Monthly Archives: May 2016

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.

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 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                        4.68               4.13      4.73
## Annualized Standard Deviation            4.52              17.35     15.27
## Annualized Sharpe Ratio (Rf=0%)          1.03               0.24      0.31
## Worst Drawdown                           5.01              59.39     52.92

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 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                          5.15              5.61
## Annualized Standard Deviation              5.66              4.93
## Annualized Sharpe Ratio (Rf=0%)            0.91              1.14
## 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        10     10        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 -0.9   -1.1
## 2016 -1.3  0.6  2.0  0.1   NA   NA   NA   NA   NA   NA   NA   NA    1.4

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.

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                                 4.83
## Annualized Standard Deviation                     3.83
## Annualized Sharpe Ratio (Rf=0%)                   1.26
## Worst Drawdown                                    5.81
##                                 World ex Europe Stocks European Stocks
## Annualized Return                                 4.84            3.93
## Annualized Standard Deviation                    15.08           15.77
## Annualized Sharpe Ratio (Rf=0%)                   0.32            0.25
## Worst Drawdown                                   62.58           55.81

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                          4.64              5.39
## Annualized Standard Deviation              6.32              4.55
## Annualized Sharpe Ratio (Rf=0%)            0.73              1.19
## 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        14     14        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   NA   NA   NA   NA   NA   NA   NA   NA   -0.8

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.

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                8.82              10.57     10.30
## Annualized Standard Deviation    6.55              15.92     15.88
## 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.

plot of chunk Opt_porfolio_charts

**Summary Performance Statistics

##                                 Benchmark 60/40 Optimal Portfolio
## Annualized Return                          8.52              8.09
## Annualized Standard Deviation              7.82              5.88
## 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 -1.1    0.4
## 2016  2.2  1.3  0.7 -0.8   NA   NA   NA   NA   NA   NA   NA   NA    3.4

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                 -0.25    3.76          -4.57    -5.58
## Annualized Standard Deviation     14.68   17.62          17.56    22.92
## Annualized Sharpe Ratio (Rf=0%)   -0.02    0.21          -0.26    -0.24
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                        0.02             4.54  2.73
## Annualized Standard Deviation            9.72             8.84  6.64
## Annualized Sharpe Ratio (Rf=0%)          0.00             0.51  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).

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                                2.54              2.73
## Annualized Standard Deviation                    5.25              6.53
## Annualized Sharpe Ratio (Rf=0%)                  0.48              0.42
## 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        12     12        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   NA   NA   NA   NA   NA   NA   NA   NA   -6.7

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

AFX Index April Update: Small up 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               3.06
## Annualized Standard Deviation   6.80
## 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 2016-03-31       <NA> -10.02        14     14       12
## 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
## 2016 -0.7  0.6 -0.6  0.6   NA   NA   NA   NA   NA   NA   NA   NA   -0.1

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

Trade Weighted Currency Indices Stretch Map

Trade Weighted Currency Indices Report

Tue May 03 22:46:56 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 arimaforecast

G10 FX Position Report Update

G10 FX POSITIONING REPORT

Tue May 03 22:48:09 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.

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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 39.18 % of maximum.

plot of chunk leverage