Investment Terminology: Standard Deviation

This is the second in a series of blogs concerning investment terminology and the topic for this article is standard deviation.  I know I said that the next article would be about systematic and unsystematic risk, but I felt that this topic should preclude that discussion and that the next article should discuss them.  According to Investopedia, standard deviation is “a measure of the dispersion of a set of data from its mean.  The more spread apart the data, the higher the deviation….In finance, standard deviation is applied to the annual rate of return of an investment to measure the investment’s volatility….it is also known as historical volatility and is used by investors as a gauge for the amount of expected volatility.”  In other words, like beta, it is a measure of risk although, unlike beta, it is not related to the market but to its own volatility or variability of returns.  Generally speaking a volatile investment has a higher standard deviation then a more stable one.

To quantify the use of standard deviation, one has to consider that the pattern of returns for an investment follows a normal, or bell, distribution, meaning that most returns are near the average with fewer returns at the extremes.  For example, if a stock’s average return is 10% per year, and the historical pattern of returns shows that the annual returns are relatively evenly distributed from 2% to 18%, but the bulk of the returns are evenly distributed around 10%, you would have a normal distribution.  While this is a wide dispersion of returns, the further you get from 10%, there is a less likely occurrence and the closer you get to 10% the more likely the return is to occur in any given year.  Then, a standard deviation of one indicates that a return will fall within a range approximately 68% of the time and a standard deviation of two indicates that a return will fall within a range approximately 95% of the time.  Again, the wider the range, the more volatile the expected returns.

Let’s apply this notion to our example stock that has an average return of 10%.  With a standard deviation of 2%, we would expect the annual return to be in the range of 8% to 12% approximately 68% of the time (one standard deviation) and between 6% and 14% approximately 95% of the time (two standard deviations).  Another stock could also have an average return of 10% but a standard deviation of 4%.  This stock would have an expected return between 6% and 14% with one standard deviation and between 2% and 18% with two standard deviations.  Obviously, the second stock is much more volatile than the first due to its much wider dispersion of returns even though they have the same average annual return.  Therefore, the second stock would generally be deemed to be riskier.

Like our discussion with beta, one can take this measure into account when choosing an individual investment or a portfolio of investments.  The difference, however, goes back to what you are measuring against.  Beta is a measure that theoretically predicts an investments return against the market.  Remember, if a stock has a beta of 1.10 and the market goes up 5% the expected return for the stock, based on beta, would be 5.5% (1.1 x 5).  Standard deviation, however, is measured against the investments own average return and is theoretically not affected by the market.  So, if the market goes up by 5% a stock could go up or down by any amount (based on standard deviation alone) but the return would likely fall within a certain range based on that stock’s standard deviation. 

As one might expect, standard deviation, beta, and other measures of risk tend to be tied together.  In other words, a stock with a low beta is likely to have a lower standard deviation than a stock with a high beta, generally speaking.  If you are building a portfolio, one can reduce the effect of a more volatile (higher standard deviation) investment by adding less volatile (lower standard deviation) investments.  The overall effect could be a portfolio with higher expected returns but lower risk.  Certainly, an investor should consider their risk tolerance and then choose individual securities or design a portfolio based, at least in part, on their tolerance for risk.  Standard deviation can help in choosing the specific investments as investors with a greater tolerance for risk may choose those with higher standard deviations and those that have less tolerance for risk may choose investments with lower standard deviations.  As mentioned, the next article will discuss systematic and unsystematic risk and how a diversified portfolio may reduce risk.  Future articles will discuss the use of alpha, style investing, and so on.

I welcome your comments.

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