 In a recent interview, George Soros captured much of the predicament that finance as a science finds itself in today, when he said, the efficient markets hypothesis has failed, and it is recognized that it has failed and therefore economists need to find a new understanding of financial markets. This is what science is. It is a trial and error. Unfortunately, we don't have a properly developed alternative, and that is what we are looking for. In the interview on CNN, he goes on to say that the approach to finance that we developed under the efficient markets paradigm is not applicable to the real world, and that he in fact made his money betting against the efficient markets hypothesis. Since the financial crisis, much of economic and financial theory has been called into question. We are increasingly recognizing the limitations of the many kinds of financial models that are dependent upon assumptions of linearity and equilibrium, that agents are rational and independent, and that the future will on aggregate generally resemble the past. This is indeed an exciting time for economics and finance, as after almost two centuries of studying equilibrium solutions created by averaging over rational actors, economists are beginning to study the emergence of non-equilibria and the general evolution of patterns in the economy. That is, we're starting to study the economy and financial markets as complex systems out of equilibrium, and increasingly doing this through a computer-based algorithmic approach. This new complexity approach is certainly a paradigm shift. One of its creators, W. Brian Arthur, describes the essence of this change in perception when he notes, really it is a shift from looking at the world in reductionist terms from the top-down and imagining everything holding everything else in equilibrium, where not much is changing at all, to looking at the world as alive. Everything is affecting everything. Dealing with complexity and non-linearity requires shifting our focus so as to look not just at the component parts, but also the overall macro system as a whole. Ideally, this means formulating some kind of overall systemic model of the financial organization we are dealing with. Even if this model may appear very basic, it helps to structure our reasoning and place our more focused analytical understanding within a broader conceptual framework. Finance serves the function of accounting for and exchanging economic value. Financial systems allow funds to be stored and moved between economic actors. They enable individuals and organizations to share and exchange ownership with the associated risks and returns. A key distinction in financial systems can be made between systems designed to enable immediate economic exchange or systems designed to enable the longer term exchange of ownership through investment. Financial systems enable the exchange of products and services via liquid capital where currencies function as a shared medium of exchange, enabling people to fluidly exchange underlying economic resources. Investment capital is concerned with the allocation of assets and liabilities over space and time with associated risks and returns. To facilitate this recording and exchanging of economic value, a financial system converts economic claims to ownership and liabilities into an information-based form of a financial asset or liability. As such, we can say a financial system is an information form of the real economy. It is an information system for the recording and exchanging of value as recorded by balance sheets and mediated by financial instruments of many kinds. Finance quantifies underlying value within the economy and creates an information representation of that in the form of what we call a financial asset. Financial assets derive their value from a contractual claim on an underlying economic asset. The point of this is that information can be more easily stored, processed, and exchanged than real economic assets. This linking, recording, and exchanging of economic value creates a network of interconnected assets and liabilities between different individuals and organizations, what we call a financial system. To serve its function, a financial system has to be able to record and move assets from one entity to another. From those who have savings to those who need it for investment, from those who are buying to those who are selling a good or a service through a currency, from one generation to another through inheritance, from individuals to public administration through taxes, from low interest nations to locations of high returns through stocks, bonds, and loans, for spreading risk through insurance, for joint investment via special purpose vehicles. This relationship between those who have capital, the investors or buyers, and those that need it, debtors or sellers, form the core of what financial systems are and do. Nodes in the network make decisions about how to allocate their capital so as to obtain the economic resources they desire through exchange or investment. Agents exchange resources or invest in other agents to generate a return on their investment or obtain the things that they desire. Financial assets are used as the medium of exchange. They serve as a standardized medium of known value for which goods and ownership can be exchanged as an alternative to bartering. The type of transaction, and type of financial instrument used to enable it, can be seen to exist on a spectrum of liquidity, which defines how widely accepted and rapidly a financial asset can be converted. Economic exchange is done through liquid capital, such as fiat currencies. Investment is done through capital markets in the form of various capital market instruments, such as bonds, stocks, commodities, and derivatives. These are all claims to ownership or claims to a portion of a revenue stream. A derivative instrument is a contract that derives its value from one or more underlying entities. Financial intermediaries, such as banks, insurance companies, hedge funds, and various forms of market makers, perform the function of aggregating resources, spreading investments, and enabling exchanges. Financial agents make exchanges to obtain the things they desire. All exchanges involve a dynamic between risk and returns. Risk defines the potential of a financial loss, and returns defines a gain. For example, when we exchange a currency for some good, it may or may not deliver the functionality we hoped for. When we invest in a company, it may or may not deliver revenue. These represent relationships between risk and returns. Through financial instruments like loans, bonds, shares, etc., financial entities connect their risks and returns with others within contractual agreements. Participants in the market aim to price assets based on their underlying value, their risk level, and their expected rate of return. Thus, the core of a financial system is the relationship between creditor and debtor, and the risk-return ratio of that connection, which defines the contractual agreements as to prices, dividends, liabilities, etc. Indeed, much of economics can be understood in terms of investment, risk, and returns, buying a house or a bicycle, starting a company, a government choosing to build a new bridge in hope that it will stimulate the economy. Combining assets makes it possible to spread risk and returns, and thus engage in larger investments without any one party needing to take on the full risk or provide the full capital investment cost. Financial systems operate at all levels, from personal finance to corporate finance to national to the global financial system. Financial markets form complex adaptive systems, evolving through an interaction between the overall system and the agents on the micro level. Actors adopt certain strategies, make investments, those strategies that prove successful become more prevalent in the system while others die out. This changes the state of the system, which then feeds back to change the success of the strategies adopted. As agents need to constantly adapt and the whole system evolves over time. A financial system is a type of information system, thus the specific form of a given financial system is heavily contingent upon the underlying information technology used to enable it. The financial system's capacity to record and share assets and liabilities is relative to the level of the underlying information technology's efficiency at recording, organizing, and exchanging financial information. As the cost of the transaction goes down and information processing capabilities go up, resources can be more easily moved around in the system and assets and liabilities shared. Coupled with this, social factors, such as legal frameworks, are key to the form of the financial system. Small systems can be defined as either simple linear systems or complex nonlinear systems. The increase in complexity is a function of the number of different component parts in the system and the degree of interconnectivity and interdependence between those elements. A simpler system is one that has few parts, with those parts being relatively undifferentiated and independent. A complex system is one that has many diverse components that are highly interconnected and interdependent. An increase in complexity changes systems in fundamental ways and the same can be said of financial systems. At a low level of complexity with few parts, limited connectivity and interdependence, simpler systems can be described as just a set of parts. Because the parts are not interdependent, they do not form synergies and thus the whole is simply equal to all of the parts, properties and dynamics summed up. As the system becomes more interconnected, it starts to take on a network structure and this increase in connections also creates greater interdependence. Greater interdependence makes the system increasingly nonlinear and as with all nonlinear phenomenon, this creates the conditions for systems level processes and emergence so that the features and dynamics of the whole is different from the sum of the parts. As systems go from simpler to more complex, they go from being linear to nonlinear. With low degrees of interconnectivity and interdependence in simpler systems, an effect can create a cause without the cause returning to its source. This is called linear causality. As we increase the interconnectivity, there are more channels for an effect to return to its cause and this creates a feedback loop between elements within the system. This feedback creates interdependence and it means that the system can change very fast as actions become coupled. What one actor does can feedback to induce another to do more of the same action, creating the possibility for compounding exponential change. The long-term dynamics of a complex system are largely a function of positive and negative feedback loops and externalities. Negative feedback is a balancing loop where the agent is connected to the costs and benefits of their actions. When the costs and benefits to the agents in the system are connected through a feedback loop to the whole, then the system is stable because there are no externalities. When the agent's actions are not connected to their consequences, there is the option for externalities, which can be both positive or negative. A positive externality is when the actions of the agent add value to the whole and thus over time it evolves to a higher level of organization. Inversely, negative externalities mean the agent's actions deplete from the whole, leading to a critical state and collapse. The asymmetry between private gains and the risk to the whole creates externalities, the tragedy of the commons, and unsustainable dynamics. Systems collapse when they become critically fragile due to externalities depleting the resources in the system. For example, when traders purchase an asset, knowing the underlying resource is not valuable but believing that the market price will go up, this is a negative externality that over time leads to a critical state as the system fills up with overpriced assets, a disconnect between real economic activity and the financial system forms, eventually leading to collapse, a housing bubble being a good example of this. Here, the negative externality is creating a disconnect between the subjective value and the objective fundamental value of the asset. The further the two depart, the more critical the system becomes. These externalities can take many forms, but they work ultimately to create a mismatch between the level of risk or value of the underlying asset and the level that is perceived by the market. The result of this is a false evaluation which enables over leverage, over exposure, and ultimately criticality as smaller changes in sentiment can have larger effects due to the lack of fundamentals and over leverage. The inherently subjective nature to the financial system and the possibility to exploit that toward the creation of credit where there is no real asset or underlying value creates instability. All of this can be understood in terms of system dynamics, feedback loops, externalities, and chaos theory. The complexity approach brings into focus connectivity and networks. After the 2008 financial crisis, many economists have come to the view that the very networked architecture of the financial system plays a central role in shaping the dynamics of the system, even more so now that it has become globally interconnected and interdependent. We increasingly recognize that to properly understand the vulnerabilities and opportunities, we have to look at the networks of connections. Here again, complexity science provides us with a new set of models and computer tools for understanding financial network structure and dynamics. The science and mathematics of networks is now almost 50 years old and advancements are being made every year. These insights from network theory can be of critical value in enabling finance to become a more mature science as they provide a mathematical basis to studying the structure of financial systems without dependence upon linear assumptions and models. A financial network is a system of financial entities that are linked through a set of connections in some way. A node in the network can be any organization with a balance sheet or any asset or liability. Connections between them can be exchanges of various forms such as that of ownership. For example, between shareholders in a company or credit and debt between borrower and lender. A financial network thus forms an interlinked system of interdependence between a group of financial entities, their assets, and liabilities. By looking at financial systems as networks, this can help us to answer some important questions that derive from the structure of relationships. For example, how important is any given node in the network as a function of their degree of connectivity and the significance of those who they are connected to? A node's real significance within a network, what is called its centrality, is not a trivial feature to analyze, and it is sometimes counter-intuitive but important to understanding which nodes play critical roles in the network. Pre-distribution is another important factor in understanding a financial network as it helps to define how centralized or distributed it is. The degree of centralization to the overall network is a major determinant of many factors such as its robustness and criticality, how resources flow across the network, and how one might go about intervening in the system. Early centralized networks represent a radically unequal level of connectivity to the nodes. Many nodes have very few connections, while some have very many. Understanding the local level rules under which agents make their decisions about which other nodes to connect to is very significant in attempting to understand the emergent overall network pattern. For example, a network formed based upon preferential attachment, where nodes connect to others based upon the level of resources or connectivity that they already have will lead to a centralized system over time and a too big to fail dynamic. Such a form of preferential attachment can be seen when banks choose to lend only to those who already have large capital accumulations, inevitably leading to a rich-get-richer effect and unsustainable concentrations in the network over time. Following such questions and constructing models based upon agents' decisions and actions, inevitably leads to the questioning of the logic under which agents are making their decisions. Financial systems are composed of agents making decisions on how to allocate their resources. Thus, to understand this system, we need to first understand something about the logic of the agents. There are two fundamentally different paradigms with respect to understanding how agents make choices and evaluate financial resources. Our actions may derive from individual deliberative reasoning, and this would be called a rational action, or they may derive from some other non-deliberative source, such as instinct and emotion, heuristic or social cues, etc. Policy finance attempts to expand our model for the agents in the system by incorporating both rational and non-rational decision making, which takes us into the domain of behavioral finance. To gain a more comprehensive and realistic model to complex financial systems, we need not only new ideas, but also new tools for modeling them. A key tool in this new approach is agent-based modeling that gives us an inherently dynamic vision of markets, as patterns are continually being created and recreated through endless computations across complex networks of interactions, just as we see in the real world. When seen in this way, financial markets show themselves not as mechanical, deterministic systems, always moving towards stability and equilibrium, but instead more like an ecosystem, continuously evolving and creating new structures and patterns. What are more traditional, general, equation-based models do not allow for is the reality of how people act and interact locally to create emergent, bottom-up patterns based upon local rules, which is, to a large extent, how markets work. People find themselves with some set of rules, some kind of local information, and then make their decisions. The interaction of these decisions leads to the overall outcomes of the market. Previously, this vision of the world was not possible for our scientific and mathematical models to deal with, because it involves very many free parameters and too much information. Prior to the advent of computer simulations, we could only write global rules and hope that the empirical data fitted into it. But today, new models from complexity theory, dealing with self-organization and emergence coupled with computer simulations, are changing this. Dealing with heterogeneous agents, making local decisions creates many parameters. It is a high-dimensional problem, and this is why large amounts of data and computer models are needed. With computers, we can define bottom-up models, where we start by asking what rules the agents are acting under, and then simulate that, leading to interaction and emergence. Solutions are no longer well-defined and closed. They're more like patterns. We are trying to simulate the rules, actions, and interactions of agents, looking at how overall patterns are created and continuously change over time. Ultimately, this approach paves the way for a future where we may be able to use big data to compute a real-time picture of what the financial system is doing at any given instance in time. No longer looking in the rearview mirror at what happened last quarter. With big data and agent-based models, we can start to move away from generalized top-down assumptions about the overall state of the financial system, and actually move towards models that are using real data, acting in real time, to compute the many interactions across the financial system, to see what emerges from the bottom-up. This changing paradigm of complexity is already proving critical to rethinking financial theory. The science of finance is young, and is changing fast. But by integrating complexity theory, we believe that it may well be key to actually studying finance as a science, in a much more realistic way than we have done in the past. The importance of rethinking our approach to finance can't be understated. As Professor Andrew Lowe notes, you all know the same scene as believing. I would argue that other times things need to be believed to be seen. Our narrative changes our behavior, which changes reality. That's what I want to leave you with. The fact that we need new narratives in finance, both from the perspective of financial advisors, but also from a societal perspective. Finance is a means to an end, not an end unto itself. This video has been an overview to the content of our e-book, Financial Complexity and Nonlinear Dynamics, a collaboration between Complexity Labs and Fasanara Capital. You can download the full e-book by clicking the link below.