Guest Blogger

My name is Matt Powell and Steven has been kind enough to invite me to use his blog to share some thoughts on risk management and modeling. I am just going to try to share some takes on some topics that I think are interesting and that help circulate ideas across different disciplines.

My background is specifically discrete mathematics, computer science, and optimization but I try to draw from practice in a variety of fields. My day job is working for Segal Consulting, primarily in defined benefit retirement plans. I am an Associate of the Society of Actuaries and an Enrolled Actuary.

Independence Dependence Correlation

Dependency

It may be odd that we are going to talk about dependency between risks before we talk about individual risks, but this issue is so key to ERM modeling that it is best to discuss it out of order.

Some of the largest ERM failures is frequently where a complex interrelationship between multiple risks causes a company failure.   The Black Swan events that Taleb is famous for discussing arises from this complex interplay between the government, company management, human frailty and the market.

Unfortunate Events

 

The Lemony Snicket book “A Series of Unfortunate Events” has led to the frequently used media phrase of “a confluence of unfortunate events”.   Since 2008, we have seen these interactions and ERM modeling has become obsessed with how to model them correctly.

In my first blog, I discussed how different techniques are used to model ERM.  The first one that was used by casualty actuaries and the Credit Derivatives market is the use of copulas or correlation matrices to set up the dependence modeling between the separate risks.  However, the Great Recession has led to the deterministic modeling in ERM.  This was because the banks were required to use multiple deterministic scenarios within their models to give them insight of the impact of the intradependency of the various risks that their book of business was exposed.  Again, Sim Segal’s ERM book discusses this approach and all of the issues behind this.

In the older ERM modeling methods, where dependency is a model assumption such as the use of correlation matrices or copulas, or the dependency that is a natural result of using the same set of stochastic scenarios in all (or most) of the corporate models, be able to come to a deep understanding of how separate risk affect each other is much more difficult than using Sim’s Value Added modeling approach.

Portfolio Effect

 

However, realize before the meltdown, dependency modeling was actually considered a positive component to ERM because through that assumption, a company’s economic capital was lower.  The idea of a portfolio effect was a major selling point for a company to introduce ERM.  This is where managment were led to believe that the interaction between their risks would actually help offset each other and so they would need to hold less capital that may be required by a regulator or a rating agency.  It was (and still is) a very popular idea that lower capital requirements gives  your company greater flexibility in their decisions and makes them more competitive.  However, historically the company equity is in a sense the last line of self-insurance that a company has to be able to continue to exist in bad times or because of bad decisions.

Motivation of ERM Models

In the first blog we discussed the four major methods that are used as the basis of ERM models.  However, other that my discussion around deterministic ERM modeling, I did not discuss why earlier ERM models were stochastic.  The stochastic models were developed to estimate an enterprise’s economic capital.  I will discuss capital modeling in a later post, but consider economic capital to be a measure of a company’s value based on the actual risks that a company is exposed to either by choice or by environment.

Financial institutions have several capital requirements placed upon them to insure their continued health and assuring their ability to meet their financial obligations.  Frequently, these requirements are placed upon them by external organizations such as regulators, rating agencies and stock analysts.  Fiscally responsible enterprises do manage their business using these external capital models, but at the same time there are uniquely positioned to understand their product and their risks, so the development of their own internal capital model would give them a much better understanding of their business.

ERM Modeling Recipes Blog

Enterprise Risk Management is a complex interaction between modeling risk and managing it. Today, I just want to discuss briefly the different styles of modeling risk.

The oldest and in some ways the most simplest to create is the stochastic model.  Here you determine the best statistical distribution that will simulate a specific risk.  As you develop these for each risk, these will be the marginals distributions that you use when you construct the multivariate distribution.  This multivariate distribution will be then used to simulate all of your risks and their interactions with each other.  Frequently, when you are aggregating your risks, you likely don’t know how the separate risks interact.  How these interact will become a major assumption in the construction of your model.

The second and more accurate modeling method is to develop stochastic scenarios, which are then used within all of your separate risk models.  The advantage of this is that the interactions between separate risks are completed determined from these scenarios.  However, the interaction assumption is now replaced by the design and creation of multiple scenarios that will task your separate risk models.  This approach, where it is more accurate regarding dependencies, immediately adds a complexity that may add days, weeks or months to the overall model design and even to the processing required to make capital estimates.

The third modeling methods is the use of proxy models.  Here, you may use scenario models to create a large set of cash flows and then you fit a model to those results such that the model can quickly process many scenarios.  Here you again have the interaction issue dealt with, but now you have a risk model of a risk model.

The fourth model is a deterministic model.  Here the need to determine economic capital is not considered.  For instance, economic capital modeling is the primary reason to use stochastic and stochastic scenario methods.  The use of deterministic scenarios to understand various risks within a company is mostly an outgrowth of the financial meltdown of the late 2000’s. Most banks had to demonstrate how their capital models were affected by various scenarios that were specified by regulatory agencies.    The deterministic approach gives a company an understanding of how their financial models are affected by various economic conditions.  Also, since the scenarios are either designed by regulators or by internal managers, the use of multiple scenarios at one time can demonstrate the interaction between these scenarios.  As has been observed over the past 10 years, frequently the Black Swan conditions arise when there is multiple interacting events that had never been anticipated.  Sim Segal’s book Corporate Value of Enterprise Risk Management: The Next Step in Business Management is an excellent source that outline how to manage using determinsitic scenarios.