In the following I us an R package BFAST designed to detect strucutural breaks in time series.The script Iteratively detects breaks in the seasonal and trend component of a time series. The first chart shows the various break and fitted regressions. The second chart shows the deviations from the regression lines and 95% interval of confidence. This could be used as an overbought/oversold indicator. Anyway, just work in progressâ€¦so any input / suggestions are always welcome as usual. Feel free to contact me at:Pierre@argonautae.com

# Author Archives: Pierre

## Time to go short VIX ?

The following analysis provides an update on some of the metrics I use to classify market risk. The word classify is more appropriate as I think that in essence you cannot forecast risk but rather attempt to adjust to it into a timely fashion. Clearly risk would not be a risk if you could forecast it accurately. However as there is generally some degree of persistence or clustering in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the VIX as a measure of global financial market risk. The same methodology can be successfully applied to other inputs such as implied currency volatility. Feel free to contact me at Pierre@argonautae.com for more detailled information on this analysis and how it can be embedded in an investment process.

My approach acknowledges that the nominal level of implied volatility is a crude metric of risk therefore I consider other measures. The VIX Volga, a measure of uncertainty of risk and the ShockIndex a measure of market dislocation. VIX Volga is simply the volatility of the VIX over a given period. This measure highlights how uncertain and unstable the level of risk has become. Though positively correlated to the level of the VIX the VIX Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX is trading at rather innocuous levels. This is not a trivial observation as the leverage undertaken by market participants tends to be an inverse function of market volatility which implies a greater vulnerability when volatility becomes uncertain at low levels and cannot be accurately budgeted for (Investors become risk seeking in low volatility environement though it is from those levels that you observe the greatest adverse changes in terms of risk). The ShockIndex is a ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It provides a measure of acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those metrics both relative to a time axis and their historical distribution. The red lines are 95% confidence intervals, the purple line identify the median. The blue line highlight are the current level. The VIX Volga and ShockIndex in the below analysis are evaluated over a period of 14 days. The medians and 95% confidence intervals are calculated over the full history going back to 1990 though some of the charts focus on the more recent years.

At close of business the **2018-10-29** the VIX was trading at **25.5** at the **84.3** percentile. The 14-day VIX Volga was estimated at **31.7** its **94.3** percentile and the shockindex at **2.6** or its **98.5** percentile.

The above charts are useful, however their visualisation is quite limiting. On the one hand we need quite a few charts to present the data on the other hand it is difficult to show the full VIX history going back to 1990 as this would make the charts unreadable. Also this does not highlight any relationship between the metrics. Therefore clustering and aggregating the whole data into a single chart could be more useful to support an investment decision. To answer this I use a mapping technique developed by Kohonen in the 1980′. It uses an unsupervised neural network to re-arrange data around meaningful clusters. Though computationally complex is a practical way to summarise multidimensional data into a low (usually 2) dimensional system.

The below chart shows how the VIX price history split into 4 distinct clusters. Those clusters are computed as a function of the VIX level , VIX volga and Shockindex.

Since 1990 the VIX traded **56** **%** of the time in Cluster 1, **33** **%** in Cluster 2, **9** **%** in Cluster 3 and **2** **%** in Cluster 4. Overall the layering provided seems quite intuitive as the increase in risk and time spent in each cluster points toward what would generally be expected from market risk regimes ranging from low to high risk.

In the chart below we zoom on the various regimes within which the VIX has been trading for the current year. so far it traded **72** **%** of the time in Cluster 1, **19** **%** in Cluster 2, **9** **%** in Cluster 3 and **0** **%** in Cluster 4.

Concluding the above analysis the below chart shows a Self Organising Map of the considered risk metrics. The data has been grouped and colored as a function of four clusters of increasing market risk regimes. Obviously as shown on the map, the minimum level of volatility pertains to cluster 1 and the highest to cluster4. The current regime and its progression from 21 days ago is also highlighted on the map.

Always happy to discuss any of the above and its possible applications, feel free to reach me at: Pierre@argonautae.co.uk

## Stock Market Risk…Its getting hot out there…

The following analysis provides an update on some of the metrics I use to classify market risk. The word classify is more appropriate as I think that in essence you cannot forecast risk but rather attempt to adjust to it into a timely fashion. Clearly risk would not be a risk if you could forecast it accurately. However as there is generally some degree of persistence or clustering in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the VIX as a measure of global financial market risk. The same methodology can be successfully applied to other inputs such as implied currency volatility. Feel free to contact me at Pierre@argonautae.com for more detailled information on this analysis and how it can be embedded in an investment process.

My approach acknowledges that the nominal level of implied volatility is a crude metric of risk therefore I consider other measures. The VIX Volga, a measure of uncertainty of risk and the ShockIndex a measure of market dislocation. VIX Volga is simply the volatility of the VIX over a given period. This measure highlights how uncertain and unstable the level of risk has become. Though positively correlated to the level of the VIX the VIX Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX is trading at rather innocuous levels. This is not a trivial observation as the leverage undertaken by market participants tends to be an inverse function of market volatility which implies a greater vulnerability when volatility becomes uncertain at low levels and cannot be accurately budgeted for (Investors become risk seeking in low volatility environement though it is from those levels that you observe the greatest adverse changes in terms of risk). The ShockIndex is a ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It provides a measure of acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those metrics both relative to a time axis and their historical distribution. The red lines are 95% confidence intervals, the purple line identify the median. The blue line highlight are the current level. The VIX Volga and ShockIndex in the below analysis are evaluated over a period of 14 days. The medians and 95% confidence intervals are calculated over the full history going back to 1990 though some of the charts focus on the more recent years.

At close of business the **2018-10-10** the VIX was trading at **23** at the **76.2** percentile. The 14-day VIX Volga was estimated at **23.5** its **85.1** percentile and the shockindex at **1.8** or its **95.1** percentile.

The above charts are useful, however their visualisation is quite limiting. On the one hand we need quite a few charts to present the data on the other hand it is difficult to show the full VIX history going back to 1990 as this would make the charts unreadable. Also this does not highlight any relationship between the metrics. Therefore clustering and aggregating the whole data into a single chart could be more useful to support an investment decision. To answer this I use a mapping technique developed by Kohonen in the 1980′. It uses an unsupervised neural network to re-arrange data around meaningful clusters. Though computationally complex is a practical way to summarise multidimensional data into a low (usually 2) dimensional system.

The below chart shows how the VIX price history split into 4 distinct clusters. Those clusters are computed as a function of the VIX level , VIX volga and Shockindex.

Since 1990 the VIX traded **43** **%** of the time in Cluster 1, **39** **%** in Cluster 2, **15** **%** in Cluster 3 and **2** **%** in Cluster 4. Overall the layering provided seems quite intuitive as the increase in risk and time spent in each cluster points toward what would generally be expected from market risk regimes ranging from low to high risk.

In the chart below we zoom on the various regimes within which the VIX has been trading for the current year. so far it traded **55** **%** of the time in Cluster 1, **23** **%** in Cluster 2, **21** **%** in Cluster 3 and **0** **%** in Cluster 4.

## Error: <text>:3:39: unexpected ',' ## 2: colnames(chartdata) <- c("Low","Moderate","High","Extreme") ## 3: chart.TimeSeries(chartdata['2007::',]), ## ^

Concluding the above analysis the below chart shows a Self Organising Map of the considered risk metrics. The data has been grouped and colored as a function of four clusters of increasing market risk regimes. Obviously as shown on the map, the minimum level of volatility pertains to cluster 1 and the highest to cluster4. The current regime and its progression from 21 days ago is also highlighted on the map.

Always happy to discuss any of the above and its possible applications, feel free to reach me at: Pierre@argonautae.co.uk

## Trade Weighted Currency Indices Stretch Map

**Trade Weighted Currency Indices Report**

**Wed Oct 10 23:39:22 2018**

The following report aims to provide a gauge to the current strenght of major currencies. For doing so I use the Bank of England Trade weighted Exchange rate indices and a standardised statistical measures of price deviation to provide an estimate of how stretched major currencies are on a trade weighted perspective.

I first calculate the T-stat of the mean price deviations over a rolling period of 61 days. The charts below show the results for each currency over the last 500 days. The purple line represents the median value since **1990-01-03** and the red lines represent the 95% confidence intervals. Therefore if the value is above or below those the deviation of the given currency would be deemed as atypical relative to what #would be expected under a normal distribution and therefore overbought/oversold.

The following Map chart shows how stretched the currencies are over time horizons ranging from 1-month to 1-year. The bigger the square the most significant the upside (green) or downside (red) of currencies over the given period.

The charts below show how the daily changes in the Trade weighted indices have correlated since January 1990 and since the begining of 2015.

Finally, the following provide an ARIMA forecast for each of the trade weighted indices. My script selects the best ARIMA fit over the previous 250-day to generate a forecast for the next 21 days.

It also shows the forecast confidence intervals.

## Trade Weighted Currency Indices Stretch Map

**Trade Weighted Currency Indices Report**

**Wed Aug 29 04:23:56 2018**

The following report aims to provide a gauge to the current strenght of major currencies. For doing so I use the Bank of England Trade weighted Exchange rate indices and a standardised statistical measures of price deviation to provide an estimate of how stretched major currencies are on a trade weighted perspective.

I first calculate the T-stat of the mean price deviations over a rolling period of 61 days. The charts below show the results for each currency over the last 500 days. The purple line represents the median value since **1990-01-03** and the red lines represent the 95% confidence intervals. Therefore if the value is above or below those the deviation of the given currency would be deemed as atypical relative to what #would be expected under a normal distribution and therefore overbought/oversold.

The following Map chart shows how stretched the currencies are over time horizons ranging from 1-month to 1-year. The bigger the square the most significant the upside (green) or downside (red) of currencies over the given period.

The charts below show how the daily changes in the Trade weighted indices have correlated since January 1990 and since the begining of 2015.

Finally, the following provide an ARIMA forecast for each of the trade weighted indices. My script selects the best ARIMA fit over the previous 250-day to generate a forecast for the next 21 days.

It also shows the forecast confidence intervals.

## Stock Market Risk Report Update…

The following analysis provides an update on some of the metrics I use to classify market risk. The word classify is more appropriate as I think that in essence you cannot forecast risk but rather attempt to adjust to it into a timely fashion. Clearly risk would not be a risk if you could forecast it accurately. However as there is generally some degree of persistence or clustering in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the VIX as a measure of global financial market risk. The same methodology can be successfully applied to other inputs such as implied currency volatility. Feel free to contact me at Pierre@argonautae.com for more detailled information on this analysis and how it can be embedded in an investment process.

My approach acknowledges that the nominal level of implied volatility is a crude metric of risk therefore I consider other measures. The VIX Volga, a measure of uncertainty of risk and the ShockIndex a measure of market dislocation. VIX Volga is simply the volatility of the VIX over a given period. This measure highlights how uncertain and unstable the level of risk has become. Though positively correlated to the level of the VIX the VIX Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX is trading at rather innocuous levels. This is not a trivial observation as the leverage undertaken by market participants tends to be an inverse function of market volatility which implies a greater vulnerability when volatility becomes uncertain at low levels and cannot be accurately budgeted for (Investors become risk seeking in low volatility environement though it is from those levels that you observe the greatest adverse changes in terms of risk). The ShockIndex is a ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It provides a measure of acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those metrics both relative to a time axis and their historical distribution. The red lines are 95% confidence intervals, the purple line identify the median. The blue line highlight are the current level. The VIX Volga and ShockIndex in the below analysis are evaluated over a period of 14 days. The medians and 95% confidence intervals are calculated over the full history going back to 1990 though some of the charts focus on the more recent years.

At close of business the **2018-08-28** the VIX was trading at **12.5** at the **15.7** percentile. The 14-day VIX Volga was estimated at **13** its **44.3** percentile and the shockindex at **0.9** or its **68.5** percentile.

The above charts are useful, however their visualisation is quite limiting. On the one hand we need quite a few charts to present the data on the other hand it is difficult to show the full VIX history going back to 1990 as this would make the charts unreadable. Also this does not highlight any relationship between the metrics. Therefore clustering and aggregating the whole data into a single chart could be more useful to support an investment decision. To answer this I use a mapping technique developed by Kohonen in the 1980′. It uses an unsupervised neural network to re-arrange data around meaningful clusters. Though computationally complex is a practical way to summarise multidimensional data into a low (usually 2) dimensional system.

The below chart shows how the VIX price history split into 4 distinct clusters. Those clusters are computed as a function of the VIX level , VIX volga and Shockindex.

Since 1990 the VIX traded **57** **%** of the time in Cluster 1, **30** **%** in Cluster 2, **11** **%** in Cluster 3 and **2** **%** in Cluster 4. Overall the layering provided seems quite intuitive as the increase in risk and time spent in each cluster points toward what would generally be expected from market risk regimes ranging from low to high risk.

In the chart below we zoom on the various regimes within which the VIX has been trading for the current year. so far it traded **74** **%** of the time in Cluster 1, **6** **%** in Cluster 2, **20** **%** in Cluster 3 and **0** **%** in Cluster 4.

Concluding the above analysis the below chart shows a Self Organising Map of the considered risk metrics. The data has been grouped and colored as a function of four clusters of increasing market risk regimes. Obviously as shown on the map, the minimum level of volatility pertains to cluster 1 and the highest to cluster4. The current regime and its progression from 21 days ago is also highlighted on the map.

Always happy to discuss any of the above and its possible applications, feel free to reach me at: Pierre@argonautae.co.uk

## More Upside for Oil ?

Whatever the market being traded, there always will be a a question being asked at one moment: How far can this thing go ? Clearly not an easy question to answer as this will invariably depends on factors that are partly unknown or difficult to estimate, such as fundamentals, market positioning or market risk amongst others. The first part is obviously to assess how atypical the move experienced in the given instrument is. This report aims to contribute to this.

The below chart shows the **WTI Spot price** over the period of **January 1986** to **April 2018** . On the **02 April 2018** it was trading around **63.05**.

In the below I plot the previous **125** days against other similar historical periods that would have closely matched the recent history. The data has been normalised so as to be on the same scale. The chart shows the latest **125** days in black, and overlay similar historical patterns in grey. It Also shows what has been the price path for the following **125** days as well as the observed quartiles.

Finally I plot the last **125** days and a trend forecast derived from an **ARIMA(0,1,0)** model as well as the 95% confidence intervals. The ARIMA model is fitted to the past **625** historical values whilst ignoring the last **125** days, therefore we can look at the recent price path against the trend forecast and its confidence intervals to gauge how (a)typical the recent move has been.

## Trade Weighted Currency Indices Stretch Map

**Trade Weighted Currency Indices Report**

**Tue Apr 03 21:34:32 2018**

The following report aims to provide a gauge to the current strenght of major currencies. For doing so I use the Bank of England Trade weighted Exchange rate indices and a standardised statistical measures of price deviation to provide an estimate of how stretched major currencies are on a trade weighted perspective.

I first calculate the T-stat of the mean price deviations over a rolling period of 61 days. The charts below show the results for each currency over the last 500 days. The purple line represents the median value since **1990-01-03** and the red lines represent the 95% confidence intervals. Therefore if the value is above or below those the deviation of the given currency would be deemed as atypical relative to what #would be expected under a normal distribution and therefore overbought/oversold.

The following Map chart shows how stretched the currencies are over time horizons ranging from 1-month to 1-year. The bigger the square the most significant the upside (green) or downside (red) of currencies over the given period.

The charts below show how the daily changes in the Trade weighted indices have correlated since January 1990 and since the begining of 2015.

Finally, the following provide an ARIMA forecast for each of the trade weighted indices. My script selects the best ARIMA fit over the previous 250-day to generate a forecast for the next 21 days.

It also shows the forecast confidence intervals.

## Stock Market Risk Report Update…

At close of business the **2018-04-02** the VIX was trading at **23.6** at the **78** percentile. The 14-day VIX Volga was estimated at **30** its **93.1** percentile and the shockindex at **1.3** or its **88.5** percentile.

Since 1990 the VIX traded **51** **%** of the time in Cluster 1, **40** **%** in Cluster 2, **7** **%** in Cluster 3 and **2** **%** in Cluster 4. Overall the layering provided seems quite intuitive as the increase in risk and time spent in each cluster points toward what would generally be expected from market risk regimes ranging from low to high risk.

In the chart below we zoom on the various regimes within which the VIX has been trading for the current year. so far it traded **60** **%** of the time in Cluster 1, **35** **%** in Cluster 2, **5** **%** in Cluster 3 and **0** **%** in Cluster 4.

## Stock Market Risk Report Update…

At close of business the **2018-03-13** the VIX was trading at **16.4** at the **43.3** percentile. The 14-day VIX Volga was estimated at **26.4** its **89.7** percentile and the shockindex at **0.9** or its **68.9** percentile.

Since 1990 the VIX traded **55** **%** of the time in Cluster 1, **34** **%** in Cluster 2, **9** **%** in Cluster 3 and **2** **%** in Cluster 4. Overall the layering provided seems quite intuitive as the increase in risk and time spent in each cluster points toward what would generally be expected from market risk regimes ranging from low to high risk.

In the chart below we zoom on the various regimes within which the VIX has been trading for the current year. so far it traded **65** **%** of the time in Cluster 1, **24** **%** in Cluster 2, **11** **%** in Cluster 3 and **0** **%** in Cluster 4.