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.

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 -0.28 3.86 -4.58 -6.16
## Annualized Standard Deviation 14.75 17.70 17.67 22.95
## Annualized Sharpe Ratio (Rf=0%) -0.02 0.22 -0.26 -0.27
## Worst Drawdown 45.25 53.05 66.41 79.38
## Corporate Bds Inflation Linked Gilts
## Annualized Return -0.41 4.72 2.80
## Annualized Standard Deviation 9.71 8.84 6.67
## Annualized Sharpe Ratio (Rf=0%) -0.04 0.53 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).

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.

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.

***Summary Performance Statistics *

## Benchmark 40Eq./60Bds Optimal Portfolio
## Annualized Return 2.60 2.69
## Annualized Standard Deviation 5.28 6.57
## Annualized Sharpe Ratio (Rf=0%) 0.49 0.41
## 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 11 11 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 0.3 NA NA NA NA NA NA NA NA NA -7.1

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