Value-at-Risk – the Ugly Duckling of Finance that Should be the Beautiful Swan

A friend and client of mine called me last week with a question, which was, “We are about to make an acquisition, but one of our shareholders is concerned with downside.  Our company is doing great right now and he’s at a point where he is more concerned with loss than he is with growth.  How do we talk him off the ledge?”  This is a classic risk analysis problem that is often addressed with sensitivity analyses, decision tree analysis, and/or gut instinct – none of which individually or collectively offers a very satisfying answer.  The reason why those approaches are unsatisfying is that they are, essentially, just made up.

Think about it – most sensitivity analyses are nothing more than robotically varying inputs (e.g. growth (+/- 1%), profit margins (+/- 1%), input prices (+/- $10), discount rates (+/- 1%)) and charting the outputs as these inputs are varied.  Most decision trees are put together with “subjective” (let’s face it, this means “made up”) probabilities, and gut instinct is just that.  Gut instinct is the Russian Roulette of M&A.  In other words, we do some more work, but we really don’t have a much greater understanding of the risk involved in the transaction.

What if there were a technique you could use to answer the downside risk question with precision and rigor?  Wouldn’t it be useful to know, for example, what is the likelihood that this M&A deal will result in a loss of (say) $5 MM in shareholder value?  Or, what if we could answer the question of what the baseline loss of value would be in the bottom 5% of outcomes?  We do have such a tool, and it’s called Value-at-Risk (VaR) analysis, and it’s been around for decades.

Value-at-Risk analysis is an elegant tool that enables us to quantify downside risk in terms of probabilities and dollars.  VaR involves modeling out the range of foreseeable outcomes within the framework of a probability distribution of those outcomes, and then selecting the risk threshold in terms of the probability of a certain value of losses or greater.  An illustration of a 5% loss threshold might look something like the following, assuming a normal distribution.


Our model results tell us that there is a 5% chance that the loss associated with this decision or commitment will be $1 million or greater.  That is a much more useful framework for identifying and considering risk in a business context than the standard toolbox.

Because VaR requires some understanding of (fairly basic) statistics to understand, VaR has been an underutilized tool, primarily the purview of hedge funds, and financial academicians.   But is VaR simply an overly-elaborate process for accomplishing something relatively simple?

In our M&A case, the VaR model may be used to quantify the downside risk to shareholder value and better inform the dialogue and decision-making around the proposed acquisition.  You can ask the reluctant shareholder, “How much value are you afraid of losing?”  He might respond, “One million dollars.”  The VaR model can quantify the likelihood of such a loss and see whether that either meets or exceeds the shareholder’s risk tolerance threshold.  Alternatively, the VaR may reveal that the deal is riskier than previously believed, causing a re-think.

Here’s another example that is an actual client case study.  A friend of mine is an attorney who was writing an indemnification agreement for a client.  The client was not willing to offer full indemnification, but was willing to provide indemnification for up to 95% of loss cases.  We ran a VaR model to find out what was the amount of damages that represented the 95% threshold, and that was the value of the indemnification limitation written into the contract.  Rather than guessing, there was a data-supported methodology to set an indemnification limit, and the deal was consummated.

Finally, and this is an older example, a client retained my practice at a prior firm to analyze the risk associated with purchasing a portfolio of distressed real estate loans.  The client wanted to know what the loss threshold was in the worst 5% of outcomes.  We built a relatively simple econometric model to link loan default rates with a relatively small number of  market and macroeconomic factors.  Because of the nature of the model and the market, the loss level at the 5% level was unacceptably high to the client, and they walked away from the deal.

  • Some other VaR analyses I think are plausible, but I have not been called upon to perform include:
  • Determining the value of the worst 5% case of outcomes in a lawsuit;
  • Determining the value of the worst 5% case of outcomes in an investment or investment portfolio;
  • Determining the value of the worst 5% case of outcomes in a currency hedge;
  • Determining the value of the worst 5% case of outcomes in a tax audit;
  • Determining the credit risk of a borrower by associating credit risk with the worst 5% case of business outcomes (such as earnings, or cash flow) for the borrower;
  • Determining the exposure on a loan guarantee with the worst 5% case of business outcomes for the ultimate borrower;
  • Determining the financial exposure for the worst 5% case of outcomes associated with a data breach;
  • Determining the financial exposure for the worst 5% case of outcomes associated with a corporate crisis (such as a plant accident, produce failure, act of employee violence, natural disaster);

I hope I have convinced you that VaR is a tool that can be used to produce satisfying and fact-based answers to numerous business questions.

Implementing VAR requires determining the range of value (loss) outcomes and the probability for each.  Technically, you could simply assign (for example) a 5% probability to an outcome and bang, you have a VaR analysis.  However, if this somehow seems a bit too easy – rather cold, if you will, I agree.  Most robust VaR analyses are accomplished using a technique called Monte Carlo simulation.

Monte Carlo simulation is one of the few cool vocabulary elements in finance.  This is fitting as I think Monte Carlo simulation is one of the coolest tools we have in finance.  Instructions on performing a Monte Carlo simulation run well beyond the scope of this blog (we may write a white paper on it later), but it’s enough if you understand that a simulation produces a range of outcomes by varying model inputs.  The model inputs have features such as mean, standard deviation, and nature of distribution, such as a “standard normal” distribution, as with a bell curve.  The inputs are then randomized, perhaps thousands of times, and the model output is calculated, recorded, and plotted for each trial.  Monte Carlo simulations are typically performed with the assistance of software, such as Crystal Ball or @Risk.  If you are comfortable with programming, you can write about a page of Visual Basic code to perform the simulation.

The parameters of the inputs (mean, standard deviation, shape of distribution) might be determined using the company’s or asset’s own historical data (e.g. revenue, margins, input costs, growth).  Alternatively, the inputs’ parameters may be estimated by analyzing similar inputs of publicly traded companies.  In some cases, you may be able to identify empirical research performed by third parties and utilize that information.  In rare cases, you may have to perform your own research.  The point is, once you determine which inputs need to be varied, it is likely simply a matter of research and analysis to determine how your inputs should be defined in your simulation model.

Once we believe we have the model correctly defined, we can run the simulation and perform the VaR analysis.  If we are seeking to identify the VaR in the 5% worst scenario, we simply identify and use the model result where 95% of the other results are higher, and 5% are lower.  In effect, a Monte Carlo simulation is the ultimate sensitivity analysis tool, and you can vary as many of the inputs as you deem necessary to produce a robust result.

VaR analysis, in spite of its powerful risk analysis capabilities, remains overlooked by executives when making critical decisions.  VaR offers answers to many high-stakes business questions that conventional models simply can’t provide in a convincing, independent way.  By using VaR, you can gain elegant and informative insight into your critical decisions.  Using VaR won’t prevent a bad outcome from happening, but it enables you to accept the risk of a given decision with eyes wide open.  Whether you decide to perform a VaR analysis yourself or seek help, the critical takeaway is that there is a tool available that can enable you to quantify your risks, empowering you to make fact-based, and likely better decisions on risk.

If you are confronted with a significant decision and are struggling with coming to terms with the risk involved, consider engaging the VaR framework.  In the right circumstances, the VaR analysis, properly performed, will give you an additional level of comfort with whichever decision you choose.

Do you have any questions about Value-at Risk analysis, or any experience using it?  Do you wish you had better tools to manage risk for yourself or for a client?  Leave a comment, or contact us to discuss your question in depth.

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