VS,

Forgetting the holes that one can drive a truck through with Beta, why not calculate it yourself?

Beta is the regression of stock returns against market returns.

A fairly quick way to do this:

***** From Yahoo! - get the last 60 month-end prices for the stock, and month-end prices for the S&P500.

Put into two columns in Excel.

***** Calculate monthly stock returns: (P1 - P0)/P0. You'll have 59 data points.

***** Calculate monthly market returns: (M1 - M0)/M0. Again, you'll have 59 data points.

***** From Excel's '**Tools**' select '**Data Analysis**'. Then select the '**Regression**'

***** The pop-up window will ask you for an '**Input Y-Range**'. Select the spreadsheet cells where

your *Stock Returns* are listed.

***** The next line asks you for an '**Input X-Range**'. Select the spreadsheet cells where your

*Market Returns* are listed.

***** Then, click the radio button under output options for '**Output Range**' Choose a blank cell

in your spreadsheet where you'd like the output to go.

Below, is the relevant data for Quality Systems (QSII), which you can cut, paste, and play with:

Month Stock Market Stock Market

End Price Level Return Return

--------------------------------------------------

Oct-00 $3.72 1,429.40

Nov-00 $3.97 1,314.95 0.0672 -0.0801

Dec-00 $3.88 1,320.28 -0.0239 0.0041

Jan-01 $4.72 1,366.01 0.2181 0.0346

Feb-01 $5.25 1,239.94 0.1123 -0.0923

Mar-01 $5.50 1,160.33 0.0476 -0.0642

Apr-01 $5.22 1,249.46 -0.0518 0.0768

May-01 $7.13 1,255.82 0.3672 0.0051

Jun-01 $6.50 1,224.42 -0.0884 -0.0250

Jul-01 $6.80 1,211.23 0.0462 -0.0108

Aug-01 $5.95 1,133.58 -0.1250 -0.0641

Sep-01 $5.23 1,040.94 -0.1218 -0.0817

Oct-01 $5.88 1,059.01 0.1244 0.0174

Nov-01 $7.43 1,139.45 0.2638 0.0760

Dec-01 $8.16 1,148.08 0.0983 0.0076

Jan-02 $8.44 1,130.20 0.0349 -0.0156

Feb-02 $8.40 1,106.73 -0.0047 -0.0208

Mar-02 $7.62 1,147.39 -0.0935 0.0367

Apr-02 $7.71 1,076.64 0.0125 -0.0617

May-02 $8.05 1,067.14 0.0441 -0.0088

Jun-02 $8.43 989.81 0.0466 -0.0725

Jul-02 $8.09 911.62 -0.0398 -0.0790

Aug-02 $8.69 916.07 0.0742 0.0049

Sep-02 $8.45 815.29 -0.0276 -0.1100

Oct-02 $10.12 885.77 0.1976 0.0864

Nov-02 $11.98 936.31 0.1833 0.0571

Dec-02 $10.05 879.82 -0.1608 -0.0603

Jan-03 $12.48 855.70 0.2413 -0.0274

Feb-03 $12.66 841.15 0.0148 -0.0170

Mar-03 $12.76 848.18 0.0075 0.0084

Apr-03 $15.19 916.92 0.1905 0.0810

May-03 $15.63 963.59 0.0290 0.0509

Jun-03 $13.63 974.51 -0.1277 0.0113

Jul-03 $17.80 990.31 0.3059 0.0162

Aug-03 $21.51 1,008.01 0.2084 0.0179

Sep-03 $20.10 995.97 -0.0656 -0.0119

Oct-03 $23.98 1,050.71 0.1930 0.0550

Nov-03 $21.40 1,058.20 -0.1076 0.0071

Dec-03 $22.30 1,111.92 0.0418 0.0508

Jan-04 $28.33 1,131.13 0.2705 0.0173

Feb-04 $22.53 1,144.94 -0.2048 0.0122

Mar-04 $22.72 1,126.21 0.0084 -0.0164

Apr-04 $21.50 1,107.30 -0.0535 -0.0168

May-04 $23.36 1,120.68 0.0865 0.0121

Jun-04 $24.55 1,140.84 0.0507 0.0180

Jul-04 $23.88 1,101.72 -0.0273 -0.0343

Aug-04 $23.82 1,104.24 -0.0023 0.0023

Sep-04 $25.26 1,114.58 0.0602 0.0094

Oct-04 $25.32 1,130.20 0.0026 0.0140

Nov-04 $30.71 1,173.82 0.2127 0.0386

Dec-04 $29.90 1,211.92 -0.0262 0.0325

Jan-05 $33.85 1,181.27 0.1319 -0.0253

Feb-05 $40.25 1,203.60 0.1892 0.0189

Mar-05 $42.34 1,180.59 0.0519 -0.0191

Apr-05 $47.58 1,156.85 0.1238 -0.0201

May-05 $60.13 1,191.50 0.2638 0.0300

Jun-05 $47.38 1,191.33 -0.2120 -0.0001

Jul-05 $57.92 1,234.18 0.2225 0.0360

Aug-05 $65.00 1,220.33 0.1222 -0.0112

Sep-05 $69.09 1,228.81 0.0629 0.0069

After you've run your regression, you'll end up with an output as per below. The important numbers are bolded for discussion:

SUMMARY OUTPUT

Regression Statistics

-----------------------------

Multiple R 0.373

R Square **0.139**

Adjusted R Square 0.124

Standard Error 0.122

Observations 59

-----------------------------

ANOVA

----------------------------------------------------------------

df SS MS F Significance F

----------------------------------------------------------------

Regression 1 0.139 0.139 9.235 0.004

Residual 57 0.855 0.015

Total 58 0.994

----------------------------------------------------------------

Standard

Coefficients Error t-Stat P-value Lower 95% Upper 95%

-----------------------------------------------------------------------------

Intercept 0.060 0.016 3.791 0.000 0.029 0.092

X Variable 1 **1.102** 0.363 **3.039** 0.004 **0.376 1.829**

-----------------------------------------------------------------------------

Okay, first-off, your calculated beta is listed in the bottom table under **Coefficients**, in the row for *X Variable 1*.

So your calculated Beta is **1.102**.

I should point out that this is where the 'free' betas available from Yahoo! or MSN end. They calculate it as per the above method (although they might use weekly returns, or 24 months, rather than 60 months, but they'll never tell you). *However*, what they don't tell you is the quality of the calculation. For example, I can tell you that the reported beta for Hidden Gem: Portfolio Recovery is statistically invalid. Yet, Yahoo! still lists it. If you use it for valuation purposes, you'll erroneously value the company too high.

So, you need to assess how statistically 'good' this beta is (and this should also illustrate the glaring problems inherent in beta). First, we ask, is our estimate of beta statistically different from zero? To do this, we run a 't-test', and you can see the regression program has considerately provided the calculated t-statistic for beta, which is **3.039**.

Now, to have confidence that our estimate of beta is statistically different from zero, we need to compare the calculated t-stat for beta agains the expected statistical value. Rather than more calc's, a quick and dirty way, is just to *make sure that the calculated t-stat is ***greater than 2**. (Note, right beside the calculated t-stat, you'll see a P-Value of 0.004, which means the probability of our beta being a result of chance and chance alone is 0.4%, or, put another way, our calculated beta is good at the 99.6% significance level). Since all this is good, we move on.

At the top of the table, you see a value for R-Squared of **0.139**. This means that **13.9%** of the variability in stock returns is attributable to the variability in the underlying market. Meaning that 86.1% of the stock return variability is attributable to other factors (boy, bet you're feeling really good about beta right about now!)

Finally, back to the bottom table, you'll see under *Lower 95%* and *Upper 95%*, two values: **0.376** and **1.829**. What these represent is a 95% confidence interval for our beta. In other words, we're 95% confident that the **'TRUE'** value of beta is somewhere between 0.376 and 1.829, as opposed to our calculated estimate of beta of 1.102. Again, you should be thinking that beta is a rather sketchy measure, right about now.

Hope that helps. Sorry about the length.

Cheers,

Jim