Earned run averages do the job for baseball pitchers. Assist-to-turnover ratios tell a similar story for basketball point guards. As do average maintenance costs for cars, on-time efficiency for airlines, etc. We use measures like these every day to assess the risks of our interests.
How much risk is involved in "owning" all of these assets? Although the measures listed above offer a reasonable picture of the risks involved in each activity, they do not combine easily to show the total risk. What technique is best at boiling down the risks of multiple assets into one number?
Value at Risk, or VaR, has come to be the leading candidate to fill this role. With this one number, risks associated with individual traders, portfolios, companies, etc. can be compared equitably. This article will explore what the past year has taught us about using VaR as a risk management tool.
Value at Risk has received much attention in the last two years because of the Securities and Exchange Commission's mandate that companies disclose their risks. The new reporting requirements, adopted in January of 1997, stipulate that all financial firms and public corporations with a market capitalisation greater than USD2.5 billion are required to begin reporting quantitative and qualitative market risk measures of their activity in derivatives and other financial instruments. For current disclosures, firms can select between providing tables of individual risk factor data, sensitivity analyses or VaR. VaR has turned out to be the most popular measure, but it is also the most confusing. What have we learned?
* Not all VaRs are created equal
* VaR is a "rear-view mirror" of the road ahead
* The underlying assumptions of VaR must be stress tested
Value at Risk was developed as a measure of overall portfolio risk. It is the first method that amalgamates the risk characteristics of varied financial instruments and represents them in one single number. This single number is an estimate of a portfolio's expected losses over a certain time interval within a specified confidence interval (CI)i, or probability level. There are three major types of VaR: Historical, Variance/Covariance, and Monte Carlo simulation. Each has advantages and disadvantages, and their results can vary wildly (see graph 2).
Not only should care be exercised when comparing different VaR numbers, but also when looking at individual VaRs. This is because VaR numbers are based on the assumption that the statistically impossible does not happen, which is a glaring falsity. Actually, the statistically impossible happens regularly, especially in emerging markets.
We start with the fact that returns of most instruments with linear price functions can be shown to reasonably fit a lognormal distribution. However, the distribution skews when major dislocations occur, such as credit downgrades, currency devaluations or political upheaval. Under the same circumstances, correlation coefficients based on historical return data also misrepresent future relationships between instruments.
Managers using historical data to anticipate future price movements are much like people using the rear view mirror to drive. If the road is reasonably straight, it is possible to keep the car on the road. But looking backward does not reveal the sharp turns that cause the drive to end disastrously. Many managers' rides came to abrupt halts in 1998, as market dislocations caused unanticipated heavy losses.
This "rear view mirror" effect is illustrated in graph 1.ii Between August of 1996 and September of 1997, all measures of portfolio VaR were essentially equal.iii However, when worldwide markets stumbled in late October of 1997, the portfolio VaR shot up, almost quintupling for the exponentially weighted VaR.iv Examples of such market dislocations abound, such as the devaluation of the baht, ruble or real and the decoupling of corporate spreads in September and October 1998.
As shown in graph 2, VaR calculations done on a portfolio containing the Thai baht prior to May 1997 would have seriously underestimated the risk involved with investing in the currency. Prior to May of 1997, the baht was pegged to the U.S. dollar and its volatility hovered at around 2-3%.v On July 2, 1997 the baht went from 24.4 THB/USD to 29.15 THB/USD, corresponding to a six-standard deviation move in one day. The chances of such a circumstance are quite prohibitive. Specifically, there is a 9.90x10-8 percent chance of a six-standard deviation move.
Perhaps more importantly, its correlation to the Japanese yen swung wildly, at one point dropping to negative 15%. An investor (or hedge fund) with a view that the baht would strengthen while hedging the positions by selling yen had the potential to lose on both trades, essentially levering up their losses. Fat-tail events, or statistically impossible price movements, turn out not to be impossible at all.
In light of these examples, it seems as if VaR is no more than an intellectual exercise without any viable practical applications. There is hope, however. The major problem with VaR is also its advantage: it is one single number that boils down all the risks inherent in a portfolio. No other risk measure can claim such a remarkable power. So the problem remains how managers can use VaR even though it is imperfect.
A possible solution is keeping in mind the question "How should my VaR change given a certain event." The answer can be used to set limits based on VaR, and consequently VaR can be used more effectively to maximize risk-adjusted returns. For example, consider a portfolio that contains the Thai baht, keeping in mind the Mexican peso crisis. During and after the Mexican government devalued the peso in late 1994, changes in Mexican forex rates and the volatilities of those rates were roughly twice as great as those experienced in the baht crisis, as displayed in graph 3. Clearly the two markets are significantly different, but it was certainly not out of the realm of possibility that Thailand could devalue its currency just as Mexico did. Therefore, limits should have been set to prepare for this radical change in VaR. Simply using the 2-3% volatility of the baht was not reasonable.
Stress testing assumptions when analysing VaR's results is not limited to currency trading. Again from graph 3, the spike in VaR around November of 1995 is due to a severe credit downgrade of the KMart bond. Like the devaluations in Thailand and Mexico, this was a statistically impossible event, and could not be predicted by a VaR model because of the fundamental assumption that history is representative of the future.
Value at risk is a complicated notion that inherently has many simplifying assumptions. Stress testing these questionable assumptions is important if the results are to be helpful.
VaR may never be practical when applied to industrial corporations because stress testing the profitability of individual products is difficult, if not impossible. Other risk measures will continue to be employed in similar situations. However, stress testing is easier for financial market participants, therefore VaR could become the most powerful statistic for risk evaluation of everything from individual traders to international behemoths such as Travelers and AXA. With the proper future market conventions, VaR has the potential to be the most powerful tool ever known for analysing risk adjusted returns.
i For example, a CI of 95% would imply that one expected
losses to be greater than the stipulated VaR for 5% of data
sampled
ii Specifically, 7.125% Treasury Bond mat 2/15/23, 7.95%
KMart Bond mat 2/1/23, 6.25% Mexican Par Bond mat
12/31/19, 7.07% Thai Kingdom Bond mat 9/30/13,
6.75% Venezuelan Par Bond mat 3/31/20
iii Daily VaR is based on three months of data with a 95%
confidence interval
iv Exponential VaR based on J.P. Morgan Risk Metrics
methodology with a 98% decay factor
v Based on three months of daily percentage returns
This week's Learning Curve was written by Patrick Thomasma, formerly an analyst at Capital Market Risk Adviors in New York.
