Let’s have a big shout out for all the divergent traders in da house….say Hey…”*Hey”*…..say Ho…”*Ho”*…say Hey Hey…… “*Hey Hey”*…say Hey Ho……”*Hey Ho”. *Today we will be mixing some beats…aka return streams…….. and looking at how we as producers in the Lab turn up or down a few dials and remix those beats at the portfolio level into high energy masterpieces.

So can you dig it?……I can’t hear you?………can you dig it?……Well it goes a little something like dis….hit it!!!!!

So the chart below represents a raw portfolio for a single momentum breakout system applied across 24 different assets between 1 Jan 2010 and 31 Jan 2019 on the M30 timeframe. The system applies the fixed fractional method on position sizing which therefore adjusts the position size of an entry decision based on current short term volatility levels……so at the individual return stream level, market volatility has already been taken into account. In super volatile market conditions, position sizes are small and in low volatility regimes, position sizes are larger. Position sizes adjust fairly quickly to volatility given the relatively short term look-back. So here is the raw portfolio result.

**Chart 1: Raw Portfolio Result – 24 Separate Return Streams**

Looks quite good as a total result doesn’t it? What is more surprising however are the equity curves of the individual return streams that comprise it.

**Chart 2: Raw Portfolio Result – Individual Return Streams of the Portfolio**

Have a closer look at tome of those return streams. Some are downright awful……however here is the important thing to note. If you elect to switch any of those poor performers off, you are automatically curve fitting the result by applying selection bias.

Let’s understand what is happening here. In the price following divergent space, we interpret the result as how the system performs against different data sets. We do not make any assessment of the nature of the data set itself….provided that each return stream is liquid and has positive skew. For example, we make no assumptions to whether we are trading grains, Forex, bonds, or metals. They simply represent different ways in which liquid data is presented to a system.

In the world of risk management we don’t care about causes or reasons of data difference as we do not attempt to apply any form of ‘selection bias’ in our future choices. Rather we care about methods that are used to lessen the impacts of adverse return streams on the overall portfolio.

Unfortunately in avoiding any form of selection bias, we must accept these return streams for what they are. It is in how they compile that is most important….and we have Chart 1 as our representative guide for the risk inherent in the entire portfolio.

So let’s now have a closer look at the performance results of the Raw Portfolio in Chart 1. We have a CAGR of 16.82% and a maximum drawdown over the period of 13.90%. Now we need to note that these results are non-compounded. In other words we have applied a fixed % of risk to each trade based on our commencing levels of equity. We are therefore not leveraging this result in the future from improved performance results. This is a very wise conservative method to apply in this game as unless you know what you are doing, the nature of compounding significantly exacerbates any volatility that is lying in that raw portfolio return stream.

Let’s see what happens by turning up the leverage dials and compounding this solution on a monthly basis. We do this by simply adjusting the fixed fractional position sizing applied to each system on a monthly basis using a multiplier that calculates the change in monthly equity. So let’s have a look at the compounding impact on the raw portfolio return stream.

**Chart 3: Compounded Result – 24 Separate Return Streams**

Ouch…… If you like pogo sticks…then perhaps you can handle that volatility…..but I certainly can’t. If you compound your portfolio you find that over the course of time the future disaster waiting to happen will happen. If you attempt to volatility adjust this compounded result, then once again you fall into a form of selection bias….or market timing bias. Unless you really know what you are doing….it is not advised.

Compounding like any form of leverage is a two edged sword. It progressively exacerbates the volatility present in a return stream. Initially it is not so bad….but over time as the equity builds the magnification present through leverage makes small volatility movements very large indeed.

So what are the other ways to improve the overall portfolio result without having to leverage yourself to death through compounding to do this?

Well if you like higher returns but can accept higher volatility you could return to your raw portfolio result and simply adopt 2x the leverage present in each return stream to effectively double the returns. You do not compound the solution over time but rather double the performance and volatility from the outset.

So what was originally a CAGR of 16.82% with a max draw of 13.90% under a 2x position sizing multiplier across the series becomes an approximate CAGR of 33.64% with a max draw of 27.8%. This is a far better result than the monthly compounded result of a CAGR of 32.07% and Max Draw of 55.05%……..so yes that is an option for those that like better bang for buck……….but there are still better options and they tend to work best together.

So what is this secret sauce to juicing up the mix?

The answer lies in both:

- Further Diversification; and
- Risk weighting the global portfolio.

Let’s look at further diversification first.

# Further Diversification

So now let’s compare and contrast the result of 24 separate return streams of Chart 1 versus 38 separate return streams of Chart 4.

**24 Return Streams: CAGR 16.82% Draw 13.90% MAR 1.21****38 Return streams: CAGR 20.24% Draw 10.43% MAR 1.94**

**Chart 4: Raw Portfolio Result – 38 separate return streams**

You can see how increasing diversification using a strategy with an edge improves the overall risk-weighted result as the array of data sources thrown at the strategy increase. That is what we mean by an edge. The ability of your strategy to perform against unseen data.

So now let’s apply a 2x position sizing multiplier across the expanded portfolio as opposed to a compounding method. Let’s see what we can achieve…..and put those headphones on.

**38 Return Streams x2: CAGR 40.48% and Max Draw of 20.86%**…….Kappoooowwwwww!!!

Now there is no guarantee that increasing diversification will improve the result….but there is a guarantee when an edge is present in your system. That’s when the ‘free lunch of a diversified portfolio’ kicks in……but if an edge is not present, you will get a soggy sandwich as opposed to any free lunch.

If you find that by diversifying into different data sets that the overall result declines, then that is a sure fire sign that your strategy does not actually have the necessary edge you need in this game. If your portfolio result improves through the addition of new data sets to the equation, then you know that it is the edge in your system that is actually contributing to this result.

# Risk Weighting at the Global Portfolio Level

If we look at each of the individual return streams of Chart 2 we will notice that each return stream has a characteristic CAGR to Max Draw relationship. The ratio used to express this relationship is the MAR ratio. Some return streams are more inherently volatile than others. As a result,some return streams unduly bias their impact on the overall portfolio. We want to remove this bias and standardise the volatility of each return stream.

Under a risk-weighted scenario, we want to make each return stream contribute an equal max drawdown to the overall portfolio so we apply a multiplier to the position size of the strategy to allow for a consistent max drawdown for each return stream over the testing period.

So this is the result we obtain by applying a risk weighting to the 24 individual strategies of the raw portfolio.

Now what needs to be remembered here is that our risk weighted assessment of the return streams is made in January 2019 based on an approximate 10 year history of return streams so the result in effect is cherry picked and reeks of selection bias in the weighting applied……however the important note to remember is this……. If you rebalance your portfolio at regular intervals using a rolling historical window of return streams your overall result will fit **somewhere between the Raw portfolio result and the Risk Weighted Portfolio Result…**as the raw result and the optimal risk weighted result are simply the spectral extremes. The actual result from re-balancing over the time series will plot somewhere hopefully mid-range between it ..so the method works…….but don’t be deceived into thinking you could have achieved the optimal risk weighted result shown in this chart.

Let’s compare and contrast the Raw Portfolio Result and the Risk Weighted Portfolio Result and include a likely assessment that plots somewhere between the two results.

**Raw Portfolio – 24 Return Streams: CAGR 16.82% Draw 13.90% MAR 1.21****Theoretical Risk Weighted Portfolio – 24 Return Streams: CAGR 12.59% Draw 5.77% MAR 2.18****Likely Risk-Weighted Result – 24 Return Streams : CAGR 14.00% Draw 8.00% MAR 1.75**

# Diversification Plus Risk Weighting

So let’s put both diversification principles and risk weighting principles to work to make that perfect funky beat.

**Raw Portfolio – 38 Return Streams: CAGR 20.24% Draw 10.43% MAR 1.94****Theoretical Risk Weighted Portfolio – 38 Return Streams: CAGR 18.18% Draw 4.30% MAR 4.23****Likely Risk-Weighted Result – 38 Return Streams : CAGR 19.00% Draw 7.00% MAR 2.71**

Okay funksters…..let’s turn up the dials on this one with a 2x position size increase………..are you ready for it………are you ready for it…………..here we go……..

**38 Return Streams x2: CAGR 38.00% and Max Draw of 14.00%**…….*Warning, warning, warning, too juiced…..too juiced…can’t compute!!!!!!*

Trade well and prosper

Rich B