## Not Even Wrong

I had a bit of a disagreement the other day with a colleague about the interpretation of beta and correlation.  He claimed that if a fund has a high beta to a particular index, that meant that it also has a high correlation to the index.  He even cited a Wikipedia article to support his point of view.  Unfortunately, it’s rather common to believe the whole story is, as the article states, that “correlation measures direction, not magnitude” and “beta takes into account both direction and magnitude.”  If that’s most of what you know about beta and correlation, then it’s easy to make the conclusion that my friend made.

Why do so many people make this mistake? Beta and Correlation are commonly used terms in traditional investing – mainly by mutual funds – and they’ve been thrown around long enough that people are familiar with the terms, so they think they understand them.  “Oh sure, I’ve heard of that before” and therefore, the person thinks to him/herself, I don’t need to know anything more about the topic.  In what’s called the Long Only world (think mutual funds), beta is regarded as a risk measure because of a simple relationship between the fund and its benchmark: beta is correlation times the fund’s volatility divided by the benchmark’s volatility.  Benchmarks are chosen to closely resemble the fund – for a technology fund, you pick a tech index as the benchmark.  For a health-care fund, you pick a health-care index.  Obviously.  A mutual fund’s benchmark is chosen because the two are highly correlated.  Mathematically, that means the correlation is close to 1.00.  So, in this case (and in this case only) beta is basically the ratio of the volatility of the fund to the volatility of the benchmark.  If beta is 1.1, that means the fund is 10% more volatile than the benchmark, and if the beta is 0.9, that means it’s 10% less volatile than the benchmark.  It all works because of the formula beta = correlation * (vol_fund / vol_index).  The problem is that people forget important aspects of the formula – like that correlation is baked into the beta – and they only remember “beta is a relative measure of volatility” or “beta is the slope of the regression line.”  Please keep in mind everything I’ve written in this past paragraph is only true for traditional long-only funds, like mutual funds. Read more of this post