Smoother than the Sum of its Parts – An Approach to Portfolio Optimization
In a previous post “Don’t be fooled by Randomness”, we discussed how the central feature of a modern efficient market is the dominance of random price action (or noise). To explain how this noise is manifested, think of the behaviour of the traders, institutions and investors who interact with the market. The participants span the spectrum of timescales from the intraday traders and High Frequency Traders (HFT) that interact with the market on the very short timescale to the very long term position traders who interact with the market on a far more selective and infrequent basis. Each of the different participant behavioural groupings vary in the outcomes they are seeking from their interactions with the market including their timing and position sizing. Putting this all together as a collective image over time, we can imagine the maelstrom of interactions and the intractable nature of predicting future price action with fidelity.
While this plethora of interactions create chart patterns (or fossilized imprints of these interactions), these signatures of interactions may simply be attributed to effective random outcomes of short term participant behaviour that have no impact on the longer term trace of price action that is reflective of gross overall behaviour.
It is the heuristic processes of the brain that make us believe that there is a meaning to every pattern, but what we don’t realise is that our brain uses pattern recognition as a rapid response basis to ascribe meaning to every sensory input we receive. It takes shortcuts given the complexity of sensory stimuli it receives and the need to respond smartly, just in case the stimuli is a real threat.
This feature is an outcome of natural selection where the senses relay information to the brain and by pattern recognition, these stimuli are compared with what is held in memory to convey a rapid meaning to the observer that may or may not be representative of the external reality. Everyone can see an image in a cloud or a constellation and many will assign a causative factor to it, however the reality may be that this feature has no more meaning to it than a pattern created from random interactions of a system.
The way we assess sensory stimuli is hard-wired in the way we are designed and a result of how we have evolved to deal with external environmental inputs such as perceived threats or perceived benefits, whether they are real or not.
Don’t believe me. Then have a look at the image below and stare at the central cross for a moment.
You will observe that the pattern starts to disappear and re-appear over time.This (Troxler Fading) is how your brain, in responding to stimuli, uses pattern recognition as a rapid response tool tool to heuristically resolve sensory inputs. Over time, as you fixate on a particular point for a period of time, an unchanging stimulus away from the fixation point will fade away and disappear. Your brain is heuristically assessing the image and rendering a result that may be contrary to the actual sensory input received.
Similar pattern recognition heuristics are applied to simple day to day tasks such as reading. For example, your brain will be able to quickly render meaning into the following paragraph simply because it utilizes the first and last letters of words as a heuristic shortcut before it fills in the gaps with later examination to resolve any further comprehension difficulties.
“I cdn’uolt blveiee taht I cluod aulaclty uesdnatnrd waht I was rdanieg: the phaonmneel pweor of the hmuan mnid. It deosn’t mttaer in waht oredr the ltteers in a wrod are, the olny iprmoatnt tihng is taht the frist and lsat ltteer be in the rghit pclae. The rset can be a taotl mses and you can sitll raed it wouthit a porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe. Scuh a cdonition is arppoiatrely cllaed Typoglycemia .
“Amzanig huh? Yaeh and you awlyas thguoht slpeling was ipmorantt.”
Now if we can accept that perhaps the brain is not the best tool to assess a complex system with fidelity, all is not lost as we can utilise mathematics (namely statistics) to peer into a complex system and utilise the principle of the Law of Large Numbers to render ‘gross statistical features’ that are more than likely to actually be real exploitable opportunities (Alpha).
Let’s take the analogy of a biased coin toss. In a narrow sample selection, there is no guarantee that this bias will be detected, however over a greater sample size, the slight bias to the coin is reflected by the gross statistical results of the entire test. This feature is a characteristic of uncertainty and attributed to the Law of Large Numbers.
Let’s assume that we are now all on the same page. I would therefore like to take you on a journey into portfolio management where we apply statistical principles to amplify non-random signals such as bias from the noise of the markets.
Translating Market Behaviour into Return Distributions
The first thing we need to understand is how the features of the price action in modern efficient markets translate to the return distributions (equity curves) that you obtain from trading activities.
Dependent on the system that you deploy to trade a given market, a profitable trade result will be generated when the price action of the market coincides with the rules of your system. An unprofitable trade result (a loss) will be generated when the price action of the market fails to observe the rules of your system.
The rules of your system dictate terms to the market in how you profit from it and furthermore the rules of your system restrict how your system responds to market uncertainty. The more prescriptive your rules are, the less breathing rule given to market uncertainty and the less your system is configured to handle market volatility. More rules actually introduce larger negative drawdowns into your system.
Given that markets are complex dynamic systems which fleetingly change market conditions at a whim, the more prescriptive your system is, the less you can endure this natural dynamic feature of markets. More robust systems in general are simpler and have less prescriptive rules. Market conditions that may be in place for a considerable period of time can and do turn on a knife edge into a very different market condition to trap the unsuspecting trader.
Now here is the rub and something to digest. For the discretionary trader out there, they may have an edge in trading a select number of market conditions when compared to a single automated system (eg. an algorithm), however to survive long term across all market conditions that can be thrown your way, you need a myriad of robust systems to achieve this.
This is the domain in which automated systems eat discretionary traders for breakfast. The human brain may be able to handle 5 different systems or so to navigate different market conditions, but a diversified portfolio of 50 plus systems across say 50 separate markets cannot be managed by that subjective grey stuff in your skull and can only be accomplished through automation.
To assist in making robust systems it is handy to broadly classify market regimes into 6 broad categories of volatile or non-volatile combinations of bear, bull or sideways congestion phases.
Most trading systems can handle say 2-3 of these 6 possible market conditions, but no single system can handle all of them and be profitable across the board. Better systems are those that can be profitable across say 2-3 different market conditions and simply preserve capital from excessive losses across the balance of market conditions.
The problem with unpredictable markets however is that you can never determine with confidence how long a particular detrimental market condition/s may last. Most of the time you survive to tell the tale….but some of the time you don’t. In this world of probabilities, that ‘some of the time’ is enough to defeat you and it is the ‘some of the time’ where risk management is your secret to survival.
Every system used to trade any market instrument or collection of market instruments generates its own distinctive equity curve and each equity curve is a unique signature of how the system constraints (created by variables) responds to prevailing market conditions. The signature created is a reflection of the sequence of profits and losses (a distribution of returns) that, when graphically portrayed, provide information about the strengths and weakness of the approach.
The equity curve provides information through the volatility of it’s return distribution that indicate whether the trade journey was a smooth enjoyable ride with limited volatility, or whether the journey was an ulcer ridden ride on a pogo stick?
For example the equity curves below in Chart 1 represent the return distributions of 3 month Treasury Bills (grey smooth line) against the orange volatile line representing the return distribution of a strategy that mirrors the performance of the S&P500 TR (Total Return including Dividends) Index.
Look closely at the profile of the equity curves (grey line and orange line). The risk-free nature of the 3 month Treasury Bill is reflected by the smooth volatility profile of the grey curve….however for this pain free ride, between 2002 to 2016 your initial $1000 investment would appreciate 1.24% (refer to CAGR) per annum and now be worth $1,199.
Now have a look at the risk-return profile of the (orange) S&P500TR Index of Chart 2 below. Ride em’ cowboy.
Chart 2: S&P500 TR Index Versus 3 Month Treasury Bill
A buy and hold approach with an investment that simulated the S&P500 would have been a nervous ride. For the joy of a 6.33% return per annum over the period, you would have experienced two nail-biting drawdowns. A drawdown of 30% on your investment almost immediately upon commencement in 2002/2003 (enough to make you question whether you had it right or wrong)…..and then a gut-wrenching drawdown of 51% in 2008/2009 associated with the GFC.
What we see here when we compare the return profiles of these two different classes of investment is the classic risk-reward trade-off. Low return with low risk versus higher return with higher risk.
Now there is a further problem with a volatile return distribution. The chart above assumes you invested $1000 on 1st January 2002. What would have happened if you had invested your hard earned $1000 in November 2007?…….*ooooops*……..you would immediately have entered a wicked drawdown where 50% of your investment would have vanished before your eyes. It would have taken until December 2011 (4 years) before you would have clawed your way out of this pit of despair and seen blue sky…….and furthermore there is no guarantee in this land of uncertainty that the investment would ever have recovered in your lifetime. Just span the last 200 years or so of market history to get an appreciation of what I am saying.
So what can we do to address the volatility of returns to hold onto the gains made but at the same time reduce our risk exposure? It’s time we started investigating the shady art of portfolio magic where you can create something from nothing.
What portfolio management is all about is to engage in a systematic method of constructing a portfolio of investments from ground up that utilises principles of risk management at all steps along the way to achieve an optimal risk-return profile.
You remember how I told you that a modern efficient market is dominated by noise with perhaps an occasional non-random feature (signal) that gives a bias to this overall noise. Well the return series of every equity curve is also representative of this noise-to-signal market feature.
The equity curve produced by a set of trading rules applied to any complex market comprises a large portion of returns that are simply the result of random price action with a smaller component of the returns being attributed to the trading outcomes arising from valid signals that are non-random in nature.
Now here is the magic trick…If you superimpose a non-correlated return series upon another by portfolio blending, two things happen.
Firstly, the noise of each return series starts cancelling each other out through a physical principle called destructive interference. The noise resulting from the combined portfolio will actually be lower than the summation of the noise of each separate equity curve.
Secondly, given the timing differences of valid signals between non-correlated series, the non-random features of each equity curve do not destructively interfere and we can generally summate both results.
The result of blending therefore “amplifies the signal to noise ratio of the return series”.
This is a very powerful feature of portfolio management that gives you a ‘free lunch’.
By blending non-correlated equity curves within a portfolio, you actually get a portfolio that has a risk-reward profile that is greater than the sum of its parts.
If you can grasp this concept……then congrats….You are now ready to understand how to construct a robust portfolio.
In a nutshell, the process of portfolio construction is a simple one. What ultimately we will be doing is to simply blend equity curves of specifically selected strategies to iron out the volatility kinks and deliver an exceptional risk-reward profile for your portfolio that is better than what each isolated component of that portfolio can otherwise achieve……
But before we commence blending the mix we need to ensure that the portfolio constituents are quality inputs……..remember in this field of statistics that garbage in equals garbage out. Like a Masterchef, you are now ready to find those key ingredients to make the perfect dish that is greater than the sum of its parts.
In the land of reality we need to understand that there is no single solution for capturing all available alpha. What we aim to achieve is to compile a diversified list of systems trading across timeframes and asset classes with the intent that each system contribution captures a small portion of available alpha yet at the same time does not contribute to excessive risk exposure for the entire collection.
If we can achieve this, then we can apply the secret sauce of Portfolio Magic by constructing composite return distributions that through careful blending, offer an enhanced risk-reward result that is greater than the sum of its parts.
Without getting into the specific details which we can explore at a later date, the following non-exhaustive list are prerequisites that you need to understand to assist you in building that perfect portfolio using robust inputs that can navigate these complex markets.
Focus on risk and the profits will simply arise from market behaviour
As traders, it is hard not to be attracted by the lure of stunning performance returns and this is where most traders tend to dedicate their efforts. The reality however is that this myopic focus fails to appreciate the other essential side of the symmetrical equation of risk-reward, namely risk.
The key requirement for your system in an efficient market is to be able to survive the storm of uncertainty comprising the incessant noise of the market, the non-random market features that may be lurking in the noise and the fairly frequent fat tails of non-random directional movement.
The central premise of this post is based on a story of survival in an unpredictable marketplace where simply having a system available at the right time and place is sufficient to exploit alpha. We can all look back in hindsight and say that we could have caught that major market move if we were there at the right time…..but a different kettle of fish for those that actually participate in these probabilistic events. How do you ensure that you are there at the right time and place without attempting to predict when those events occur?
The answer is a simple but challenging one. You must have your systems turned on 24/7 that are capable of surviving market uncertainty and be capable of exploiting alpha when it rears its head when market conditions are favorable to your system. You must be present and riding that wave of opportunity even through you will never know when that wave turns into a tsunami.
Look for small amounts of alpha which can then be consolidated by a portfolio into large alpha
Modern efficient markets as discussed are characterised by randomness, but occasionally within this noise there is a slight bias that leads to exploitable opportunities (arbitrage). The ephemeral opportunities in a modern market quickly gets exploited as algorithms and traders adapt to these new opportunities. Alpha appears here and there at unpredictable times and we need to recognise that there is no single solution that can capture all that is available. The market is dynamic and as such certain systems may have their time in the sun capitalizing on an exploitable opportunity but quickly that opportunity is arbitraged away until a new opportunity is identified by a system pioneer. Finding the appropriate solution for harvesting alpha for all market conditions (the holy grail) is like searching for a needle in a haystack…..so a piece of advice that may save you years of frustration…..just don’t do it. There are other ways to skin a dead cat using a portfolio solution.
Provided that each contributing component of the portfolio has positive expectancy (an edge) and contributes modest alpha to the entire portfolio, by being able to survive the storm of uncertainty through a broad range of market conditions, we can then compile a powerful portfolio solution that gets the best bang for buck in terms of risk-reward for your finite investment capital.
Use as much Data as Possible
Use as much data history as you have at your disposal that is representative of as many market conditions as possible in assessing your investment universe for candidates that may be suitable for your portfolio……..and you may have a better chance of riding the storms. In statistical terms, the more data you have the better. There is no upper limit or ideal sample size, as an entire population of data is always more preferable to a mere sample of it.
The significant degree of non-predictive ‘noise’ in an efficient market has the ability to fool you. What you may think is a profitable strategy that uses a small data set, may just be simple luck. Never underestimate randomness in the market. It is everywhere and is attributed to the complex interactions that occur between its participants.
You will never be able to determine with 100% certainty whether your system has a statistical edge…..the best you will be able to achieve is determine the degree of accuracy within a defined confidence interval.
Predicting these markets is a futile exercise. The best we can come up with is whether or not your system has survived over an extended history of market conditions. The assumption therefore is that history repeats…. but unfortunately to have any confidence in this statement, means that you need to have as much history as you can get your hands on that spans as great a range of potential market conditions as possible.
Fortunately we have studies on the last 800 or so years of market history from the days of the great ‘tulip bubble’ that lead us to concluding that certain market behaviours associated with human nature are persistently repeatable, namely fear and greed. This simple lesson from history of repeatable human behaviour is what the diversified systematic trend follower predates on.
Having faith in a historical data set is not a perfect assumption as new market conditions may emerge that we have never experienced before….but it is the best that we can hope for. As humans we tend to have short memories especially when markets are booming. The best tip I can give to you is start taking your history lessons seriously and remember….Lest we Forget!!!!!
While events such as the Swissy de-peg (above) have the potential to knock a trader who is overexposed in a particular asset for six, the diversified portfolio manager that has significant cross-asset diversification can ride out these calamities with limited impact.
Complete market failure ‘Force majeure’ is also something you need to always keep in the back of your mind. It may just happen. Let’s say that a World War 111 breaks out….then what would be the impacts on your portfolio? Unfortunately we can never totally eliminate risk but at least we can learn from history to identify ways to mitigate risks that have been prevalent in the past.
Choose Liquid Instruments
Liquidity is a valuable risk management lever during adverse times. You may not appreciate its significance until that very time you want to get extract yourself from a painful loss. When you need liquidity, it may not be there.
Liquidity relates to the ability for you to turn your investments into the most liquid instrument being cash. Low liquidity can be responsible for significant volatility in your return profile. The point about liquidity is that it only rears its ugly head when times are tough for investors or when are facing extreme volatility such as a market crisis.
The result of low liquidity is an equity curve that may have attractive strongly rising equity curves in periods of boom, but look for long enough and you will find that these periods of boom are periodically interspersed with significant periods of bust.
If you think that the S&P500 TR is too risky for your liking, then it is time to smell the thorns and realise that the equity curve associated with illiquid instruments can be even more pronounced.
This is not to say that traditional liquid markets cannot become illiquid at times, but in this context, liquidity is a relative measure. If an exchange has a high volume of trade that is not dominated by selling, the price a buyer offers and a seller accepts will be fairly close. During market routs however, this principle is tested, with buyers demanding deep discounts, but in general the impact of lower market liquidity for highly liquid instruments is less than illiquid markets such as real-estate.
Finite capital is a limitation that severely affects your ability to diversify
When assessing potential candidates for inclusion in your portfolio you need to be able to assess the strengths and weaknesses of each return series in terms of risk weighted returns. This is essential as your finite capital constraints mean that you need to select from alternative offerings to produce the healthiest overall portfolio.
The impact on finite capital constraints rears its head during a drawdown. Let’s assume that you have only $100,000 as trading capital. A single trading strategy using position sizing that over the course of an extended data set (say 10 years of history) has a drawdown of 50% means that half your available trading capital will need to be allocated as a risk measure to that strategy. This therefore severely restricts your ability to diversify into other systems.
Before we commence any investment we need to have a sound understanding of our personal risk tolerances. Without that knowledge you may find that under very normal market conditions (such as a short term unfavourable market condition), that the drawdown impact may exceed your risk tolerance leading to detrimental investment decisions that result in you abandoning a potentially very successful investment strategy.
For example, none of us would expect the stock market to experience an unfavourable drawdown of 50%, but simply refer to your history books as in black and white we have a history of experiences such as this throughout the stock market record.
Understand using the Law of Large Numbers what the Maximum adverse excursion of your system will be
To understand the risk of an investment, a long term equity curve provides an understanding of the history of volatility of that instrument over time. We can also use statistical measures such as the Annualized Sharpe Ratio to provide an indication of the volatility of the distribution of returns…..however my preferred ratio is the Return to Drawdown ratio (or alternatively Adjusted CAGR).
The reason for my preference for using Drawdown as a risk measure is that I like to know in $ terms, the impacts on my portfolio as a worst case scenario. I like to carefully consider this maximum drawdown against my personal risk tolerance and consider how I would psychologically fare in the midst of this horrible event.
The problem with drawdowns is that you never know how low they could go, or how quickly your portfolio can recover to levels pre-drawdown. The questions you will be asking yourself during this time are truly damaging to the psyche. Is my system broke?……will I ever dig myself out of this?…..are we going to zero?………what will my wife and family say?……am I just a gambler?……that 1% return offering by my bank now looks attractive!!!.. etc, etc, etc.
The problem with using the maximum drawdown as a measure of system risk is that the actual drawdown is a feature arising from a series of adverse trade events or importantly the sequence of losing trades that you may have. Change the sequence of trades and you have a new losing sequence that produces a different maximum drawdown.
To overcome this problem of relying on a unique historic maximum drawdown of a system as a representative measure of risk, we can apply a Monte Carlo simulation (reorders the trade sequence) to the trade history of a backtest to assess where the actual back test plotted within this Monte Carlo sequence.
If you find that your distribution of returns using actual historical data plots in the upper of lower quadrants of the Monte-Carlo Distribution, this provides important information on whether your historical backtest and maximum drawdown is representative of the average of the entire potential distribution.
The chart of the left (above) shows a back-test result which plotted in the higher range of the entire Monte Carlo distribution. This suggests that your result is not representative of the average of the sample and in relative terms, the trade sequence of the backtest produced a better result than average. As a result, you would not use the historical results as a proxy measure to assess the risk-reward profile of the contributing system.
The curve on the right hand chart however falls in the middle of the distribution of returns and is more likely to be representative of your future result. As a result, your historical backtest could be regarded as a useful proxy measure or benchmark.
Once you are happy with an equity curve that is representative of the sample of return distributions, we can then more reliably use the maximum drawdown of that series as a guide to assessing maximum adverse risk.
Now remember, the old adage to apply is to assume that your worst drawdown is always ahead of you. What this means is that the longer you are in this game, the greater probability of a consecutive run of losing streaks. As a precautionary tale the way you should treat the maximum drawdown experienced in the past 10 years or so using the Monte Carlo simulation above to validate the result, is to then assume that your future worst drawdown will be twice as large. This really ups the ante and ensures you stretch yourself in finding the best possible ingredients for your portfolio.
Finite investment capital is a major obstacle for diversification. One way to overcome this obstacle to an extent, is to use Return to Drawdown Ratios as a method to select between investment alternatives. This way you are able to hone in on those investments that offer superior risk weighted return metrics for your portfolio allowing you to get a bigger bang for your finite buck. The Return to Drawdown ratio allows you to rank different investments and determine the scalability of your investments in your portfolio in accordance with your risk appetite.
CAGR is an acronym for Compound Annual Growth Rate. Having a knowledge of the adjusted CAGR allows you to compare risk weighted performance returns against alternative investments. To calculate adjusted CAGR, what we do is take the raw CAGR of a particular investment (say 15%) and take note of it’s maximum drawdown (say 52%). Now let’s say our maximum risk tolerance is 30%. The adjusted CAGR needs to re-weight the raw CAGR to reflect a 30% drawdown. To achieve this apply the following formula (Raw CAGR/Max Drawdown) x Max Drawdown tolerance) = (0.15/0.52)x 0.30 = 8.65%. We can apply the Adjusted CAGR formula to all our alternative investments so we can rank them all in terms of their risk adjusted return result.
For example let’s compare two return series, but before we do we conclude that a 30% drawdown is our risk tolerance level:
Example 1 = a $100K investment in system 1 that offers an annualised raw return (or CAGR) of 15% per annum between 2002 and 2016 and a max drawdown 60% or a ($60K) hit to the portfolio at some point in time.
Example 2 = a $100K investment offering a 10% raw CAGR between 2002 and 2016 and max drawdown of 10% or a ($10K) hit to the portfolio at some point in time.
A focus on return alone would make you conclude that example 1 was the better alternative. Now let’s look at the risk adjusted return result using Adjusted CAGR.
Example 1 = 0.15/0.60 x 0.30 = 7.5%
Example 2 = 0.10/0.10 x 0.30 = 30%
While the raw returns suggest that Example 1 is preferable, a risk weighted comparative assessment clearly concludes that Example 2 is far better …..In fact 4x as preferable. What this means is that pound for pound, Example 2 is a far better investment offering as it offers much steadier returns with lower risk.
Become familiar with Correlation between Return Series
It is the risk-reward relationships that are the most important aspect to portfolio management…..not simply raw returns. Asset correlation is a very powerful feature that the Portfolio Manager has up his/her sleeve to drive strong returns within managed risk constraints.
Without going in to too much detail here, as asset correlation has already been discussed in prior posts, how assets move in in relation to each other defines the extent of correlation in the return series between them.
Assets by virtue of their relational dependency can move in concert together (positively correlated eg. approaching +1), or be diametrically opposed (perfectly anti-correlated) in their relative movements (approaching -1).
This relational dependency (approaching +1 or -1) between a pair of assets produces unsustainable growth in the portfolio returns during boom times but acts as a double edged sword offering dramatic drawdowns during bad times.
Importantly for a portfolio manager, a correlated portfolio exacerbates the volatility of returns whereas an un-correlated portfolio smooths the distribution of returns.
Principles of diversification seek to reduce this correlation to as close to zero as possible, thereby when one asset in the portfolio is entering a drawdown, another asset is entering a draw-up. The result for the portfolio being a linear equity curve as opposed to a volatile return series.
Let’s assume a return series relative to a portfolio has a correlation of +1. This means that the return series moves in concert with the overall portfolio. When the portfolio is encountering a drawdown, the instrument is also in a drawdown phase. The cumulative impact of that instrument to the overall portfolio therefore exacerbates the drawdown of the portfolio.
What a portfolio manager would therefore seek to do would be to search for a return distribution that offered a -1 correlation to that instrument and thereby to together produce a 0 correlation (+1 plus -1) to that portfolio and thereby minimise the risk impact on the overall portfolio while benefiting from the two returns of both asset series.
Let’s look at an example.
Refer to the highlighted row in the Table 1 that provides performance results of the Dreiss Research Corporation. A portfolio comprising the Diversified Program offered by Bill Dreiss offers a very solid return of 17.65% CAGR between 2002 to 2016, however this heady return entails suffering a maximum drawdown over the period of 51.44%. While this drawdown may be too much to stomach for a trader engaging in a single system, it is this sort of return distribution that is music to the ears of the Portfolio Manager who may be eager to include by allocation a portion of this return distribution into his portfolio to leverage performance returns, provided he can water down the drawdown impact on the entire portfolio.
Let’s see if a Portfolio Manager can cheat by jumping onto the back of Bill Dreiss’s stunning performance and include an asset in his portfolio that assists in smoothing this rocky road while at the same time benefiting from the great results of Bill.
What we are looking for then is a return distribution that serves to dampen the volatility. We can see that the Dreiss Research Program has very little correlation with the S&P500 TR index. Refer to the highlighted column “S&P 500 Correl”. Look at how the Dreiss program correlates with this index at -0.02. This is as about uncorrelated as you can get (zero being perfectly uncorrelated). Ideally we would be looking for a return series that was anti-correlated with the Dreiss Research Program (offering a correlation approaching -1), however an uncorrelated return series will do the trick.
Let’s have a look at the equity curves of Dreiss against the S&P500 TR Index before we blend them.
Closely look at the green line (Dreiss equity curve) and the blue line (S&P500 TR). You will see that when Dreiss is performing strongly, the S&P500 TR Index is entering a drawdown and vice versa. Just by a visual interrogation of the equity curves you can identify if the different return series are correlated or not.
Now let’s look at the key performance statistics to see how this compares down the track with a blended result simply using correlation as a guide.
Now, when we blend these two return streams into a new portfolio, we want to capitalise on the positive qualities (the returns of Dreiss) while at the same time, plugging those nasty drawdown periods and in particular that incurred in 2012. So let’s merge the two income streams with an equal weighting applied to each and see the result.
The red equity curve represents the blended result. Now remember we are not focusing on the actual raw return. What we need to focus on are the risk-reward metrics. The reason for this will become obvious shortly.
Here are the performance results when compared to Dreiss alone:
Concentrate on those risk-reward metrics that have been highlighted and in particular the Return to Drawdown ratio. What this tells you is that the blended result has a higher relative risk-reward ratio and delivers more bang for buck with less ulcers. The scaled CAGR is a comparative measure assuming your max risk tolerance is a 40% drawdown. Pound for pound the blended result produces an adjusted CAGR of 21.41% for a max drawdown of 40% whereas the Dreiss program alone produces a scaled CAGR of 13.72% for the same 40% drawdown.
Under finite capital constraints you can therefore allocate more of your portfolio to the blended result than to Dreiss alone and supercharge your performance results.
Understand Methods of Diversification
While asset diversification or timeframe diversification can reduce your risk exposure to a degree, as more and more markets are becoming correlated, turning to other methods of diversification such as system diversification is becoming more and more important.
While you have little control over the correlation that may exist between different markets or timeframes, where you do have control is in your system design, which can be specifically configured to possess a unique equity curve that addresses a portfolio’s weakness by plugging the volatility gaps.
What this is saying is that system diversification and specifically your ability to design systems to respond to particular market conditions is your ideal tool for portfolio management.
Only consider systems in your selection that offer Positive Expectancy
Each contributing system to your overall portfolio must have positive expectancy. It is not essential that this positive expectancy is high, but provided each system contributes weak alpha to the portfolio, then we can cook this up to produce stunning returns in a portfolio.
Identifying systems with positive expectancy is one of the harder challenges of this game…..but is a critical feature of portfolio robustness. What this protects against is the likelihood that a failure in one element will bring down the entire portfolio.
The principle of ‘quality in and quality out’ is in play here. A system with a ‘true edge’ by definition has been able to survive what history has thrown at it and has still been able to produce a return stream that more than compensates for the frictional costs of trading.
Simply blending non-correlated return streams that have not had a demonstrated track record over recent market history is not going to get you anywhere.
Using a Diversified Portfolio allows you to employ simpler system ingredients
Holding a trade in your portfolio indefinitely increases risk to your portfolio. Think of the risk associated with an unrealised trade as a slowly heating pressure-cooker. The only way to extinguish risk is to exit from a trade. Have you ever been in a position where your investment has declined substantially in value and as a result of you not taking any action to extinguish the risk, the loss exacerbates. Well, as a result of this feature, contrary to what many may think, buy and hold strategies typically have the greatest volatility in return profiles. How we release this risk pressure through trade management is critical for the portfolio manager.
While setting stops is an essential feature of risk management for a single system to release this risk potential, under a diversified portfolio where any individual component may only represent say 0.5% – 2% of your total portfolio, then the need for a traditional stop as a release valve is not an urgent necessity.
However this does not mean that we abandon the risk of an adverse event for a single instrument. What we do however is to engage a different type of exit such as a time based stop or a performance based exit approach that prevents us from unnecessarily introducing drawdowns into our portfolio.
Remember I mentioned that the rules of your system apply constraints to the way price action must unfold for you to be profitable. A classic stop loss is a significant constraint that more often than not, unnecessarily extracts you from a trade and introduces a drawdown into your system. Under a diversified portfolio where you can give your trades greater freedom to breathe, this limiting constraint is lifted allowing you the luxury of seeking simpler strategies that would not be considered by a single system trader.
Understand the Benefits of Positive Skew
It is essential that you understand if your system components have negative or positive skew. Skewness is a term in statistics used to describe asymmetry from the normal distribution in a set of statistical data.
For a diversified portfolio we are after systems with positive skew, namely, lots of small losses with the occasional big win.
A single system trader who does not have the capability to enjoy the benefits of diversification usually elects the converse negatively skewed strategy. Namely a strategy with lots of small wins interspersed with the occasional large loss.
Negative skew strategies have the ability to lull you into a false state of confidence as you believe that you have found the Holy Grail, only to then find, when market conditions change, that you have the mother of all problems on your hands.
Does this remind you of a Martingale strategy (commonly referred to as the Gamblers fallacy)? I hope so, as Martingale’s and their averaging down variants have the mother of all negative skews.
It is essential for risk management purposes that you blow off risk steam in your portfolio by being prepared to cut losses short and allowing your winners to run. Yes you will have more volatile return distribution profiles in each single portfolio addition, but as discussed, you can iron out this volatility through blending methods. Having a volatile profile of individual system components is a sure sign that you have release valves in place to ‘blow off’ intrinsic risk from your portfolio. A single system with an almost linear equity curve is a massive warning bell for the Portfolio Manager indicating either a system component that is curve-fitted, or a Martingale Variant or simply the result of a particular market condition.
Convergent strategies such as mean reversion tend to be negative skewed and offer great, almost perfect equity curves for a period of time and high win rates attracting traders who do not like admitting they can be wrong…..until the pressure cooker blows and it is too late to defend. RIP Long Term capital management (LTCM).
Hopefully this post has provided some food for thought for those who may be struggling to find a consistent return in these modern mature markets. There is a solution, but that solution requires you to recognise that there is no single winning system or Holy Grail.
You have to be prepared to cheat and use portfolio construction as a method to ride market uncertainty, but to do this you need to divert your attention from system returns and focus on the all-important risk management aspects of generating these returns.
There is a reason we say that with increased return comes increased risk. These two common features of every investment are co-dependent features.
Thankfully this post provides a few clues in how you can use well-known risk management methods to at least ensure that you can optimize the risk-return relationship.
Trade well and prosper