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MANAGEMENT’S DISCUSSION AND ANALYSIS
JPMorgan Chase & Co.
78 JPMorgan Chase & Co. / 2006 Annual Report
To calculate VAR, the Firm uses historical simulation, which measures risk
across instruments and portfolios in a consistent and comparable way. This
approach assumes that historical changes in market values are representative
of future changes. The simulation is based upon data for the previous twelve
months. The Firm calculates VAR using a one-day time horizon and an expected
tail-loss methodology, which approximates a 99% confidence level. This means
the Firm would expect to incur losses greater than that predicted by VAR esti-
mates only once in every 100 trading days, or about two to three times a
year.
IB Trading and Credit Portfolio VAR
IB trading VAR by risk type and credit portfolio VAR
2006 2005
As of or for the year ended Average Minimum Maximum Average Minimum Maximum At December 31,
December 31, (in millions) VAR VAR VAR VAR VAR VAR 2006 2005
By risk type:
Fixed income $56 $35 $ 94 $ 67 $ 37 $ 110 $44 $89
Foreign exchange 22 14 42 23 16 32 27 19
Equities 31 18 50 34 15 65 49 24
Commodities and other 45 22 128 21 7 50 41 34
Less: portfolio diversification (70)(c) NM(d) NM(d) (59)(c) NM(d) NM(d) (62)(c) (63)(c)
Trading VAR(a) 84 55 137 86 53 130 99 103
Credit portfolio VAR(b) 15 12 19 14 11 17 15 15
Less: portfolio diversification (11)(c) NM(d) NM(d) (12)(c) NM(d) NM(d) (10)(c) (10)(c)
Total trading and credit
portfolio VAR $ 88 $ 61 $ 138 $ 88 $ 57 $ 130 $ 104 $108
(a) Trading VAR does not include VAR related to the MSR portfolio or VAR related to other corporate functions, such as Treasury and Private Equity. For a discussion of MSRs and the corporate functions,
see pages 53–54 and Note 16 on pages 121–122 of this Annual Report, respectively. Trading VAR includes substantially all trading activities in IB; however, particular risk parameters of certain prod-
ucts are not fully captured, for example, correlation risk.
(b) Includes VAR on derivative credit valuation adjustments, hedges of the credit valuation adjustment and mark-to-market hedges of the accrual loan portfolio, which are all reported in Principal transac-
tions revenue. This VAR does not include the accrual loan portfolio, which is not marked to market.
(c) Average and period-end VARs are less than the sum of the VARs of its market risk components, which is due to risk offsets resulting from portfolio diversification. The diversification effect reflects
the fact that the risks are not perfectly correlated. The risk of a portfolio of positions is therefore usually less than the sum of the risks of the positions themselves.
(d) Designated as not meaningful (“NM”) because the minimum and maximum may occur on different days for different risk components, and hence it is not meaningful to compute a portfolio
diversification effect.
Investment Bank’s average Total Trading and Credit Portfolio VAR was $88 mil-
lion for both 2006 and 2005. Commodities and other VAR increased due to
continued expansion of the energy trading business, while Fixed income VAR
decreased due to reduced risk positions, as well as to lower market volatility
compared with 2005. These changes also led to an increase in portfolio diver-
sification, as Average Trading VAR diversification increased to $70 million, or
45% of the sum of the components, during 2006; from $59 million, or 41% of
the sum of the components, during 2005. In general, over the course of the
year, VAR exposures can vary significantly as positions change, market volatility
fluctuates and diversification benefits change.
VAR back-testing
To evaluate the soundness of its VAR model, the Firm conducts daily back-testing
of VAR against daily IB market risk-related revenue, which is defined as the
change in value of Principal transactions revenue less Private Equity gains/losses
plus any trading-related net interest income, brokerage commissions, underwrit-
ing fees or other revenue. The following histogram illustrates the daily market
risk-related gains and losses for IB trading businesses for the year ended
December 31, 2006. The chart shows that IB posted market risk-related gains on
227 out of 260 days in this period, with 29 days exceeding $100 million. The
inset graph looks at those days on which IB experienced losses and depicts the
amount by which VAR exceeded the actual loss on each of those days. Losses
were sustained on 33 days, with no loss greater than $100 million, and with no
loss exceeding the VAR measure.