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# SouthTrust Corporation (SOTR) Message Board

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• larrywalker larrywalker Dec 1, 1997 8:07 PM Flag

## SouthTrust's Risk

I strongly suspect that the beta analysis for Southtrust is merely an academic pursuit, since its present identity is likely to be short lived. This bank has to be in the crosshairs of several larger acquisitive banks. (But, I have been wrong before. *L*)

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• Larry,

I'm glad you caught my oversimplification of stock betas. Its been a few years since I took graduate level finance in the MBA program. Now what does Beta mean? A lot of disservice has been done to Beta in the popular press because of trying to simplify
the concept. A beta of 1.5 does not mean that is the market goes up by 10 points, the stock will go up by 15 points. It doesn't even mean that if the market has a return (over some period, say a month) of 2%, the stock will have a return of 3%. To understand Beta, look at the equation of the line we just fitted:

stock return = alpha + beta * index return

Therefore, by computing the derivative, we can write:
Change in stock return = beta * change in index return

So, truly and technically speaking, if the market return is 2% above its mean, the stock return would be 3% above its mean, if the stock beta is 1.5.

One shot at interpreting beta is the following. On a day the (S&P-type) market index goes up by 1%, a stock with beta of 1.5 will go up by 1.5% + epsilon. Thus it won't go up by exactly 1.5%, but by something different.

So in a diversified portfolio, the beta of stock X is a good summary of its risk properties with respect to the "systematic risk", which is fluctuations in the market index. A stock with high beta responds strongly to variations in the market, and a stock with low beta is relatively insensitive to variations in the market.

E.g. if you had a portfolio of beta 1.2, and decided to add a stock with beta 1.5, then you know that you are slightly increasing the riskiness (and average return) of your portfolio. This conclusion is reached by merely comparing two numbers (1.2 and 1.5). That parsimony of computation is the major contribution of the notion of "beta". Conversely if you got cold feet about the variability of your beta = 1.2 portfolio, you could augment it with a few companies with beta less than 1.

If you had wished to figure such conclusions without the notion of beta, you would have had to deal with large covariance matrices and nontrivial computations.

Beta is the sensitivity of a stock's returns to the returns on some market index (e.g., S&P 500). Beta values can be roughly characterized as follows:

�b less than 0
Negative beta is possible but not likely. People thought gold stocks should have negative betas but that hasn't been true. �b equal to 0 Cash under your mattress, assuming no inflation �beta between

0 and 1
Low-volatility investments (e.g., utility stocks) �b equal to 1
Matching the index (e.g., for the S&P 500, an index fund) �b greater than 1
Anything more volatile than the index (e.g., small cap. funds) �b much greater than 1 (tending toward infinity)
Impossible, because the stock would be expected to go to zero on any market decline. 2-3 is probably as high as you will get.

Hope thi s helps clear up the beta debate.