Monthly Archives: December 2015

G10 FX Implied Volatilities: Cheap or Expensive ?

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

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

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

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

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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.

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At close of business the 2015-12-02 the G10 FX volatility index was estimated at 9.9 % at the 83.3 percentile. The 14-day G10 FX Volga was estimated at 5.3 % its 76.1 percentile and the shockindex at 0.7 or its 78.5 percentile.

The above charts are useful, however their visualisation is quite limiting. On the one hand we need quite a few charts to present the data on the other hand it is difficult to show the full 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 59 % of the time in Cluster 1, 30 % in Cluster 2, 8 % 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.

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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 66 % of the time in Cluster 1, 24 % in Cluster 2, 10 % 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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US MUTUAL FUND FLOWS REPORT UPDATE

Wed Dec 02 15:13:06 2015

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

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During the month of November we have seen flows of US$ -22.4Bn in Domestic equities,US$ -0.16Bn in international equities, US$ -4Bn in Hybrid products,US$ -5.83 Bn in taxable bond funds and US$ 2.1Bn in non taxable bond funds.

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The Charts below shows the distribution in percentage terms of the US$ -16.5Bn that have flowed into US$ Mutual funds over the last 12-month.

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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.

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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.

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AFX Index November Update: Good 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

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**Summary Performance Statistics **

##                                  AFX
## Annualized Return               3.20
## Annualized Standard Deviation   6.80
## Annualized Sharpe Ratio (Rf=0%) 0.47

Drawdowns Table

##          From     Trough         To  Depth Length To Trough Recovery
## 1  2010-11-30 2014-06-30 2015-01-30 -11.43        51     51       44
## 2  2004-01-30 2004-09-30 2008-10-31 -10.76        58     58        9
## 3  2015-04-30 2015-10-30       <NA>  -8.34         9      9        7
## 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  -6.37        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 -0.8  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  1.9  3.3  0.3   -5.8
## 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  0.2   11.5
## 2009 -1.1 -0.6 -2.2 -2.7  4.5 -0.7 -0.6 -0.7  1.6 -0.8  0.8 -0.7   -3.1
## 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   -1.1
## 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   NA   -2.3

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 .

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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.

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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                                 4.88
## Annualized Standard Deviation                     3.83
## Annualized Sharpe Ratio (Rf=0%)                   1.28
## Worst Drawdown                                    5.81
##                                 World ex Europe Stocks European Stocks
## Annualized Return                                 5.42            4.65
## Annualized Standard Deviation                    15.15           15.80
## Annualized Sharpe Ratio (Rf=0%)                   0.36            0.29
## 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.

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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.

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**Summary Performance Statistics **

##                                 Benchmark 60/40 Optimal Portfolio
## Annualized Return                          5.03              5.78
## Annualized Standard Deviation              6.34              4.52
## Annualized Sharpe Ratio (Rf=0%)            0.79              1.28
## 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         9      9        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   NA    4.5

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

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.

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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                8.85              10.62     10.43
## Annualized Standard Deviation    6.55              16.00     15.96
## Annualized Sharpe Ratio (Rf=0%)  1.35               0.66      0.65
## Worst Drawdown                  11.42              52.51     44.04

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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**Summary Performance Statistics **

##                                 Benchmark 60/40 Optimal Portfolio
## Annualized Return                          8.58              8.13
## Annualized Standard Deviation              7.86              5.90
## Annualized Sharpe Ratio (Rf=0%)            1.09              1.38
## 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   NA    1.5

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

US Investor Allocation Update

The following is a generic asset allocation report from the perspective of a US investor. I use the Barclay US all treasury index, the MSCI World ex US and the MSCI US 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.

plot of chunk Summary charts
The below summary performance statistics show that a US investor would have got the best risk adjusted return by holding a broad basket of US treasuries. 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. US stocks.

##                                 US Treasuries World Ex US Stocks US Stocks
## Annualized Return                        4.61               4.26      4.86
## Annualized Standard Deviation            4.55              17.37     15.31
## Annualized Sharpe Ratio (Rf=0%)          1.01               0.24      0.32
## Worst Drawdown                           5.01              59.39     52.92

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 costs of 0.25% of adjusted notional for each monthly rebalancement. The performance is compared to the return of a portfolio composed of 60% US treasuries and 40% US equities.

plot of chunk Opt_porfolio_charts

**Summary Performance Statistics **

##                                 Benchmark 60/40 Optimal Portfolio
## Annualized Return                          5.18              5.74
## Annualized Standard Deviation              5.69              4.95
## Annualized Sharpe Ratio (Rf=0%)            0.91              1.16
## Worst Drawdown                            19.43              7.29

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2007-12-31 2008-10-31 2008-12-31 -7.29        13     13       11
## 2 2009-01-31 2009-06-30 2010-06-30 -4.74        18     18        6
## 3 2003-06-30 2003-07-31 2004-02-29 -4.59         9      9        2
## 4 2015-08-31 2015-09-30       <NA> -4.57         5      5        2
## 5 2004-04-30 2004-05-31 2004-09-30 -3.31         6      6        2

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 2002  0.5  0.9 -2.2  2.1  0.6  1.1  2.2  2.1  2.4 -0.9 -0.8  2.2   10.1
## 2003 -0.3  1.6 -0.4  0.5  3.0 -0.5 -4.1  0.5  3.0 -1.2  0.1  1.3    3.4
## 2004  0.9  1.2  0.6 -3.1 -0.3  0.7  0.2  1.8  0.7  1.5  0.7  1.8    6.8
## 2005  0.1  0.5 -0.9  0.7  1.0  0.9 -0.4  2.0  0.7 -2.2  1.7  2.9    7.1
## 2006  3.9 -0.2  2.2  3.6 -3.0  0.0  0.9  2.1  0.4  2.1  1.9  0.7   14.6
## 2007  0.2  1.2  1.2  2.4  0.2  0.0  0.6  0.5  2.2  1.9  0.6 -0.5   10.4
## 2008 -0.9  1.1  0.2 -0.1 -0.4 -1.8 -0.5  0.3 -2.4 -2.4  5.0  3.5    1.6
## 2009 -3.2 -0.6  2.2 -1.9 -1.1 -0.2  0.4  0.9  0.8 -0.1  1.4 -2.7   -4.0
## 2010  1.6  0.4 -0.9  1.1  1.7  1.9  0.7  2.0  0.0 -0.2 -0.7 -1.8    5.8
## 2011  0.0  0.1 -0.1  1.3  1.4 -0.4  1.6  2.2  1.2 -0.1  0.5  1.0    8.6
## 2012  1.2  0.2 -0.1  1.0  0.1  0.4  1.1  0.3  0.2 -0.5  0.6 -0.3    4.3
## 2013  0.2  0.7  0.8  1.2 -1.3 -1.3  1.1 -1.1  1.4  1.6  0.4 -0.1    3.7
## 2014  0.3  1.3 -0.1  0.6  1.4  0.4 -0.5  1.9 -1.0  1.6  1.6  0.0    7.7
## 2015  0.3  1.0 -0.2 -0.1  0.3 -1.5  1.5 -3.6 -1.0  3.2 -0.1   NA   -0.2

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                  0.08    4.41          -4.23    -4.86
## Annualized Standard Deviation     14.96   17.92          17.86    23.16
## Annualized Sharpe Ratio (Rf=0%)    0.01    0.25          -0.24    -0.21
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                       -0.16             4.73  2.58
## Annualized Standard Deviation            9.87             8.80  6.65
## Annualized Sharpe Ratio (Rf=0%)         -0.02             0.54  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_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                                2.68              4.39
 Annualized Standard Deviation                    5.31              6.16
 Annualized Sharpe Ratio (Rf=0%)                  0.50              0.71
 Worst Drawdown                                   6.02              5.05

Drawdowns Table

      From     Trough      To      Depth   Length To Trough Recovery
 2015-06-29 2015-09-29       <NA> -5.05         7      7        4
 2013-05-30 2013-06-27 2014-02-28 -4.59        10     10        2
 2010-09-29 2011-01-31 2011-09-29 -4.52        13     13        5
 2012-04-29 2012-06-28 2013-02-28 -2.22        11     11        3
 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  NA    4.6

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

BIS Trade Weighted Indices Clusters

I have always been keen on clustering methods as they are a practical way to visualise meaningful relationships that may exist in the somehow chaotic financial markets….. I thought that I would apply such methodology to the trade weighted indices published by the BIS. Obviously this could easily be used within other context such as multi-asset, macro-fundamentals etc….if you want a natter about this or just to exchange some ideas on the subject, contact me at Pierre@argonautae.co.uk…

The following charts look how the monthly changes in the Trade weighted indices have correlated since January 2000.

plot of chunk correlation

The below plot the minimum spanning tree for the TWI indices. The distance between the nodes being a function of the above correlations. Some groupings are quite intuitive…some other less so…My R script uses visNetwork to provide a dynamic chart that can be manipulated…I will add further controls such as Zoom later…

EURUSD Calendar Heat Map

I stumbled on a few snippets of code that allow to display data into a really neat calendar heatmap. I merged some of my own code with it to calculate rolling T-Stats which I then bound within a -1/+1 interval by using a normal probability density function. So here is the result applied to the spot EURUSD …I can of course use that with any time series…so you may end up seeing a few more charts of those going forward….

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