To Infinity and Beyond – Making the Most of your Finite Capital
One of the most overlooked aspects of retail trading is the efficient deployment of trading capital.
According to many ‘wise old trading sages’ you may hear in some notable trading books and on many a trading forum such mantras as “only risk 1%-2% of your trading equity per trade”….or something thereabouts. This advice means well and is more a statement about capital protection and living to fight another day….however if you take the time to invest your efforts in portfolio management, you will see how this ‘sage advice’ unfortunately significantly caps your aspirations to make better use of your finite capital.
This article titled “To Infinity and Beyond’ provides a recipe to the trader seeking to compound their net wealth through the use of sound portfolio management principles that address the risk inherent in a number of return streams. It is not about picking the systems offering the best returns, but rather the process of how you go about managing the volatility of a variety of return streams that have a slight edge which then allow you to compile a robust selection of trading strategies that can navigate a broad array of different market regimes. Once you have achieved this aim, this is when you can reach to ‘infinity and beyond’ through position sizing and effective capital allocation in delivering a large ‘bang for buck from your limited $’.
Shortly we will be releasing some trading tools on our website that will assist the trader in expertly crafting their own robust portfolios using the techniques explored in this article, but before we do, it is time to think beyond the trading system itself as a panacea for your woes, and invest your thoughts in the power of portfolio magic.
So before we get started, we shall take a quick overview of the major principles we need to take into account when we compile a diversified portfolio.
What is a Return Stream?
Now we use the term ‘return stream’ quite a bit in this article so it is best to understand what it is. For any asset whose value alters over time, the return stream is a running statement of the appreciation or depreciation of the price of that asset. From art works to precious metals, to stock values, to ‘you name it’…….. every financial asset offers a return stream over time which may comprise an income yield and a component associated with capital appreciation or depreciation. The techniques that we deploy in this article are far reaching and can be deployed to a vast array of financial products each of which produce a return stream that uniquely defines the risk to reward relationship of that asset.
In terms of trading a liquid instrument, a return stream represents your equity curve associated with your trading activities. It is a derivative signature expressed in terms of $ that represents how your trading system has performed in navigating the financial markets.
When your system trades during favorable market conditions your equity curve rises and your drawdown profile falls, and when your system trades during unfavorable conditions, your equity curve falls and your drawdown profile rises.
So let’s have a look at a single return stream associated with a single trading strategy for the GBPUSD on the hourly timeframe (H1) and see what it tells us.
Graph 1 – Single System Return Stream – GBPUSD H1 44441183
By forensically examining the equity curve and it’s associated drawdown profile, you can quickly assess those periods where your system performed, under-performed or stagnated. For example I have highlighted those regions on the Equity Curve and Drawdown profile above that provides useful information about how your system has performed over the market conditions thrown at it over an extended period of time (in this case since April 2003 to Jan 2019.
Now every asset and every collection of assets has a return stream and this derivative signature provides essential information that a portfolio manager uses to compile their portfolio as it provides information on the strengths and weaknesses of that return stream over a range of different market conditions.
For example, here is a return stream of a portfolio comprising 18 separate systems.
Graph 2 – Portfolio Return Stream of 18 Systems
Now the simple difference between the return stream offered by a single strategy and the return stream of a compiled portfolio is that a portfolio compiles the discreet return streams of each contributing system into a single compilation. For example here are the individual return streams of the 18 separate systems that compile the portfolio of Graph 2.
Graph 3 – Individual Return Streams of Consolidated Portfolio Return Stream of 18 Systems
What is important to note is that the return stream (or equity curve) is a unique representation of how that asset or collection of assets performs in accordance with market conditions. Unless the collection of individual return streams are perfectly correlated, each return stream possess unique differences that have value to the portfolio manager in reducing the adverse volatility of the return stream of the consolidated portfolio.
The signature of the equity curve is an important principle to understand in compiling portfolios as the name of the game, to wealth creation and weathering market uncertainty, is in how you compile a portfolio from the individual return streams so that overall, the portfolio return stream (equity curve) has positive momentum (with limited stagnation periods) and limited adverse volatility (aka weak spots or deficiencies). Remember that beneficial volatility is good and makes you king of the world ….so don’t be mean to all types of volatility.
To achieve this end, like a puzzle, you superimpose the standardized risk weighted return streams on top of each other to address the weak spots in each return stream as a collective…but we will get to this later. It sounds more complicated than it is…but if you are good at visual puzzles, that’s all you need to this game. Forget the quantitative statistics and heavy mathematics as visual methods work best in portfolio compilation.
Why can a diversified portfolio deliver so much more bang for buck on finite capital than a single system?
So this is the question you really need to ask, as once you understand it….you will never trade a single system alone again. Diversification of return streams is the key.
Let’s look at the performance metrics of the the single system displayed in Graph 1 above (highlighted in brown below).
Table 1 – Performance Metrics of Single System
The highlighted (brown) row in Table 1 provide performance metrics of the single system which produced the equity curve of Graph 1. Of particular note are the following columns.
Open Bal = $10,000 The opening balance allocated to the strategy to produce the following performance metrics.
CAGR = 2.2%. The CAGR column represents the compound annual growth rate of the strategy over the 16 year period. For a possible edge to be present in a system, then we need a positive CAGR over a large time series. This value does not need to be great….but we just need it to be positive.
Draw = 10.36% The Draw column represents the maximum drawdown of the strategy over the 16 year period.
MAR = 0.21 The MAR column is an important risk-weighted metric that represents the overall volatility of the strategy, by dividing the CAGR by the Draw. Higher MAR ratios are less volatile than lower MAR ratios. While we prefer strategies with higher MAR ratios, it is very important to also consider the skew of the strategy as high MAR ratios with negative skew should be avoided.
Skew = 6.07 The skew column is an important metric that represents the overall bias in the frequency of the return distribution towards many small losses with occasional large wins (high positive skew) or many small wins with occasional large losses (high negative skew). Now I have previously written at length on the benefits of divergent strategies with positive skew so I won’t rehash it here.
So let’s put this all together. We have an individual strategy with an opening balance of $10K that has a possible edge in delivering an overall positive CAGR of 2.2% over the 16 year period but is accompanied by a 10.36% drawdown over the period. The MAR ratio is therefore relatively unappealing but the strategy is divergent and does have good positive skew.
Now imagine you are a retail trader who is dependent on this strategy as their daily bread and butter. It is very unlikely that they would even consider this strategy given the paltry returns. They could of course scale up the returns with position sizing (aka increasing leverage) to deliver the CAGR, but this will come at a cost associated with increased drawdowns. For example let’s say you want to allocate your entire capital of $50K towards this single strategy but to make ends meet and pay some of the bills you wanted a CAGR of at least 10% per annum as opposed to the current 2.2% per annum. This is simply done by multiplying the position sizing of the strategy by 5 times…..so let’s see the impact.
For the privilege of increasing your CAGR to 10.24% per annum with a $50K allocation, your drawdown has now increased to a whopping 48.74%. Would you really have the stomach to tolerate this? Can you now see why so may retail traders face risk of ruin. They typically trade above their pay grade using leverage with the expectation of higher returns and rarely take any heed of the associated increased risk that accompanies that increased return.
Unfortunately the very volatile nature of the strategy in isolation also prevents you from applying other further forms of portfolio treatment such as compounding your returns through the reinvestment of profits. Given the very volatile nature of the single strategy, compounding the strategy will simply lead to risk of ruin very smartly.
These are the reasons for the statement that there are better ways to get bang for buck from your finite capital through a portfolio of diversified systems. So let’s see this principle in action.
Let’s look at the scenario now where we compile the 18 instruments of the portfolio from Table 1 above without any further position sizing treatment or leverage and allocate the same $50,000 capital over the portfolio as opposed to the single system. You will note that no system on it’s own have anything to crow about in terms of their risk weighted signature (MAR ratio), but what they do have is different equity curve signatures….and this is where the free lunch resides in portfolio management. So what is the result of simply compiling all the 18 systems together with no mathematics or science involved.
How do you like them apples. With the same $50,000 capital allocation you have now ramped up your CAGR in the uncompounded scenario to 9.8% with a maximum drawdown of 4.84% for the entire time series. Even better for the monthly compounded solution (profits reinvested) where CAGR reaches a staggering 22.24% with a commensurate very acceptable drawdown of 7.74%.
Take some time to be marveled by this principle. The reason for this hocus pocus is attributed to the low correlated nature of the individual return streams where the weakness of each individual return stream is diluted through the superposition of return streams that do not have the same equity curve signature. What this method does is attack the risk embedded in each individual strategy as opposed to the former method of simply multiplying your profit result by 5 times.
Remember that we cannot control profits….but we can control risk. Given the duality between risk versus return, by addressing your risk at the single system level, you are massaging the risk-return relationship at the global portfolio level which then allows you to play some additional tricks in boosting the earnings potential of your finite capital.
But we can do better than this raw compilation of 18 strategies through a few additional simple steps. Let’s move on to them….but before we do….a note about compounding.
The principle of compounding is an old one which you will have learnt at school. In this example each month the portfolio equity is calculated and ‘marked to market. This value is then used as a basis to recalculate position sizing based on the new level of equity. For compounding to take full effect, profits need to be fully reinvested back into the portfolio. Now the compounding impact of this theoretical exercise does not take into account your tax position, so the reality is that these levels are a theoretical benchmark only. Furthermore, any funds you withdraw from the portfolio, significantly dilutes the effects of compounding which is a long term exponential acceleration.
Below is an example of the uncompounded equity curve of the raw portfolio and the monthly compounded equity curve. Look how long it takes for the impact of the compounding principle to take hold….but when it does, it is a sight to see. Compounding, like leverage however is a two edged sword. This exponential impact applies to losing return streams in the same manner that it applies to winning return streams so take heed.
Risk-weighting the Portfolio
Ok, so let’s assume I have sold you on the broad principle of trading a diversified suite of uncorrelated return streams, what can we now do to bring home more of the bacon for our finite $50K capital?
If you refer back to Table 1 of the Raw portfolio you will see that each system produces a different CAGR and Drawdown maximum. For example the raw CAGR for each system ranges between 0.7% and 9.0% with drawdowns ranging between 1.83% and 32.52%. What this variance means is that each system has not been normalised in terms of their risk-weighted return. Therefore those systems with higher CAGR and higher Drawdowns will bias the results of the portfolio in their favour. The result of a bias towards certain systems can put the entire portfolio at risk as a failure in one of these bigger biases can result in total portfolio destruction.
As a risk management measure we want to be sure that each system has therefore been scaled in accordance with their risk weighting. In other words that each system has a standardized risk weighting.
The way we do this is to apply a desired maximum drawdown for each system and then scale each system using a multiplier of it’s position sizing to come to that desired maximum drawdown tolerance. For example, let’s assume that System 1 in the Raw Portfolio has a CAGR of 8.6% and a Max Drawdown of 32.52%. To risk weight this system to a desired maximum drawdown of say 20%, we apply a multiplier of 0.62 (0.62 x 32.52% = 20%) to the position sizing of that system.
So now let’s have a look at the risk weighted treatment of the raw portfolio in Table 1 base on a chosen weighting of a maximum 20% drawdown for each individual system. Note that this does not mean that the drawdown for the global portfolio will also be 20%. How the return streams compile determines the end result at the portfolio level.
Table 2 – Performance Metrics of Risk Weighted Portfolio
Refer to the Multiplier column of Table 2. This is the multiplier we apply to each system of the Raw Portfolio to standardise the risk weighting of each contributing system.
So let’s see what this has now achieved at the portfolio level by referring to the rows ‘Risk Wt Portfolio’ and ‘Risk Wt Portfolio Compounded’.
Take a good look at those risk weighted performance statistics and be once again amazed. The uncompounded CAGR is now 13.45% with a maximum drawdown of only 4.1%. The compounded solution offers a CAGR of a staggering 43.25% and maximum drawdown of 14.45%.
Below are the equity curves and drawdown profile of the uncompounded and compounded Risk weighted solution.
Now what needs to be remembered is that we have achieved this through risk treatment measures as opposed to simply increasing position sizing (leverage) to lift profitability. This is where the shady art of portfolio management takes a bow. It is through risk management that we accelerate our wealth building principles, not through a myopic focus on profits only.
But come on Rich, the title of this article is “To Infinity and Beyond”. There must be more that we can do?
Okay dear readers, I leave you in this article with the secret sauce of how I then further compile my systems using visual equity curve matching. This is my preferred method that I apply to blending a portfolio as opposed to a more conventional approach by using correlation statistics. By mapping the equity curves against each other, so much more information is revealed than a single correlation statistic.
Portfolio Compilation Through Equity Curve Assembly
We left the portfolio previously at the ‘Risk Weighted’ Treatment stage. Below is a table that reflects the current risk weighted portfolio before we apply further treatments.
The performance statics and equity curve at this point in the treatment stage is as follows.
Now the first step of the following treatment process looks at the skew of the individual strategies in the risk weighted portfolio and eliminate those convergent strategies with extreme negative skew. The reason we do this is to ensure that no return stream has the potential to significantly compromise the overall portfolio. For those wishing to know more on the damaging impacts of negative skew, then please refer to the prior Blog post on the subject.
The table below highlights (in blue) two systems in the portfolio with extreme negative skew. Their individual equity curves are very appealing in their linear ascent with little volatility, however they can be toxic to the portfolio when market conditions change and you are left with a string of very large consecutive losses.
So…now that we have removed these two ‘convergent’ systems from the compiled portfolio and now only have 16 ‘divergent’ systems to play we unfortunately find that this risk management process has reduced the MAR of the compiled portfolio from a prior 2.99 to 2.88 which reduces the capital efficiency.
So we now need to make this deficiency up and push on towards infinity through a bit of equity curve matching…..so how do we do this?
Let’s look closely at the drawdown profile of the compiled compounded portfolio as it stands now. Look closely at the drawdown peaks and identify the weak spots. I have highlighted these with red circles.
If we can reduce these drawdown spikes, then we reduce our maximum drawdown of the portfolio and may improve our MAR ratio. So what we need to do is closely examine the equity curves of the individual systems in the portfolio and see which systems contribute to this weakness.
This is where the game turns into a puzzle and we align each of our individual equity curves with the global portfolio to map where the weakness resides.
Let’s start on the major drawdown weakness of December 2018 and refer to the table below which maps the equity curves of the individual systems against the equity curve of the total portfolio. I will highlight (in green) the systems that are contributors to this weakness. I will also highlight what I regard as the major contributor (in blue). Note the deterioration in equity of these highlighted strategies in December 2018.
So let’s turn off the system highlighted in blue and now observe the result.
The peak drawdown of December 2018 has now been addressed and a new max drawdown in August 2012 has been identified.
Without going into the blow by blow story, I simply repeat this process outlined above by trialing various system exclusions that contribute to this drawdown weakness until I am left with a solid MAR ratio that I am happy with. The process I undertook for this example left 11 systems remaining.
…..but now have a look at the revised performance metrics of the compiled portfolio.
We have now lifted our MAR ratio above the risk weighted solution to a whopping 3.20 with only 11 systems in the portfolio.
Sure, you may say that the CAGR of the compounded risk weighted solution of 43.25% is higher than the compiled solution of 30.61%…however you are missing the point. What I can now do is reduce my capital allocation to $30,000 and achieve a 49.11% CAGR with a similar maximum drawdown to the risk weighted solution of 16%. This is how we get bigger bang for buck for our finite capital.
So okay, the title of this article ‘to infinity and beyond’ was perhaps a bit far fetched…as we have to stop somewhere in our tinkering …… but hopefully it gives you some insight into how some powerful portfolio blends can be used to garner magnificent returns with far lower volatility that can otherwise be achieved by single systems.
So if you like this method of portfolio construction, then stay tuned as we will have some powerful tools available in our shop shortly to make this a seamless exercise.
Now before I go, I need to spell out in BOLD about the assumptions that lurk in this article. This article is about managing risk from known historical returns. The results achieved have been achieved through the application of risk management principles that have already happened. There is no guarantee that the method described here will produce the same terrific results. In fact when selection bias has it’s last word, you should always adopt a far more prudent outlook of any future due to the inherent uncertainty that lies within.
However what we can at least say is this. At least the risk management measures adopted have accounted for the risk inherent in the market of the past, which is what risk management is all about. We can never protect ourselves against all possible risks. However….the risk framework that resides in this particular treatment does allow for a degree of uncertainty by always cutting losses short and allowing for unlimited possible upside……but it has no say in the actual ultimate future performance associated with market conditions as the techniques deployed are not predictive in nature.
So this is not about any form of predictive outlook. This technique is simply about managing known or predictable risks by plugging the weaknesses of a past condition and by allowing for unpredictable uncertain events to offer potential significant upside.
In later articles I will start to guide you through the process of how you use these techniques as a basis to step you forward into an uncertain regime and adapt your portfolio mix as you go to progressively enhance the robustness of your portfolio over time.
Trade well and prosper