Economic Capital modeling – Importance of Attribution Walk

Abstract

Financial Risk Management is important to any financial institute and hence understanding of what impacts the financial risk is key issue. Economic Capital is one of the most acceptable measures of financial risk. Clear understanding of what impacts Economic Capital and by how much assures robust risk management. We in this paper provide a procedural framework by which a risk manager will be able to understand the impact of variables leading to the change in Economic Capital.

Introduction

Since the 2008 financial crisis, businesses have become more keenly aware of the value of their credit ratings. Accordingly, to strengthen financial risk management processes, financial firms have begun to charge economic capital to their operations based on their processes. Economic capital is the amount of equity necessary to cover possible unexpected losses that arise from an organization’s procedures. Typically, this charge covers the risk of loss over a year, but may be longer. Economic capital charges will also depend on the confidence level that businesses want to reach for covering losses of this type. Ultimately, charging operations for economic capital will drive better risk management practices and improve business profitability.

As the concept of charging for economic capital is not relatively new, but still businesses face a host of challenges with implementation. One of the key challenges we want to focus is on analysis of change in Economic Capital on consequent calculations. Later we emphasize its importance by presenting practical business cases explaining the importance.

A Brief Note on Economic Capital and it’s Modeling

Economic capital analysis refers to ongoing efforts by banks to assure themselves and regulators that they hold sufficient capital to absorb losses to their portfolio, over a relatively short horizon and with a specified degree of confidence (usually 99%, though with some variations).

The desire to have a defined level of assurance about capital adequacy means that economic capital modeling inherently deals with probabilities. In an economic capital modeling exercise, the risk manager thus attempts, by various means, to summarize the likely outcomes for the bank’s portfolio as a whole in a joint probability distribution. By using the joint distribution of investment returns, rather than individual return distributions, the diversification of risk within the portfolio is given its due. As a result, the bank can economize on capital while also being reasonably well assured that a chosen extreme quartile of the joint return distribution will account for the majority of anticipated outcomes[1].

Attribution Walk

Typically the Economic Capital is set aside every first quarter of the year for the business which is has financial risk. But a periodic watch is kept to monitor the adequacy of the Economic Capital. This periodic watch is kept by running the Economic Capital model and recalculating the Economic Capital with the latest business data. The time between two Economic Capital calculations depend on business to business. They may vary from daily, weekly to quarterly.

If the Economic Capital model is run of standalone basis, the Economic Capital numbers appear reliable to the business as long as they are on expected lines. During volatile periods, large change in the Economic Capital numbers is observed. If the Economic Capital model is standalone one, it will be difficult to pin point the exact reason of these changes. Even during nonvolatile periods, we can observe un-expected large change in Economic Capital due to change in the model variables.

Attribution walk is a process where we analyze the change in Economic Capital by step by step change in the model variables and hence study the impact of each model variable. Attribution walk give us direction to further deep dive the Economic Capital calculation process in case we find unexpected change in numbers.

Hence attribution walk will help us to analyze the change in the Economic Capital from two consecutive runs, by demonstrating quantitatively the impact of each variable in step by step manner. In attribution walk, we calculate the Economic Capital repeatedly by sequentially changing one variable at a time. We will explain the process of attribution walk by some practical industrial examples.

In all the examples we assume that we are running the Economic Capital numbers on quarterly basis and Q1 runs have already been done and we are calculating the Q2 numbers. These examples only demonstrate how an attribution walk can be implemented. We do not attempt to suggest any modeling approach for a given problem.

Credit Risk Economic Capital Calculation

Suppose there is a bank holding company which has a portfolio of loans. The loan portfolio will have its expected probability of default. Economic Capital of such a portfolio is typically calculated by Monte Carlo Simulation[3]. A loss distribution is formed and required percentiles of losses are extracted from the distribution. Typically key inputs of the model are:

  1. Exposure at Default
  2. Probability of Default
  3. Loss Give Default
  4. Correlation value for the portfolio

We use the above 4 variables in our Economic Capital model and calculate the Economic Capital. In attribution walk we repeat the Economic Calculations by changing the variables sequentially one at a time.

The steps of attribution walk will be sequentially:

Variables as of Quarter

EAD

PD

LGD

Correlation

Economic Capital 1

Q2

Q1

Q1

Q1

Economic Capital 2

Q2

Q2

Q1

Q1

Economic Capital 3

Q2

Q2

Q2

Q1

Economic Capital 4

Q2

Q2

Q2

Q2

We can have any order of change in the variable values.

Now we have Economic Capital calculated in Q1. Economic Capitals (1, 2, 3 and 4) give us sequential path of the change from Q1 to Q2. At any state if there is an unexpected change we can deep dive those numbers and analyze them.

Economic Calculation for a Cargo Leasing Business

Suppose a company has cargo leasing business. They had various types of carriers which they will lease to their customers. Among many risks in the business; key are Market and Credit risk. Credit risk will be dealt by a similar approach as above in the organization. We will deal with the market risk part here. Market risk is defined as business’s inability to redeploy their cargo at lease rate which was above their cost price. The market risk also includes business’s inability to utilize all the cars in storage. The risk manager would want to calculate economic capital which he would recommend to the corporate office to keep aside so that the rail business remains a going concern with respect to market risk.

One more aspect of risk is that such leasing businesses will have some fixed initial lease terms of their carriers. They will be because of the existing contracts. This will be changing every month because new lease contracts being initialized and old ones getting aged or terminated. Hence typical variables will be

  • Utilization of each carrier
  • Lease rate of each carrier
  • Initial Lease Period

The steps of attribution walk will be sequentially:

Variables as of Quarter

Lease Rate

Utilization

Initial lease period

Economic Capital 1

Q2

Q1

Q1

Economic Capital 2

Q2

Q2

Q1

Economic Capital 3

Q2

Q2

Q2

 

Once the numbers are calculated we will be able to analyze the step by step changes in the Economic Capital numbers. Now we have Economic Capital calculated in Q1. Economic Capitals (1, 2 and 3) give us sequential path of the change from Q1 to Q2.

Economic Capital Calculation for an Insurance Portfolio

Suppose an Insurance company has cash flow based product lines. Each product line will have cash flows based on assets and liabilities. These cash flows will be impacted by the change in interest rates. The risk manager would like to calculate the Economic Capital for the surplus. Typically Duration Convexity based approach is used to analyze such risk[4]. The key risk variables are:

  • Duration and convexity of the assets and liability cash flows
  • Market values of the cash flows

The steps of attribution walk will be sequentially:

Variables as of Quarter

Duration

Convexity

Market Value

Economic Capital 1

Q2

Q1

Q1

Economic Capital 2

Q2

Q2

Q1

Economic Capital 3

Q2

Q2

Q2

 

Once the numbers are calculated we will be able to analyze the step by step changes in the Economic Capital numbers. Now we have Economic Capital calculated in Q1. Economic Capitals (1, 2, and 3) give us sequential path of the change from Q1 to Q2 and hence demonstrating the impact due to change in the values of the input variables.

Further Research – Change of Sequence of Parameter Changes

We discussed three examples of implementation of attribution walk in Economic Capital modeling. We took a sequence in changing the parameters. The change in the Economic Capital will not be same for the change in the value of the parameters because the relationship between the model output and variable may not be a linear one.

It is left for the business judgment to find the most relevant sequence.

Conclusion

Economic Capital calculation is important to achieve targeted credit rating for a financial organization. Hence understanding those numbers and how they change, what parameter impacts them the most becomes important for risk managers as well as business managers. Especially for business managers, the models are typically black boxes and any unexpected change in the output is not acceptable unless proper reasoning is presented. Attribution walk helps the risk manager in two ways: giving him clarity in the impact of each variable and hence logic to present their impact to the business managers. Secondly helps him monitor the input data and gives him right direction to explore in case there is some genuine error in the calculation process.

References:

  1. “Stress Testing and Economic Capital: An Integrated Framework” by Ethan Cohen-Cole, Matt Sekerke and James Zuberi
  2. “Measuring and Optimizing Portfolio Credit Risk: A Copula Based Approach” by Annalisa Di Clemente and Claudio Romano, titled
  3. “Options futures and other derivatives” by John C Hull
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