Going Visual on GBP-USD With an Interactive Google Calendar Heat Map….

I stumbled on a few snippets of code that allows to display data into a really neat interactive calendar heatmap and line chart. I merged some of my own code to calculate rolling T-Stats which I then bound within a -1/+1 interval by using a normal probability density function and here is the results applied to the GBP-USD historical rates published by the bank of England/

The line charts shows the historical price of the GBP-USD whereas the calendar heatmap shows the rolling 21-day color coded T-stat of the GBP-USD daily logarithmic returns… Not rocket science but a quite visual way to illustrate when the GBP-USD was historically overbought/oversold….

 



GBPUSD 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 GBP-USD over the period of January 1975 to February 2017 . On the 17 February 2017 it was trading around 1.2431626.

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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(0,1,5) 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.

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Oil and US Trade weighted Index Relationship

The below plot is a bi-density chart of the WTI spot rate versus the Fed USD Trade weighted index (Weekly data since February 1986). The contour lines delimit the empirical joint distribution. The yellow line is the best fit derived from a quantile regression. The dotted red lines delimit the quantiles for the Oil price. The bold red cross hair lines show where both the USD TWI and the oil Price is at the most recent point….

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Gold and USD Trade weighted index

The below plot is a bi-density chart of the Gold spot rate in US$ versus the Fed USD Trade weighted index (weekly data since  January 1979). The contour lines delimit the empirical joint distribution. The yellow line is the best fit derived from a quantile regression The dotted red lines delimit the quantiles for the Gold price. The bold red cross hair lines show where both the USD TWI and the Gold Price is at the most recent point.

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Weekly Changes in G10 FX Trade Weighted Indices

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%.

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Trade Weighted Currency Indices Stretch Map

Trade Weighted Currency Indices Report

Sat Feb 11 17:23:03 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.

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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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% Changes of GBPUSD across 250 to 5-day time-horizon

As a follow up of my previous post on boxplots I thought that I would expand my script to visualise the appreciation/depreciation of one specific values accross differnt time frames. In the below analysis I use the daily GBPUSD exchange rate that I grab from the Bank of England Website.

The blue dots represent the most recent observations for the given time frames, the orange dots are the outliers over the period 1975 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%.

The % change is presented in terms of USD relative to GBP. So from the below chart we can see that the USD appreciated by close to 17% against GBP which is within a 95% interval of confidence. And so on for teh other time frame….

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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.

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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                  1.25    4.51          -3.79    -5.85
## Annualized Standard Deviation     14.21   17.22          16.94    22.48
## Annualized Sharpe Ratio (Rf=0%)    0.09    0.26          -0.22    -0.26
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                        0.56             6.09  2.84
## Annualized Standard Deviation            9.74             9.69  6.92
## Annualized Sharpe Ratio (Rf=0%)          0.06             0.63  0.41
## 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).

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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.

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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.

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**Summary Performance Statistics

##                                 Benchmark 40Eq./60Bds Optimal Portfolio
## Annualized Return                                3.38              3.65
## Annualized Standard Deviation                    5.59              6.83
## Annualized Sharpe Ratio (Rf=0%)                  0.60              0.53
## Worst Drawdown                                   6.90             12.90

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2015-06-30 2016-02-29       <NA> -12.9        22     22        9
## 2 2013-05-31 2013-06-28 2014-02-28 -4.59        10     10        2
## 3 2010-09-30 2011-01-31 2011-09-30 -4.52        13     13        5
## 4 2012-04-30 2012-06-29 2013-02-28 -2.22        11     11        3
## 5 2014-03-31 2014-06-30 2014-08-29 -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 -5.7 -1.8  0.9 -0.1  1.6 -0.5  3.0  5.3 -0.7 -1.6 -3.5  3.0   -0.2
## 2017  0.3  1.8   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA    2.1

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

GBPUSD 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 GBP-USD over the period of January 1975 to February 2017 . On the 09 February 2017 it was trading around 1.2528188.

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(0,1,5) 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.

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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.

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At close of business the 2017-02-10 the VIX was trading at 10.8 at the 1.5 percentile. The 14-day VIX Volga was estimated at 8.2 its 14.1 percentile and the shockindex at 0.7 or its 48.7 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 57 % of the time in Cluster 1, 31 % 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.

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In the chart below we zoom on the various regimes within which the VIX has been trading for the current year. so far it traded 62 % of the time in Cluster 1, 19 % in Cluster 2, 20 % in Cluster 3 and 0 % in Cluster 4.

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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.

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