## Philippe Jorion's

## Orange County Case:

# 3.3 Duration and VAR

Value-at-Risk is directly linked to the concept of duration in
situations where a portfolio is exposed to one risk factor only,
the interest rate.
Duration measures the exposure to the risk factor.
Value-at-Risk incorporates duration with the probability of an adverse
move in the interest rate.
Define duration again

## Duration and VAR

Previously, we computed the VAR of a $100 million portfolio invested in
a 5-year note. At the 95% level over one month, the portfolio VAR was
found to be $1.7 million.
Can we relate this number to the portfolio duration?
The typical duration for a 5-year note is 4.5 years.
Assume now that the current yield *y* is 5%.
From historical data, we find that the worst increase in yields over a
month at the 95% is 0.40%.
The worst loss, or VAR, is then given by
*
Worst Dollar Loss =
Duration x 1/(1+y) x Portfolio Value x Worst Yield Increase
*

VAR = 4.5 Years x (1/1.05) x $100m x 0.4%

which is also $1.7 million!
Thus the value at risk is directly related to the concept of duration.

The VAR approach, however, is more general, because it allows
investors to include
many assets such as foreign currencies, commodities and equities,
which are exposed to other sources of risk than interest rate movements.

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