Calculating Beta
By Thomas Stridsman
©2001, Reprinted with permission of Active Trader magazine (www.activetradermag.com)
Beta is typically calculated using monthly prices over a period of at least two years, generating 24 monthly “observations.” However, it can be calculated on any time frame. Statistically speaking, the more observations used in the beta calculation and the longer the time interval between the observations, the more reliable the forecast. At least in theory, that is, because — as with so many other technical indicators — beta lags market action, and the more observations and the longer the time between them, the more it will lag.
To calculate beta, first measure the percentage price changes from one period to the next for both an individual stock and its corresponding market index. Then create a regression line (a “best-fit” line that best approximates the slope of the data) of the two time series, using the change in the index as the independent variable against which to compare the change in the stock price.
While many technical analysis packages allow you to perform intermarket calculations, this type of statistical analysis is more computer intensive than normal technical analysis, which can make it a very slow process. Therefore, you’re probably better off using a spreadsheet program, such as MS Excel. A sample spreadsheet illustrating the following example can be found at www.activetradermag.com/ code.htm.
In Excel, simply use the “slope” function, which measures the slope of a regression line running through your data, with the independent variable (the change in index) on the horizontal axis and the dependent variable (the corresponding change in the stock price) on the vertical axis. The resulting Excel formula looks like this:
=SLOPE(O3:O26,G3:G26)
where:
O3:O26 denotes the column and rows containing the index price changes.
G3:G26 denotes the column and rows containing the stock price changes.
In this case we placed the first formula in cell R26 and then filled all rows in column R with the same formula, all the way down to the bottom of the sheet, so the formula in cell R27 will be =SLOPE(O4:O27,G4:G27), and so on. When done, column R will hold a series of values that show how beta has changed from one period to the next.
Charting beta
One program that works well with Excel when making calculations such as this is MetaStock. More so than other programs of its genre, MetaStock has made it very easy to copy and paste data between MetaStock and other Windows programs.
In MetaStock, first create and save two charts — one holding the index, and one the stock you’d like to compare it with, as shown in Figure 1(above), which compares the S&P 500 index with Alcoa (AA). Then copy and paste both series into Excel. Remember to paste them both as links, so the spreadsheet will change with the contents of the MetaStock charts. Figure 2 (below) shows what this looks like, with the index pasted into columns A-F and the stock into columns I-N.
The next step is to use different lengths of the slope formula given earlier, and then copy those columns and paste them as links back into MetaStock. When done, you should have a chart resembling the one in Figure 3 (below), where the red line shows a one-year beta, the yellow line a two-year beta and the blue line a four-year beta, all based on monthly observations. Interestingly, if you compare the beta values in Figure 3 to the most recent eight months or so in the S&P 500 and Alcoa (see Figure 1), you’ll notice that while the S&P has continued to move lower, Alcoa has bucked the trend and reached new highs. Despite this, Alcoa’s beta values are still positive, and even slightly above 1.
How can this be, when a positive beta value means that the stock is likely to move in the same direction as the index? This is because Alcoa has still moved in the same direction as the index during a majority of the period. It just so happens that when the index has staged a small positive move, Alcoa has staged a large one, and when the index has staged a small negative move, Alcoa has staged an even smaller one.
One conclusion of analysis like this is that Alcoa is a good candidate for long trades in those months you believe the index will move higher, or a good place to park your money those months you believe the index will move lower. The only thing that seems to be keeping Alcoa from moving even higher is the general negative bias of the market.
To get a feel for the current relationship between the index and the stock, you also could produce a “scatter chart” in Excel. This is done by first highlighting the appropriate number of changes in the market value for both the index and the stock (columns G and O, in Figure 2) and then using the “scatter” selection in Excel’s chart wizard. Figure 4 (bottom) shows what this looks like.
Notice in Figure 4 how most dots, no matter the color, are located in the upper right and lower left quadrants of the chart, which means more often than not, when the index moves in a specific direction, Alcoa also moves in that direction. This reflects a positive beta, despite the fact that Alcoa has bucked the trend during the most recent months.
