asset Pricing Model (CAPM), created by Jack Treynor, William Sharpe, John Lintner and Jan Mossin. These individuals received the Nobel Prize in Economics for their work on the model. Beta allows for an investor to compare the relative riskiness of owning certain assets.

Skill level:
Easy

### Things you need

• Graphing calculator

## Instructions

1. 1

Find the rate of return of the asset in question and the rate of return of the portfolio. In the CAPM, "the portfolio" refers to a portfolio which contains "all risky assets." The rate of return of the portfolio is replaced by the rate of return of the market benchmark, the Standard & Poor's 500. The S&P 500 is used as the portfolio because it is said to contain assets which replicate the effects of owning all risky assets. Therefore, the rate of return for the portfolio will be the rate of return of the S&P 500 over the specified period of time.

The rate of return is calculated as follows:

(current value of asset - initial value of asset)/(initial value of asset)

For example, if you want to find the rate of return of a stock that was worth £52 two months ago and is worth £65 now, the calculation would be: (\$100 - £52)/(\$80) = .25, or 25 per cent

In the same example, if the S&P 500 was at £520 two months ago and is at £715 now, the calculation would be: (\$1,100 - £520)/(\$800) = .375, or 37.5 per cent.

In the beta formula, rate of return is used as a decimal.

2. 2

Find the covariance between the rate of return of the asset in question and the rate of return of the portfolio. Put simply: Cov(rate of return of asset, rate of return of portfolio).

Covariance is calculated as follows: Cov(X,Y) = E[(X-E[X])(Y-E[Y])]

Simplified: E[XY]-E[X]*E[Y]

Covariance can be found as a function on your calculator. In this equation, X and Y are the variables representing the asset and the portfolio, respectively. E is the expected value for each variable. Expected value is "the sum of the values of a random variable divided by the number of values." It can be estimated or calculated by summing the respective probabilities of the asset and portfolio reaching your determined price levels.

Expected value can also be found as a function on your calculator.

3. 3

Divide the answer from step 2 (covariance between rate of return of asset and portfolio) by the variance of the rate of return of the portfolio. Variance is calculated as follows: Var(X) = E[(X - µ)^2], where E is the expected value and µ is the mean. Variance can be found as a function on your calculator.

The final calculation for beta is as follows: [Cov(rate of return of asset, rate of return of portfolio)]/[Var(rate of return of the portfolio)]

The beta for the market (the portfolio) is always 1. If the beta of an asset is 2, it is considered to be twice as risky as the market.

#### Tips and warnings

• Though the beta calculation is very complex, the beta for any stock can be found published on many free finance websites, such as Yahoo! Finance and Google Finance. Using this method can save you a great deal of time.
• Though the beta calculation is very thorough, it must be used with other tools in order to make a truly informed investment decision.

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