Monday, March 14, 2011

An animated view of standard deviation

Today's animated post provides an overview of standard deviation; a very important measure for us performance measurement types!

2 comments:

  1. Stephen Campisi, CFAMarch 14, 2011 at 7:51 PM

    So much of the "debate" around standard deviation is little more than an exercise in semantics, along with much ado about statistical nuances. There is more to criticize about the idea of an expected return being an imperfect measure of the change in a client's wealth. After all, the expected return is simply a short term number, while most clients are long term investors. It seems that a geometric return is the better statistic to estimate the client's reasonable increase in wealth over time. That's what they really want to know. Also, expected returns are easily distorted by outliers, so if anything, a median return is probably the better statistic to represent a representative short term return. Why is there no complaint about the problems of expected return and its overuse and misuse with clients? It seems that return estimates pose the bigger problem.

    But back to the "favorite" bad boy of risk: standard deviation. The context of risk for investments really deals with the issue of uncertainty of return over the short run, comparing the short run expectation with the return one may experience in any particular period. In this context (which is the context that most investors consider to be the relevant explanation of risk) then standard deviation is the right measure of risk. In plain English, it measures the general difference in return between what one might expect and what one actually experiences in any given period. For example, one might say that, based on a sampling of return data, that an investment can be expected to return 10% plus or minus 20%, so that the reasonable range of returns that one may experience in any period would likely lie between -10% and + 30%. One might further extrapolate that the return that one would achieve over the long term would be in the range of about 8 percent. These are reasonable inferences and expectations, where risk is nicely measured by the size of the gap between expectation and what one actually experiences in the short run.

    Standard deviation is not a particularly ambitious statistic. It's easy to measure, highly intuitive and serves a reasonable purpose. Perhaps the performance world should stop torturing it in the hopes of getting it to confess more than it knows.

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  2. Steve, your wisdom and insights are exceptional on topics like this. I have a book from the early part of the 20th century that deals with uncertainty, and the problem is that it's not measurable. Anything ex ante is potentially flawed. As for confessing more than we know, that will be the day. I guess you're right that standard deviation IS the "favorite bad boy" of risk; it ain't going anywhere, is it?

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