Financial Risk, the Art of Statistical Modeling & Challenges With Machine Learning
“The reality is, risk is a variable. Those in the financial world know it.”- Jason Fried
Financial risk management is being formally practiced for decades if not centuries using conventional as well as unconventional methods to help identify and manage the risk of financial loss. However, since last few decades it has emerged as a formal discipline of study and research.
Today financial risk management has evolved into a business function with a sharp focus on identification, assessment, reporting, monitoring and management of financial risk, than just being a department of treasury.
Post 2007-08 financial crisis, the banks and financial institutions all over the world are experiencing deepening regulations with a need for broadening the scope of financial risk management.
With ever changing socioeconomic environment, dynamics in the financial markets, advancements in technology and evolving customer expectations, no wonder, there would be even more pressing need to manage financial risks in an informed way.
Statistical Models, Mathematical Measures and Quantitative Methods as Foundations of Financial Risk
The foundation of financial risk has always been mathematical and/or rather statistical. Financial risk is one of the important element of core concepts of financial theory and practice in general.
For example, quantitative finance as a field of applied math, deals with the application of mathematical modeling for various financial market activities (e.g. CAPM for options pricing), but at its core lies the concept of managing financial risk (e.g. valuations and risk models).
Similarly financial engineering, a multidisciplinary field that stems from engineering techniques, mathematics & computer programming, more importantly has financial theory & financial risk at its core (e.g. Derivatives, Modern Portfolio Theory and Asset Pricing).
The Art of Statistical Modeling
Financial risk management deals with more than ten different types of risks but market and credit risks are the two most talked about broader risk classes besides the operational (residual) risk. Many statistical models, mathematical measures and quantitative methods are widely used as important tools in financial risk management for risk identification, assessment & measurement.
Since we are talking about financial risk from a generalized standpoint of a probabilistic event/s which may or may not occur, the focus of this discussion is more on statistical modeling.
Managing credit risk for that matter, makes extensive use of statistical models for estimating default probabilities, credit ratings, calculating credit exposure of derivatives, CVA, DVA and credit VaR (ex. Vasicek’s model).
Market risk too uses statistical risk models for calculating Value-at-Risk (VaR) and Expected Shortfall (ES) measures, pricing and valuations of derivatives, returns, spreads and yields, calculating the Greeks, modeling and forecasting trends, seasonality and cycles (MA, AR, ARMA models), calculating volatility, correlations and copulas (EWMA, GARCH), to name a few.
However, the statistical models are not just ordered mathematical instructions and assumptions acting on the sample data which help us to understand the interactions between two or more variables. If we notice carefully, they have an identity of their own, a character & a legacy of performance if they manage to stand the test of time.
These models are imagined, conceived and built with an intention of solving a specific problem or for a specific purpose by those who understand the fact that financial risk is not just a random phenomenon that appears due to human errors, variable market conditions or otherwise — it has a trend, cycle or pattern which can be identified and modeled.
Statistical modeling is an art in itself, and for that one has to be an artiste who can imagine, explore and interpret the dance of variables, conditions and assumptions.
Let’s take an example of Value-at-Risk (VaR) measure which is widely used in market risk management to provide a summarized single number downside risk of a portfolio.
The Basel Committee on Bank Supervision (BCBS) via its 1996 amendment requires all the banks to hold capital for market and credit risk, post that there are further revisions (e.g. FRTB) for required capital requirements.
Traditionally, the capital requirement for market risk calculation uses VaR with n=days and x=percentile, where the variable n is time horizon & variable x is confidence interval (example n=10 days, x=99%). The bank is required to hold capital that is k times VaR measure, where k is bank specific, decided depending upon factors like how well tested a banks VaR estimates are.
The intention is to provide estimates such as “I am x% certain that the loss would not be more than v ($) dollars in the next n days”. Here, v is VaR for a portfolio and is function of two variables i.e. n & x. To get the best VaR estimates with high confidence level, one has to explore the historical data (hence, historical simulation is one of the methods to calculate VaR).
That’s not all though, we also have scenarios analysis, stressed VaR and back testing, which adds fuel to imagination to help get the best or rather accurate VaR estimates.
VaR is undoubtedly a standard method to calculate summarized portfolio risk, but Expected Shortfall (ES) provides better estimates as a risk measure. Here, however the intent differs. While VaR focuses more on the probabilistic possibility of a loss for a given time horizon, the ES talks about how much that loss would be.(Ref. Risk Management and Financial Institutions, 4th Ed. John C. Hull, pg. 259, Sec.12.4)
One can even calculate marginal, incremental and component VaR (& ES) for sub portfolios. Euler’ theorem can be used when a risk measure for a complete portfolio is allocated to sub portfolios. There are tools and techniques for back testing, stress testing, extreme value theory (EVT) for precisely measuring the “tails” to improve VaR estimates with high confidence levels.
Its JPMorgan where the development and wider use of VaR as a risk measure ‘happened’ out of the frustration of receiving a detailed, long and cryptic 4.15 risk report which did not help the top executives to understand & make quick decisions. Eventually the “Markowitz portfolio theory” was adapted to develop VaR report.
This is just a tip of the iceberg and there are many more statistical models used as tools for financial risk management, each one of them is used for a specific purpose.
Machine Learning — Implementation in Financial Risk Management, Promises & Challenges
Due to the advancements in computer science & technology, the ability to process large amount of structured as well as unstructured data in near real time has made it possible for Machine Learning (ML) to emerge as a business enabler. This ability has opened up new avenues for business data analytics and found its applications in almost every business domain/function.
Applied machine learning has many use cases in banking and finance too, and it ranges from algorithmic trading, credit risk modeling, and fraud detection to virtual financial advisers (risky business, isn’t it?). No surprise ML has also found its application in financial risk management.
Statistical Modeling vs Machine Learning
Machine learning has its roots in core sciences like mathematics & statistics along with engineering and computer science. Machine learning essentially needs a solid understanding of probability and statistics, linear algebra, advanced calculus, coordinate geometry as well as optimization & simulation techniques etc.
If we notice carefully, exactly the same (and more) areas of knowledge are a mandate to understand and apply financial risk management in practice. To strengthen the argument we can take an example of linear regression, which is one of the machine learning class of algorithms under supervised learning that is used for predicting continuous dependent variable. The same is also used in financial risk models and has similar aspects of regression, estimating coefficients, calculating standard error, hypothesis testing, confidence levels, optimization etc.
If that is the case, then one might ask a question as to, “If we have machine learning that has much more processing power and improved accuracy in predictions, do we really need statistics in financial risk management?” The answer to this question is not straight forward though and there are different schools of thoughts around this notion. The context or the problem in hand would play a major role in making a fairly balanced and pragmatic assessment of these two. But in the current scheme of things the generalized answer is — ‘No’ — machine learning is not a substitute for statistical methods in any area of its application, let alone financial risk.
There is a fundamental difference between statistical modeling and machine learning and that is of the intention or purpose, what we expect from each one of them.
If we try to understand the basic difference between the two, there are many arguments that can be made as pros and cons for each one of them — when and where to use those. But everything boils down to their intention & ability to interpret the model. The statistical models, be it descriptive or inferential — the intent more often is to understand the correlation between variables, their inter dependence. For machine learning however, the intent is to predict and that’s its real strength.
The ability to interpret is important for those who are going to use the model because along with the statistical findings or inferences a model provides, the users are also going to apply their business acumen or domain experience to make decisions.
Modeling is indeed a form of creative expression & the choice of variables along with assumptions act as a medium to imagine possibilities and explore various alternatives — this is interpret-ability of a model which in turn enables leveraging the domain expertise of the model developer or model user. Unless we factor-in this need for domain expertise in statistical or machine learning models, we are landing into an unknown territory, which is a risk in itself. Statistical models certainly score over machine learning models when it comes to interpret-ability.
Conclusion
Though machine learning promises real time, high volume data processing to produce accurate predictions, it’s still a black box processing. Here machine learning models strikingly differ from statistical modeling in two ways, the intention behind building a model and their interpret-ability.
The ability to interpret the model is as one of the emotional needs of the modelers and business users as it adds an important dimension to every statistical model — the dimension of being an artiste. The model is a creative expression of their domain expertise, business acumen and judgement!
It would be foolish to say that this challenge with machine learning models that we face today as humans can never be solved, eventually it will happen.
Till then let us appreciate and enjoy the art of statistical modeling and all that stat!
