JPY TWI 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 JPY TWI over the period of January 1990 to September 2016 . On the 23 September 2016 it was trading around 152.1843.

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(3,1,2) 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

GBP TWI 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 TWI over the period of January 1990 to September 2016 . On the 23 September 2016 it was trading around 77.4078.

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(0,1,0) 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

Mon Sep 26 22:22:12 2016

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.

plot of chunk linechart

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.

plot of chunk rolling chart

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.

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

plot of chunk correlation
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.

plot of chunk arimaforecastplot of chunk arimaforecastplot of chunk arimaforecast

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 2016-09-23 the VIX was trading at 12.3 at the 10.8 percentile. The 14-day VIX Volga was estimated at 23 its 84.1 percentile and the shockindex at 1.7 or its 95 percentile.

The above charts are useful, however their visualisation is quite limiting. On the one hand we need quite a few charts to present the data on the other hand it is difficult to show the full VIX history going back to 1990 as this would make the charts unreadable. Therefore clustering and aggregating the whole data into a single chart should be useful to the end user. To answer this I use a mapping technique developed by Kohonen in the 1980′. It uses an unsupervised neural network to re-arrange data around meaningful clusters. Though computationally complex is a practical way to summarise multidimensional data into a low (usually 2) dimensional system.

The below chart shows how the VIX price history was split into 4 distinct clusters. Those clusters where computed not only as a function of the VIX level but also as a function of the other variables, namely VIX volga and Shockindex.

Since 1990 the VIX traded 59 % of the time in Cluster 1, 29 % in Cluster 2, 9 % in Cluster 3 and 2 % in Cluster 4. Overall the layering provided seems quite intuitive as the increase in risk and time spent in each cluster points toward what would generally be expected from market risk regimes ranging from low to high risk.

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 65 % of the time in Cluster 1, 19 % in Cluster 2, 15 % 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.co.uk

JPY TWI 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 JPY TWI over the period of January 1990 to September 2016 . On the 06 September 2016 it was trading around 149.6833.

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(3,1,2) 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

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 2016-09-06 the VIX was trading at 12 at the 8.4 percentile. The 14-day VIX Volga was estimated at 8.4 its 15.2 percentile and the shockindex at 0.7 or its 50.3 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. 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.co.uk

US MUTUAL FUND FLOWS REPORT UPDATE

Wed Sep 07 21:51:43 2016

Fund flows are important as they reflect the general investor preference for a specific asset class given current and expected economic conditions and market risk. They may also highlight non-sustainable market positioning. The ICI in the US tracks about 98% of the inflows and outflows in US mutual funds and makes its data freely available on its website. The following is a summarised report of the data it publishes every Wednesday. The first charts shows the cumulative inflows/outflows in each of the asset classes buckets since 2007

plot of chunk cumulative

During the month of August we have seen flows of US$ -26.5Bn in Domestic equities,US$ -7.72Bn in international equities, US$ -0.091Bn in Hybrid products,US$ 19.1 Bn in taxable bond funds and US$ 6.97Bn in non taxable bond funds.

plot of chunk month to date
The Charts below shows the distribution of the US$ -195Bn that have flowed into US$ Mutual funds over the last 12-month.

plot of chunk distribution

The below charts show the monthly inflows/outflows for each type of fund and plot them both within their 95% confidence intervals and also relative to their historical distribution. This provides a level of information in respect of how “out of line” or not the current month inflows/outflows may be relative to their past history. In the distribution charts The current month is highlited in blue whereas the vertical red lines represent the 95% confidence intervals.

plot of chunk flowdistribution

The chart below plot the inflows/outflows T-statistics for each of the funds cathegories considered. The Map chart provides information for period ranging from 2 years to 3 months.The greater the square the more important the inflows (green) outflows(red) over a given period.

plot of chunk flowmap

UK Investor Allocation Update

The below is a generic asset allocation report produced from the perspective of a UK investor. I use the Barclay UK Gilts all maturities index, the MSCI World ex UK and the MSCI UK Gross indices (i.e dividends re-invested) as proxies for bonds and equities holdings. As time goes I will add a few more asset buckets such as EM, commodities and properties. So see this as a first attempt to an evolutive product.

The below charts shows the rolling 36-month return, volatility and risk adjusted return for each of the assets used in the final portfolio. Clearly equities 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 below summary performance statistics show that a UK investor would have got the best risk adjusted return by holding a broad basket of Gilts. Over the long term the returns would have been quite similar accross asset classes. However the risk as expressed by the annualised volatility of the monthly returns and the maximum drawdown would have been at it highest for equities and particularly for World Ex. UK stocks.

##                                 Gilts World Ex UK Stocks UK Stocks
## Annualized Return                9.09              10.91     10.48
## Annualized Standard Deviation    6.59              15.90     15.82
## Annualized Sharpe Ratio (Rf=0%)  1.38               0.69      0.66
## Worst Drawdown                  11.42              52.51     44.04

In the following I use a mean-variance model to compute the weights of the portfolio that maximises the information ratio on the efficient frontier.The model is optimised for “long only” and weights adding to one constraints. I use 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.

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_chart
Using the above weights I then calculate the return of the portfolio for the folowing period assuming a cost of 0.25% of adjusted notional for each monthly rebalancement. The performance is compared to the return of a portfolio composed of 60% Gilts and 40% UK equities.

plot of chunk Opt_porfolio_charts

**Summary Performance Statistics

##                                 Benchmark 60/40 Optimal Portfolio
## Annualized Return                          8.78              8.38
## Annualized Standard Deviation              7.83              5.94
## Annualized Sharpe Ratio (Rf=0%)            1.12              1.41
## Worst Drawdown                            13.54             11.26

Drawdowns Table

##         From     Trough         To  Depth Length To Trough Recovery
## 1 1994-01-31 1994-05-31 1995-05-31 -11.26        17     17        5
## 2 1990-01-31 1990-04-30 1990-11-30  -9.49        11     11        4
## 3 1986-09-30 1986-09-30 1987-01-31  -6.06         5      5        1
## 4 2009-01-31 2009-01-31 2009-08-31   -5.1         8      8        1
## 5 2008-01-31 2008-06-30 2008-12-31  -5.07        12     12        6

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 1984  1.6 -1.9  4.1  0.2 -4.4  1.7 -1.6  7.0  2.9  2.1  2.1  0.9   14.6
## 1985  1.6  1.8 -1.1  0.7  1.4  0.2  1.1  1.8  1.2  1.0  0.8  0.8   11.3
## 1986 -0.1  5.0  7.2  1.9 -0.2 -0.5  0.2  2.4 -6.1  1.0  0.0  3.1   13.9
## 1987  3.6  2.9  3.2  2.2  1.3 -1.0 -1.1 -0.5  0.6 -2.3 -0.4 -0.3    8.1
## 1988  2.9  2.0  1.0 -0.1  0.4  0.3  1.0 -1.7  2.7  1.8 -1.8  1.5   10.0
## 1989  3.2 -0.3  0.8  0.8  0.0  0.8  3.5  0.6 -1.3  0.8  0.1  1.9   11.1
## 1990 -3.5 -2.1 -2.5 -1.7  5.8  2.0 -0.3 -1.3 -0.8  3.9  3.0  0.3    2.8
## 1991  3.7  1.9  1.2  0.4  0.3  0.3  2.3  1.9  2.4  0.4 -0.4  1.3   15.8
## 1992  2.5  1.3 -2.4  4.1  2.1 -0.4 -0.2 -1.0  4.0  5.2 -1.0  2.5   16.6
## 1993  1.3  2.2  0.8 -1.3  0.5  3.3  2.4  3.4  0.1  1.3  1.9  3.6   19.8
## 1994 -0.1 -3.6 -3.3 -1.1 -3.7  0.5  1.4  0.9 -1.2  1.0  2.1 -0.5   -7.4
## 1995  1.1  0.5  1.4  1.3  3.6 -2.2  2.3  1.4  0.4  1.2  3.7  1.3   15.9
## 1996  0.9 -1.9  0.2  1.9 -0.5  1.6 -0.1  0.7  2.1  0.0  2.3 -0.9    6.3
## 1997  2.3  1.1 -1.7  1.9  2.2  1.0  1.6  0.0  3.8  0.2  0.6  1.8   14.8
## 1998  1.9  0.2  1.7  0.9  1.2 -0.3  0.9  3.1  3.2  0.0  3.1  2.2   18.1
## 1999  1.1 -1.7  0.8  0.1 -1.6 -0.1 -1.0  1.2 -2.2  2.1  1.6 -0.5   -0.2
## 2000 -1.7  1.7  1.4  0.9  0.5  0.4  0.0  0.0  0.4  1.0  1.8  0.6    7.2
## 2001  0.5 -0.4 -0.3 -0.9 -0.6 -0.4  1.9  1.1 -0.9  3.3 -0.2 -2.0    1.0
## 2002  1.2 -0.4 -1.5  0.7 -0.1  1.2  0.2  2.2  0.3  0.1 -0.1  1.0    4.7
## 2003  0.3  1.0 -0.6  1.2  2.4 -0.5 -1.1  0.4  0.4 -1.4  0.4  2.4    4.7
## 2004 -0.4  1.0  0.5 -0.7 -0.9  1.1  0.1  1.6  1.1  1.0  1.3  0.8    6.6
## 2005  0.1 -0.1  0.3  0.9  2.3  1.6  0.0  1.1  0.3 -0.4  1.8  1.6    9.6
## 2006  0.9  0.3 -0.6 -1.2 -0.7  0.0  1.3  0.9  0.6  1.2  0.0 -0.6    2.1
## 2007 -1.3  1.4 -0.2  0.3 -0.3 -1.0  1.2  1.1  0.7  1.6  0.2  1.5    5.1
## 2008 -2.0  0.3  0.2 -0.1 -1.3 -2.2  1.4  2.7 -2.3 -1.1  3.9  5.0    4.4
## 2009 -5.1  0.2  2.7 -0.1 -0.3  0.4  0.3  4.2  0.7 -0.4  1.2 -2.0    1.6
## 2010  0.1  0.1  1.4  0.4  1.5  0.8  0.5  4.0  0.2 -1.0 -0.8  0.6    7.7
## 2011 -1.8  1.0  0.2  2.1  1.0 -0.6  2.7  0.5  2.4  2.4  1.7  1.6   13.2
## 2012  0.7 -0.5 -0.6 -0.3  2.8 -0.1  1.9  0.1 -0.3 -0.6  1.1 -0.2    4.0
## 2013  0.5  2.0  1.9  1.0 -1.1 -2.6  2.2 -2.1  0.7  1.8 -0.7 -0.6    2.9
## 2014  0.6  1.0  0.2  0.4  1.4 -0.5  0.7  3.5 -0.9  1.3  3.3  0.8   11.8
## 2015  4.0 -2.1  1.6 -1.1  0.6 -3.5  1.9 -1.6  0.2  0.5  0.9 -1.1    0.4
## 2016  2.2  1.3  0.7 -0.8  1.5  5.8  2.4  2.4   NA   NA   NA   NA   15.5

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

European Investor Allocation Update

The following is a generic asset allocation report produced from the perspective of a EU investor. I use the Barclay EURO Governement all maturities index, the MSCI World ex Europe and the MSCI EUrope Gross indices (i.e dividends re-invested) as proxies for bonds and equities holdings. As time goes I will add a few more asset buckets such as EM, commodities and properties. So see this as a first attempt to an evolutive product.

The below charts shows the rolling 36-month return, volatility and risk adjusted return for each of the assets used in the final portfolio. Clearly equities 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 below summary performance statistics show that a EU investor would have got the best risk adjusted return by holding a broad basket of European Governement Bonds. Over the long term the returns would have been quite similar accross asset classes. However the risk as expressed by the annualised volatility of the monthly returns and the maximum drawdown would have been at it highest for equities and particularly for World Ex. Europe stocks.

##                                 Euro Governement Bonds
## Annualized Return                                 4.96
## Annualized Standard Deviation                     3.83
## Annualized Sharpe Ratio (Rf=0%)                   1.29
## Worst Drawdown                                    5.81
##                                 World ex Europe Stocks European Stocks
## Annualized Return                                 5.20            3.99
## Annualized Standard Deviation                    14.98           15.68
## Annualized Sharpe Ratio (Rf=0%)                   0.35            0.25
## Worst Drawdown                                   62.58           55.81

In the following I use a mean-variance model to compute the weights of the portfolio that maximises the information ratio on the efficient frontier.The model is optimised for “long only” and weights adding to one constraints. I use 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.

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_chart
Using the above weights I then calculate the return of the portfolio for the folowing period assuming a cost of 0.25% of adjusted notional for each monthly rebalancement. The performance is compared to the return of a portfolio composed of 60% Euro Gov. Bonds and 40% Euro equities.

plot of chunk Opt_porfolio_charts

**Summary Performance Statistics

##                                 Benchmark 60/40 Optimal Portfolio
## Annualized Return                          4.76              5.58
## Annualized Standard Deviation              6.27              4.53
## Annualized Sharpe Ratio (Rf=0%)            0.76              1.23
## Worst Drawdown                            22.62              9.39

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2007-11-30 2008-06-30 2009-08-31 -9.39        22     22        8
## 2 2015-04-30 2015-09-30       <NA> -8.16        18     18        6
## 3 2010-09-30 2011-03-31 2012-01-31  -5.8        17     17        7
## 4 2013-05-31 2013-06-30 2013-10-31  -2.2         6      6        2
## 5 2006-03-31 2006-05-31 2006-08-31 -2.17         6      6        3

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 2002  0.6  0.0 -0.8  0.6  0.0  1.0  1.0  1.3  1.4 -0.3  0.7  1.6    7.0
## 2003  0.9  1.0 -0.4  0.2  2.1  0.1 -1.4  0.4  1.3 -1.0 -0.3  1.3    4.3
## 2004  0.6  1.4  0.8 -0.9 -0.5  0.7  0.7  1.2  0.5  0.9  1.3  0.8    7.6
## 2005  1.3 -0.3  0.5  1.2  1.4  1.3 -0.1  0.9  0.5 -1.4  0.5  1.3    7.2
## 2006  0.0  0.6 -0.3 -0.2 -1.7  0.1  1.3  1.7  1.0  1.5  0.2  0.5    4.7
## 2007  0.5 -0.2  0.7  1.5  0.6 -0.5 -0.6  0.3  0.3  1.6 -1.5 -0.8    1.8
## 2008 -2.8  0.2 -1.2  0.7 -0.9 -3.5  0.8  1.3 -1.5  0.9  3.7  1.2   -1.0
## 2009 -1.1  0.8  1.2  0.6 -1.2  1.2  1.8  0.5  0.6  0.1  0.6 -0.8    4.2
## 2010  0.5  1.2  0.6 -0.7  1.1 -0.3  0.9  2.6 -1.2 -0.5 -2.6 -0.3    1.4
## 2011 -0.5  0.2 -1.0  0.3  1.0 -0.5  0.1  1.9  0.6 -1.2 -1.6  3.9    3.2
## 2012  2.6  1.8  1.0 -0.2  0.4  0.0  2.7  0.3  1.0 -0.3  1.1  0.6   11.0
## 2013  0.2  1.9  2.2  1.6 -0.3 -1.9  1.4 -1.1  1.1  2.2  0.9  0.0    8.4
## 2014  0.9  1.0  0.9  0.6  2.0  1.4  1.2  2.7  1.0  1.3  1.8  1.5   16.2
## 2015  3.1  2.7  1.9 -1.8 -0.1 -3.4  2.4 -5.1 -0.2  3.3  1.8 -2.3    2.2
## 2016 -1.2  0.5  0.7 -0.9  1.6  1.9  1.2 -0.2   NA   NA   NA   NA    3.7

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

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                  0.76    4.31          -3.86    -5.70
## Annualized Standard Deviation     14.44   17.55          17.25    22.74
## Annualized Sharpe Ratio (Rf=0%)    0.05    0.25          -0.22    -0.25
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                        1.27             6.59  3.70
## Annualized Standard Deviation            9.75             9.64  6.77
## Annualized Sharpe Ratio (Rf=0%)          0.13             0.68  0.55
## 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                                3.92              4.04
## Annualized Standard Deviation                    5.46              6.72
## Annualized Sharpe Ratio (Rf=0%)                  0.72              0.60
## Worst Drawdown                                   6.90             12.90

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2015-06-29 2016-02-29       <NA> -12.9        17     17        9
## 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 -5.7 -1.8  0.9 -0.1  1.6 -0.5  3.0  5.3  0.3   NA   NA   NA    3.0

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