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February 10th, 2019, 09:10 AM   #11
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The problem is so vaguely stated as to be almost impossible to respond to.

Yes, if you have a data set where numbers lower than the mean are more desirable, of "higher value" in economic jargon, than numbers equal to or greater than the mean, then using the standard deviation as a criterion of desirability does not make sense. In that case, some other criterion, perhaps skew or possibly a specially designed statistic, would make sense. We choose our tools to fit the task at hand.

But once you start talking about beta, you are well into the realm of financial economics. As I have explained, risk in economics is concerned with variance around the expected value (mean); indeed, risk is quantitatively defined in terms of the standard deviation around the expected value. And it is assumed, as an empirical matter, that as the variance around the expected value increases, the market value usually decreases. Consequently, in theory, which abstracts from temporary deviations from the normal, market value is assumed to be a function of expected value and risk, with a positive partial differential with respect to expected value and a negative partial differential with respect to risk.

Now you seem to have confused beta with the standard deviation. A standard definition of beta is the variance of one data set divided by its covariance with another data set. So beta is not a measure of one data set on its own. It is a measure that by its terms compares one data set against another data set. Strictly speaking, it is not even meaningful to talk about a data set's beta; it makes sense only with respect to two different data sets. Now in practice, a data set is usually being compared to a standard reference data set that is not explicitly mentioned but implicitly understood. In that case, people do refer to a data set's beta, but there are two data sets in mind.

So to take a simple concrete example, if a stock has a beta < 1 when compared to a general index of stocks, the probability is that you will lose relative to the stock market if the market in general goes up. If a stock has a beta > 1 when compared to a general index of stocks, you will lose relative to the stock market if the market in general goes down. Beta tells you under what circumstances a specific stock will probably out-perform the market and under what circumstances a specific stock will probably under-perform the market. The greater the deviation, the worse off you will probably be if the market goes in a direction opposite to your expectations.

Talking about beta as though it is a standard deviation is to show ignorance of what beta is.

Last edited by JeffM1; February 10th, 2019 at 09:55 AM.
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February 10th, 2019, 10:26 AM   #12
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Quote:
Originally Posted by omeradmani View Post
The same is the case when higher numbers of the SD are desirable.
The values that you are talking about are already addressed in the expected value.

Moreover, in economics, the degree to which higher numbers have higher value is shown by the numbers themselves.

Are you under some delusion that "value" is determined solely by the standard deviation? Where did you get that weird idea from?
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