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Value-at-Risk

Gordon Yeager, a manager in Ernst & Young LLP's Risk Management and Regulatory Practice, explains how value-at-risk can be used as a corporate forecasting tool.

The VAR Debate: Matching Objectives with the Application

Much has been written in this publication recently on the correctness of value-at-risk (VAR). Philippe Jorion and Nassim Taleb argued their points quite elegantly in "The Jorion-Taleb Debate” (April). I found myself agreeing with nearly every point raised by both men. However, the debate, and the majority of the articles on this subject, are quite narrowly focused on how VAR is applied.

The more people speak about VAR and the more articles are written, the more defined its use becomes. This is a bit unusual, considering that VAR calculations came into prominence as much as a way to provide risk-adjusted return measures as to estimate potential risk. Now the focus of debates and articles seems to be limited to the measure's use as an estimation of short-term losses for derivative portfolios and the oft-quoted statement, "There is a 95 percent confidence level that the portfolio will lose no more than $1 million in the next 24 hours.” In addition, VAR seems to be perceived to have value only as a control measure that includes all of a firm's risk positions, and few address its use as a strategic or planning tool.

The real focus of potential VAR users should not be on the measure's perceived correctness, but rather on the definition of the firm's measurement objectives and the matching of them with a customized application. VAR and its methodologies are far too powerful and flexible to be confined to a narrowly defined application. The focus of VAR should also not be on debating the proper methodology, time period and confidence interval. Each methodology has its own merit, and once the proper measurement application is thoroughly defined, choosing between variance/covariance, historical simulation and Monte Carlo simulation is not a difficult task. One certainly would not use variance/covariance to determine the probability of exercising a portfolio of barrier options over a 12-month period, and it would be overkill to use Monte Carlo simulation when determining the overnight risk on a portfolio of treasury bills.

Customized VAR Applications

In designing VAR programs for a variety of end-users, we have found a number of valuable nonstandard uses for the measure. We would be the first to admit that the application of VAR that has been the focus of current debate has little benefit for the vast majority of corporations. However, based on the ability of VAR to produce probabilistic forecasts for potential cash flows, we have identified dozens of useful applications for any organization.

The key in identifying these applications is a focus on the current state of the organization and its concerns. For instance, a company that needs assistance in choosing an overseas expansion strategy can use VAR to produce foreign investment hurdle rates that are risk-adjusted and more accurately depict potential returns for a project in Argentina vs. one in Germany.

VAR can also be used to help corporations evaluate the risk of their business operations. By modeling a corporation's exposed cash flows, treasury can provide senior management with an estimate of the risk that is inherent in its business and help to address the "Should we hedge?” question. The ability to handle a number of different risks with potential offsets is key in this application. Without VAR, the ability to estimate the risk of a long Deutsche mark and short French franc position requires the use of caveat-laden scenario analyses.

VAR also has unique applications in the investment environment. The ability to evaluate the diversification benefit of alternative asset classes and managers and the incremental risk that they add to the portfolio is an excellent use of the measure. VAR can also be used to update investment guidelines. Typically every investment policy has limits set on asset allocation to ensure diversification and reduce risk (such as concentrating only 10 percent of the portfolio's value in small-cap stocks). These limits are often arrived at in a somewhat arbitrary fashion, however. With VAR, one can determine what those limits translate to in terms of risk. A sample portfolio created from these asset-allocation guidelines can serve as a valuable benchmark to guide investment decisions.

The common thread in these alternative applications is their use as decision-making tools. VAR should not be considered an answer to a company's risk management concerns; rather it is a tool that can provide valuable decision-enhancing information.

A case study

One detailed example of a customized VAR application involves a U.S.-based company hedging its net income translation exposure. This exposure arises from international operations with non-U.S. dollar functional currencies. The net income figures of these operations must be translated to U.S. dollars to produce a consolidated net income number. Even though these net income numbers are not exposed from a cash flow point of view, many companies hedge them in order to protect their consolidated net income forecasts. Although the correctness of this type of hedging could be debated at great length in another series of articles, the purpose of this example is to highlight the VAR application utilized.

This particular company had been hedging its net income exposure for a number of years using at-the-money options. (Net income exposure is typically hedged with options because of the desire to avoid realized foreign exchange losses that cannot be offset by gains from the exposure.) In each of the last three years, the currency markets had moved in the company's favor and the options had expired worthless. Senior management questioned the strategy and requested that treasury do two things—evaluate alternative strategies and provide more information on potential strategy performance.

Treasury's mandate for this hedging program was to deliver the budget rates used to translate the net income forecasts into dollars. Stated another way, treasury wanted to ensure that the consolidated U.S. dollar net income forecast was not missed because of currency fluctuations. With a thorough definition of the company's objectives, a proper measurement process could be formulated.

Sample Output
Forecasted USD Value: $1,254,321
Strategy
Alternatives
Hedge
Cost
95%
Value-At-Risk
Probability of
Missing Value
Stress
Test
Unhedged
  0 1,209,667 47.5% 1,103,802
Gain/(Loss) vs. Budget   (44,654)   (150,519)
Strategy #1
100% ATM Options (40,264) 1,253,196 1.7% 1,253,167
Gain/(Loss) vs. Budget   (1,125)   (1,154)
Strategy #2
50% ATM Options (20,132) 1,241,907 18.3% 1,180,316
Gain/(Loss) vs. Budget   (12,414)   (74,005)
Strategy #3
100% 2% OTM Options (23,205) 1,231,743 23.4% 1,227,980
Gain/(Loss) vs. Budget   (22,578)   (26,341)

The process used a multistep Monte Carlo simulation to forecast future values of the net income exposures and alternative hedge strategies. Each strategy's VAR was calculated using a one-year time period and a 95 percent confidence interval. The most valuable measure for the client, however, was the determination of each strategy's probability of missing the forecasted net income target. Determining the probability associated with a dollar amount, rather than determining the dollar amount associated with a probability, was an important distinction for the company. It may even allow the determination of the probability of option exercise.

When this information and the results of defined fixed scenarios were combined with the hedge costs of each hedge strategy, senior management was provided with the information requested. A sample report is shown on the opposite page. This information is not produced to provide an answer but to provide information to aid decision-making. This is a key point about VAR that has been overlooked in much of the debating. The real value of the measure is to provide information to make more complete decisions.

Despite these beneficial applications, all VAR proponents must caution users on the measure. The very nature of the measure requires it to be used in tandem with some type of stress testing, since the far tails of the distribution are the real concerns. Nothing associated with VAR is about certainty, and it can be debated whether the derivatives debacles of the recent past would have been avoided had VAR been used.

Our experience with VAR, however, has shown it to be a very powerful tool when a firm carefully outlines its risk measurement objectives and matches them with a proper application of the measure. The benefits of risk measures that enable more informed decisions to be made are difficult to debate.


Gordon Yeager can be reached at gordon.yeager@ey.com.
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