Many institutions have adopted value at risk (VAR) as a way to measure portfolio
risk. Hendricks discusses the VAR methodology and the various VAR approaches in
use today. Using simulated portfolios examined over a long period of time, he
looks at how the various VAR approaches perform in measuring risk and how they
differ among themselves. Overall, at a 95 percent confidence level, all the VAR
approaches examined measure risk accurately, but at a 99 percent confidence
level, VAR measures tend to understate the actual risk.
The surge in financial market trading activity and the increasing complexity of financial
instruments make it difficult for traders, managers, analysts, and investors to know the
financial risks borne by an institution. Value at risk (VAR) addresses this uncertainty
by providing a measure of how much portfolio value could decline over a specified period
of time (at some level of confidence) as a result of movements in the financial markets.
A daily VAR of $10,000,000 at a 95 percent confidence level means that 95 percent of the
time, the portfolio is expected to lose no more than $10,000,000 in one day. Given the
growth in the use of VAR models, the author examines how well VAR models perform in
practice.
The author investigates the three most common VAR models: (1) the equally weighted
variance–covariance approach, (2) the exponentially weighted
variance–covariance approach, and (3) the historical simulation approach. The
first two approaches are similar in that they assume price changes are normally
distributed and serially independent. But empirical evidence shows that distributions of
financial price changes have fatter tails than those predicted by the normal
distribution, which may cause VAR measures to underestimate true portfolio risk because
the VAR measure is designed explicitly to capture performance at the tails of price
change distributions (i.e., the “bad” outcomes). The first two approaches
differ from each other in how past data are to be weighted in estimating the variances
and covariances of future market movements. The equally weighted approach assumes that
data are to be weighted equally over a historical period whereas the exponentially
weighted approach gives more weight to recent observations relative to earlier
observations.
The third VAR approach uses historical data to simulate the portfolio's performance. In
other words, how would the portfolio perform if the market behaved exactly as it did in
the past? The portfolio performance data are then used to calculate VAR measures at the
desired confidence level. An attractive feature of this VAR method is that it does not
make the assumptions of normality or serial independence. Instead, it assumes that the
market will behave as it did in the past. If the historical period contains price-change
distributions with fat tails, then their impact on the portfolio's performance will be
reflected in the VAR measure.
Hendricks also investigates how well the risk measures produced by various VAR models
compare with the actual performance of different portfolios. Do the approaches measure
risk accurately? Do the approaches perform differently at a 95 percent confidence level
than at a 99 percent confidence level? What are the trade-offs in VAR performance if
long-term or short-term historical observation periods are used as inputs to the VAR
model?
To answer these and other questions, the author generates 1,000 randomly selected foreign
exchange portfolios (without option positions) and calculates VAR estimates for each
portfolio during the period from 1983 to 1994. For each portfolio and each day in the
sample period, the author calculates 12 one-day VAR estimates that are variations of the
three basic VAR approaches described previously. The author then assesses the
performance of each VAR approach—each measured separately at the 95 percent and 99
percent confidence levels—using nine performance criteria.
Overall, no single VAR approach is clearly superior to the others. All the VAR approaches
accurately measure the level of risk at the 95 percent confidence level and produce
estimates roughly similar in average size. At the 99 percent level, VAR measures are
somewhat less accurate and tend to understate risk. As expected, the historical
simulation approach, which does not assume normality, produces larger risk measures at
the 99 percent level than do the variance–covariance approaches. The exponentially
weighted approach tends to track portfolio risk over time better than the other two
approaches. The results also show that the largest daily portfolio losses can be several
times larger than the VAR measure. This finding highlights the fact that VAR measures
are not to be treated as “upper bounds” for expected portfolio losses. Other
risk measurement methods (e.g., scenario analysis and stress testing) must be used to
gauge maximum portfolio losses over a specified holding period.