Category Archives: Asset allocation

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                  3.50    4.55          -3.51    -5.50
## Annualized Standard Deviation     15.86   17.08          16.83    22.35
## Annualized Sharpe Ratio (Rf=0%)    0.22    0.27          -0.21    -0.25
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                        0.69             6.28  3.06
## Annualized Standard Deviation            9.70             9.62  6.91
## Annualized Sharpe Ratio (Rf=0%)          0.07             0.65  0.44
## 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                                4.82              3.82
## Annualized Standard Deviation                    6.55              6.76
## Annualized Sharpe Ratio (Rf=0%)                  0.74              0.57
## Worst Drawdown                                   6.90             12.90

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2015-06-30 2016-02-29       <NA> -12.9        24     24        9
## 2 2013-05-31 2013-06-28 2014-02-28 -4.59        10     10        2
## 3 2010-09-30 2011-01-31 2011-09-30 -4.52        13     13        5
## 4 2012-04-30 2012-06-29 2013-02-28 -2.22        11     11        3
## 5 2014-03-31 2014-06-30 2014-08-29 -1.75         6      6        4

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 2010   NA   NA   NA -0.2  0.4  1.0 -0.9  4.4 -0.1 -2.6 -0.4  0.9    2.3
## 2011 -2.3  1.0  0.5  0.5  0.9 -0.6  2.0 -0.8  1.9  0.7  1.5  1.4    6.6
## 2012  1.7 -0.1  0.1 -1.9  0.2 -0.5  1.3  0.4 -0.7 -0.8  0.4  0.3    0.5
## 2013 -0.3  1.7  2.1  0.1 -1.4 -3.2  3.0 -1.4  1.1  1.1 -0.9  0.1    2.1
## 2014  0.7  1.9 -0.6 -1.0  0.7 -0.9  0.2  3.0 -1.7  1.5  4.6  0.4    8.8
## 2015  5.4  1.1  0.7 -1.0  2.7 -3.8  2.7 -3.3 -0.5  2.9 -2.2 -1.6    3.0
## 2016 -5.7 -1.8  0.9 -0.1  1.6 -0.5  3.0  5.3 -0.7 -1.6 -3.5  3.0   -0.2
## 2017  0.3  1.8  0.8  1.0   NA   NA   NA   NA   NA   NA   NA   NA    4.0

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                  3.46    4.54          -3.51    -5.51
## Annualized Standard Deviation     15.71   17.15          16.90    22.44
## Annualized Sharpe Ratio (Rf=0%)    0.22    0.26          -0.21    -0.25
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                        0.68             5.83  2.93
## Annualized Standard Deviation            9.73             9.69  6.95
## Annualized Sharpe Ratio (Rf=0%)          0.07             0.60  0.42
## 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                                4.71              3.44
## Annualized Standard Deviation                    6.38              6.81
## Annualized Sharpe Ratio (Rf=0%)                  0.74              0.51
## Worst Drawdown                                   6.90             12.90

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2015-06-30 2016-02-29       <NA> -12.9        23     23        9
## 2 2013-05-31 2013-06-28 2014-02-28 -4.59        10     10        2
## 3 2010-09-30 2011-01-31 2011-09-30 -4.52        13     13        5
## 4 2012-04-30 2012-06-29 2013-02-28 -2.22        11     11        3
## 5 2014-03-31 2014-06-30 2014-08-29 -1.75         6      6        4

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 2010   NA   NA   NA -0.2  0.4  1.0 -0.9  4.4 -0.1 -2.6 -0.4  0.9    2.3
## 2011 -2.3  1.0  0.5  0.5  0.9 -0.6  2.0 -0.8  1.9  0.7  1.5  1.4    6.6
## 2012  1.7 -0.1  0.1 -1.9  0.2 -0.5  1.3  0.4 -0.7 -0.8  0.4  0.3    0.5
## 2013 -0.3  1.7  2.1  0.1 -1.4 -3.2  3.0 -1.4  1.1  1.1 -0.9  0.1    2.1
## 2014  0.7  1.9 -0.6 -1.0  0.7 -0.9  0.2  3.0 -1.7  1.5  4.6  0.4    8.8
## 2015  5.4  1.1  0.7 -1.0  2.7 -3.8  2.7 -3.3 -0.5  2.9 -2.2 -1.6    3.0
## 2016 -5.7 -1.8  0.9 -0.1  1.6 -0.5  3.0  5.3 -0.7 -1.6 -3.5  3.0   -0.2
## 2017  0.3  1.8 -1.2   NA   NA   NA   NA   NA   NA   NA   NA   NA    1.0

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                  1.25    4.51          -3.79    -5.85
## Annualized Standard Deviation     14.21   17.22          16.94    22.48
## Annualized Sharpe Ratio (Rf=0%)    0.09    0.26          -0.22    -0.26
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                        0.56             6.09  2.84
## Annualized Standard Deviation            9.74             9.69  6.92
## Annualized Sharpe Ratio (Rf=0%)          0.06             0.63  0.41
## Worst Drawdown                          32.18            14.86  8.49

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

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                                3.38              3.65
## Annualized Standard Deviation                    5.59              6.83
## Annualized Sharpe Ratio (Rf=0%)                  0.60              0.53
## Worst Drawdown                                   6.90             12.90

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2015-06-30 2016-02-29       <NA> -12.9        22     22        9
## 2 2013-05-31 2013-06-28 2014-02-28 -4.59        10     10        2
## 3 2010-09-30 2011-01-31 2011-09-30 -4.52        13     13        5
## 4 2012-04-30 2012-06-29 2013-02-28 -2.22        11     11        3
## 5 2014-03-31 2014-06-30 2014-08-29 -1.75         6      6        4

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 2010   NA   NA   NA -0.2  0.4  1.0 -0.9  4.4 -0.1 -2.6 -0.4  0.9    2.3
## 2011 -2.3  1.0  0.5  0.5  0.9 -0.6  2.0 -0.8  1.9  0.7  1.5  1.4    6.6
## 2012  1.7 -0.1  0.1 -1.9  0.2 -0.5  1.3  0.4 -0.7 -0.8  0.4  0.3    0.5
## 2013 -0.3  1.7  2.1  0.1 -1.4 -3.2  3.0 -1.4  1.1  1.1 -0.9  0.1    2.1
## 2014  0.7  1.9 -0.6 -1.0  0.7 -0.9  0.2  3.0 -1.7  1.5  4.6  0.4    8.8
## 2015  5.4  1.1  0.7 -1.0  2.7 -3.8  2.7 -3.3 -0.5  2.9 -2.2 -1.6    3.0
## 2016 -5.7 -1.8  0.9 -0.1  1.6 -0.5  3.0  5.3 -0.7 -1.6 -3.5  3.0   -0.2
## 2017  0.3  1.8   NA   NA   NA   NA   NA   NA   NA   NA   NA   NA    2.1

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

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                  1.03    4.19          -4.00    -5.84
## Annualized Standard Deviation     14.31   17.35          17.06    22.61
## Annualized Sharpe Ratio (Rf=0%)    0.07    0.24          -0.23    -0.26
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                        0.60             6.08  2.97
## Annualized Standard Deviation            9.81             9.77  6.94
## Annualized Sharpe Ratio (Rf=0%)          0.06             0.62  0.43
## 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                                3.40              3.42
## Annualized Standard Deviation                    5.62              6.89
## Annualized Sharpe Ratio (Rf=0%)                  0.60              0.50
## Worst Drawdown                                   6.90             12.90

Drawdowns Table

##         From     Trough         To Depth Length To Trough Recovery
## 1 2015-06-30 2016-02-29       <NA> -12.9        20     20        9
## 2 2013-05-31 2013-06-28 2014-02-28 -4.59        10     10        2
## 3 2010-09-30 2011-01-31 2011-09-30 -4.52        13     13        5
## 4 2012-04-30 2012-06-29 2013-02-28 -2.22        11     11        3
## 5 2014-03-31 2014-06-30 2014-08-29 -1.75         6      6        4

Monthly Returns

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec YEARLY
## 2010   NA   NA   NA -0.2  0.4  1.0 -0.9  4.4 -0.1 -2.6 -0.4  0.9    2.3
## 2011 -2.3  1.0  0.5  0.5  0.9 -0.6  2.0 -0.8  1.9  0.7  1.5  1.4    6.6
## 2012  1.7 -0.1  0.1 -1.9  0.2 -0.5  1.3  0.4 -0.7 -0.8  0.4  0.3    0.5
## 2013 -0.3  1.7  2.1  0.1 -1.4 -3.2  3.0 -1.4  1.1  1.1 -0.9  0.1    2.1
## 2014  0.7  1.9 -0.6 -1.0  0.7 -0.9  0.2  3.0 -1.7  1.5  4.6  0.4    8.8
## 2015  5.4  1.1  0.7 -1.0  2.7 -3.8  2.7 -3.3 -0.5  2.9 -2.2 -1.6    3.0
## 2016 -5.7 -1.8  0.9 -0.1  1.6 -0.5  3.0  5.3 -0.7 -1.6 -3.5  3.0   -0.2

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                  0.64    3.99          -4.18    -6.46
## Annualized Standard Deviation     14.33   17.41          17.10    22.61
## Annualized Sharpe Ratio (Rf=0%)    0.04    0.23          -0.24    -0.29
## Worst Drawdown                    45.25   53.05          66.41    79.38
##                                 Corporate Bds Inflation Linked Gilts
## Annualized Return                        0.40             6.06  2.78
## Annualized Standard Deviation            9.82             9.63  6.95
## Annualized Sharpe Ratio (Rf=0%)          0.04             0.63  0.40
## 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                                3.02              3.29
## Annualized Standard Deviation                    5.58              6.73
## Annualized Sharpe Ratio (Rf=0%)                  0.54              0.49
## 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        19     19        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 -0.7 -1.6 -1.7   NA   -1.3

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

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

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                        4.71               4.10      4.98
## Annualized Standard Deviation            4.51              17.24     15.15
## Annualized Sharpe Ratio (Rf=0%)          1.05               0.24      0.33
## 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                          5.29              5.69
## Annualized Standard Deviation              5.61              4.89
## Annualized Sharpe Ratio (Rf=0%)            0.94              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 2016-06-30 -4.57        11     11        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  0.5  1.8  1.2 -0.4   NA   NA   NA   NA    4.5

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