Money Week

I wish I knew what was, but I’m too embarrasse­d to ask

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Standard deviation (SD) is the most widely-used measure of “dispersion”, or in financial markets, “risk”. That may sound technical but it’s actually quite straightfo­rward to understand. It is based on the idea that any population is “normally distribute­d” (it follows a “bell curve” pattern) – in other words, whether it contains the height of every UK adult male, or the annual return from the FTSE 100 over 100 years, most members of a normallydi­stributed group will bunch around the arithmetic average (the “mean”) for the whole.

For the heights example, this would be the sum of every man’s height divided by the number of men in the UK. So a randomly chosen man in the UK will on average be close to, say, 5’10” – with only a few people significan­tly above or below that “mean” height (these are so-called “outliers”).

SD quantifies the average dispersion of a given measuremen­t (in this case, heights or equity returns), above or below the mean figure. In other words, it’s a measure of how widely the data varies from the mean.

Given a normal distributi­on, about two-thirds of all the data points in a set should lie with one SD of the mean, and almost 100% should lie within three SDs. The higher the SD, the

wider the spread of the data – or the greater the risk that a randomly chosen man from your data set is nowhere near the average of 5’10”, or that the return from equities next year is way above or below the past 100-year average.

SD can also be applied to other aspects of financial markets. For example, as noted above, in GMO’s definition, a market which has moved more than two SDs away from the mean is in bubble territory. This, according to GMO, is something that should happen once every 44 years, but in fact happens once every 35, which reflects the fact that markets do not follow a “normal” random distributi­on but are instead driven by human behaviour.

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