S&P 500 Path Analysis

The Fed just told us that its policy was at appropriate level and that there was no bias for hike or cut. Personally I think this is rather good news but the short term reaction as been for a small sell off. I guess any excuse is good for short term players to sell the relief rally that occurred in Q1…I am still looking for a clean break of 3000….

The below chart shows the S&P 500 cumulative return over the period January 1985 to May 2019 .At Close of business 01 May 2019 it was trading at 2923.

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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.

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Finally I plot the last 125 days and a trend forecast derived from an ARIMA(2,1,3) 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.

plot of chunk arimaplot

Calm Blue Sea for the Stock Markets….

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.

plot of chunk riskchart

At close of business the 2019-05-01 the VIX was trading at 14.8 at the 33.6 percentile. The 14-day VIX Volga was estimated at 9.4 its 25.5 percentile and the shockindex at 0.7 or its 46.5 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 53 % of the time in Cluster 1, 33 % 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.

plot of chunk cluster_chart

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 61 % of the time in Cluster 1, 25 % in Cluster 2, 14 % in Cluster 3 and 0 % in Cluster 4.

plot of chunk ytdriskchart

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.

plot of chunk SOM_chart

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

GBPUSD Break Analysis…

In the following I us an R package BFAST designed to detect structural 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 progress…so any input / suggestions are always welcome as usual. Feel free to contact me at:Pierre@argonautae.com

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Time to look at GBPUSD ?

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 among 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 GBP-USD over the period of January 1975 to March 2019 . On the 26 March 2019 it was trading around 1.3215277.

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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.

plot of chunk pattern

Finally I plot the last 125 days and a trend forecast derived from an ARIMA(3,1,0) 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.

plot of chunk arimaplot

Trade Weighted Currency Indices Stretch Map

Trade Weighted Currency Indices Report

Thu Mar 28 07:11:34 2019

The following report aims to provide a gauge to the current strength 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.

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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.

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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.

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

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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.

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Stock Market Risk 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 re balancing 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 detailed 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.

plot of chunk riskchart

At close of business the 2019-03-27 the VIX was trading at 15.2 at the 35.7 percentile. The 14-day VIX Volga was estimated at 15.2 its 57.8 percentile and the shockindex at 0.9 or its 72.6 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 39 % of the time in Cluster 1, 34 % in Cluster 2, 23 % in Cluster 3 and 3 % 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.

plot of chunk cluster_chart

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 51 % of the time in Cluster 1, 18 % in Cluster 2, 31 % in Cluster 3 and 0 % in Cluster 4.

plot of chunk ytdriskchart

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.

plot of chunk SOM_chart

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

AFX Index

In 1996 I co-wrote a paper which laid out the basis of a currency trend following index which we called the AFX. The paper went on to be published in 1998: Lequeux, P. and Acar, E. (1998) “A Dynamic Benchmark for Managed currencies Funds”, European Journal of Finance Vol.4. Our aim was to provide a framework to benchmark currency managers which at the time were primarily trend following in respect of their investment approach. Incidentally we probably coined the first FX smart beta index. To be clear the “raison d’etre” of the AFX was not specifically  to generate alpha but rather more to express a level of return and correlation consistent with the typical currency trend follower manager so as to be used as a tool for style analysis and performance evaluation. There clearly better techniques to accurately capitalise on currency trends. The paper we produced went on to be quoted in many research papers and the index to be used by many market practitioners and central banks in their own research. The methodology underpinning the benchmark was extending on previous published research which investigated the statistical properties of trading rules. The design which is transparent and relatively simple relies on 3 simple moving averages of order 32, 61 and 117 days to switch exposures to currency from long to short (and vice versa) as a function of the unfolding market trends.The simple moving average method was chosen amongst a large array of technical indicators because it was and still is one of the most popular trading rule amongst systematic traders. and therefore the returns of the index bear a high level of correlation to many currency manager peer group indices and also single managers.

Originally the index was computed using settlement price from the CME and also weightings derived from the triennial foreign exchange survey conducted by the BIS. As an attempt to make the index available to a broader audience of academics and market practitioners for research purpose I decided to somehow revisit some of the practical aspects of the AFX design. Namely data source availability , transparency and replicability. In that respect the re balancing of the weights in the index which are based on the most recent BIS triennial survey are now reset on the first business day of the year following the publication of the survey. Instead of using CME futures the index is now calculated using London market close (4PM) sourced from the Bank fo England database and short term interest rates sourced from the Federal Reserve Bank of St Louis database. The new iteration of the index is  strongly correlated to its predecessor whilst now having a greater level transparency and applicability which should be helpful to many academics and market practitioners who use it in their own research.

The most recent index monthly returns can be downloaded in a CSV format here whilst the return of the old version of the index can be found there. The R code that downloads the data and computes the returns of the index can be found here. The following link provides a list of most of the papers that have referenced and or used the index

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Stock Market Risk: Back to the Blue Sea…

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.

plot of chunk riskchart

At close of business the 2019-02-15 the VIX was trading at 14.9 at the 34.1 percentile. The 14-day VIX Volga was estimated at 9.8 its 28.2 percentile and the shockindex at 0.5 or its 17.4 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. 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, 32 % in Cluster 2, 10 % 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.

plot of chunk cluster_chart

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 67 % of the time in Cluster 1, 18 % in Cluster 2, 15 % in Cluster 3 and 0 % in Cluster 4.

plot of chunk ytdriskchart

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.

plot of chunk SOM_chart

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

Time to Buy Oil ?

Oil seems awfully undervalued on a technical basis….

The below chart shows the WTI Spot price over the period of January 1986 to January 2019 . On the 08 January 2019 it was trading around 49.73.

plot of chunk chartdata

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.

plot of chunk pattern

Finally I plot the last 125 days and a trend forecast derived from an ARIMA(4,1,1) 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.

plot of chunk arimaplot

Stock Market Risk…Overdone ?

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.

plot of chunk riskchart

At close of business the 2019-01-03 the VIX was trading at 25.1 at the 83.3 percentile. The 14-day VIX Volga was estimated at 32.6 its 94.7 percentile and the shockindex at 1.8 or its 95.3 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 49 % of the time in Cluster 1, 35 % in Cluster 2, 14 % 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.

plot of chunk cluster_chart

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, 19 % in Cluster 2, 21 % in Cluster 3 and 0 % in Cluster 4.

plot of chunk ytdriskchart

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.

plot of chunk SOM_chart

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