
All About Value at Risk
Value at Risk
FAQ
I am not sure what are the most frequently
asked questions about VaR, but I have made a stab
at it here. If you have any suggestions for additions to this list, I
would welcome them. If you have a
question, suggest a Q for the FAQ by clicking here
What is VaR? What's the difference
between EaR, VaR, and EVE? Should the "a" be
capitalized in VaR (VAR)? What's statistics got to
do with it? What's the tail of a loss
distribution? What does VaR say about
the "tail" of the loss distribution? What does VaR assume as a
risk measure? What's market
risk? What is
VaR used for? How is VaR
calculated? What is Monte
Carlo? What is
Historical Simulation? What is
RiskMetrics? What is the
Variance/Covariance Matrix or Parametric method? What is a "linear"
exposure? What
is a "non linear" exposure? What is Stress
Testing? What
is Backtesting? What do regulators think
of VaR? What
is a lookback period? What does VaR have to do
with maximization of shareholder wealth? What's the difference
between a confidence level and a confidence interval? How does VaR for
corporates differ from VAR for financial firms? What is the most
accurate VaR method? What is the minimum
number of simulations that should be run in Monte Carlo VAR? What confidence level
should I use?; Is 99% more conservative than 95%? What time horizon should
I use?
What is VaR? I think of Value at Risk as a measure of potential loss from an
unlikely, adverse event in a normal, everyday market environment. VaR is
denominated in units of a currency, e.g., US dollars. To get more
concrete, VaR is an amount, say D dollars, where the chance of losing more
than D dollars is, say, 1 in 100 over some future time inderval, say 1
day. This is a probabalistic statement, and therefore VaR is a statistical
measure of risk exposure. The calculation of VaR requires the application
of statistical theory. [top]
What's the difference between
EaR, VaR, and EVE? Earnings at Risk typically
looks only at potential changes in cash flows/earnings over the forecast
horizon. Value at risk looks at the change in the the entire value over
the forecast horizon. Economic Value of Equity also looks at value change,
but typically over a longer forecast horizon than VAR (up to 1 year). In a
trading enviornment, where profit and loss are equivalent to changes in
value, EaR and VaR should be the same. [top]
Should the "a" be capitalized
in VaR (VAR)? When at work I capitalize, but in
less formal situations I don't. Actually, it's less confusing if you
don't, since VAR (capital "a") also stands for "Value Added Reseller" and
"Vector Auto Regression." [top]
What's statistics got to do
with it? Var is actually a piece of information
about the distribution of possible future losses on a portfolio. The
actual gain or loss won't be known until it happens. Until then it's
uncertain; a random variable. Information about the behavior of a random
variable is called a statistic. As you may guess, there are many
statistics about a portfolio returns, for example the expected return. The
VaR is a very useful statistic for risk managers, but it's unlikely that
it's the only statistic that has some usefulness. Nevertheless, it is the
statistic focused on almost exclusively. Now for the tricky stuff. VaR
itself is a random variable, because not only is the portfolio's future
return unknown, but the distribution of the portfolio's return must be
guessed at by inference from observable data. That means that the
calculated VaR is really itself just an estimate of the true VaR. So you
could estimate a VaR of the distribution of the VaR! Most people are
content with estimating confidence intervals for any estimated parameter,
becuase the confidence interval tells you how precise is your estimate.
[top]
What's the tail of a loss
distribution? The tail is that portion of the
loss distribution that contains the outlying (i.e., bad) events). Problem
is, no one seems to know exactly where the tail begins. Which can be a
problem for some measures of risk. However, a lot of research is going on
in this area, so stay tuned. [top]
What does VaR say about the
"tail" of the loss distribution? Not much really.
If your VaR model assumes some shape for the entire distribution of
portfolio return, then everything you need to know about the tail is
embedded in that assumption [top]
What does VaR assume as a
risk measure? Just about every VaR model assumes
that the portfolio under consideration doesn't change over the forecast
horizon. This is a fiction, especially for trading portfolios, but trying
to incorporate forecasts of position changes into a model forecasting
returns is very complicated. VaR models also assume that the historical
data used to construct the VaR estimate contains information useful in
forecsting the loss distribution. Some VaR models go further and assume
that the historical data themselves follow a specific distribution (e.g.,
a "normal distribution" in RiskMetrics(TM)). [top]
What's market
risk? Market risk is usually defined as the risk
to loss in a financial instrument from an adverse movement in market
prices or rates. What's adverse? Well, it depends. If you own a bond, then
a rise in interest rates is adverse, but if you have lent/sold a bond, it
is a fall in rates that is adverse. Generally people classify sources of
market risk into four categories, interest rates, equities, foreign
exchange and commodities. [top]
What is VaR used
for? Not a food additive, yet. Originally VaR was
used as an information tool. I.e., it was used to communicate to
management a feeling for the exposure to changes in market prices. Then
market risk was incorporated into the actual risk control structure. I.e.,
trading limits were based on VaR calculations. Now it is commonly used in
the incentive structure as well. I.e., VaR is a component determining
riskadjusted performance and compensation. Interestingly, the theory of
VaR has not kept pace. While we understand it's usefulness as an
information tool, it's not clear how it fits into the "shareholder wealth
maximization" paradigm of modern financial theory. [top]
How is VaR calculated?
It depends on the method used,
variance/covariance, Monte Carlo, historical simulation. Generally, it
involves using historical data on market prices and rates, the current
portfolio positions, and models (e.g, option models, bond models) for
pricing those positions. These inputs are then combined in different ways,
depending on the method, to derive an estimate of a particular percentile
of the loss distribution, typically the 99th percentile loss. [top]
What is Monte
Carlo? A small principality in Europe. But you
knew that. It is a simulation technique. First make some assumptions about
the distribution of changes in market prices and rates (for example, by
assuming they are normally distributed), then collecting data to estimate
the parameters of the distribution). The Monte Carlo then uses those
assumptions to give successive sets of possible future realizations of
changes in those rates. For each set, the portfolio is revalued. When
done, you've got a set of portfolio revaluations corresponding to the set
of possible realizations of rates. From that distribution you take the
99th percentile loss as the VaR. [top]
What is Historical
Simulation? Like Monte Carlo, it is a simulation
technique, but it skips the step of making assumptions about the
distribution of changes in market prices and rates (usually). Instead, it
assumes that whatever the realizations of those changes in prices and
rates were in the past is what they can be over the forecast horizon. It
takes those actual changes, applies them to the current set of rates, then
uses those to revalue the portfolio. When done, you've got a set of
portfolio revaluations corresponding to the set of possible realizations
of rates. From that distribution you take the 99th percentile loss as the
VaR. [top]
What is
RiskMetrics? It is a particular implementation of
the Variance/Covariance approach to calculating VaR. It is particular, not
general, because it assumes a particular structure forthe evolution of
market prices and rates through time, and because it translates all
portfolio positions into their component cash flows (or "equivalent") and
performs the VaR computation on those. It is really responsible for
popularizing VaR, and is a perfectly reasonable approach, especially for
portfolios without a lot of nonliearity. [top]
What is the
Variance/Covariance Matrix or Parametric method? This is a very simplified and speedy approach to VaR
computation. It is so, because it assumes a particular distribution for
both the changes in market prices and rates and the changes in portfolio
value. Usually, this is the "normal" distribution. The neat thing about
the normal is that a lot is known about it, including how to readily
obtain an estimate of any percentile once you know the variances and
covariances of all changes in position values. These are normally
estimated directly from historical data. In this method the VaR of the
portfolio, is a simple transformation of the estimated variance/covariance
matrix. So simple that it doesn't really work well for nonlinaer
positions. [top]
What is a "linear"
exposure? A linear risk is one where the change
in the value of a position in response to a change in a market price or
rate is a constant proportion of the change in the price or rate. [top]
What is a "non linear"
exposure? Everything that's not linear. For
example, options are thought of as nonlinear exposures, because they
respond differently to changes in the value of the underlying instrument
depending on whether they are inthemoney, atthemoney, or
outofthemoney. [top]
What is Stress
Testing? I think of stress testing as measure of
risk exposure that's complementary to VaR. Stress testing is a measure of
potential loss as a result of a plausible event in an abnormal market
environment. Two types of stress testing are popular. The first is based
on economic scenarios. Pretend your portfolio experiences the 1987 or 1997
stock market crash again. The second is "matrix" based. Change a bunch of
assumptions about correlations and variances and see what happens. Neither
is statistical in nature, in contrast to VaR. That is, you don't know the
probability of any particular scenario. [top]
What is
Backtesting? Backtesting is a statistical process
for validating the accuracy of a VaR model. Banking regulators require
backtesting for banks that use VaR for regulatory capital. It involves a
comparison between the number of times the VaR model underpredicts the
subsequent day's loss, versus the number of time such an underpreduction
is expected. If losses exceeding VaR have a 1 in 100 chance of occuring,
then we expect to see 2 or 3 of those in a year. There is a lot of debate
about whether backtesting is meaningful, because it is difficult to
validate a model based on a few extreme events  not enough data.
What do regulators think of
VaR? Lovehate, I think. Love first. Banking
regulators internationally have agreed to allow banks to use VaR models to
calculate regulatory capital. Don't ask why banks have minimum capital set
by regulators, as that is a different FAq. In the USA, the securities
regulator allows corporates to use VaR to express their exposure to market
risk in their annual and quarterly regulatory public financial filings.
Now hate. Regulators aren't sure that VaR is the "right" measure of risk?
Nor are they sure how much weight should be given to it in risk
management. They really aren't sure whether VaR should be extended to the
measurement of other kinds of risk, such as credit risk. [top]
What is a lookback
period? It is the period of history that is used
to collect data used in the computation of VaR. This is important, because
if the data is inappropriate for the forecast, the forecast is no good.
[top]
What does VaR have to do
with maximization of shareholder wealth? Excellent question. A precise answer isn't possible yet. This
is troublesome, as one hopes that it is being used in ways that are
consistent with the concept of shareholder wealth maximization, but we
can't be sure. [top]
What's the difference
between a confidence level and a confidence interval? Pet peeve coming up. While VaR is an estimate of a percentile
of the loss distribution, it is commonly referred to as a confidence
level. This is because we say, we are 99% confident that the loss will not
exceed $XX. It's more exact to refer to VaR as a percentile estimate.
Because VaR is a statistical estimate, it is an uncertain amount itself,
and that uncertainty can be encapsulated in a statistical concept called a
confidence interval  I am 95% sure that the VaR actually lies between $AA
and $BB. It's too confusing to talk about a confidence interval around a
confidence level. [top]
How does VaR for corporates
differ from VAR for financial firms? The use of
VaR for nonfinancial firms is still evolving. Currently it is mostly
focused on either VaR for derivatives and hedging instruments only or VaR
for cash flows, i.e., EaR. [top]
What is the most accurate
VaR method? Accuracy is in the eye of the
beholder. A general answer to this question is not possible, because it
will depend on the nature of the portfolio and the data used in the
estimation of VaR. Several studies comparing methodologies were conducted
a few years back, typically with linear portfolios, either equities or fx.
These tended to show that the variancecovariance approach was better when
short histories of market prices were used, because Monte Carlo and
Historical Simulation would under estimate the 99th percentile. With
longer histories MC and HC were equal to or better than VCV. But I don't
recommend you generalizing from these studies, because of their limited
scope. Because of this, it is very important to have an estimate of
precision for every VaR estimate (A confidence
interval). [top]
What is the minimum number
of simulations that should be run in Monte Carlo VAR? I know that one major bank uses 500 simulations for its Monte
Carlo VaR. Again, the answer depends on the complexity of the portfolio.
Linear instruments, fewer simulations. But MC has its own peculiarities
that affect accuracy. For example, some MC routines use "variance
reduction." These are "tricks" used to improve accuracy for a given
simulation size. With variance reduction techniques (e.g., Antithetic
Variates), the fewer simulations needed for a given accuracy. Remember
that underlying every MC is some distribution from which observations of
market rates are sampled. So assumptions about the distribution and
shortcuts taken to reduce the "dimensionality" of the distribution will
also have a cost in accuracy which should require more simulations for a
given level of accuracy. [top]
What confidence level should
I use?; Is 99% more conservative than 95%? I know
this is really two questions. The underlying question really is, what
percentile of the return distribution gives me better information about
risk exposure? If the portfolio return distribution were normally
distributed, it wouldn't matter, because every percentile is expressible
as a constant times the standard deviation of the return, the standard
deviation being the only real information you need for risk assessment in
the normal distribution case. The tradeoff between choice of percentiles
in the real world in which we live is really about accuracy. It is more
difficult to accurately estimate a point farther out in the tail of the
distribution of returns, because there is less observable data to use in
the estimation. However, you may wish to look farther out in the tail if
you believe that your portfolio return distribution is more "fattailed"
(you may think of it as when the ratio: 99 percentile/95 percentile is
greater than if the ratio were calculated for a normally distributed
return distribution). If there's more going on out there in the tail, you
may want to focus on it more. However, simply because 99th percentile VaR
yields a bigger VaR does not mean that using a 99th percentile rather than
a 95th percentile VaR is a more conservative of a measure of risk. All it
means is that you are looking at a point farther out in the tail and
calling that your risk exposure. Whether you use 95 or 99, you are
generating an estimate of risk from the same distribution of returns.
[top]
What time horizon should I
use? The standard time horizon (that period over
which the VaR forecast is made) is one day for most financial businesses
with active trading portfolios. The logic for this horizon is that it
would take less than one day to either exit or hedge out all the market
risk in any position, so that's really how long is the exposure. This
reasoning suggests that the horizon should be tuned to the interval to
close out the market exposure. This is a bit simplified, because it
ignores liquidity issues (large positions may take longer to exit, simply
because they are large), differences among portfolio instruments (it is
not reasonable to employ a one day horizon for some positions and a
multiday horizon for others, and then to aggregate them for portfolio VaR
calculations), and consistency with credit VaR calculations (typically
using a much longer horizon, thereby making aggregation complicated 
ignoring all the other theoretical issues in aggregating credit and market
risk). These two problems have no completely satisfactory solutions. So,
it may be best to identify a singly horizon that best fits the portfolio's
characteristics and use that for everything when calculating VaR. [top] Page
created by: Barry Schachter. This
page: http://www.GloriaMundi.org/var/FAQ.html
