Case study: standard deviation in stock analysis

January 12, 2020

Introduction

It is my free personal finance research. I like to get up to Stern finance MBA level, so I have to push myself to understand the basics, the first one I like to work on is standard deviation.

How to work on standard deviation

I like to extract one example fro the article related to standard deviation topic. Here is the article.

The calculation to work on I have to go over word by word, and then quickly review the statements.

4 standard deviation an average return of 10 percent per year, how to calculate the fund's future return?
 Answer:
68% change to range between 6 and 14 percent, 10+/- 4% or its 10 percent average plus or minus the standard deviation of four, according to morningstar.
68% - normal distribution 95% of time, the return would be between 2 and 18 percent, or two standard deviations of the mean.

If you simply bought the fund on the basis of its 10 percent average return you might be pretty shocked to make just 2 percent of 6 percent.

Large standard deviation

Active traders like this volatility because it offers lots of opportunities to buy low and sell high. But people investing for retirement or college generally don't want big swings - not the downward ones, anyway.

Hold on to wait out the down periods

Holding an investment for a long time can overcome the damage from volatility. In that case, you're more likely to benefit from the average return and can afford to wait for a downturn to reverse. So if you like the average returns of a fund that has a large standard deviation, plan to hold on to wait out the down periods.

Standard deviation. This is defined as "the square root of variance." The math is tricky but generally this measures how much an investment wanders off of its average path, like a drunk who can't walk the white line. The bigger the standard deviation, the greater the risk. "Clients can relate to this measure as they understand the real world impact of volatility on their cash-flow decisions," Middleton says.

[See: 7 Ways to Trade Volatility with ETFs and ETNs.]

Morningstar it calculates standard deviation for mutual funds by looking at returns over the previous 36 months. The average return for that period is figured and standard deviation shows how much the monthly returns differed from the average.

A fund that gained or lost 1 percent each month like clockwork would have a standard deviation of zero, because there was no variation at all.

If a fund has a standard deviation of four and an average return of 10 percent per year, the fund's future returns have a 68 percent chance to range between 6 and 14 percent, or its 10 percent average plus or minus the standard deviation of four, according to Morningstar. And 95 percent of the time, the return would be between 2 and 18 percent, or two standard deviations of the mean.

If you simply bought the fund on the basis of its 10 percent average return you might be pretty shocked to make just 2 percent or 6 percent.

Of course, not everyone hates investments with large standard deviation. Active traders like this volatility because it offers lots of opportunities to buy low and sell high. But people investing for retirement or college generally don't want big swings – not the downward ones, anyway.

Holding an investment for a long time can overcome the damage from volatility. In that case, you're more likely to benefit from the average return and can afford to wait for a downturn to reverse. So if you like the average returns of a fund that has a large standard deviation, plan to hold on to wait out the down periods.