By: Alpha Male

Before an unfortunate laboratory accident (involving mice trained to recognize Greek letters) left Alpha Male with strange  blogging superpowers, he was a mild-mannered marketing executive with a $300 million long/short equity hedge fund. While at said hedge fund, Alpha Male learned a useful lesson about Beta:

All Betas are not created equal.

This statement may sound trite. Of course Betas are not created equal! You can have betas to an infinite number of factors from the S&P500 to the price of zinc to bond spreads, right? And by the same token, just because your portfolio has a beta-weight net exposure to the S&P500 of zero does not mean it has a beta-weighted net exposure of zero to zinc or spreads.  Besides, Betas assume normality – which is not always a safe bet.

True and True and “True”.  But I am referring here to betas to the same factor and I am assuming returns are normally distributed.

You can’t imagine the frustration experienced by the portfolio management team when a 1.0 beta stock falls out of bed on a day when the market was down only slightly. Why did this happen in the absence of news that might push it out of bed? On the same day, a stock with a beta of 0.9 might even have been up slightly. What gives?

The problem is that beta has been elevated by Bloomberg and Morningstar to cult status. Too often, investors blindly expect beta to predict short term security behavior. Perhaps in the 1970s when typical portfolio turnover was still under 500x a year, beta was a more useful measure. But it’s not a very useful metric in today’s short-term (hedge fund) investing world.

A quick trip back to finance class will illustrate why.

The formula for beta can be re-arranged so that beta can be described as the product of market correlation and volatility (indexed to the market, or as a % of the market). In other words beta is just correlation grossed up or down depending on the volatility of the stock.

So a stock might have a 1.0 beta because it has a 0.5 correlation and a volatility that is 2x that of the market’s, or it might have a 1.0 beta because it has a 0.95 market correlation and a volatility that is only about 5% higher than the market’s.

Obviously, I would trust a 1.0 beta under the second scenario more than I would under the first. In fairness, many investors are not oblivious to this. They will often ask to know the r-squared of the beta provided to them.

But r-squared is a marginalized statistic that is generally treated as an add-on to the beta. It’s an after-thought that is, at best, treated as a footnote. But since r-squared is the correlation, it should get a promotion. As the math to the left suggests, beta is simply an adjustment to the far more important number: correlation, not the other way around.

What if a 1.0 beta stock had a correlation of 0.2 and a volatility 5x that of the market? Why even bother calculating a beta in this case?  What could beta possible tell us? Essentially, this beta would tell us that over a very long time period, the stock will have a 1.0 market correlation. Such a stock apparently marches to the beat of its own drum. But given a long enough time period, it will in fact track the market.

Still, in the short term you might as well flip a coin to guess where the stock will go each day. An over-reliance on beta has obfuscated the discussion of the short term behavior of stocks.

For those, like Alpha Male, who are more graphically inclined, a scatter plot of the market vs. an individual stock comes in handy:

Figure 1 shows the axes for our scatter plot:

Figure 2 shows a stock with a 1.0 beta. It happens to have a high market correlation (low r-squared) as depicted by the tight range of dots around the regression line.

Figure 3 compares this stock with another stock that has a 0.5 Beta. Note that it has the same volatility as our first stock, but its beta (slope) is still only 0.5.

Since we have determined that the beta is simply the product of the correlation and the (relative) volatility, the correlation must also be 0.5. (The shaded area in Figure 4 represents one standard deviation)

Now let’s take that 0.5 correlation stock and double its volatility (i.e. lever it up). This would disperse the data points as in Figure 5 – essentially “stretching” the data points vertically.

Note that the regression line for this new blown-out set of data points now has a higher slope. In fact, as Figure 6 illustrates, its slope (beta) is now back at 1.0.

So what a stock or fund lacks in terms of market correlation it can make up for with extra volatility in order to achieve a given beta.  As a result, betas may or may not say anything about short term behavior – it all depends on the correlation.  Betas simply can’t be published, read and used without the proper context.

The morale is: don’t become part of the “Cult of Beta”.

- Alpha Male

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