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Standard Deviation

by Craig Moser on December 14, 2018

Measuring gains and/or losses on investments begins when you purchase the investment. Also known as the reference point, the impact going forward shows investment returns aren’t in a straight line. So how do we measure, and what should we expect?  That’s where standard deviation comes in.

Many people use a benchmark like the S&P 500 to determine if their investments are doing good or bad.

After a major market declines, the next few years typically look pretty good if you buy what just took a serious decline. However, this isn’t a very objective way to measure since you’re using a low as your reference point.

Comparing a broadly diversified portfolio against a portfolio with purely stock is another way some people measure returns. This scenario makes it difficult to understand why you’re either doing better or worse than that single investment category. Again, it’s just not a good comparison to only a single stock index unless (and if) you own anything other than large US “blend” style stocks.

Average vs. Volatility

Standard deviation is the statistical term that measures the amount of variable or dispersion around an average. In other words, it’s a measure of volatility. You could call it the “wobble factor”.  Generally speaking, dispersion is the difference between the actual value and the average value. Sort of your “batting average”, but not what happens every time you get up to bat. Sometimes you swing and miss, while other times you connect and get on base.

The larger the dispersion or variability is, the higher the standard deviation is. In other words, you can have a “high flyer”, but drops in this type of investment also has the same downside volatility when the investment goes down. The smaller the dispersion or variability around your average return, the lower the standard deviation. A steadier outcome rather than peaks and valleys.

Investment professionals can use standard deviation to measure expected risk and determine the significance of certain price movements. Risk doesn’t mean high sustainable return, but it does mean you may make a higher than normal return. It also means you may lose more than someone taking less risk. Standard deviation values depend on the price of the underlying security.  They are only standards to use for comparison and all investments are not the same.

Historical standard deviation values are also affected when a security experiences a large price change over a period of time. An example would be measuring March 2009 versus October 2007, where one was a market bottom and the other a market top.

The current value of the standard deviation can be used to estimate the importance of a move or set an expectation of ranges of outcomes over a particular time frame.

This assumes price changes are normally distributed with a classic bell curve. However, there are times when price changes for securities are not always normally distributed. Despite this, professionals can still use normal distribution guidelines to gauge the significance of a price movement. When things are not normal then it usually is time to react in some way either positively or negatively.

In A Normal Distribution

68% of the observations fall within one standard deviation (this is normal range for most investment professionals). Most portfolios are designed around this single deviation from the average set of parameters.

95% of the observations fall within two standard deviations. So, you are 2X as volatile either up or down when these occur- not normal.

99.7% of the observations fall within three standard deviations. We rarely experience 3X volatility but when that happens you should be cautious as you are in a very extreme environment. You may have heard the phrase a black swan event. This is a good parameter.

A move greater than one standard deviation would show above average strength or weakness, depending on the direction of the move.

Using these guidelines, investors can estimate the significance of a price movement and if your portfolio “rules” tell you to either lighten or increase exposure to a particular asset class due to an excess of volatility, you typically improve your outcomes over time.

As with all indicators, the standard deviation should be used in conjunction with other analysis tools.

It’s usually better to measure using the most appropriate benchmark comparison to what you actually own in your portfolio to give yourself a fair comparison of your progress and understand that you will need to have patience with market-based investments as they change like the wind blows.

Over time you should make money and during volatile times you should reduce your exposure to those assets that are in current decline in order to help better preserve principal.

So, volatility will occur both in upwards trends and unfortunately in downward trends.

Basically, fully liquid, marketable securities move up and down around their average returns so expect changes rather than anticipating only positive returns with no retracements.

Standard Deviation: What It Is

Standard deviation is a measure of how much an investment’s returns can vary from its average return. It is a measure of volatility and in turn, risk.
Sorry for the math but…….
The formula for standard deviation is:
Standard Deviation = [1/n * (ri – rave)2]½
where:
ri = actual rate of return
rave = average rate of return
n = number of time periods
For math-oriented readers, standard deviation is the square root of the variance.

Let’s assume that you invest in Company XYZ stock, which has returned an average 10% per year for the last 10 years. Next you determine the risk by comparing your stock to Company ABC stock. To answer this, let’s first take a closer look at the year-by-year returns that compose that average:

Return Chart

One investment was steadier while the other had higher highs and lower lows but given 10 years of returns both had the same average return. One big difference is that if you keep most of your principal in lower volatility investments during major market corrections you will likely not have as much loss to recover, so you can have better or more consistent outcomes over time.

Averages can be deceiving.

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