We’ve all seen volatility in nature in the form of waves, strong winds and other physical processes. Naturally, it affects stock market returns too.

The best way to describe it is as a measure of the distribution of the returns of a given security. Consequently it is presented as **standard deviation or variance**.

I use either a ready made volatility index based on options prices, calculate it from historical data or just go for the square root of time.

I am a retail investor, therefore, I am interested in the volatility of individual stocks and market indices. No one wants to buy a stock only to see it going down day after day.

Volatility affects different investors in different ways. Day traders experience the highest volatility while long term investors the lowest. This is probably why long term investing is promoted by financial media as the best option. I personally disagree as people have different goals and personalities.

The implication is that some may want to be more engaged in the market than others or to take more risk. Furthermore, I don’t see why we should be put in boxes all the time. Nothing can prevent a value investor from day trading every now and again if he or she wishes to do so.

## The VIX

Unfortunately the FTSE 100 volatility index (VFTSE) was discontinued so I’ll have to go with its American counterpart, the **S&P 500 VIX**.

The VIX is a statistical measure which represents the market’s future expectation of risk based on options prices. Here is a chart comparing the S&P 500 (green) and the VIX:

Volatility expands during periods of uncertainty so some call it the ‘fear gauge’. I think that uncertainty is probably a more accurate definition. You can see it went through the roof during the covid-19 crash. It is fair to say that the beginning of the pandemic was a very ambiguous period for the stock market.

The most important point is that no one knows if there is going to be a dramatic expansion. If in doubt check out the performance of **Credit Suisse’s ETN XIV**. It was an inverse volatility index which was short selling VIX futures. Here is the chart of this product:

It seems that it is not such a good idea to short the VIX. The more pressing matter is how does volatility affect the average retail investor.

My personal take is that there is a degree of causality between volatility and time. This is why VIX futures are usually in contango, meaning that volatility is priced higher the further out in time we go.

It is the same in financial forecasting as any model will become less and less accurate the longer the period. After all who knows what will happen in twenty years or even five.

### Your investment style determines your volatility exposure

The confusing part is that day traders experience the highest volatility of all due to the fluctuation of stock prices even though the share price moves are of a smaller amplitude.

Having said that, a daily move can be a few percentage points which is where the volatility comes from.

Another factor is that most day traders and short term traders use leverage as no one would trade 1 share of SPY for a $3 profit.

Leverage is widely available in the UK via **CFD** products which amplify profits but can have a devastating effect on losses.

A value investor on the other hand could have easily slept through the 2018 market correction and the 2020 crash. Then why does all of this matter? Can’t we just buy an index fund and forget about all this? Some can, some can’t. A few of us have the urge to find the latest potential blockbuster stock, to outperform the market or just to have a bit of fun on the way to retirement.

## The square root of time

The √t is an important element of the Black-Scholes options pricing model. So instead of calculating the standard deviation of returns you can just use the square root of time.

For example, the S&P 500 standard deviation is around 17% this year, while for √250 trading days we get 15.8% which goes up to 19% if you use √365. Chances are that the S&P 500 will stay within this range about 68% of the time and it will reach 31.6% about 95% of the time (a 2 standard deviation move).

However, this may not necessarily be the case as market crashes happen more often than statistics imply. Moreover, the accuracy of this method increases the longer the time period probably due to the lower volatility of returns.

## Volatility of individual stocks

A lot of people end up buying an individual stock for one reason or another, usually seeking profits. Intuitively I know that if I buy a utility company it will never turn into the next Amazon.

But what if I wanted to buy a dividend stock, Vodafone for example. What kind of share price can I expect next year?

I could take some historical data, calculate the standard deviation and derive the expected move from there or adjust the square root of time for individual stock volatility.

Alternatively I can use ready made data to come up with an assumption. I prefer to do the latter as I have already compared the methods and they yield a similar result.

Vodafone’s volatility index sits at around 37% so based on this and some other data from the option chain I’d expect an 80% probability to move within ±21.5% until April 2021. This is all based on math so I’d take it with a pinch of salt.

If Vodafone declare that they have no money left, rest assured the share price will sink like the Titanic. Stock price has gone to zero or near zero every now and again so the risk is real.

## Conclusion

Statistics can rarely be used in isolation but they help us to build an expectation of the outcome of a given trade.

From a probabilistic perspective the purchase of stock is either a 50:50 or 53:47 (due to overall positive drift in the market) bet.

Therefore, it is important to do our homework before routing any orders as no one buys stock to lose money. I usually use statistics, current market conditions and company data to make informed market decisions.