Understanding Volatility, the Standard Deviation and the Semi-Deviation

“The true investor welcomes volatility…” 

Warren Buffet

Have you ever wondered what metrics are available for investors to help them choose between similar portfolios, besides returns?

In this post, I´ll be giving a quick intro into the standard deviation (SD) as a measure of volatility. This will be swift, but sufficient for understanding the concept, and also its difference compared to the semi-deviation, another volatility metric also explained in this post. 

The Standard Deviation

Without going into the maths, the SD gives the probability that returns from an asset or portfolio will fall within a certain distance from the average return of that asset or portfolio. And to explain it as simply as possible, these are the basic guidelines:

  • The probability that a return in the future falls within 1 SD below or above the average return for that asset is approximately 68%.
  • The probability that it falls within 2 SDs below or above the average return for that asset is approximately 95.5%.
  • And within 3 SDs below or above the average return for that asset is approximately 99.7%.

Source: Towards Data Science

For example: 

If the portfolio average return is 5.0% with an SD of 3.0% there is a:

  • 68% probability that future returns will be between 2.0% and 8.0% (Average – 1 SD and Average + 1 SD) 
  • 95.5% probability that it will be between -1.0% and 11.0% 
  • 99.7% probability that it will be between -4.0% and 14.0%

You can see that there is a 0.3% probability that any given return falls beyond 3 SD-s from the mean, either positive or negative. If you split this, there is only a 0.15% (0.30/2) probability that returns fall below 3 SDs from the average return.

This is what is known as tail risk and could become what is called a “Black Swan Event”, which is an event that, although having a very low probability of actually happening, has terrible consequences. The 2008 financial crisis and COVID-19 are good examples.

What is Semi-Deviation?

Imagine you have two assets to choose from, Asset “A” and Asset “B” with the returns and SD shown in the table.

Asset A Asset B
Period Returns Period Returns
1 8% 1 17%
2 -5% 2 0%
3 12% 3 -2%
Mean 5% Mean 5%
StandardDev 8.89% StandardDev 10.44%

If you could choose only one, you would probably choose Asset A, and you would be correct to do so using this information. 

But there is an issue with that… The (SD) measures the probability that future returns fall within a certain distance from the average return, either above or below the mean. The SD makes no difference between a return above or below the average return, if they are both at the same distance from the average. Sounds weird?

Consider either of the assets in the example above with a mean return of 5.00%. The SD would be equally increased if one of the returns is either 9.00% or 1.00%. Why? Because they are both equally distant from the average return of 5.00%. And this is precisely where the SD falls short… 

Investors would not consider these two returns in the same way. Upside volatility is desirable, while downside volatility is not. Here is where the semi-deviation comes into place. It is a measure of downside risk, not affected by upside returns.

In our example, Asset B has a higher standard deviation, and the same mean return of 5.00%, however it has a lower semi-deviation of 4.97% versus 5.77% for Asset A. This happens because Asset B´s SD is increased compared to Asset A by that very large return of 19.00%. But this is something good, not bad! The fact that the semi-deviation is lower shows that the probability of having returns below the average return is lower. 

You would now probably choose Asset B instead of A… And you would be correct to do so! That’s because they go together! The takeaway from this is that although the SD is widely used as a volatility metric, it does not show the whole picture and should be used alongside the semi-deviation. 

Alejandro Echavarri Garrido is a Chilean asset manager with an academic and professional background in finance. He has a Master’s degree in both Finance and Business Administration and has worked as an investment advisor in both Switzerland and Chile.

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