8.5 HISTORIC OR BACK SIMULATION APPROACH. A major criticism of RiskMet-
rics is the need to assume a symmetric (normal) distribution for all asset returns.^23
Clearly, for some assets, such as options and short-term securities (bonds), this is
highly questionable. For example, the most an investor can lose if he or she buys a
call option on an equity is the call premium; however, the investor’s potential upside
returns are unlimited. In a statistical sense, the returns on call options are nonnormal
since they exhibit a positive skew.^24
Because of these and other considerations discussed below, the large majority of
FIs that have developed market risk models have employed a historic or back simu-
lation approach. The advantages of this approach are that (1) it is simple, (2) it does
not require that asset returns be normally distributed, and (3) it does not require that
the correlations or standard deviations of asset returns be calculated.
8 • 14 MARKET RISKAverage DEAR Minimum DEAR Maximum DEAR
Name for the year 2000 during 2000 during 2000
Bank of America $42 $25 $53
Bank One 14 8 19
Citicorp 45 28 96
First Union 10 5 16
FleetBoston Financial 40 28 59
J.P. Morgan Chase 28 18 43
*The figures are based on these banks’ internal models, i.e., they may be based on method-
ologies other than RiskMetrics—see below.
Source:Year 2000 10-K reports for the respective companies.
Exhibit 8.6. Daily Earnings at Risk for Large U.S. Commercial Banks, 2000* (in millions of
dollars).
(^23) Another criticism is that VARmodels like RiskMetrics ignore the (risk in the) payments of accrued
interest on an FI’s debt securities. Thus, VARmodels will underestimate the true probability of default
and the appropriate level of capital to be held against this risk (see P. Kupiec, “Risk Capital and VAR,”
The Journal of Derivatives, Winter 1999, pp. 41–52). Also, Johansson, Seiles, and Tjarnberg find that be-
cause of the distributional assumptions, while RiskMetrics produces reasonable estimates of downside
risk of FIs with highly diversified portfolios, FIs with small, undiversified portfolios will significantly un-
derestimate their true risk exposure using RiskMetrics (see, F. Johansson, M. J. Seiles, and M. Tjarnberg,
“Measuring Downside Portfolio Risks,”The Journal of Portfolio Management, Fall 1999, pp. 96–107).
Finally, a number of authors have argued that many asset distributions have “fat tails” and that RiskMet-
rics, by assuming the normal distribution, underestimates the risk of extreme losses. See, for example,
Salih F. Neftci, “Value at Risk Calculations, Extreme Events and Tail Estimations,”Journal of Deriva-
tives, Spring 2000, pp. 23–37. One alternative approach to dealing with the “fat-tail” problem is extreme
value theory. Simply put, one can view an asset distribution as being explained by two distributions. For
example, a normal distribution may explain returns up to the 95% threshold, but for losses beyond that
threshold another distribution such as the generalized Pareto distribution may provide a better explana-
tion of loss outcomes such as the 99% level and beyond. In short, the normal distribution is likely to un-
derestimate the importance and size of observations in the tail of the distribution which is after all what
value at risk models are meant to be measuring (see, also, Alexander J. McNeil, “Extreme Value Theory
for Risk Managers,” Working Paper, Department of Mathematics, ETH Zentrom, Ch-8092, Zurich,
Switzerland, May 17, 1999).
(^24) For a normal distribution, its skew (which is the third moment of a distribution) is zero.