My investigation was prompted by a casual observation that the Beta value reported on one website varied a lot compared to the Beta value on another website....How can that be???

Well here are the reasons:

Beta calculations are nothing more than looking at the change in value of a share price (on a percentage basis) compared to the change in value of an index for the same time frame (on a percentage basis).

Then for a fixed period of time you create a scatter graphical plot (think of a target hit by a shotgun blast) and then run a regression analysis to determine the SLOPE of the best straight line through the data (this is the BETA value) and the R-squared value which tells you the goodness-of-fit.

A perfect of the data would have an R-squared value of 1...the lower the r-squared value the more scattered the data (think of a wide spacing between the dots of data as opposed to following the best line)

To Answer YOUR question: the R-squared value is NOT the same as the BETA...R-squared tell you how good that the data fit the best straight line. the Beta is the slope of the line (your formula there is correct.)

Why is the R-squared value important?

Well it is quite easy for two widely different plots of data to have the same best straight line through them...however their R-squared values can be different. You use the R-squared value to compare the QUALITY of the Beta result.

Let us say data set #1 has a beta of 1.3 and an R-squared of .1
another data set #2 has a beta of 1.3 and an R-squared of .6

Are these stocks the same?? NO...they are both more volatile than the index they are being compared to.....however data set #2 has a higher R-squared value so it will MORE RELIABLY follow that index than data set #1 since its values are tighter together.

Now Why are PUBLISHED Beta values unreliable??

1. They DON'T indicate which index they are being compared to. They are ASSUMED to be compared to the S&P500 but you are never sure...and even if they are, is this the appropriate index for comparison.

Shouldn't a Hi-Tech stock use the NASDQ for its beta as there are more Hi-tech stocks in its group...better yet have the comparison made to a sub index which is totally composed of Hi-tech companies...makes more sense to me than having a comparison to a general overall index.

Gold stocks perhaps be compared to the end-of-day price of Gold itself....that seems a more reliable beta number if following that commodity. Why should a gold mine be compared with data that includes drug companies...makes no sense to me.

also you have the problem of comparing Beta's of stocks that list in 2 countries

Take Research in Motion [RIMM: NASD; TSX: RIM]

https://www.theglobeandmail.com/globe-inv...
https://finviz.com/quote.ashx?t=rimm

In Canada the Beta is 2.13 as measured on the Canadian website the Toronto Globe and Mail
In the USA the Beta is 1.69 as measured in the USA using the website FinViz

A significant difference...who is right? probably both...the USA result is based on probably the S&P500 while the Canadian result is based on the TSE composite Index most likely...but you don't know.

Both charts track each other as far as share price goes...so...which beta do you go with??? A big decision there...I would suppose it would depend on the companies you are comparing to...Are they predominately in the USA (probably the case) or in Canada....it is a decision but you have no guidance on the matter...well perhaps now you will think about it more.

2. The websites do not publish WHEN the beta was calculated. A beta based on 5 years of data is hardly comparable to one of 2 years of data or one year...was it calculated say for one year back from today or was that last one year calculation done 6 months ago....you have no way of knowing how these numbers are calculated

3. Websites do not publish the TYPE of DATA used....is it weekly close or daily close...both can be used both and will give you different results for Beta and r-squared numbers

For me using published data is useless for all the reasons listed above. Are Beta and r-squared numbers in theory useless....I have not said that...it is just that the published ones (unless they describe how they are calculated AND are industry/appropriate index specific) are useless.

It is not hard to set up a spread sheet and calculate your own Beta and r-squared values based on an index that is more appropriate than a general S&P 500

It is only when you do that can you make reliable decisions basis on the number you get

I personally use a bear/bull beta which I find far more useful. I've talked about in my custom platform thread. But short version, I think it's more useful to know how a stock performs against the benchmark in a particular market cycle.

Mike