# How does volatility affect structured products? Part 2: Clock patterns, fat tails and cones

In the second part of our series on the impact volatility has on structured products, Benedict Peeters, founder and CEO of Finvex Group, the independent Belgian consulting firm which provides specific financial services to investment managers, financial advisers, banks, insurers and research houses, talks about clock patterns, fat tails and cones.

“Finvex works on reducing volatility in portfolio’s and indices. We are very much focused on volatility analysis but also on extreme risk. Because volatility is a measure of the so called normally distributed risk. If you look at volatility alone, I am speaking about historical and accurate estimated volatility, then volatility is a measure which takes into account that the distribution of prices of shares have a normal Gaussian distribution. This approach underestimates the extreme movements that happen in real life. As if there is a clock pattern around the range around which the value of a share could fluctuate up and down. So the centre of the clock is set at zero return and then you say the probability that the share rises by 3% is higher than the probability that the share rises by 10% and higher than the probability that the share rises by 15%. If you would draw this against a curve you would draw a clock, left and right.

“With volatility, when it is distributed normally, you are saying that the probability that something gets average yield is much higher than the probability that it is extremely high or extremely low. A share which is very volatile has a clock pattern which is flatter while a share which is less volatile will have a volatility distribution which looks more like a cone.

“Each share has its own normal distribution but in the real world, when it comes to risk, a share is not just defined by volatility because there are also other risk measures. There are also things such as skew, where a share is, as they say, skewed towards one side, the symmetrical and asymmetrical aspect of the distribution. But also, more importantly, the fat tails, the kurtosis effect as they say. I will give an example of the financial markets: if today you would take the S&P 500 or the S&P 100 and you say, this has historically a volatility of between 15% and 20% and that would be the only criteria, an event like a stockmarket crash of 35% would occur only once every 10,000 years.

“If you would merely view volatility you say the stockmarket has a volatility of 15% and you say how likely is it that a downwards movement of 30% or 40% would take place in one day, the chances are – according to the normal distribution – that this would almost never happen. Actually the chances are so minimal that by taking volatility as a benchmark, you will have a wrong picture of the actual risk. Because actual risks are that stocks often have more average movements but also more extreme movements than is apparent from a normal distribution.

“If you are looking at a normal distribution you say the return closest to the average will be the most common and returns which are different from the average will be built in a cone-like formation. You are basically drawing a hat, which is the volatility. The more you move towards extremes, especially the extremely negative and positive, the less frequently it occurs. The reality is that if you look at the distribution of individual shares, but also at stockmarkets, there is no such distribution. There are more average performances but unfortunately also more extreme results. Especially extreme results on the downside.

“Someone who is just looking at volatility as a measure of risk is making a huge mistake. It is very important to also do the extreme risk analysis. The option prices using old models, such as Black - Scholes, which are based on volatility, what happened with those models is that the volatility was artificially bumped to take into account the fact that there are some deviations from the normal distribution.

“In reality, if you have sophisticate models, you do take volatility into account, with other factors as gamma, with extreme risks. If you buy a product with capital protection but this capital protection has a knockout element where if for example the Eurostoxx 50 decreases by more than 30% you lose the capital protection. If you only look at volatility of the Eurostoxx 50 and look at how often this happens, then, based on volatility you will say ‘that will almost never happen’. While historically, if you go back 20 years, you come across many observations in which the knockout could have happened.”

**Related stories: **

**How does volatility affect structured products? Pt 1**