I always liked boxplots. I think they provide a great and very visual way to position current data relative to their history whilst highlighting outliers. This is particularly useful as it helps to put recent moves in context of their past opportunities and possibly highly reversals and/or opportunities. To illustrate this I wrote a quick script in R to grab the BOE G10 Trade weighted indices from the website of the bank of England and posititon the most recent one week move relative to its history of weekly move going back to 1990.

The blue dots represent the most recent observations, the orange dots are the outliers over the period 1990 to date. The boxes emcompasses the observations that fall between the 25% and 75% quantiles. The Blue lines in the box are the median value over the sample and the “wiskers” represent an interval of close to 95%.

# Trade Weighted Currency Indices Stretch Map

**Trade Weighted Currency Indices Report**

**Tue Jul 04 20:51:00 2017**

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.

# G10 FX Implied Volatilities: Cheap or Expensive ?

The following report provides a granular analysis of implied volatilities within G10 FX. I use primarily the same formatting than for my G10FX positioning report to estimate how extended the 1-month FX implied volatilities are over various time horizon.

The first set of charts shows the historical T-stat of the 1-day changes in 1-month implied volatilities over a rolling period of 61-days. This is my statistical metric to quantify how stretched the implied volatilities are, but clearly other time period could be used as shown further down on in that report. The purple line represents the median value since 1996 and the red lines represent the 95% confidence intervals. Therefore if the value is above or below those the deviation of the given implied volatility should be deemed as atypical relative to what would be expected under a normal distribution (I am not saying that implied volatilities have a normal behaviour to be clear….) and therefore overbought/oversold.

The below charts shows the current implied volatilities relative to their historical distributions since 1996. Once again the red lines delimit the 95% confidence intervals and the purple line the median value. The blue line indicates the most current level of 1-month implied volatility.

Finally the below shows a stretch map of the T-Stats to help visualise how much implied volatilities have departed from their equilibrium levels over time horizons ranging from 1-month to 6-month. The bigger the square the most significant the observed upside (Green) or downside (Red) of the implied volatility over the given period.

# GBPUSD Implied Volatility Level and Steepness of Volatility Curve

I recently have read a paper titled The yen/dollar exchange rate in 1998: views from options markets written by the Bank of England back in November 1998. This got me to think of how I could best represent in one chart the relationship between the slope of the implied volatility term structure of and the nominal level o the 1-month volatility. In the following example I have applied this to the GBPUSD implied volatility as I thought this would be interesting to look at in the light of the forthcomint BREXIT negotiations and tonight elections….

Anyhow to do this, I regress the 1, 3, 6 and 12-month GBPUSD implied volatilies against their time values for the period 1996 to Mayr 2017 (i.e 5513 volatility curves). I derived the volatility curve slopes t_stats for each day and then classified the 1-month volatilities into three groups as a function of the significance level of the slope t-stats. The chart below shows the 1-month implied volatiliy over the full period. When the volatility curve slope was positvely significant at 95% critical threshold the data is shown in green, When there was a signicantly negative slope at the 95% critical threshold the data is shown in red and pale blue for the remainder. I think this is a neat way highlight that time of high volatility are associated with a volatility curve that slope downwardly and vice-versa.

Below are the

# US Stock Market Risk Report Update…

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 **2017-05-12** the VIX was trading at **10.4** at the **0.7** percentile. The 14-day VIX Volga was estimated at **13.6** its **47.3** percentile and the shockindex at **0.9** 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 1990 the VIX traded **50** **%** 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 **53** **%** of the time in Cluster 1, **27** **%** in Cluster 2, **19** **%** 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

# UK Polls Update … Significant gains for Labour…..

OK it is election time again here in the UK and the Conservatives have the upper according to many polls and surveys monitoring the voting intention of UK voters. Though there are many surveys and polls the data available is quite noisy and also inconveniently irregularly spaced. This makes it difficult to detect trends and evaluate possible scenarios. In an attempt to bring some clarity I use UK polls survey results since the May 2010 sourced from the UK Polling Report website. They provide the results of 2221 polls made since may 2010. I First aggregate the data by calculating the weekly means of all the surveys, generating a sample of 350 weekly estimates. As shown in the below charts this greatly reduces the noise in the data .

As of the week ending 2017-06-01 the average percentage of intention to vote was standing at **45.74** % for the Conservatives, **38.3** % for Labour, **8.87** % for the LDEM, **4.61** % for UKIP and **2.48** % for the Green party.

The following charts show for each party the historical distribution of the percentage of vote intention (since 05/2010 for Conservatives, Labour and LDEM; 04/2012 for UKIP and 07/2012 for the Green party), the current level at which it stands (vertical green line) and its mean over the whole sample (blue line).

Finally the below provides an arima forecast of the percentage of vote intention by party and the 95% confidence intervals based on the previous 52 weeks of data. Each forecast is based on the best fitted ARIMA over the history used.

# Non Farm Payrolls time again…

It is NFP time again, sweepstakes must be rife on trading floors around the world…..So it is time to use my NFP forecasting model which leverages on both an ARIMA forecast and a simple linear regression using the ADP as the independent variable to generate a mixed forecast of the NFP.

Not surprisingly the ADP and the NFP data releases are positively correlated, thoug this has been significantly time varying. Also the NFP tend to be generally twice as volatile than the ADP numbers, highlighting their challenging nature for a forecaster.

## ADP NFP ## Min. :-845.95 Min. :-823.00 ## 1st Qu.: 23.17 1st Qu.: 20.75 ## Median : 144.57 Median : 138.50 ## Mean : 83.18 Mean : 85.72 ## 3rd Qu.: 212.27 3rd Qu.: 230.50 ## Max. : 383.98 Max. : 524.00

In the below chart I use a 24-month rolling Granger Causality test to investigate the causality at a lag of one between ADP and NFP releases. The chart shows the P-values of the test which indicate in which way the causality,if any, flows. Clearly sometime the ADP has been a leading indicator, other times not.

In the below I use an optimising algorithm to find the best ARIMA over the entire sample so as to generate a trend forecast of the NFP. The wide confidence intervals clearly highlight that those forecasts are associated with a high degree of of uncertainty.

Finally I use a mixed model to generate an estimate of what the next NFP release will be. The forecast is derived both from a linear regression model forecast with the ADP as the independent variable and also from the forecast generated by the previously fitted ARIMA model.

The LM model forecasts an NFP release of : **253,618** whilts the ARIMA calls for a release of: **178,689** . This contributes to a mixed model forecast of : **218,792**

# US Stock Market Risk Report Update…

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 **2017-05-12** the VIX was trading at **10.4** at the **0.7** percentile. The 14-day VIX Volga was estimated at **13.6** its **47.3** percentile and the shockindex at **0.9** 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 1990 the VIX traded **56** **%** of the time in Cluster 1, **31** **%** 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 **66** **%** of the time in Cluster 1, **13** **%** 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

# Trade Weighted Currency Indices Stretch Map

**Trade Weighted Currency Indices Report**

**Mon May 29 07:01:07 2017**

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.

# UK Polls Update

OK it is election time again here in the UK and the Conservatives have the upper according to many polls and surveys monitoring the voting intention of UK voters. Though there are many surveys and polls the data available is quite noisy and also inconveniently irregularly spaced. This makes it difficult to detect trends and evaluate possible scenarios. In an attempt to bring some clarity I use UK polls survey results since the May 2010 sourced from the UK Polling Report website. They provide the results of 2198 polls made since may 2010. I First aggregate the data by calculating the weekly means of all the surveys, generating a sample of 347 weekly estimates. As shown in the below charts this greatly reduces the noise in the data .

As of the week ending 2017-05-14 the average percentage of intention to vote was standing at **50.3** % for the Conservatives, **32.23** % for Labour, **9.56** % for the LDEM, **5.55** % for UKIP and **2.36** % for the Green party.

The following charts show for each party the historical distribution of the percentage of vote intention (since 05/2010 for Conservatives, Labour and LDEM; 04/2012 for UKIP and 07/2012 for the Green party), the current level at which it stands (vertical green line) and its mean over the whole sample (blue line).

Finally the below provides an arima forecast of the percentage of vote intention by party and the 95% confidence intervals based on the previous 52 weeks of data. Each forecast is based on the best fitted ARIMA over the history used.