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Standard Deviation of Returns & Investment Volatility

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  • 0:02 What Is Standard Deviation?
  • 2:26 Range of Expected Returns
  • 5:33 Lesson Summary
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Lesson Transcript
Instructor: Brendan Verma

Brendan was a Financial Advisor for 10 years and has completed all 3 levels of the CFA Program.

Volatility of returns is a key consideration when evaluating investments. In this lesson we look at how standard deviation can be used to compare the riskiness of assets for better decision-making while investing.

What Is Standard Deviation?

Standard deviation is a measure of the variation, or dispersion, in data. It tells us how spread out the values are around their mean. It is calculated by subtracting each value in a data set from its mean, squaring the value, averaging all squared values, and finally taking the square root of the average.

When studying the volatility of investment returns, we are particularly interested in two uses of standard deviation:

  1. Comparing the measure of the variation, or dispersion, in data
  2. Determining the range of expected returns for an investment

Let's examine how an investor could use standard deviation to compare stocks:

Mark is a newbie investor. He's considering his first investment in stocks. Although he is looking for high returns, he doesn't want his first investment to turn out badly. He decides to compare two well-known but different companies. TooSoft is a long-standing technology company with a global presence and stable earnings growth. Its stock has returned an average of 8% per annum (p.a.). to investors, and has a standard deviation of 15% per year. Mark is also considering a relatively new social media market leader, FaceNote. With returns of 15% p.a., FaceNote has a higher standard deviation of 25% p.a.

A quick comparison shows which stock is expected to have greater variability of returns. Riskier investments are characterized by higher standard deviation. When Mark looks at the options before him, he can easily determine that FaceNote is the riskier of the two stocks, as it has higher standard deviation. It also tells Mark that, although FaceNote has higher expected return, its return is expected to vary considerably more than TooSoft. Mark can use this information to decide if he is comfortable to invest in a stock that offers potential for higher return, but also carries the risk of larger fluctuations.

To help investors like Mark, investment companies and research providers use standard deviation to classify investments into high, medium, and low risk. This helps investors choose between alternatives, keeping their own preferences for risk in mind. An investor looking for preservation of capital would find low standard deviation stocks more attractive because of their stable, less varying nature, whereas a more aggressive investor would seek high standard deviation investments that could offer the potential for higher returns.

Range of Expected Returns

Mark can dig deeper into his analysis of the stocks and determine the expected range of returns for them. This will help him decide if the return potential is worth the risk.

Assuming the expected investment returns can be approximated with a normal distribution curve, a bell-shaped curve, 68% of TooSoft's expected returns should lie within one standard deviation above and below the average, 95% within two standard deviations, and 99.7% within three standard deviations.

The formula to calculate expected return ranges, using standard deviation, is:

Average - (n * Standard Deviation), to Average + (n * Standard Deviation)

Calculating these ranges for TooSoft gives us the following:

One standard deviation would be:

8% p.a. - (1*15% p.a.), to 8% p.a. + (1*15% p.a.)

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