Driving Complexity-To-Target: Application to Portfolio Design

Driving the complexity of a given system to a prescribed target value has numerous applications, ranging from engineering (who wouldn't want a simpler design that performs according to specs?) to management, advanced portfolio design, wealth management or investment strategy.

But more than just complexity it is also the robustness of systems that is of most concern. When considering portfolios both diversification and volatility are of concern
We know that in system design (and this applies to portfolios) the mini-max principle, whereby you maximise something (e.g. the expected return) while minimising at the same time something else (e.g. risk) leads to inherently fragile solutions. Taking simultaneously many things to the limit is of course possible but the price one pays is a rigid and fragile solution: you basically push yourself into a very tight corner of  the design space where you have little margin of manoeuvre in case things go wrong. And things do go wrong. Especially if you think that most things in life are linear and follow a Gaussian distribution you should prepare yourself for a handful of surprises.

Portfolio diversification and design can be accomplished differently based on complexity and, in particular, on these two simple facts:

• High complexity increases exposure - a less complex portfolio is better than a more complex one.
• A less complex portfolio accomplishes better diversification (more or along the lines of the MPT and Markowitz logic).

Let us see an example. Suppose you want to build a portfolio based on the Dow Jones Industrial Average Index and its components. Without going into unnecessary technicalities, below is an example of our first portfolio. We observe that:

Its complexity is 64.3 (pretty close to the critical value of 68.75)
Entropy is 823
Robustness is 66.8%
Rating: 2 stars

Nothing to celebrate.

Suppose now that you wish to increase the robustness to, say, 85%. Using our Complexity-To-Target Technology it is possible to "force" the robustness of the portfolio to this target value. Since robustness and complexity are linked it is possible to do this either for robustness or complexity or even both. The new portfolio is illustrated below.

Complexity is now 50.9
Entropy is 542 - this tells us that the behaviour of the portfolio is substantially more predictable
Robustness is 84.9%
Rating: 4 stars

The hubs of the portfolio (red discs) have now changed but that is another matter.



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Software Complexity and What Brought Down AF447

After the recovery of the black boxes from the ill-fated Air France flight 447, it has been concluded that pilot error, coupled with Pitot-tube malfunction have been the major causes of the tragedy. It appears, however, that this is yet another "loss of control" accident. Based on black box data, the aircraft stalled at very high altitude. But, you cannot stall an A330. By definition. The airliner (and many other fly-by-wire aircraft) is software packed to such an extent that it won't let you stall it even if you wanted to commit suicide. That's the theory. But in reality, you don't fly an airliner - you fly the software.  The degree of automation is phenomenal. That is precisely the problem.
Pilots say that they have become button pushers. Here are some comments on the AF447 accident taken verbatim from a Professional Pilots blog:

"We need to get away from the automated flight regime that we are in today."

"Pilots must be able to fly. And to a better standard than the autopilot!"
"To be brutally honest, a great many of my co-pilot colleagues could NOT manage their flying day without the autopilot. They would be sorely taxed."
"It will cost a lot of money to retrain these 'button pushers' to fly again, ..."
"It appears as if the sheer complexity of the systems masked the simplicity of what was really going on. "
"Just so I understand correctly, then there is no way to take direct control of the aircraft unless the computer itself decides to let you, or perhaps more correctly stated, decides you should. Sounds like Skynet in "The Terminator". "

This accident is a very complex one. It is not going to be easy to understand why the plane really came down. It will take time to analyse the data thoroughly and to understand why highly trained pilots pulled the nose up when the stall alarm went off. The theory is that they must have received a large volume of information of very highly confusing nature in order to do so. Apparently, they managed to crash a flyable aircraft.


We have our own view as to the nature of the problem, not to its cause. We believe that it is the excessive complexity of the system that is to be blamed. Modern aircraft carry over 4 million lines of code. That is a huge amount of real-time code. The code, organised into modules, runs in a myriad of modes: "normal law", "alternate law", " approach", "climb", etc., etc. The point is however this. No matter what system you're talking of, high complexity manifests itself in very unpleasant manner - the system is able to produce surprising behaviour. Unexpectedly. In other words, a highly complex system can suddenly switch mode of behaviour, often due to minute changes of its operating conditions. When you manage millions of lines of code, and, in addition, you feed into the system faulty measurements of speed, altitude, temperature, etc., what can you expect? But is it possible to analyse the astronomical number of conditions and combinations of parameters that a modern autopilot is ever going to have to process? Of course not. The more a SW module is sophisticated - number of inputs, outputs, IF statements, GOTO, read, write, COMMON blocks, lines of code, etc., etc. - the more surprises it can potentially deliver. But how can you know if a piece of SW is complex or not? Size is not sufficient. You need to measure its complexity before you can say that it is highly complex. We have a tool to do precisely that - OntoSpace. It works like this. Take a SW module like the one depicted below.

It will have a certain number of entry points (inputs) and produce certain results (outputs). The module is designed based on the assumption that each input will be within certain (min and max) bounds. The module is then tested in a number of scenarios. Of great interest are "extreme" conditions, i.e. situations in which the module (and the underlying algorithms) and, ultimately the corresponding HW system in question is "under pressure". The uneducated public - just like many engineers - believe that the worst conditions are reached when the inputs take on extreme (min or max) values. This is not the case. Throw at your SW module hundreds of thousands or millions of combinations of inputs - you can generate them very efficiently using Monte Carlo Simulation techniques - and you will see extreme conditions, which do not involve end values of the inputs, to emerge by the dozens. And once you have the results of a Monte Carlo sweep just feed them into OntoSpace. An example with 6 inputs and 6 outputs is shown below.

 

The module, composed of four blocks (routines) has been plugged into a Monte Carlo loop (Updated Latin Hypercube Sampling has been used to generate the random values of the inputs). As can be observed the module obtains a 5-star complexity rating. Its complexity is 24.46. The upper complexity bound - the so-called critical complexity - is equal to 34.87. In the proximity of this threshold the module will deliver unreliable results. Both these values of complexity should be specified on the back of every SW DDD or ADD (Detailed Design Document and Architectural Design Document). So, this particular module is not highly complex. The idea, of course, is simply to illustrate the process and to show a Complexity Map of a SW module. In other words, we know how to measure the complexity of a piece of SW and to measure its inclinations to misbehave (robustness).
 
But how complex is a system of 4 million lines of code? Has anyone ever measured that? Or its capacity to behave in an unexpected manner? We believe that the fate of AF447 was buried in the super-sophisticated SW which runs modern fly-by-wire airliners and which has the hidden and intrinsic ability to confuse highly trained pilots. You simply cannot and you should not design highly sophisticated systems without keeping an eye on their complexity. Imagine purchasing an expensive house without knowing what it really costs or embarking on a long journey without knowing how far you will need to go. If you design a super sophisticated system and you don't know how sophisticated is really is it will one day turn its back on you. It sounds a bit like buying complex derivatives and seeing them explode (or implode!) together with your  favourite bank. Sounds familiar, doesn't it?



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Model-free methods - a new frontier of science

When we make decisions or when we think our brain does not use any equations or math models. Our behaviour is fruit of certain hard-wired instincts and experience that is acquired during our lives and stored as patterns (or attractors). We sort of "feel the answer" to problems no matter how complex they may seem but without actually computing the answer. How can that be? How can a person (not to mention an animal) who has no clue of mathematics still be capable of performing fantastically complex functions? Why doesn't a brain, with its immense memory and computational power, store some basic equations and formulae and use them when we need to make a decision? Theoretically this could be perfectly feasible. One could learn equations and techniques and store them in memory for better and more sophisticated decision-making. We all know that in reality things don't work like that. So how do they work? What mechanisms does a brain use if it is not math models? In reality the brain uses model-free methods. In Nature there is nobody to architecture a model for you. There is no mathematics in Nature. Mathematics and math models are an artificial invention of man.  Nature doesn't need to resort to equations or other analytical artifacts. These have been invented by man but this doesn't mean that they really do exist. As Heisenberg put it, what we see is not Nature but Nature exposed to our way of questioning her. If we discover that "F = M * a" that doesn't mean that Nature actually  computes this relationship each time a mass is accelerated. The relationship simply holds (until somebody disproves it).

Humans (and probably also animals) work based on  inter-related fuzzy rules which can be organised into maps, such as the one below. The so-called Fuzzy Cognitive Maps are made of nodes (bubbles) and links (arrows joining the bubbles). These links are built and consolidated  by the brain as new information linking pairs of bubbles is presented to us and becomes verifiable. Let's take highway traffic (see map below). For example, a baby doesn't know that "Bad weather increases traffic congestion". However, it is a conclusion you arrive at once you've been there yourself a few times. The rule gets crystallised and remains in our brain for a long time (unless  sometimes alcohol dissolves it!). As time passes, new rules may be added to the picture until, after years of experience, the whole thing becomes a consolidated body of knowledge. In time, it can suffer adjustments and transformations (e.g. if new traffic rules are introduced) but the bottom line is the same. There is no math model here. Just functions (bubbles) connected to each other in a  fuzzy manner, the weights being the fruit of the individuals own experience.

 

As a person gains experience, the rules (links) become stronger but, as new information is added, they can also become more fuzzy. This is the main difference between a teenager and an adult. For young people - who have very few data points on which to build the links - the rules are crisp (through two data point a straight line passes, while it is difficult for 1000 points to form a straight line - they will more probably form something that looks like a cigar). This is why many adults don't see the world as black or white and why they tend to ponder their answers to questions. Again, the point is that there is no math model here. Just example-based learning which produces sets of inter-related Fuzzy Cognitive Maps that are stored in our memory. Clearly, one may envisage attaching a measure of complexity to each such map.

OntoSpace, our flagship product, functions in a similar manner. It doesn't employ math models in order to establish relationships between the parameters of a system or a process. Essentially, it emulates the functioning of the human brain. 

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Is it Possible to Make Predictions?

Prediction of the future has always been man's dream. However, there is an overwhelming amount of physical evidence that this is quite impossible. This is because the future is permanently under construction. Therefore, as every second passes, the future is changed. The cause of this are the laws of physics. If the future were predictable with all likelihood we would have different physical laws and life would probably not even exist.

But man is a subborn species. The unhealthy desire to predict the future has pushed mathematicians to devise utterly  unnatural methods which, in virtue of prolonged and often distorted use, are now deeply rooted in the practises in virtually all spheres of social life. Scientists speak of predictive models, just as the economists, the weather man, etc. Some people believe in horoscopes while others buy lucky  lottery numbers.

Much of the contemporary "predictive machinery" is based on statistics - looking back in time, building some model of what has actually happened, extrapolating into the future. The concept of probability plays a central role here. Bertrand Russel is known to have said, back in 1929, that "probability is the most important concept in modern science, especially as nobody has the slightest notion what it means". In fact, probability is not a physical entity and it is not subjected to any laws in the strict scientific meaning. As a matter of fact, there are no laws of probability. If a future event will take place, it will do so irrespective of the probability that we may have attached to it. If an extremely  unlikely event will happen, it's probability of occurrence is already 100%.

Predictions are of major interest in the realm of uncertainty. Clearly, one can predict with a high degree of accuracy when an object will hit the ground when it is dropped from a certain height (providing it is not a feather). What we are more concerned with is the desire to predict phenomena and events of interest to economists, investors, managers or politicians.

But there is another problem with predictions. Suppose you do indeed know with certainty that an event of interest to you will happen at a specific time in the future.  You will surely take action based on that knowledge. What this can cause, however, is a change in the chain of events such that you inevitably alter that event. As an example, suppose that you are extremely wealthy and that you know the exact value of certain stocks some months in advance. You will immediately start to buy and /or sell massive amounts of these stocks. This will surely cause other investors to react. Inevitably, the flow of events will be such that the predicted values of these stocks will not be the ones you knew with "certainty". What does this mean? It means that you can only verify a prediction if you do nothing. The moment you act based on your knowledge of the future you automatically alter it and the prediction cannot be verified.  Consequently, the phrase "predictive model" is an oxymoron. As mentioned, because of the way the laws of physics work, the future is permanently under construction. And if you add Goedel to the picture ...... The Creator is indeed very smart!

So, it seems that our efforts to devise some sort of predictive analytical machinery is futile. The current planetary meltdown of the economy eloquently underscores this fact. The severity and depth of this crisis has not been predicted (had this been the case we would have taken measures, right?) and this speaks of the quality of the contemporary economic and econometric models and of their predictive capability. With all respect, their predictive capability is not too exciting.

In actual fact, we still don't even really understand the crisis and its multiple causes. But how can one speak of predicting phenomena which  are poorly understood? Shouldn't we change the order of things? Shouldn't we try to first understand better the dynamics of   highly complex interconnected  and turbulent economic systems and devote less resources to fortune telling and high-tech circle-squaring? How about:

• Taking a holistic view of things, analysing systems of entities not single entities.
• Searching for recognisable patterns, not repeatable details. The closer you look the less you see!
• Moving from sophisticated (and subjective) models to model-free approaches.
• Developing a new kind of maths, which is less "digital" and closer to reality.
• Dedicating more effort to understanding the way things work, the way Nature works.

What cannot be achieved should not be pursued. Our efforts and resources should be focused on real problems that admit real solutions. Omnis ars naturae imitatio est.

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FREE account for Measuring Business Complexity and Rating

If you wish to measure the complexity of your business, or assess its Resilience Rating, just follow these instructions:


1. go to http://www.rate-a-business.com/index.php

2. login as User: freerating    Pwd: freerating


Don't forget to read the short tutorial!




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Beyond the concepts of Risk and Risk Management

The current economic crisis indicates that conventional risk assessment, rating and management techniques don’t perform well in a turbulent and global environment. AAA-rated companies and banks have suddenly failed, demonstrating the limitations of not only risk management techniques but also the need to re-think the expensive and sophisticated Business Intelligence and Corporate Performance Management infrastructure that modern corporations have relied on. But what are the origins of the financial meltdown that is spilling over into the real economy? Why is the economy increasingly fragile? We identify three main causes: excessively complex financial products, globalized financial markets that lack regulations and usage of subjective computational models that are naturally limited to less turbulent scenarios.

Models are only Models. No matter how sophisticated, a model is always based on a series of assumptions. More sophistication means more assumptions. Classical risk evaluation models, because of their subjective nature, are inherently unable to capture the unexpected and pathological events that have punctuated human history, not to mention the economy. But there is more. Conventional Business Intelligence is unable to cope with the hidden complexity of a modern global corporation precisely because it thrives on unrealistic mathematical models. Once defined, a model is condemned to deliver only what has been hard-wired into its formulation. However, a difficulty in analysing our inherently turbulent economy and, more specifically, financial instabilities, lies in the fact that most of the crises manifest themselves in a seemingly unique manner. Life very rarely follows a Gaussian distribution and the future is constantly under construction.

  

Excessively complex financial products have spread hidden risks to every corner of the globe. Their degree of intricacy is such that they are often beyond the control of those who have created them. Derivatives of derivatives of derivatives …. The speculative use of such products creates an explosive mixture. Because of the global nature of our economy, and due to its spectacular degree of interconnectedness, such products are an ideal vehicle for creating and transmitting uncertainty.

Uncertain and global economy. It is because of the laws of physics that our economy is increasingly uncertain, unstable and interconnected. This means that it is becoming increasingly complex and turbulent. Conventional methods that rely on mathematical models are unable to capture and embrace this complexity, not to mention predict crises. The increase of complexity is inevitable and globalization is an inevitable consequence of the growth of complexity.

Complexity is a fundamental property of every dynamical system. Like many things, it can be managed provided it can be measured. As for most things in life, when managed, complexity becomes an asset. When ignored, it becomes a liability, a time bomb. Because of the laws of physics, the spontaneous increase of complexity in all spheres of social life is inevitable. Like for most things in life, every system possesses its own maximum level of sustainable complexity. Close to this limit, known as critical complexity, it becomes fragile, hence vulnerable. This is the fundamental reason why each corporation should know its value of complexity, as well as the corresponding critical value.

  

Complexity can be measured. Ontonix is the first company to have developed and marketed a radically innovative and unique technology for rational quantification and management of complexity. Introduced in 2005, OntoSpace™, our flagship product, is the World’s first complexity management system. While others struggle with definitions of complexity, we have been measuring the complexity of banks, corporations, financial products, mergers, or crises already since 2005. Our complexity measure is objective. It is natural. No fancy mathematics, statistics or exotic models. A 100% model-free approach guarantees an objective look at a corporation.

Hidden and growing complexity is the main enemy of a corporation. A corporation may still be profitable but close to default. Highly complex systems are difficult to manage and may suddenly collapse. Excessive complexity is the true source of risk.

  

Critically complex systems become almost impossible to manage, hence are vulnerable and greatly exposed to both internal and external sources of uncertainty.  

Complexity X Uncertainty = Fragility™. This simple yet fundamental equation has been coined by Ontonix and establishes the philosophy and logic behind our technology and services offering. The bottom line is simple: a complex business process, operating in an uncertain environment, is a fragile mix. Since the uncertainty of the global economy cannot be easily altered, in order to operate at acceptable levels of fragility one must necessarily reduce the complexity of the corresponding business model. Based on this logic Complexity Management goes beyond Risk Management and establishes a new underlying paradigm for a superior and holistic form of Business Intelligence. A technology of the Third Millennium.

Conventional techniques provide insufficient to insure against all future contingencies.

There are numerous recent examples of AAA-rated corporations that have suddenly defaulted or are in serious difficulty. The collapse of the Lehman Brothers Bank is a prominent case.  Based on the financial highlights of the bank in the period 2004-2008, our analysis has indicated how a quickly increasing complexity provided crisis precursors, hinting more than a year before default that the system was in difficulty. Evidently, the management was unaware that complexity was sky-rocketing as it is invisible to conventional methods. 

The bottom line: manage complexity.

 

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