VAR for Enterprise Risk Management

Value-at-risk for banks graphic

Two risk managers were discussing their fear of flying and crashing to their deaths in an airplane.  One of the risk managers stated that he had a morbid fear of being on a plane that is blown up by an onboard bomb.  The second risk manager asked how he handled this fear, to which the first risk manager replied - “Simple, I bring on board with me a bomb that I have control over, and of course I would never detonate it.”  “How does that help?” said the second risk manager.  The first risk manager replied, “The chances of there being two bombs on the same plane are over 27 trillion one.”

If we didn’t get a chuckle out of you that is OK as if nothing else the joke illustrates a point of causation in enterprise risk management, which is currently a hot topic in banking. Astute risk managers understand the fallacy in the first risk manager’s logic in that the odds of any bomb blowing a plane up is materially the same.  To help bankers better understand risk, today we want to demystify value-at-risk (VAR) so that community banks can have another tool in their arsenal and apply the methodology to multiple areas of the bank.

What Is Value-at-Risk?

VAR is currently the most important measure of risk at the national banks and not just on the trading floors and capital markets, but also in their commercial divisions.  VAR is the centerpiece of almost every risk-adjusted return-on-capital loan pricing model; it is also the gold standard for measuring market risk and can be an invaluable tool in quantifying risk in general.  Most regulators are familiar with the concept and endorse the measure.  In fact, in recent regulatory pronouncements, regulators have specifically referenced VAR as an important risk measurement tool.

VAR was first presented in 1986 at Bankers Trust and was applied for that firm’s fixed income portfolios.  Since then, VAR calculations have made tremendous advances and can be applied to any risky asset (a loan, a vendor agreement, or even an employment contract).

In the shortest, but least understood words, VAR is a risk-adjusted probabilistic approach to risk management.  That means that we assign probabilities to various risky outcomes and then order the outcomes from best to worse.  We then state the loss at worst-case levels.  When measuring VAR, we need to state the potential loss in value of an asset (or portfolio) over a defined period for a given confidence interval. Therefore, there are three key elements of VAR: 1) A specified level of loss in value; 2) A fixed time period over which risk is assessed; and, 3) A confidence interval.

How To Use VAR In Credit

For example, suppose that we have a VAR on a $1mm loan for 5 years equal to $200k at 95% confidence level.  The specified loss in value in our example is $200k, the time period is the 5-year life of the loan, and the confidence interval is 95% (we calculate that there is only a 5% chance that the value of the loan will drop more than $200k over the 5-year term).  VAR is neutral to the type of risk assessed which is the poetry of the measure.  We can use VAR to capture credit, market, interest rate, reputation or legal risk.  Any risk that can be distributed with probability of occurrence over time can be quantified using VAR.

Let us consider a $1mm, 5-year fixed rate loan, priced at 4%, with an expected 1.5% probability of default (PD) per annum and 30% severity of loss (loss given default).  Based on simple VAR models, the credit VAR for the loan is $107,578 at the 95% confidence interval.  In other words, we would expect that out of 100 similar loans, only 5 loans would have a credit loss greater than $107,578 over the 5-year period.  This $107,578 figure is only the credit VAR.  We need to add VAR related to other risks associated with any loan.

From our example above, we can also easily calculate the market VAR (possibility of losses associated with interest rate movement), liquidity VAR (possibility that we cannot fund this loan in the future), documentation VAR (for example that our security interest is not perfected), and add these VARs together (adjusting for correlation between them) to arrive at total risk for the loan.  We can do the same for multiple loans (again adjusting for correlation) to come up with a VAR for the entire portfolio.  

 

For the example of the loan above, the VAR for market risk is $64,449.  We can share a short white paper on how to measure market VAR for loans (or hedges) here.  The graph below shows the VAR exposure on our 5 year loan in the purple line (which peaks at $64k around 2.5years into the life of the loan).

VAR graphic

Conclusion

Some bankers are intimidated by VAR as a risk measure for commercial loans, however, the concept is not complex and off-the-shelf models (many bankers use Excel add-ins) are available for almost any application.  Using VAR will not only help your bank quantify risk, but will help your bank communicate about risk. This is a huge step forward in risk management as the lack of risk communication in our industry is one of our major shortcomings. When your board says they want you to increase (or decrease) risk, you now have a framework for discussing how and how much.

Further to this point, bankers using VAR can now see what risks are correlated and which risks are casual. Using VAR to measure your loan portfolio risk may help avoid unwittingly bringing multiple loan bombs to your bank.