The Probability of Normality

As an option seller you want the market to stay within the range prognosticated by implied volatility. But what is the historic probability that markets behave as expected? And what other analysis could be done to enhance your chances and find the periods when it is wise to sell an at the money straddle? This article will try to give some answers to this question.

The normal distribution cone

implied volatility cone

implied volatility cone

The chart above shows a one- and two- standard deviation cone of implied volatility. S&P on top, the 30 day at-the-money implied volatility at the bottom. If you would sell an 30 day at the money straddle and hold it until expiry, you would win if the market is within the one standard deviation cone at expiry. But as you can see, this is not always the case. Sometimes future market moves are under estimated by the current implied volatility, and this would result in a losing trade.

Statistics of normality

Normal distribution is only a mediocre assumption for market behaviour, and as Nicholas Taleb has shown in his books, the next black swan is just around the corner and you must not expect that things are normal distributed all the time.

S&P500 25 day returns

S&P500 25 day returns since 1980

Notice the fat tails on the left and the right shifted bell curve, the actual 25 day returns of S&P500 (since 1980) look quite different than you would expect from a normal distribution assumption.

And these differences to normal distribution are the cause why you will not get a 68% winning rate if you do a backtest on the one standard deviation cone shown at the beginning. Have a look at the table below:

implied volatility check

probability to be within a 1 standard deviation cone after 25 working days

The probability to be within the price range prognosticated by the 30 day ATM options volatility is by no means near the values you would have expected. Using the last 3000 daily bars to run this analysis, you can clearly see that not a single stock of the current DOW 30 stocks shows the expected value of 68%.  That’s no good news to options sellers. You have got a higher than expected probability that things go wrong. The 30 day at the money implied volatility seems to under estimate future volatility.

Adding an edge

One way to add an edge and bring the winning rate up might be to observe the relationship between the historic volatility of the market and the current implied volatility.

SPY implied vola cone

SPY implied vola cone

The chart above shows the 30 day at the money  implied volatility (black) and the historical volatility (red), based on the previous 30 daily bars. If you would sell an ATM straddle only if the implied volatility is above the historic volatility, meaning that the market seems to exaggerate volatility, it unfortunately would not have the expected result.

implied above historical volatility

implied above historical volatility

Compare the results on the left and right table: The left shows the probability to be within the range prognosticated by 30 day implied volatility after 25 trading days. The right side shows the results if you would have done this bet only if the current implied volatility is above the 30 day historic volatility. I can’t see a big difference, there obviously is no edge in following this approach. Nevertheless it can be seen in many books on options trading!

Adding edge, attempt number 2

The basic idea of the attempt above, although it does not deliver the expected edge, is not too bad. As markets tend to calm down after a high volatility, the attempt to define areas of high volatility could be fruitful. Only selling options when implied volatility is high and thus placing a bet that things will be fine in the future is something I would also do in real trading.

To get better results, one can do the following: Compare the current implied volatility to the lowest levels during history and then only sell a straddle if current volatility is way higher. On the chart below you see how I do it in everyday trading. I am waiting until implied volatility has at least reached levels twice as high as the lowest levels on the 30 days before.

areas of high implied volatility

areas of high implied volatility

These areas give you a way better chance to stay within the prognosticated area than an average day would give you. Beside that, you get the highest premium for your short options and a high probability that volatility will contract, thus making the trade even more lucrative. See the statistics below and judge for yourself:

probability in high vola areas

probability in high vola areas

The right table gives you the probability to stay within the area prognosticated by the at the money implied volatility. The right table shows the probability if you only place this bet when the current implied volatility is at least twice as high as its lowest levels on the 30 days before. This does not happen every day, see the number of occurrences, but it improves the chance for a winning trade vastly. Your probability now is higher than the 68% a one standard deviation cone would suggest.

Further reading

Have a look at the article on the statistics of VIX It shows why it is important to sell volatility only when it is high.

IV percentile will also be of interest, it shows the mean reverting properties and some statistics on VIX

 

Thanks to tradesignal for the software to run the tests and Refinitiv for the implied volatility data.

Tradesignal customers can find the code for the implied volatility projection cone over here

VIX and S&P 20 day returns relative to VIX level 1990-2019

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Daily Extremes – Significance of time

Analysing at which time daily market extremes are established shows the significance of the first and last hours of market action. See how different markets show different behaviour and see what can be learned from this analysis.

Probability of Extremes

A day of trading usually starts with a lot of fantasies for the future, then we try to survive the day and end it with a lot of hope for tomorrow. This psychological pattern can also be shown when analysing intraday market data. A high level of fantasies usually leads to a strong market movement, and thus market extremes can often be seen near the beginning or the end of the trading session. Continue reading

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Noisy Data strategy testing

Algorithmic trading adds noise to the markets we have known. So why not add some noise to your historic market data? This way you can check if your algorithmic trading strategies are fit for the future. Learn how to generate noisy data and how to test your strategies for stability in a noisy market.

Synthetic market data?

Continue reading

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Backtesting Market Volatility

If you want to trade volatility, you can place a bet on the option market. Just buy an at the money put and call, and at expiry day you will either win or lose, depending on the actual market move since you bought the straddle and the price you paid for the straddle. To put it simple, if the market moves more than you paid for the two options you will win, otherwise you will lose. This article is about a back test of volatility. Continue reading

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Demystifying the 200 day average

The 200 day average is considered as a key indicator in everyday technical analysis. It tells us if markets are bullish or bearish. But can this claim be proved statistically, or is it just an urban legend handed down from one generation of technical analysts to the next? Let’s find out and demystify the 200 day moving average. Continue reading

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KVOL Volatility part 2

How to calculate volatility based on the expected return of a straddle strategy has been shown in part 1 of fair bet volatility KVOL.

Using and Displaying K-Volatility:

KVOL uses the given amount of historic returns to calculate an expected value of an at the money put and call option. The sum of these prices are the historic fair value for implied volatility. It can be used to compare current market implied volatility to historic fair values.

Beside calculating KVOL for a specific return period it can also be used to show it as a projection indicator on the chart.

The example on the chart gives such an expectation channel for the s&P500 at the beginning of each month. The 250 days before are used to calculate KVOL. The line underneath the chart is running KVOL for 13 trading days.

Simplified trading:

to win, with higher volatility expected: you would have bought a straddle at the beginning of the month, expiring at the end of the month. You should not have paid more than a KVOL for 25 bars (working days to expiry) would have suggested. You win if the chart is outside of the projection at the end of the month.

The shown example uses the 250 daily bars before  the beginning of the month to calculate the returns and the price of KVOL. The projected lines represent the winning boundaries of the straddle at expiry.

Continue reading

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Statistics of VIX

The CBOE volatility index VIX  measures the market’s expectation of future volatility. This article will show you some key statistics of VIX and help you to decide if it is better to buy or to sell volatility.

Statistics of VIX

The spikes to the top and the long phases of relatively low volatility are reflected in a left-leaning distribution diagram and a long tail towards the higher levels. The median value is 17%, meaning 50% of the prices are above (below) this level.

The next chart shows the distribution of returns over 25 trading days. The median price movement being slightly shifted to the negative area shows the mean reverting characteristics of volatility.

Buy or sell volatility?

Analysing the level of VIX and the returns afterwards yields an even more interesting picture:

The green line gives the 25 bar percentage returns of VIX, with VIX noting above 25, the red line gives the returns with VIX below 15. Observe the median of the two lines:

The median 25 bar return with VIX above 25 (green) is around -15%, only 20% of the returns are positive when VIX is currently above 25. Sell volatility.

The median returns with VIX currently below 15 (red) is above 0% and with a fat tail to positive returns. Buy volatility. (data from 2004-2018)

Adverse movement of VIX

The above chart suggests that going short on volatility, if VIX is above 25, seems to be a good idea. But it is not without risk. The chart below shows what can go wrong during the next 25 days. The distribution diagram gives the maximum adverse movement of the VIX, with VIX currently trading above 25.

The green line, VIX currently above 25, shows a +10% median maximum up movement over the next 25 days. So do not expect a short vola position to be without risk. Some adverse movement has to be expected.

On the other side, the distribution of the maximum loss of the VIX during a 25 day period shows a median of below -20%. This represents the profit potential of a short volatility position.

Conclusion of VIX statistics:

If you plan to short volatility wait until VIX is trading above 25. If you want to buy volatility, do so if VIX is trading below 15.

 

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