dividualDEARs (in thousands of dollars), we get
The equation indicates that considering the risk of each trading position as well as
the correlation structure among those positions’ returns results in a lower measure of
portfolio trading risk ($39,969) than when risks of the underlying trading positions
(the sum of which was $53,090) are added. A quick check will reveal that had we as-
sumed that all three assets were perfectly positively correlated (i.e., ij= 1), DEAR
for the portfolio would have been $53,090. Clearly, even in abnormal market condi-
tions, assuming that asset returns are perfectly correlated will exaggerate the degree
of actual trading risk exposure.
Exhibit 8.5 shows the type of spreadsheet used by FIs such as J.P. Morgan Chase
to calculate DEAR. As you can see, in this example positions can be taken in 15 dif-
ferent country (currency) bonds in eight different maturity buckets.^22 There is also
a column for FX risk (and, if necessary, equity risk) in these different country mar-
kets, although in this example the FI has no FX risk exposure (all of the cells are
empty).
In the example in Exhibit 8.5, while the FI is holding offsetting long and short po-
sitions in both German and French bonds, it is still exposed to trading risks of
$48,000 and $27,000, respectively (see the column Interest DEAR). This happens be-
cause the French yield curve is more volatile than the German and shocks at differ-
ent maturity buckets are not equal. The DEARfigure for a U.S. bond position of long
$20 million is $76,000. Adding these three positions yields a DEARof $151,000.
However, this ignores the fact that German, French, and U.S. yield shocks are not
perfectly correlated. Allowing for diversification effects (the “portfolio effect”) re-
sults in a total DEARof only $89,000. This would be the number reported to the FI’s
senior management. Exhibit 8.6 reports the average, minimum, and maximum daily
earnings at risk for several large U.S. commercial banks at year-end 2000. J.P. Mor-
gan Chase was exposed to a maximum of $43 million in 2000.
Currently, the number of markets covered by J.P. Morgan Chase’s traders and the
number of correlations among those markets require the daily production and updat-
ing of over 450 volatility estimates () and correlations (). These data are updated
daily.
$39,969 21 .4 21 10.77 21332 21 .1 21 9.32 213324DEAR portfolio 31 10.77 22 1 9.32 22 13322 21 .2 21 10.77 21 9.32 28 • 12 MARKET RISK(^22) Bonds held with different maturity dates (e.g., six years) are split into two and allocated to the near-
est two of the eight maturity buckets (here, five years and seven years) using three criteria:
- The sum of the current market valueof the two resulting cash flows must be identical to the mar-
ket value of the original cash flow. - The market riskof the portfolio of two cash flows must be identical to the overall market risk of
the original cash flow. - The two cash flows have the same signas the original cash flow.
See J.P.Morgan, RiskMetrics—Technical document, November 1994 and Return to RiskMetrics: The
Evolution of a Standard, April 2001. http://www.jpmorganchase.comorwww.riskmetrics.com.
1 > 2