In Part 1 of our 3 Part article titled “Creating a Powerful Blend from Scratch”, we commenced the portfolio optimization process by selecting our primary system upon which we would then apply diversification principles across instruments and asset classes to achieve a bigger bang for buck in terms of risk-weighted returns for our finite investment capital. Part 2 of this installment article focuses on how we go about this blending exercise.
Selecting the Ingredients and Back Test Horizon
In deciding where to start in our selection of instruments for this portfolio blend and in determining the extent of the back-test that we undertake to test for robustness, we will simply apply the following broad rules:
- Always use liquid instruments;
- Ensure that you do not focus your selection on any particular asset class. Asset classes by their very nature tend to comprise instruments that are highly correlated. As a Portfolio manager we are seeking low or better still un-correlated contributors to the blended composite to dampen the volatility of returns. As a result, ensure that you select your instruments paying attention to the need to achieve equal representation of instruments from each asset class;
- Use a back test horizon that captures as many different market conditions as possible to test for system robustness. In this example, we will be going back 7 years or so to 1 January 2010 as we unfortunately have a limited data history available. At least this 7 year period provides a significant period of time that includes a variety of different market conditions…..but the more data history you have over a greater variety of different market conditions….the better.
For the purposes of demonstration we will be blending a portfolio of 24 liquid instruments to showcase the power of diversification. You will see as we build the blend that while the marginal utility of additional instruments decreases with an increased portfolio universe (in other words, a portfolio of greater than say 20 instruments does not significantly improve risk-weighted returns), the more diversified you become means the less risk exposed you are to any single instrument (provided that they your instrument selection are generally uncorrelated).
Now many Portfolio Managers will say that there is no point to going beyond a 20 instrument universe across asset classes….but I beg to differ. We are seeking the most robust long term sustainable solutions so the more we diversify, the less risk exposed we become to the possible ‘Black Swan’ market conditions facing a single instrument.
Furthermore instrument (market) diversification allows you to span hundreds of different data series and only trade those market conditions where momentum is extreme and less likely to be simply a random price fluctuation. For example a big trend or momentum move on a single instrument may only occur 1-3 times a year….so with 100 different liquid data series, that may give you say 300 opportunities a year to only pull the trigger on the best examples. This feature ensures that the symptom of potential over-trading is reduced…which is one of the major reasons in an efficient market that a trader comes undone.
Anyway….without too much more waffling let’s get our hands dirty and start our foray into Portfolio Blending with two major Forex pairs….the almighty EURUSD and EURJPY. For the purposes of back-testing we will be using a great back-testing kit which quickly and accurately conducts back-tests within the Metatrader (MT4) environment.
Portfolio Blend – 2 Instruments (EURUSD + EURJPY)
Portfolio Return Streams (Equity Curve) – EURUSD + EURJPY
While the performance results are strong for this equal weighted blend of two Forex trading pairs, clearly the volatility of returns need to be dealt with. As more and more instruments are added to the portfolio we will see how we can smooth things off to create a wicked portfolio performer.
At this stage of the game with only 2 instruments included, diversification benefits are not significantly revealing themselves. The blend of instruments (adopting a 17 x position sizing multiplier) produces a 24.1% CAGR over the 7 year period with a maximum drawdown (albeit during tough mean reverting times for trend following) of 21.94%.
Now onto the 3rd instrument for inclusion, namely CADJPY.
Portfolio Blend – 3 Instruments (EURUSD + EURJPY + CADJPY)
Through the simple addition of CADJPY to the portfolio we have effectively doubled our CAGR to 47.1% for the 7 year period without adding to our drawdown which now lies at 21.02%.
It is worthwhile having a good look at the equity curve above as it reveals something about trend following (momentum) in terms of correlation. Over the extended time series we achieved benefits from fairly low correlation between the 3 instruments…….. but during particular periods of heightened volatility (Nov 2014 to Jan 2016), all 3 instruments became highly correlated. You need to keep in mind that while correlation is very useful as a tool to construct a portfolio, a better appreciation of how to use correlation is by visual analysis of the composite equity curves.
For example refer to the equity curves below of the individual contributors. I have highlighted periods of varying correlation of return distributions.
Still only early days as we have only 3 instruments tested with 21 to go. Hopefully this process of portfolio build gives you some great ideas on how to improve your overall performance returns using the power of diversification’s free lunch. Our ultimate aim is to smooth the equity curve and reduce the volatility of return distributions.
With the inclusion of 3 instruments we are starting to see the benefits of diversification kick in. Namely, the improved risk weighted returns associated with the flattening of the portfolio equity curve. Let’s see how we go with 4 instruments through the addition of XAUUSD (gold) which we recognise as possessing low correlation with respect to the majority of instruments contained in the Forex asset class.
Portfolio Blend – 4 Instruments (EURUSD + EURJPY + CADJPY + XAUUSD)
We have had to tame the multiplier a bit from 17x to 12x as we spread trading risk over more instruments and this is to be expected as we increase the size of the portfolio. Through the addition of XAUUSD we have further increased our CAGR from 47.1% to 50.1% for the 7 year period while slightly reducing our maximum drawdown from 21.02% to 20.33%. Now this might not seem much but let’s now have a look at the annual returns each year.
You will see that through the inclusion of this uncorrelated instrument to the portfolio, the poor periods of performance with a portfolio of 3 instruments such as 2011 (with 15.9% Gross return) now becomes a solid year of performance in 2011 for 4 instruments (with a 70.7% Gross return).
Let’s have a detailed look at the contributing equity curves to see why.
In those particular periods of time when the balance of the portfolio was in drawdown, XAUUSD and its negatively correlated nature came to the rescue delivering strong performance returns and assisting in flattening the portfolio’s equity curve.
Things are coming on nicely where the benefits of diversification are clearly beginning to take shape. With the addition of XAUUSD we saw CAGR lift to 50.1% for the 7.6 year period with a max drawdown of 20.33%.
If you closely look at the equity curves and how they blend through addition and subtraction you will see that clearly there is room for another negatively correlated instrument….so this provides a clue as to our next instrument for selection and testing………namely XAGUSD (Silver).
Portfolio Blend – 5 Instruments (EURUSD + EURJPY + CADJPY + XAUUSD + XAGUSD)
Through the addition of XAGUSD we have further increased our CAGR from 50.1% to 59.0% for the 7 year period while slightly reducing our maximum drawdown from 20.33% to 19.5% with some very attractive annual returns.
So where to now? What new instrument do we add to the mix to hopefully improve things further? It’s time to have a look at the contributing equity curves again.
Two weak spots have been identified that we would like to fill (refer to chart above). We obviously need to select a further instrument that is non-correlated to our instruments already that include Forex pairs and precious metals…..you guessed it…..now it’s time to add a few indices.
Next stop DJI30. Let’s see what further joy we can bring to the portfolio through diversification.
Portfolio Blend – 6 Instruments (EURUSD + EURJPY + CADJPY + XAUUSD + XAGUSD + DJI30)
Now let’s refer to the individual results of the DJI30 in isolation. A CAGR of 4.1%, a maximum drawdown of 6.8% and a risk weighted MAR ratio of 0.60. Not very impressive in isolation is it? Surely this relatively poor performer will not offer any significant performance benefits to the total performer?
Now it is easy to get complacent and assume that the performance results in isolation are no big deal….and hence drop that instrument and look for something with bigger bang for buck……but you need to be very aware that it is how this instrument contributes overall to portfolio robustness which is the critical ingredient…..and in this regard we need to remember that what we were searching for was an instrument that could fill the drawdown gaps. From such humble beginnings look what this individual contribution of DJI30 does to the overall performance metrics of the portfolio.
Through the simple addition of what appeared to be an average performer in isolation….we have accelerated our CAGR from 59.0% to 76.8% for the entire 7 year period while retaining our max drawdown to approximately 20% (19.1%) using a position multiplier of 14x.
That’s it…..take some time to digest this as it is a BIG DEAL.
Just look at the Gross annual returns below. Can you see any red in there? Sure we still need to subtract Holding Costs (eg. SWAP) and slippage from these backtest results….but there is more than enough joy to spread around.
We are flying high using a multiplier of 14x to produce a CAGR of 76.8% with a max draw of 19.1% for the period 1 Jan 2010 to 16 August 2017. Why bother diversifying any further with results like these….I hear you cry?
Well despite the euphoria we have the following to deal with:
- Our trade sample is still far too low (501 trades over 7 years or about 1 trade every 5 days on average) for our liking to give us the required confidence to commit large capital towards this strategy. We need to increase the sample size significantly to make us even more convinced that this exercise has not been a cherry picked one (hindsight bias or selection biased).
- For the purposes of deploying this strategy we are neutral in our preferred choice of instruments. Our only requirement is that it is tradable and highly liquid. The assumption that a particular market is more suited for mean reverting strategies or trending/momentum strategies is a red-rag to a bull for those with an understanding of market complexity and statistics. What may not be trending today, last year or 5 years ago…..may on a hairpin change market condition to a trending one.
Remember it is the fat tails that drive us….not the normal noise of the market…..and fat tails occur unpredictably in any market irrespective of its apparent ‘normal’ day to day machinations.
We may just have been lucky in our choice of 6 instruments for the portfolio from a vast potential universe to select from. It is only through greater diversification and the Law of Large numbers that any statistical aberration from selection bias will be smoothed out. Think of a biased coin………..How many tosses does it take to determine the coin has a bias? Well there is no finite answer apart from the tendency for the bias to be detected as the sample size increase. This is the principle we need to take to our portfolio construction.
So given that we need to diversify further, where to now. What new instrument do we add to the mix to hopefully improve things further?
Let’s review the individual returns of the portfolio to search for clues.
The DJI30 certainly nailed the weak patches of the equity curve….but there is room for more drawdown reduction between October 2013 and December 2013……mmmmmmm……..more equities……so let’s see how the FTSE contributes to the growing portfolio.
Now the moral of the story for our next instrument inclusion (FTSE) leaves us with some critical ideas that are essential in the portfolio creation story. Here are two extremely important points that you need to remember when portfolio blending……which is counter-intuitive to a trader simply trading a single instrument for their livelihood.
- Firstly do not assume that just because an instrument delivers a negative overall return that it might not assist in stabilizing the volatility of returns of a broader portfolio. As a broad assumption you actually do not need each individual return stream to have a positive slope. The key take-out is to focus on the correlation contribution that an additional instrument makes to the overall portfolio and NOT necessarily its profit contribution.
- Our focus is on risk management and NOT profits. Remember that for a market with ‘fat tails’ which does not necessarily conform to a Gaussian distribution, that by simply strictly managing risk at all times and letting profits run….you are virtually guaranteed with the Law of Large Numbers that in the longer term you will be profitable. Follow this principle and you will not be disappointed. Remember that the vast majority of traders out there cannot get this into their skulls and that is why trend following/momentum will endure in the long term.
Ok….now let’s get into it……let’s see what the FTSE brings to the mix.
Portfolio Blend – 7 Instruments (EURUSD + EURJPY + CADJPY + XAUUSD + XAGUSD + DJI30 + FTSE)
First, look at the results of the FTSE in isolation. A terrible result with a CAGR of -1.8%, a maximum drawdown of 18.9% and a MAR ratio of -0.09. Surely we should not be considering including this poor performer in the portfolio?
Well just to demonstrate the key points raised previously in regards to portfolio blending that is very counter-intuitive in nature, look now at the result for the overall portfolio.
Despite the inclusion of a poor performer and applying a 14 x position size multiplier across the entire portfolio, the CAGR was 74.0% (previously 76.8%)…so a slight reduction in $….but here is the kicker….the max draw was only 17.3% (previously 19.1%). So pound for pound in terms of the MAR ratio (CAGR/Drawdown) our risk weighted return is now 4.29x as opposed to the previous 4.02x……. I bet you didn’t think that would occur?
What in effect has happened is that the *relatively* small losses associated with FTSE have less detrimentally affected the entire portfolio that the *relatively* large gains in reduced drawdown……nifty eh!
Now up to this point we have probably provided enough practical demonstration to allow the reader to start blending their own secret recipes themselves…….however we will now take you to the tail end of this blending exercise where we have blended 24 individual instruments that in isolation address the portfolio weaknesses and together help to make a robust performer with excellent risk-weighted returns.
What you will notice as you progressively diversify your portfolio is that at a point in time, adding to the blend does not necessarily materially affect the underlying performance metrics…..this is a good sign that you have avoided over-fitting…….while there is little change to performance, what is being achieved in this technique is a growing sample size, increased trade frequency and a commensurate reduced trade risk % ……..plus this process of diversifying the blend has built your confidence levels in recognizing that this technique is applicable to any liquid instrument. As a result, you do not need to worry that your instrument choice reflects selection bias.
So where did we end up? For the purposes of this practical demonstration we called it a day at 24 instruments drawn from a broad spectrum of different asset classes.
Here are the preliminary results.
Portfolio Blend – 24 Instruments
Test Period – 1st January 2010 to 16th August 2017
Trade sample size: 1,176
Win Ratio: 43.8%
Maximum Drawdown: 11.6%
MAR ratio: 5.28
Portfolio Composition Return Profiles
Having compiled a blend that we are comfortable with, before we can pluck the courage up to launch into our live trading, now comes the time to remove any bullish euphoria and focus on the reality of live trading. We do this to dampen our expectations and ensure our risk weightings are correctly applied for live conditions. This is where the brutal reality of the frictional costs of trading need to take center stage….as we inevitably incur additional costs to that anticipated from our back tests attributed to the realities of live trading.
Stay tuned for Part 3 of this installment article of “Creating a Powerful Portfolio Blend from Scratch” where we need to dampen down our performance expectations to take into account the realities of live trading as compared to the results of back-testing.
Trade well and prosper