Economic Capital Modeling With Limited Data

Introduction

Since the 2008 financial crisis, businesses have become more keenly aware of the value of their credit ratings. Accordingly, to strengthen 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. This is due to limitations posed by limited and/or un-reliable data; it is challenging to establish an accurate and reliable economic capital framework. Consequently, the following discussion addresses the issue of data limitations and how to approach it when calculating economic capital. This is a common problem faced from the perspective of market, credit and operational risk. We discuss scenarios where these situations may arise, identify the challenge and how to deal with it.

Scenarios where the challenges can arise

  1. The problem of limited and/or unreliable data frequently arises for those businesses that handle infrequently traded assets. Unlike shares of stock that can be openly traded on an exchange, these are generally unconventional assets. Examples include real estate, plantation assets, and private equities. The limited frequency of trading for these types of assets qualifies them as illiquid.
  2. The problem also manifests itself when organizations are new and do not have sufficient historical experience regarding their processes.
  3. Lastly, business segments that pioneer new opportunities in underdeveloped markets or asset classes face similar difficulties in measuring these types of risk.

Considerations

Small Dataset: The amount of economic capital an institution may desire to hold depends, in part, on the level of confidence the institution is interested in. For example, having sufficient capital and loss reserves to cover losses 99% of the time equates to a 1% confidence level. For institutions with limited data, a methodology to calculate such an extreme circumstance will be a significant challenge. An analysis to satisfy such a high confidence interval requires substantial data.

Solution: One potential option is to use an industry-wide index as a proxy. The portfolio profile of the index should be similar to the subject business. Bear in mind, the profiles of the subject and proxy portfolio may change over time. Consequently, you may need to find and alternative index or abandon this approach. You can request alternative relevant data from the peer organizations. In that case, it is very important to combine the analytical conclusions with an external market study as well as an independent party reports to reach a decision.

Unknown Distribution of Available data: In some cases, business data does not fit into a known data distribution. In other cases, business data may fit an identifiable distribution fit, but it may not make practical business sense. For example, it is highly probable that the historical returns of an illiquid portfolio will not follow a normal distribution. They may turn out to be log normally distributed (after taking account that each return is shifted in positive quadrant). The distribution may be justified by the data at hand, however as a practical matter, it may not make sense as it implies a positive return at all times.

Solution: You may need to study the available data from a number of perspectives before you can identify an appropriate distribution. Given the limited data, you cannot do an in-depth analysis, however you can do some basic research to observe the attributes of the data.  These observations include:

  1. Observing the maximum and minimum values of the data.
  2. Establishing the variance and standard deviation (σ) of the data.
  3. Lay out possible distributions and list out the properties of the distributions that are satisfied by the data.
    1. (i.e., assuming a normal distribution, are all the data points covered in ±nσ (n is number which refers to the required confidence interval)? Similar analyses can be done based on other distributions. A chart of ±nσ range should be completed for all distributions considered.
    2. The chart should contain those distributions that appear to be nearest to the data distribution.
  4. Using the information gathered from the first 3 steps, you can build a scenario analysis using the past experiences from the portfolio. You can supplement this analysis by performing an external study of the market on which the assets are based. Independent party reports can also be included to reach a conclusion.

You can apply expert judgment to the results from the steps above to establish an economic capital measurement.

Diversification Benefit: The challenges of limited data in the context of economic capital are exacerbated when you try to integrate a benefit for diversification. Businesses that operate in different sectors have lower risk profiles than those that operate in singular or limited sectors. Multi-sector businesses experience diversification benefits. The benefit assumes that losses from one business in one sector may be offset by profits in another business in another sector. To maximize the diversification benefit, you need to ensure that the businesses you invest in are least positively dependent on each other. To measure the benefit, you need to accurately measure the dependency of the businesses you have invested in. As such, it is difficult to measure the dependency among businesses with limited data.

Solution: One possible technique can be to combine data of similar businesses. This improves data density while automatically including a diversification benefit in the combined portfolio. Following the combination of businesses, you can perform the same four steps from above and add the expert judgment to calculate an economic capital measurement.

Conclusion

Data is a natural phenomenon, but models are man-made. Consequently, there are no models that can completely capture all available data and predict all future behavior. This problem only gets worse when there is limited and unreliable data. The points discussed above are only offered as suggestions to deal with the problem of limited data. The key point is that there are a limited number of options available from a modeling perspective to deal with thin datasets. Consequently, modelers and business experts have to analyze business problems from alternative perspectives to achieve the best result. They need to compliment the model with alternative scenarios (through other more similar distributions), similar businesses (through expert judgments and independent studies) to support the output delivered by the model.

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