We can estimate beta for a stock or portfolio of stocks relative to the overall stock market using simple linear regression analysis. The reader might recall the following equation from an earlier course in statistics. However, prior work in statistics is not necessary to grasp the following concepts. In simple equation form we have:

where α = the alpha or intercept term, β = the beta or slope coefficient that shows the size of the impact that market returns (R_{MKT}) have on stock returns (R_{i}), and e_{i} = an error term reflecting the fact that changes in market returns are not likely to fully explain changes in stock returns. This straight line is shown in Figure LE12.1.

There are computer software programs and sophisticated financial calculators that can perform the necessary calculations and find the beta coefficient with little effort. Spreadsheet software can perform this analysis, too. In addition, we can estimate beta the "long way" by using relatively simple calculations that can be done by hand or by using a simple calculator. We will demonstrate the long way of estimating beta so that the reader can develop a better understanding of the underlying process.

Let's begin by using the monthly returns over a recent six-month period between the market as measured by the S&P 500 and Microsoft (in practice, beta is often computed using ...

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