Monthly Archives: January 2016

UK Assets Only Investor Dynamic ETF Allocation Portfolio Update

The following report provides analyticals in respect of an investible ETF multi-asset dynamic portfolio for UK assets only investors (I am clearly not saying nor advising that you should invest in such porfolio, I am just producing this for general information). For my allocation exercise I used Ishares ETF. My choice for the Ishares was purely driven by the fact that they have the longest price history. However, bearing in mind that Ishare Equity ETF have a total expense ratio of 0.40% , I therefore would rather use Vanguard or State street ETFs when available for implementation as they have a far much more reasonable TER (close to 10 bps). So my choice of IShares ETF probably affects negatively the numbers shown in the below.

I used the FTSE 100 , FTSE 250, FTSE high Div. ,UK Property , Corporate Bonds, Inflation Linked bonds and Gilts ETFs as my investible universe. The description of each ETF can be accessed by clicking on the assets and following the web link.

The below charts shows the rolling 36-month return, volatility and risk-adjusted return for each of the assets considered. Clearly equities and property have a higher volatility than bonds but also higher/lower localised returns highliting that timing is key in unlocking those higher returns.

plot of chunk Summary charts
The summary performance statistics show that over the period April 2007 to date a UK investor would have had the best risk adjusted return by holding a broad basket of Inflation linked bonds and the worse by investing in the Property index which suffered hugely during the financial crisis.

##                                 FTSE100 FTSE250 FTSE HIGH Div. Property
## Annualized Return                 -0.58    4.01          -5.00    -5.10
## Annualized Standard Deviation     14.88   17.78          17.77    22.95
## Annualized Sharpe Ratio (Rf=0%)   -0.04    0.23          -0.28    -0.22
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                       -0.24             4.47  2.55
## Annualized Standard Deviation            9.81             8.81  6.62
## Annualized Sharpe Ratio (Rf=0%)         -0.02             0.51  0.39
## Worst Drawdown                          32.18            14.86  8.49

Below I show the Markowitz Efficient Frontier based on the past 36-month return series. Each investible asset, the minimum variance and tangent portfolio are shown on the plot as well as the in-sample 36-month annualised returns. The Green line is just the risk free line (I assumed zero risk free).

plot of chunk frontier

I then used a mean-variance model to compute the weights of the portfolio that maximises the risk return ratio on the efficient frontier.The model is optimised for “long only” and weights adding to one constraints. I used a rolling window of 36-month to estimate the returns, volatility and correlation input fed into the Markovitz model. The use of a rolling window implies that the momentum effect in the input is captured by the optimisation. Therefore if an asset becomes more attractive through time in terms of its risk adjusted return and/or diversification potential its participation into the final portfolio should increase and vice versae as time goes. The two charts below show how the optimised portfolio weights have changed throughout time and also what were the weights at the end of the last month.

plot of chunk weights_chartplot of chunk weights_chart
Using the above weights I then calculate the return of the portfolio for the folowing period assuming a transaction cost of 0.15% of adjusted notional for each monthly rebalancement so as to factor in bid-ask spreads. The performance is compared to the return of a portfolio composed of 40% Gilts and 60% UK equities.

plot of chunk Opt_porfolio_charts

**Summary Performance Statistics 

##                                 Benchmark 40Eq./60Bds Optimal Portfolio
## Annualized Return                                2.23              3.72
## Annualized Standard Deviation                    5.33              6.17
## Annualized Sharpe Ratio (Rf=0%)                  0.42              0.60
## Worst Drawdown                                   6.91              7.49

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2015-06-29 2016-01-06       <NA> -7.49         9      9        8
## 2 2013-05-30 2013-06-27 2014-02-28 -4.59        10     10        2
## 3 2010-09-29 2011-01-31 2011-09-29 -4.52        13     13        5
## 4 2012-04-29 2012-06-28 2013-02-28 -2.22        11     11        3
## 5 2014-03-30 2014-06-29 2014-08-28 -1.75         6      6        4

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 2010   NA   NA   NA -0.2  0.4  1.0 -0.9  4.4 -0.1 -2.6 -0.4  0.9    2.3
## 2011 -2.3  1.0  0.5  0.5  0.9 -0.6  2.0 -0.8  1.9  0.7  1.5  1.4    6.6
## 2012  1.7 -0.1  0.1 -1.9  0.2 -0.5  1.3  0.4 -0.7 -0.8  0.4  0.3    0.5
## 2013 -0.3  1.7  2.1  0.1 -1.4 -3.2  3.0 -1.4  1.1  1.1 -0.9  0.1    2.1
## 2014  0.7  1.9 -0.6 -1.0  0.7 -0.9  0.2  3.0 -1.7  1.5  4.6  0.4    8.8
## 2015  5.4  1.1  0.7 -1.0  2.7 -3.8  2.7 -3.3 -0.5  2.9 -2.2 -1.6    3.0
## 2016 -1.6   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA   -1.6

If you need more information or have questions about the above, feel free to contact me at Pierre@argonautae.com

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.

plot of chunk chartsplot of chunk charts

##       ADP                 NFP           
##  "Min.   :-825.57  " "Min.   :-824.00  "
##  "1st Qu.: -38.73  " "1st Qu.: -38.50  "
##  "Median : 132.84  " "Median : 121.00  "
##  "Mean   :  51.59  " "Mean   :  59.66  "
##  "3rd Qu.: 199.56  " "3rd Qu.: 212.00  "
##  "Max.   : 342.63  " "Max.   : 518.00  "

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.

plot of chunk causality

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.

plot of chunk arimachart

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 : 260,304 whilts the ARIMA calls for a release of: 223,604 . This contributes to a mixed model forecast of : 243,480

EURUSD Update….

 

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 EURUSD Spot Price over the period of December 1998 to January 2016 . On the 05 January 2016 it was trading around 1.0745.

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(0,1,2) 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

AFX Index October Update: Bad month for currency trend followers …..

Passive currency indices do not reflect any of the money management skills necessary to generate profit out of the Foreign Exchange market. Evidently there is no value in holding a long (or short) position in any currency over the very long term. For this reason passive currency benchmarks fail to adequately describe the performance of currency funds because they do not have an embedded timing process to imitate the short/long currency positions that an active manager would take. For that reason correlation between passive currency indices and currency managers peer group indices tends to be low.

The AFX, aims to replicate the risk/return profile of the average currency manager by using the returns of technical trading rules, namely trend following trading rules. The index was designed by Lequeux & Acar (1998). The timing embedded in the index relies on the buy/sell signals generated by three moving averages. So as to cover a broad spectrum of time horizons the ex-ante statistical properties of technical indicators were used to build the index on the basis of ex-ante measurable criteria of risk reduction and transaction costs. Finally the index uses a weighting scheme derived from the estimated turnover in currency market as reported by the triennial survey on foreign exchange turnover conducted by the Bank for International Settlements. The index is calculated gross of any fee or risk free income and as such express the typical directional market opportunity that was available in G10 FX.

A full description of the index can be found in : Lequeux, P. and Acar, E. (1998) “A Dynamic Benchmark for Managed currencies Funds”, European Journal of Finance Vol. 4.

The historical returns of the AFX Index can be downloaded by through the following link: AFX Historical data

plot of chunk risk_profile

**Summary Performance Statistics 

##                                  AFX
## Annualized Return               3.09
## Annualized Standard Deviation   6.69
## Annualized Sharpe Ratio (Rf=0%) 0.46

Drawdowns Table

##                   From              Trough                  To  Depth
## 1  2010-11-30 00:00:00 2014-06-30 23:00:00 2015-01-30 00:00:00  -11.5
## 2  2004-01-30 00:00:00 2004-09-30 23:00:00 2008-10-31 00:00:00 -10.81
## 3  2015-04-30 23:00:00 2015-12-31 00:00:00                <NA>  -9.29
## 4  1993-05-31 23:00:00 1995-01-31 00:00:00 1995-04-30 23:00:00  -7.85
## 5  1988-01-29 00:00:00 1988-04-28 23:00:00 1988-11-30 00:00:00  -7.79
## 6  1991-07-31 23:00:00 1991-08-29 23:00:00 1991-12-31 00:00:00  -7.21
## 7  1995-05-31 23:00:00 1995-07-31 23:00:00 1996-04-30 23:00:00  -6.22
## 8  2009-01-30 00:00:00 2009-04-30 23:00:00 2010-05-31 23:00:00  -5.93
## 9  1992-01-31 00:00:00 1992-04-30 23:00:00 1992-08-31 23:00:00   -5.7
## 10 2002-08-29 23:00:00 2002-11-29 00:00:00 2003-05-29 23:00:00  -5.37
##    Length To Trough Recovery
## 1         51     51       44
## 2         58     58        9
## 3         10     10        9
## 4         24     24       21
## 5         11     11        4
## 6          6      6        2
## 7         12     12        3
## 8         17     17        4
## 9          8      8        4
## 10        10     10        4

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 1984 -0.6 -0.7 -0.7  0.1 -0.4  2.5  3.9 -1.5  3.4 -0.4  0.9  1.9    8.5
## 1985  1.5  4.0 -2.4 -1.3 -0.3 -0.6  5.6 -0.1  0.0  0.6  3.3  0.0   10.1
## 1986  1.4  5.0 -1.4  1.2  0.0  0.4  3.8 -0.1 -1.2  0.8 -0.9  0.8    9.9
## 1987  3.2  0.1  1.3  3.0 -2.1 -1.8  1.6  0.2 -1.0  0.0  4.7  5.0   14.3
## 1988 -5.8 -0.3 -0.2 -1.6  1.2  4.9  0.9  1.2 -1.6  0.9  3.1 -2.9   -0.2
## 1989  3.1 -2.5  3.1  0.3  4.8 -0.2 -1.2 -0.8 -2.0 -1.1  0.8  2.2    6.4
## 1990 -0.4  0.5  0.7 -0.2  0.2 -1.3  3.4  1.5  0.3  2.8 -0.6 -1.4    5.7
## 1991 -1.8 -1.1  6.5 -0.2 -1.1  2.8 -3.3 -4.0  3.4 -1.3  1.9  5.3    7.0
## 1992 -4.5 -1.0  1.4 -1.7  0.7  3.7  1.6  4.3 -1.2 -0.8  1.7 -0.7    3.6
## 1993 -2.8  2.0  1.3  1.7 -0.3 -1.8  0.2 -3.2  0.0  0.0 -0.2 -0.4   -3.3
## 1994 -1.5  0.3  0.1  0.9 -0.8  2.6 -0.7 -1.6 -0.2  1.8 -1.2 -1.1   -1.5
## 1995 -0.8  1.7  6.5  0.5 -4.2 -1.9 -0.2  4.5 -1.0  0.7 -0.9 -0.1    4.7
## 1996  3.3 -1.8  0.9  1.9  0.2  0.4 -0.4 -0.8  0.9  1.8  0.2  1.4    7.9
## 1997  4.0  1.3 -0.9  1.6 -2.3  0.7  2.9 -1.5 -0.5  0.2  1.5  0.1    7.2
## 1998 -0.7 -2.1  2.8 -1.5  1.6 -0.8 -0.7 -1.4  1.1  4.1 -2.5  0.1    0.1
## 1999 -0.4  0.7  0.6  0.6  0.4  0.4 -1.1 -0.7  0.9 -1.6  2.4 -0.5    1.8
## 2000  1.8  0.8 -0.7  1.1 -0.5 -2.0  0.0  0.9  0.1  2.0 -0.6  4.4    7.3
## 2001 -0.3 -1.4  2.6 -2.7  1.2 -0.3 -0.9  1.7 -0.8 -0.7 -0.5  0.3   -2.0
## 2002  1.3 -1.9 -1.6  1.2  2.0  4.3  0.0 -1.6 -1.7 -1.6 -0.6  2.8    2.8
## 2003  1.2 -0.5 -0.5  0.5  2.5 -1.8 -1.3  0.9  1.2 -0.2  0.7  3.0    5.7
## 2004 -0.5 -0.4 -0.8 -0.9 -0.9 -1.9 -1.4 -3.0 -1.5  2.0  3.3  0.3   -5.7
## 2005 -2.7 -0.4  0.3 -0.5  3.0  2.7 -1.1 -1.0  0.3  0.3  1.6 -1.7    0.7
## 2006 -1.4 -0.9 -1.6  2.1  1.0 -1.0 -0.5  0.5 -0.1 -0.2  1.9 -0.5   -0.8
## 2007 -0.1 -0.9 -0.8  1.2 -0.2  0.0  0.1 -0.9  1.4  0.8  0.6 -1.3   -0.3
## 2008  0.7  0.9  1.6 -1.6 -1.2 -1.8 -0.9  4.2 -0.6  8.5  1.5  0.3   11.5
## 2009 -1.1 -0.4 -2.6 -2.1  4.7 -0.8 -1.0 -1.0  1.6 -0.5  0.8 -0.7   -3.0
## 2010  0.7  1.3 -0.1 -0.2  3.1 -1.1  1.2 -0.5  2.4  0.7 -0.7 -1.7    5.0
## 2011 -1.3  0.2  0.7  2.6 -3.1 -1.8 -0.3 -2.9  3.5 -4.1 -0.2  2.0   -4.8
## 2012 -0.9  0.8 -0.6 -1.2  3.3 -3.2  0.9 -1.2  1.3  0.3 -0.1  2.2    1.5
## 2013  2.1 -0.2  0.5 -1.4 -0.7 -2.6 -0.9 -0.9  1.6 -0.6  0.3  1.8   -1.2
## 2014 -2.6  0.2 -0.8 -1.1 -0.2 -0.1  0.3  1.6  3.5  0.8  2.5  1.4    5.5
## 2015  2.5 -0.3  1.8 -1.6 -0.4 -2.7 -0.7 -0.6 -1.1 -1.5  2.3 -3.4   -5.6

The AFX is positively correlated to main peer group indices highlighting that currency managers are typically directional in their investment style. The below charts shows the 24-month rolling correlation of the AFX with the BTOP FX Index .

plot of chunk rolling_correl

If you need more information or have questions about the above, feel free to contact me at pollux@argonautae.com

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.

plot of chunk riskchart

At close of business the 2016-01-04 the VIX was trading at 20.7 at the 63.9 percentile. The 14-day VIX Volga was estimated at 28.4 its 91.9 percentile and the shockindex at 1.8 or its 96.4 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 1990 the VIX traded 49 % of the time in Cluster 1, 39 % 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 53 % of the time in Cluster 1, 28 % in Cluster 2, 19 % in Cluster 3 and 0 % in Cluster 4.

plot of chunk ytdriskchart

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.

plot of chunk SOM_chart

Always happy to discuss any of the above, feel free to reach me at: Pierre@argonautae.com

Brazil 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 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.

plot of chunk riskchart

At close of business the 2016-01-04 the VIX Brazil was trading at 46.9 at the 91.8 percentile. The 14-day VIX Brazil Volga was estimated at 25.3 its 84.3 percentile and the Brazil shockindex at 0.5 or its 51.6 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. 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 42 % of the time in Cluster 1, 37 % in Cluster 2, 15 % in Cluster 3 and 6 % 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 48 % of the time in Cluster 1, 36 % in Cluster 2, 4 % in Cluster 3 and 12 % in Cluster 4.

plot of chunk ytdriskchart

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.

plot of chunk SOM_chart

Always happy to discuss any of the above, feel free to reach me at: pollux@argonautae.com

Europe 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 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.

plot of chunk riskchart

At close of business the 2016-01-05 the VIX Europe was trading at 26.2 at the 65.7 percentile. The 14-day VIX Europe Volga was estimated at 26.1 its 86 percentile and the Europe shockindex at 1.1 or its 89 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 48 % of the time in Cluster 1, 37 % in Cluster 2, 13 % 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 46 % of the time in Cluster 1, 41 % in Cluster 2, 13 % in Cluster 3 and 0 % in Cluster 4.

plot of chunk ytdriskchart

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.

plot of chunk SOM_chart

Always happy to discuss any of the above, feel free to reach me at: Pierre@argonautae.com

G10 FX Position Report Update

G10 FX POSITIONING REPORT

Mon Jan 04 23:48:55 2016

The following report aims to provide a gauge to the current market positioning in G10 FX. It focuses on US$ crosses and uses a standardised statistical measures of price deviation as well as a regression methodology to produce an estimate of how stretched currency exchange rates are and also to evaluate how currency managers are likely to be positioned and leveraged in G10 Currency. I use the BTOPFX in the report but can do the computations for any other peer group benchmark.

G10 FX STRETCH MAP

The stretch indicator looks at how much exchange rates are extended by calculating the T-stat of the mean price deviation over a rolling period of 61 days. The charts below shows the results for each currency pairs over the last 500 days. The spot prices are expressed as 1 unit of foreign currency versus the USD. The purple line represent the median value since 2005 and the red lines represent the 95% confidence intervals. Therefore if the value is above or below those the deviation of the given exchange rate would be deemed as atypical relative to what would be expected under a normal distribution and therefore overbought/oversold.

plot of chunk stretch line chart

The below shows the above calculated T-stats but this time relative to their historical distributions. Once again the red lines delimit the 95% confidence intervals and the purple line the median value. The blue line indicates the most current value of the T-stat.

plot of chunk stretch distribution

The following Map chart shows how stretched G10 FX exchange rates are over time horizons ranging from 1-month to 6-month. The bigger the square the most significant the upside (green) or downside (red) of the exchange rate over the given period. All the exchange rates are quoted on CCY-US$ basis so red indicate a depreciation of a given CCY against US$ and green an appreciation versus the US$.

plot of chunk stretch map

Estimated Currency Managers Positioning in G10 FX

To determine the sensitivity of currency managers to exchange rates and therefore their current positioning we regress the daily returns of the BTOPFX index against the daily logarithmic returns of G10 FX rates. We then calculate the T-stat for each of the regression’s slope coefficients. The higher the T-stat the higher the sensitivity to a given currency and therefore likely positioning. Using the regression weights as well as the variance of the independent and explanatory variables as input we can then easily deduce an estimation of the current risk utilisation of the typical currency manager as inferred by the values of the BTOPFX.

The below shows the T-stat of the regression’s slope coefficients over the last 500 days. The purple line represents the median value since 2005 and the red lines represent the 95% confidence intervals. Therefore if the value is above or below the red lines the positioning in a currency would be deemed as extreme and therefore the risk of unwinding would be greater since the market inventory would likely be close to its highest. Probably highlighting a good environment to enter a contrarian trade.

plot of chunk sensitivity line chart

The sensitivity of currency managers returns to changes in G10 FX rates relative to their historical distribution is shown below. Once again the red lines are the 95% confidence intervals and the purple line the median value. The blue line indicates the most current value of the T-stat. If this one is either side of the intervals of confidence it indicates a potentially overextended market positioning in the given currency.

plot of chunk sensitivity distribution

The exposure to the US$ is derived from the combined sensitivities to the other currencies and is shown in the same fashion than for the other currencies. Namely against an axis of time and relative to its historical distribution.

plot of chunk USD sensitivity

The below Map chart shows the currency managers sensitivity to G10 FX exchange rates over time horizons ranging from 1-month to 6-month. The bigger the square the most significant the sensitivity to a currency the exchange rate over the given period. Long positioning is shown in green and short in red.

plot of chunk sensitivity map

Estimated Leverage

As explained previously the level of risk utilisation of currency managers and therefore their gearing can easily be derived by using the regression coefficients and the variances of both the independent and explanatory variables. The chart below shows the rolling estimation of risk utilisation as well putting it in respect of its historical distribution. Average Risk utilisation over the last 61 days is estimated at 27.5 % of maximum.

plot of chunk leverage

AFX Index December 2016 Update…

Passive currency indices do not reflect any of the money management skills necessary to generate profit out of the Foreign Exchange market. Evidently there is no value in holding a long (or short) position in any currency over the very long term. For this reason passive currency benchmarks fail to adequately describe the performance of currency funds because they do not have an embedded timing process to imitate the short/long currency positions that an active manager would take. For that reason correlation between passive currency indices and currency managers peer group indices tends to be low.

The AFX, aims to replicate the risk/return profile of the average currency manager by using the returns of technical trading rules, namely trend following trading rules. The index was designed by Lequeux & Acar (1998). The timing embedded in the index relies on the buy/sell signals generated by three moving averages. So as to cover a broad spectrum of time horizons the ex-ante statistical properties of technical indicators were used to build the index on the basis of ex-ante measurable criteria of risk reduction and transaction costs. Finally the index uses a weighting scheme derived from the estimated turnover in currency market as reported by the triennial survey on foreign exchange turnover conducted by the Bank for International Settlements. The index is calculated gross of any fee or risk free income and as such express the typical directional market opportunity that was available in G10 FX.

A full description of the index can be found in : Lequeux, P. and Acar, E. (1998) “A Dynamic Benchmark for Managed currencies Funds”, European Journal of Finance Vol. 4.

The historical returns of the AFX Index can be downloaded by through the following link: AFX Historical data

plot of chunk risk_profile

**Summary Performance Statistics 

##                                  AFX
## Annualized Return               3.09
## Annualized Standard Deviation   6.83
## Annualized Sharpe Ratio (Rf=0%) 0.45

Drawdowns Table

##          From     Trough         To  Depth Length To Trough Recovery
## 1  2010-11-30 2014-06-30 2015-01-30 -11.48        51     51       44
## 2  2004-01-30 2004-09-30 2008-10-31 -10.76        58     58        9
## 3  2015-04-30 2015-12-31       <NA>   -9.4        10     10        9
## 4  1993-05-28 1995-01-31 1996-01-31  -7.86        33     33       21
## 5  1988-01-29 1988-04-29 1988-11-30  -7.79        11     11        4
## 6  1991-04-30 1991-08-30 1991-12-31  -7.17         9      9        5
## 7  2009-01-30 2009-04-30 2010-05-31  -6.26        17     17        4
## 8  1992-01-31 1992-04-30 1992-07-31  -5.77         7      7        4
## 9  2002-07-31 2002-11-29 2003-05-30  -5.68        11     11        5
## 10 1989-06-30 1989-10-31 1990-07-31  -5.58        14     14        5

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 1984 -0.6 -0.7 -0.7  0.0  0.8  1.4  4.1 -1.7  3.9 -0.9  0.9  1.9    8.5
## 1985  1.5  4.0 -1.5 -2.3 -0.4 -0.3  6.7 -1.5 -1.5  2.1  3.3  0.0   10.1
## 1986  1.4  5.0 -1.3  2.2 -1.1  0.3  3.7  0.1 -1.3  1.0 -0.9  0.8    9.9
## 1987  3.2  0.1  2.3  1.7 -1.6 -1.9  1.7 -0.1 -0.5 -0.2  4.7  5.0   14.3
## 1988 -5.8 -0.3 -0.2 -1.6  1.3  4.2  1.8  0.7 -1.5  0.9  3.1 -2.9   -0.2
## 1989  3.1 -2.5  3.1 -0.3  5.6 -0.5 -1.6 -0.9 -1.6 -1.1  0.8  2.2    6.4
## 1990 -0.4  0.5  0.7 -0.1  0.1 -1.2  3.8  1.1 -0.2  3.3 -0.6 -1.4    5.7
## 1991 -1.8 -1.1  7.9 -1.8 -0.9  2.3 -2.7 -4.2  3.6 -1.6  1.9  5.3    7.0
## 1992 -4.5 -1.0  0.8 -1.1  0.5  3.8  1.7  3.7 -0.6 -0.7  1.7 -0.7    3.6
## 1993 -2.8  2.0  0.5  2.6 -0.1 -1.2 -0.5 -3.3  0.1  0.0 -0.2 -0.4   -3.3
## 1994 -1.5  0.3  1.4 -0.4 -0.9  2.9 -1.1 -1.5 -0.2  1.8 -1.2 -1.1   -1.5
## 1995 -0.8  1.7  6.5  0.2 -3.8 -2.0 -0.5  4.9 -1.1  0.7 -0.9 -0.1    4.7
## 1996  3.3 -1.8  0.6  2.0  0.4  0.3 -0.1 -1.0  0.8  1.8  0.2  1.4    7.9
## 1997  4.0  1.3 -0.3  1.3 -2.6  0.7  2.3 -0.9 -0.4  0.1  1.5  0.1    7.2
## 1998 -0.7 -2.1  2.6 -1.3  1.5 -0.5 -0.8 -1.9  0.9  4.7 -2.5  0.1    0.1
## 1999 -0.4  0.7  0.7  0.6  0.7 -0.5 -0.5 -0.8  0.2 -0.8  2.4 -0.5    1.8
## 2000  1.8  0.8 -0.7  1.4 -1.1 -1.7 -0.2  1.9 -0.7  2.0 -0.6  4.4    7.3
## 2001 -0.3 -1.4  2.6 -2.1  0.8 -0.5 -1.0  1.8 -0.9 -0.6 -0.5  0.3   -2.0
## 2002  1.3 -1.9 -1.3  0.3  2.6  4.7 -0.4 -1.5 -1.7 -1.6 -0.6  2.8    2.8
## 2003  1.2 -0.5 -0.5  0.1  2.9 -1.9 -1.1  0.7  0.7  0.3  0.7  3.0    5.7
## 2004 -0.5 -0.4 -1.0 -0.7 -1.0 -1.8 -1.3 -3.0 -1.5  2.0  3.3  0.3   -5.7
## 2005 -2.7 -0.4  0.0 -0.2  2.6  2.2  0.2 -1.6  0.6  0.3  1.6 -1.7    0.7
## 2006 -1.4 -0.9 -1.6  1.9  1.2 -1.1 -0.6  0.6 -0.1 -0.2  1.9 -0.5   -0.8
## 2007 -0.1 -0.9 -0.8  1.2 -0.4  0.1  0.3 -1.0  1.6  0.6  0.6 -1.3   -0.3
## 2008  0.7  0.9  2.8 -2.5 -1.5 -1.9 -0.7  4.2 -0.9  8.8  1.5  0.3   11.5
## 2009 -1.1 -0.4 -2.2 -2.8  4.5 -0.7 -0.6 -0.7  1.6 -0.8  0.8 -0.7   -3.0
## 2010  0.7  1.3  0.1 -0.3  3.1 -0.7  0.7  0.1  1.1  1.4 -0.7 -1.7    5.0
## 2011 -1.3  0.2  0.3  3.0 -3.2 -1.6 -0.2 -2.9  3.2 -4.1 -0.2  2.0   -4.8
## 2012 -0.9  0.8 -0.6 -1.2  3.3 -3.3  0.8 -1.1  1.2  0.4 -0.1  2.2    1.5
## 2013  2.1 -0.2  0.7 -1.8 -0.5 -2.6 -0.4 -1.5  1.5 -0.5  0.3  1.8   -1.2
## 2014 -2.6  0.2 -0.9 -0.9 -0.2 -0.1  0.5  1.4  3.5  0.7  2.5  1.4    5.5
## 2015  2.5 -0.3  1.9 -1.3 -1.0 -2.5 -0.7 -1.2 -0.5 -1.5  2.3 -3.4   -5.6

The AFX is positively correlated to main peer group indices highlighting that currency managers are typically directional in their investment style. The below charts shows the 24-month rolling correlation of the AFX with the BTOP FX Index .

plot of chunk rolling_correl

If you need more information or have questions about the above, feel free to contact me at pollux@argonautae.com

G10 FX Risk Report Update

The following analysis uses a proprietary G10 FX implied volatility index which I created quite a few years ago. The index is a G10 FX 1-month implied volatility index which weights are derived from the BIX FX triennal surveys for the year 2001,2003 & 2007. If you want more information on the exact formulation of the index feel free to contact me pollux@argonautae.com for a chat. For the time being suffice to say that the G10 FX volatility index is a broad and accurately weighted measure of G10 FX risk.

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, namely Volga and the ShockIndex. The Volga is simply the volatility of the G10 FX volatility index over a given period. This measure highlights how uncertain and unstable the level of risk in G10 FX has become. Though generally positively correlated those measures of risk can diverge from time to time. You can have a high level of volga whilst G10 FX volatilities are 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 for. The ShockIndex is the ratio between the Volga and the G10 FX volatility index 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 in FX markets.

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 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 1996 though the charts shows only the recent years.

plot of chunk riskchart

At close of business the 2016-01-04 the G10 FX volatility index was estimated at 8.8 % at the 71.9 percentile. The 14-day G10 FX Volga was estimated at 6.1 % its 83.5 percentile and the shockindex at 0.6 or its 69.4 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 G10 FX volatility Index history going back to 1996 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 G10 FX Volatility Index history was split into 4 distinct clusters. Those clusters where computed not only as a function of the G10 FX Volatility Index level but also as a function of the other discussed variables, namely Volga and Shockindex.

Since 1996 the G10 FX volatility Index traded 32 % of the time in Cluster 1, 38 % in Cluster 2, 24 % in Cluster 3 and 6 % 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 G10 FX Volatility Index hasevolved for the current year. so far it remained 59 % of the time in Cluster 1, 17 % in Cluster 2, 25 % in Cluster 3 and 0 % in Cluster 4.

plot of chunk ytdriskchart

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.

plot of chunk SOM_chart