A Primer on Volatility

6th Dec '20 by Nick Ray

7 comments 807 reads

Volatility is a very useful guide to many aspects of a stock's behaviour but I think for a lot of people it is either hard to understand, or maybe just seems to be a "magic" number which is difficult to interpret.

People sometimes express surprise that a stock has fallen by 40% and taken out a stop-loss when Stockopedia is reporting that the stock has a volatility of 160%. An understanding of volatility would greatly reduce any surprise in such a case.

Originally I planned to post some rules of thumb about what values of volatility mean, but I realised that simply perpetuates the idea that volatility is some deeply mysterious metric.

In fact it is based on a very simple - even obvious - idea which becomes much more user-friendly after you have tried working the volatility out for yourself.

So instead I will give what I hope is a very accessible explanation of how volatility is computed and then point out some rules of thumb afterwards.

A Worked Example

Volatility is formally defined as the standard deviation of a stock's returns. So let's do a worked example.

A "return" is just the change in price divided by the original price, usually expressed as a percentage. So consider the following sequence of ten daily returns:

	1	2	3	4	5	6	7	8	9	10
returns	4	-3	2	2	-1	3	1	2	-3	3

This represents a stock increasing by 4% then falling by -3% and so on. Graphically the stock is doing this:

To compute the volatility, we first find the 'mean' (i.e. average) daily change:

(4 -3 +2 +2 -1 +3 +1 +2 -3 +3)/10 = 1

On the chart above, I have plotted in red what the mean return sequence of prices would look like. As expected it gets to (nearly) the same end point but in a smooth way.

Then we subtract the mean from each return to get the deviation from the mean:

	1	2	3	4	5	6	7	8	9	10
returns	4	-3	2	2	-1	3	1	2	-3	3
deviations	3	-4	1	1	-2	2	0	1	-4	2

Now what we want is to find the mean (i.e. average) deviation from the mean.

But if we just add them up we will get zero:

(3 -4 +1 +1 -2 +2 +0 +1 -4 +2) = 0

(This should be obvious to you from the definition. We subtract the mean ten times so we have subtracted the sum of the returns from the sum of the returns. Hence zero.)

An obvious way…

Unlock with Email

Unlock with Google

Already have an account?
Login here

Macro

6th Dec '20

Thankyou, Nick. Much appreciated.

pka

Nick, Thanks very much for your excellent explanation of volatility.

7th Dec '20

Being able to calculate the Sharpe ratio from the SR volatility measure is a positive.

However, one of the strange things about Stockopedia is that the "full quote" which contains the volatility measure is not available for ETFs.

And one of the asset classes that you might most want to use the Sharpe ratio for is ETFs - along with Investment Trusts.

... Another topic for the "in development" list?

Of course Ed might say, "first things first". And the momentum view of a folio which contains ETFs does not yet include the "Price Change %", the "Rel Strength", or indeed the "Price versus MA" or "Price versus 52w High".

... So, a lot of areas for improvement.

... And of course I would also like to see Sortino added to the above, too.

8th Dec '20

Nick,

You wrote:

"So volatility is a measure of how difficult the market finds it to price the stock. It is not a measure of risk but uncertainty or confusion. In that sense it is a kind of "Value" metric. If the market does not know how to value a stock it will have higher volatility."

That is a very perceptive and excellent observation which I have not come across before. However, I think a stock with high volatility is riskier than one with low volatility, in the sense that the probability of a large percentage fall from the current share price is greater with the more volatile stock. Against that, the probability of a large percentage rise from the current share price is also greater with the more volatile stock, because volatility works in both directions.

Something you didn't mention in your article is the "low volatility anomaly", the observation that low-volatility stocks have higher returns than high-volatility stocks in most markets studied:

https://en.wikipedia.org/wiki/Low-volatility_anomaly

HumourMe

That is a very perceptive and excellent observation which I have not come across before. However, I think a stock with high volatility is riskier than one with low volatility, in the sense that the probability of a large percentage fall from the current share price is greater with the more volatile stock. Against that, the probability of a large percentage rise from the current share price is also greater with the more volatile stock, because volatility works in both directions.

Assuming absolutely no trend then this is one view.

Assuming a range bound share or a trend, with a significant alpha, then being towards the edge of a predicted envelope might imply a short term reversal. This then supports buy the dip.

As well as 'closing' volatility there is also 'average true range' that reflects intraday movement. High ATR is more difficult as you encounter wild intraday swings.

It is possible to have high ATR and low volatility and vice versa. These two types of volatility are often conflated, but are really different entities.

Some traders seek low 'true range' entries, with low volume, believing they represent low demand/supply; the expectation is that this imbalance is easily tipped one way or the other by demand/supply appearing, increasing the probability of a large price movement (volatility expansion). The advantage of this setup, if the effect is real, is that it can offer tight stops. If the effect isn't real and you are disciplined with position sizing and the stops another advantage is that you get longer to learn before you lose your money.

pdesai

9th Dec '20

Thank you Nick for an excellent article,I am now slightly better educated!

coniston

Thanks for sharing Nick.

A Primer on Volatility

A Worked Example

Unlock the rest of this article with a 14 day trial

About the Author

Nick Ray

7 comments

Unlock the metrics for all these stocks and more...

Unlock the metrics for all these stocks and more...