What is Value at Risk approach?
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VAR. A technique which uses the statistical analysis of
historical market trends and volatilities to estimate the
likelihood that a given portfolio's losses will exceed a
certain amount. Value at risk is frequently calculated for
either one day or two week periods, and is generally given
as an X percentage chance that the portfolio will lose Y
dollars.
Largest loss likely to be suffered on a portfolio position
over a holding period (usually 1 to 10 days) with a given
probability (confidence level). VAR is a measure of market
risk, and is equal to one standard deviation of the
distribution of possible returns on a portfolio of
positions.
The amount or percentage of value that is at risk of being
lost from a change in prevailing interest rates (similarly
defined for things other than interest rates as well). The
sensitivity of the value of a single financial instrument,
a portfolio of financial instruments, or an entire entitys
balance sheet to changes in interest rates can be
calculated. The resulting sensitivity is the amount of
value at risk. See earnings at risk for an alternative
measure of interest rate risk. VAR, sometimes called equity
value at risk or EVAR, can be calculated by at least four
different mathematical expresions. The simplest and least
accurate measure of VAR is the difference between the
calculated economic value of equity (EVE) under one
projected rate scenario and the calculated EVE under a
different projected rate scenario.
Value at risk (VAR or sometimes VaR) has been called
the "new science of risk management", but you do not need
to be a scientist to use VAR. Here, in part 1 of this
series, we look at the idea behind VAR and the three basic
methods of calculating it. In Part 2, we apply these
methods to calculating VAR for a single stock or
investment.
The Idea behind VAR
The most popular and traditional measure of risk is
volatility. The main problem with volatility, however, is
that it does not care about the direction of an
investment's movement: a stock can be volatile because it
suddenly jumps higher. Of course, investors are not
distressed by gains! (See The Limits and Uses of
Volatility.)
For investors, risk is about the odds of losing money, and
VAR is based on that common-sense fact. By assuming
investors care about the odds of a really big loss, VAR
answers the question, "What is my worst-case scenario?"
or "How much could I lose in a really bad month?"
Now let's get specific. A VAR statistic has three
components: a time period, a confidence level and a loss
amount (or loss percentage). Keep these three parts in mind
as we give some examples of variations of the question that
VAR answers:
What is the most I can - with a 95% or 99% level of
confidence - expect to lose in dollars over the next
month?
What is the maximum percentage I can - with 95% or 99%
confidence - expect to lose over the next year?
You can see how the "VAR question" has three elements: a
relatively high level of confidence (typically either 95%
or 99%), a time period (a day, a month or a year) and an
estimate of investment loss (expressed either in dollar or
percentage terms).
In financial mathematics and financial risk management,
Value at Risk (VaR) is a widely used risk measure of the
risk of loss on a specific portfolio of financial assets.
For a given portfolio, probability and time horizon, VaR is
defined as a threshold value such that the probability that
the mark-to-market loss on the portfolio over the given
time horizon exceeds this value (assuming normal markets
and no trading in the portfolio) is the given probability
level.
For example, if a portfolio of stocks has a one-day 5% VaR
of $1 million, there is a 5% probability that the portfolio
will fall in value by more than $1 million over a one day
period, assuming markets are normal and there is no
trading. Informally, a loss of $1 million or more on this
portfolio is expected on 1 day in 20. A loss which exceeds
the VaR threshold is termed a “VaR break.”
The 10% Value at Risk of a normally distributed portfolio
returnsVaR has five main uses in finance: risk management,
risk measurement, financial control, financial reporting
and computing regulatory capital. VaR is sometimes used in
non-financial applications as well.
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