Standard Deviation
What is standard deviation?
Standard deviation is a statistical measure of the dispersion—or variance—of a set of values. In finance, this measure is often used to represent how much an investment’s return (or value) might be expected to fluctuate over time. This is a common way of measuring portfolio risk. The higher the standard deviation, the more volatile the portfolio.
Using the normal distribution as an example, the graphics below illustrate the likelihood that the value of a random variable in a data set is likely to occur within certain ranges. For reasons discussed throughout this page, the normal distribution is a flawed model for simulating investment returns.
Is it a good measurement of portfolio risk?
Kind of, but it has its limitations. In theory, we can calculate the standard deviation of historical returns easily—it’s just math. But due to the characteristics of the probability distributions often used to model investment performance, this approach has some pretty glaring flaws (see here).
It’s also flawed in that it calculates total volatility. That is, it treats downside risk (losses) and upside “risk” (gains) equally. But it’s only downside risk that we’re really concerned about, because that’s how we lose money. If the value of an investment only ever moves in the good direction (up), price fluctuations (and high standard deviations) would always be welcome. Unfortunately, no such investment exists.
So why is it used if it’s imperfect?
Despite its flaws, standard deviation has some good qualities. It’s reasonably well understood, widely used and easy to implement in practice. And to be fair, it’s actually a fine tool for measuring portfolio volatility much of the time. The biggest problem is those pesky “outliers” (extreme market events, or "Black Swans”), which the normal distribution fails to appropriately account for. This is why we’ve fattened the tails in the probability models for Honest Math. We believe assigning higher probabilities to those damn birds is a more practical approach to modeling investment performance.
Can I know the exact probability of achieving my goals?
In case we haven’t made this point clear yet: No. It is impossible to measure actual probability with respect to your portfolio. The world is strange and unpredictable. Your life, which is subject to countless random variables, doesn’t fit nicely inside the contours of a bell curve. And your portfolio, just like your life, is disproportionately impacted by infrequent but extreme events (“Black Swans”) that can’t be perfectly modeled using the normal distribution, or any probability distribution, for that matter.
