Standard Deviation

Standard deviation measures how closely returns track their long-term average. Standard deviation measures volatility risk.

How Is it Useful?

Despite being the oldest way of looking at risk, standard deviation remains applicable. Highly volatile investments are hard for some people to stomach. Also, for those investors who are prone to taking the worst action at the worst time (e.g. chasing returns, or buying high and selling low) highly volatile investments offer many opportunities to make mistakes.

What Is a Good Number?

Generally speaking, a lower standard deviation means less uncertainty on a period-to-period basis, which is desirable. The lowest standard deviation possible would be zero. Standard deviations will vary from asset class to asset class, so context is important in distinguishing whether a standard deviation is considered good or bad.

What Are the Limitations?

Standard deviation does not distinguish between the returns that fall above the average and below the average, so a manager is punished equally for “good” upside deviation and “bad” downside deviation. Also, standard deviation makes no provision for the timing of returns. There is no distinction between a situation where the bad returns were randomly scattered over a long time frame or a scenario when all the bad returns occurred within a small time frame.

What Do the Graphs Show Me?

Below we see two return series. The upper one exhibits a high standard deviation and the bottom one shows a low standard deviation. The straight red line represents the long-term, average annual return for each series. As it turns out, the long-term average returns are identical. However, on a month-to-month basis the upper graph’s returns tend to stray further from the red line. Therefore the fund in the upper graph exhibits greater volatility, larger standard deviation, and more substantial risk.

What Are Typical Values?

One of the striking aspects of standard deviation is that there is surprisingly little variation across decades. From a returns perspective, the difference between the bull markets of the 1980s and 1990s and the bear markets of the 2000s was extreme. However, looking at the standard deviations across decades, the numbers remain somewhat stable. Overall bonds exhibit the lowest volatility, while emerging markets and small cap stocks have displayed the highest.

Math Corner: 

Standard deviation is a well-known statistical tool used across many industries in order to determine just how representative the mean value of an overall set of data is. The process of squaring the differences is used to remove negative values. Otherwise the positive and negative values would net out to zero.


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