Making VAR More Flexible
Mark Garman, president of Financial Engineering Associates,
explains how a new methodology, delta value-at-risk, can help traders and
risk managers use VAR more effectively for strategic decision-making.
In every risk manager's tool kit, there is available a value-at-risk
(VAR) system that acts as the trash compactor for the entire company, compressing
diffuse, firm-wide risk information into a single number. At cutting-edge
institutions, however, risk managers want something more versatile than
this one-dimensional number. A simple VAR number may indicate that you have
a risk problem, but doesn't tell you how to solve it. Ideally VAR should
provide actionable information and help companies answer the following questions:
how do individual trades affect total firm-wide VAR? How much will a hypothetical
hedge decrease total VAR? Which trade, out of several, will have the greatest
effect on firm-wide VAR?
VAR, as it is currently practiced at most banks, cannot provide this
information for a variety of reasons. First, VAR's single-number approach
is designed to reduce the market's natural complexity; it is impossible
to "reverse engineer" VAR to, for example, recover the cash flows
that were fed into the original VAR number or reassemble the individual
trades from the cash flows. Second, VAR even at its most reductive is still
a time-consuming process for institutions with very large portfolios. This
means that if you want to look at how a particular trade will affect your
firm-wide VAR, you must run a baseline VAR on an existing portfolio, add
the new trade to your portfolio, rerun VAR for the entire firm, and take
the difference between the two.
How can you turn your plain-vanilla VAR report into a robust decision-support
tool? Well, at Financial Engineering Associates (FEA) we have developed
a new methodology to address these questions and more. Known generically
as "DelVAR," this new approach focuses on simplifying the calculation
of incremental changes of firm-wide VAR. This allows us to minimize the
horsepower required to run VAR and related functions such as risk-based
trading limits in real time.
Of course, to understand DelVAR, it is first necessary to consider how
standard VAR-type analysis works. In order to ensure VAR calculations speed
along at a good clip, it is necessary to break down all the trades in your
portfolio into their component cash flows which, in turn, are netted according
to their maturities. These cash flows are then run through a variance/covariance
matrix. That matrix is generated according to a number of assumptions that
the user makes at the outset. The basic assumptions include the time period
over which P&L will vary, how different market factors are correlated,
how volatility numbers are generated, and the confidence or probability
that the resulting VAR figure will indeed accurately reflect the effect
of actual market fluctuations on P&L.
Calculated in this fashion, standard VAR makes it quite difficult to
determine the effect of any single "what-if" or actual trade on
the total portfolio. The only way to do this under the old methodology is
to split the new trade into its component cash flows, then fold everything
into the existing portfolio and recalculate VAR for the total portfolio.
The difference between the "before" VAR and the "after"
VAR is what we call the incremental VAR of the single trade.
Enter DelVAR, Stage Left
DelVAR eliminates the problems described above by calculating not only
total VAR, but also an additional quantity that we will call "gradient"
VAR, the cash flow direction in which VAR is increasing the fastest. Gradient
VAR can be determined by plotting a sort of VAR "terrain map"
of cash flow combinations. The cash flow combinations with lowest VAR appear
in the center of the map, with oval bands extending upwards towards their
outer limits as VAR increases. The total VAR of the portfolio can be identified
as the terrain "height" of a cash flow "point" on this
In the chart at right we have mapped two simple cash flows, one representing U.S. dollar flows with a certain maturity and the other representing Deutsche
mark flows with some maturity. (In a real-life situation, of course, the
terrain map would likely be N-dimensional and more complex.) From point
"P," which represents the portfolio's cash flows, it is possible
to extrapolate the gradient VAR, which is represented by the white arrow.
This is the cash flow direction in which VAR increases most quickly.
In order to evaluate a new trade's effect on VAR, all you must do is
compare the direction of the line between the point representing the trade's
cash flows on the terrain map and point "P" to the direction of
the gradient VAR line. If the direction of this new line is within 90 degrees
of the gradient VAR line, this particular deal will increase the portfolio's
total VAR. If the angle is greater than 90 degrees, the deal will decrease
Putting DelVAR into practice
How can DelVAR provide actionable information while simultaneously reducing time and energy spent on portfolio-wide calculations? Consider the following
suggested procedure: at the designated start of a day-long trading period,
calculate both total VAR and DelVAR (i.e. the "gradient" VAR).
As new trades are executed (or considered, as the case may be), plot their
cash flows and compare these against the initial DelVAR. This process generates
an approximate incremental VAR without the arduous recalculation of portfolio-wide
Drawbacks to Consider
The incremental VAR resulting from the calculations described above is
only an approximation because the system does not recalculate total VAR
every time a trade is registered. Generally speaking, however, the approximation
will be quite close to the actual incremental VAR, except under some conditions.
The DelVar method is vulnerable to two such conditions: extremely large
trades that represent a considerable portion of the total portfolio, and
cases in which the sum of the daily accumulation of trades is a large fraction
of the whole portfolio. Both could throw off the DelVAR method because point
"P"-or the total VAR-would have been calculated without these
large, "influential" deals. For firms that occasionally have large
trades or ultra-high-volume trading, it may make sense to recalculate total
VAR and DelVAR after such periods.
Dare to Compare
One of the most important uses of DelVAR is to compare how a variety
of different trades (or hedges, in the case of corporates) could potentially
affect the total VAR of a portfolio. In this case, however, it is critical
to remember that large trades will always affect VAR more than small trades
no matter what they are. The trick here is to factor out the size effect
by measuring the potential impact of different deals on total VAR by examining
incremental VAR per unit of trade. To this end, you can choose to measure
deal size in terms of any of the following: the cash flows it generates;
its individual VAR; its potential return; its market price; the capital
it requires; or its notional value. Whatever size measure you choose must
be maintained throughout the comparisons.
Once you have determined how you are going to measure size (and have
selected a standard trade "unit") you can divide each trade's
incremental VAR by the number of units to arrive at incremental VAR per
unit. (You can also simply calculate incremental VAR for a single unit.)
Using this method you can compare the relative "riskiness" of
I believe DelVAR increases computational efficiency while giving users
more "proactive" decision support information than standard VAR
alone. In other words, it can help your trash compactor become a multi-function
appliance that can also suggest new recipes for lowering risk.
Outlook, FEA's value-at-risk add-in software, contains VARDelta, FEA's
version of DelVAR (patent pending).