Category Archives: Market Risk

The following report 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 in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the CBOE Emerging markets ETF Volatility Index (VIX Emerging markets) as a measure of Emerging stock markets risk. The same methodology can be successfully applied to other inputs. Feel free to contact me at Pierre@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two 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 Emerging markets 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 Emerging markets the VIX Emerging markets Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX Emerging markets 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 therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report 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 the charts shows only the recent years.

At close of business the 2016-10-17 the VIX Emerging markets was trading at 23 at the 47.7 percentile. The 14-day VIX Emerging markets Volga was estimated at 18.9 its 67.8 percentile and the Emerging markets shockindex at 0.8 or its 64.9 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. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. 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 was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 03/2011 the VIX Emerging markets traded 51 % of the time in Cluster 1, 34 % in Cluster 2, 9 % in Cluster 3 and 5 % 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 64 % of the time in Cluster 1, 35 % in Cluster 2, 1 % in Cluster 3 and 0 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned 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, feel free to reach me at: Pierre@argonautae.co.uk

The following report 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 in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the CBOE China ETF Volatility Index (VIX China) as a measure of stock market risk for China . The same methodology can be successfully applied to other inputs. Feel free to contact me at Pierre@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two 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 China 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 China the VIX China Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX China 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 therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report 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 the charts shows only the recent years.

At close of business the 2016-10-17 the VIX China was trading at 25.1 at the 43.9 percentile. The 14-day VIX China Volga was estimated at 13.6 its 51.4 percentile and the China shockindex at 0.6 or its 58.4 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. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. 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 was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 03/2011 the VIX China traded 76 % of the time in Cluster 1, 12 % in Cluster 2, 9 % in Cluster 3 and 4 % 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 98 % of the time in Cluster 1, 2 % in Cluster 2, 0 % in Cluster 3 and 0 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned 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, feel free to reach me at: Pierre@argonautae.co.uk

The following report 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 in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the CBOE Brazil ETF Volatility Index (VIX Brazil) as a measure of stock market risk for Brazil . The same methodology can be successfully applied to other inputs. Feel free to contact me at pollux@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two 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 Brazil 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 Brazil the VIX Brazil Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX Brazil 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 therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report 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 the charts shows only the recent years.

At close of business the 2016-10-17 the VIX Brazil was trading at 33 at the 58.7 percentile. The 14-day VIX Brazil Volga was estimated at 18.2 its 64.9 percentile and the Brazil shockindex at 0.5 or its 48.4 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. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. 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 was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 03/2011 the VIX Brazil traded 60 % of the time in Cluster 1, 22 % in Cluster 2, 3 % in Cluster 3 and 14 % 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, 12 % in Cluster 2, 8 % in Cluster 3 and 6 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned 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, feel free to reach me at: pollux@argonautae.com

The following report 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 in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the EURO STOXX 50® Volatility (VIX EUROPE) as a measure of stock market risk for Europe. The same methodology can be successfully applied to other inputs. Feel free to contact me at Pierre@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two 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 Europe 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 Europe the VIX Europe Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX Europe 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 therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report 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 the charts shows only the recent years.

At close of business the 2016-10-18 the VIX Europe was trading at 19.1 at the 25.9 percentile. The 14-day VIX Europe Volga was estimated at 17 its 55 percentile and the Europe shockindex at 0.8 or its 72.4 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. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. 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 was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 03/2011 the VIX Europe traded 39 % of the time in Cluster 1, 47 % in Cluster 2, 12 % 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 44 % of the time in Cluster 1, 44 % in Cluster 2, 12 % in Cluster 3 and 0 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned 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, feel free to reach me at: Pierre@argonautae.co.uk

The following report 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 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. Feel free to contact me at Pierre@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two 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 therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report 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 the charts shows only the recent years.

At close of business the 2016-09-30 the VIX was trading at 13.3 at the 19.1 percentile. The 14-day VIX Volga was estimated at 25.1 its 87.7 percentile and the shockindex at 1.9 or its 96.9 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. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. 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 was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 1990 the VIX traded 49 % of the time in Cluster 1, 37 % 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 55 % of the time in Cluster 1, 25 % in Cluster 2, 20 % in Cluster 3 and 0 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned 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, feel free to reach me at: Pierre@argonautae.co.uk

The following report 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 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. Feel free to contact me at Pierre@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two 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 therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report 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 the charts shows only the recent years.

At close of business the 2016-09-23 the VIX was trading at 12.3 at the 10.8 percentile. The 14-day VIX Volga was estimated at 23 its 84.1 percentile and the shockindex at 1.7 or its 95 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. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. 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 was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 1990 the VIX traded 59 % of the time in Cluster 1, 29 % 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, 19 % in Cluster 2, 15 % in Cluster 3 and 0 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned 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, feel free to reach me at: Pierre@argonautae.co.uk

The following report 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 in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the CBOE Emerging markets ETF Volatility Index (VIX Emerging markets) as a measure of Emerging stock markets risk. The same methodology can be successfully applied to other inputs. Feel free to contact me at Pierre@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two 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 Emerging markets 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 Emerging markets the VIX Emerging markets Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX Emerging markets 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 therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report 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 the charts shows only the recent years.

At close of business the 2016-08-30 the VIX Emerging markets was trading at 20.5 at the 27.5 percentile. The 14-day VIX Emerging markets Volga was estimated at 9.7 its 2.4 percentile and the Emerging markets shockindex at 0.5 or its 12 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. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. 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 was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 03/2011 the VIX Emerging markets traded 51 % of the time in Cluster 1, 33 % in Cluster 2, 8 % in Cluster 3 and 8 % 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 62 % of the time in Cluster 1, 34 % in Cluster 2, 4 % in Cluster 3 and 0 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned 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, feel free to reach me at: Pierre@argonautae.co.uk

The following report 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 in risk regimes, using a dynamic classification may be a useful approach for portfolio rebalancing and hedging. In this report I use the CBOE Brazil ETF Volatility Index (VIX Brazil) as a measure of stock market risk for Brazil . The same methodology can be successfully applied to other inputs. Feel free to contact me at pollux@argonautae.com for more information on the subject.

In my approach I recognise that the nominal level of implied volatility is a crude metric of risk therefore I also use two 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 Brazil 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 Brazil the VIX Brazil Volga is not necessarily dependent on it. You can have a high level of volga whilst the VIX Brazil 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 therefore cannot be accurately budgeted fo r. The ShockIndex is the ratio between the Volga and VIX at the beginning the historical window chosen to evaluate the Volga. It quantifies sharp changes and acceleration in risk levels. Historically it has proven to be a good classifying measure for market event risks.

The below charts shows those three measures both relative to a time axis and their historical distribution. The red lines are the 95% confidence intervals, the purple line the median. The blue line highlight the current level. The VIX Volga and ShockIndex in this report 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 the charts shows only the recent years.

At close of business the 2016-08-30 the VIX Brazil was trading at 33.5 at the 61.1 percentile. The 14-day VIX Brazil Volga was estimated at 9.2 its 7.7 percentile and the Brazil shockindex at 0.3 or its 5.1 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. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. 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 was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 03/2011 the VIX Brazil traded 60 % of the time in Cluster 1, 22 % in Cluster 2, 3 % in Cluster 3 and 15 % 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 73 % of the time in Cluster 1, 12 % in Cluster 2, 8 % in Cluster 3 and 6 % in Cluster 4.

Finally the below chart shows a Self Organising Map of the above mentioned 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, feel free to reach me at: pollux@argonautae.com