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Strategies & Market Trends : A.I.M Users Group Bulletin Board
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To: LemonHead who wrote (12915)9/22/2000 10:37:51 AM
From: labestul  Read Replies (1) of 18928
 
You gotta be kidding. You must be trying to bring Savage out of the Wood work. My pencil is round not square rooted.

Well I'm out!!! Now isn't that your worst nightmare!

Actually this reminds me a filly that I once owned who would only race in the dark. She was a real night mare.

And then again was the elected leader of my home town who insisted on attending every city council meeting dressed in a full set of silver armor. He was without a doubt the very worst KNIGHT MAYOR I have ever known!

But now on to some Greek things. A question was raised about r squared in relation to beta. This arises in the context of measuring investment return on stocks (among other things).

Suppose I draw a graph as follows. Along the horizontal line I have the return on the overall market which could be represented by a stock index for example. Now suppose along the vertical axis I have the return of a particular stock in which I am interested. Finally suppose I have the history of returns over a prior period (one year for example). Then for each date I could mark a point on my graph. For example if on January 2nd of last year the index return had been 10% and the stock's return had been 12% I would mark a point 10 units to the right and 12 units up from the center of my graph. I would do this for all my data.

I could then ask myself two questions:

(1) does the group of points suggest any pattern to me?

(2) if yes, can I use this pattern to project what will happen to my stock return if the market return reaches such and such a level?

One approach to resolving these two question is to use a mathematical technique and set of formulae called linear regression. This technique assumes that the answer to the first question is YES and that there is a strait line relationship between the market return and individual stocks rate of return. The formal equation of this line involves two estimated parameters called alpha and beta. These parameters are estimated using a technique which minimizes the distances between the plotted points on the graph and the corresponding points on the estimated line. This particular techniques is called "least squares error minimization" (or variations thereon). It is however not necessary to know how this technique works simply to interpret and use the results.

For those who remember basic analytic geometry BETA is simply the SLOPE of the regression line. But weather or not one remembers is irrelevant. We all know that one use of BETA is as a measure of the volatility of the stocks return (and hence also its price) in relation to the market.

The problem with this whole approach however is that we have made an implicit assumption that the relationship between the overall market return and that of the stock's return is LINEAR (i.e. a strait line). In practice this might not be true. We could check this in at least two ways.

First we could obtain the data upon which the calculations for BETA were made and then plot this data in a graph. We might then be able to see if all of the points tend to lie along or close to a strait line. Not only would this be a lot of work but in general we don't have that data.

Therefore the mathematical technique of linear regression also produces a measure of fit called r squared (sometimes RHO squared ......... but that's Greek to me). The closer that r squared is to one ... the better the fit ... that is the more the graph of dots resembles a strait line.

And so in a nutshell that's it. R-squared is a measure of how confident we are in the BETA.

Hope this helps,

Barry
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