with a minimum value of 3 (i.e., Capital charge (DEAR)×() ×(3)). In
general, the multiplication factor makes required capital significantly higher
than VAR produced from private models.However, to reduce the burden of capital needs, an additional type of capital can
be raised by FIs to meet the capital charge (or requirement). For example, suppose
the portfolio DEARwas $10 million using the 1% worst case (or 99th percentile).^42
The minimum capital charge would be:^43
Capital provides an internal insurance fund to protect an FI, its depositors and other
liability holders, and the insurance fund (e.g., the FDIC fund) against losses. The BIS
permits three types of capital to be held to meet this capital requirement: Tier 1, Tier 2,
and Tier 3. Tier 1 capital is essentially retained earnings and common stock, Tier 2 is
essentially long-term subordinated debt (over five years), and Tier 3 is short-term sub-
ordinated debt with an original maturity of at least two years. Thus, the $94.86 million
in the example above can be raised by any of the three capital types subject to the two
following limitations: (1) Tier 3 capital is limited to 250% of Tier 1 capital, and (2) Tier
2 capital can be substituted for Tier 3 capital up to the same 250% limit. For example,
suppose Tier 1 capital was $27.10 million and the FI issued short-term Tier 3 debt of
$67.76 million. Then the 250% limit would mean that no more Tier 3 (or Tier 2) debt
could be issued to meet a target above $94.86 ($27.1 ×2.5 = $67.76) without additional
Tier 1 capital being added. This capital charge for market risk would be added to the
capital charge for credit risk and operational risk to get the FI’s total capital requirement.
Exhibit 8.11 lists the market risk capital requirement to the total capital requirement
for several large U.S. bank holding companies as of the first quarter of 2000. Notice
how small the market risk capital requirement is relative to the total capital require-
ment for these banks. Only J.P. Morgan (prior to its merger with Chase) and CIBC
have ratios greater than 10%. The average ratio of market risk capital required to total
capital required for the 16 bank holding companies is only 4%.^44 Moreover, very few
banks, other than the very largest (above), report market risk exposures at all.
Capital charge 1 $10 million 2 12102 132 $94.86 million2108.7 BIS REGULATIONS AND LARGE BANK INTERNAL MODELS 8 • 25(^42) Using 2.33rather than 1.65.
(^43) The idea of a minimum multiplication factor of 3 is to create a scheme that is “incentive compati-
ble.” Specifically, if FIs using internal models constantly underestimate the amount of capital they need
to meet their market risk exposures, regulators can punish those FIs by raising the multiplication factor
to as high as 4. Such a response may effectively put the FI out of the trading business. The degree to
which the multiplication factor is raised above 3 depends on the number of days an FI’s model underes-
timates its market risk over the preceding year. For example, an underestimation error that occurs on
more than 10 days out of the past 250 days will result in the multiplication factor being raised to 4.
(^44) D. Hendricks and B. Hirtle, in “Bank Capital Requirements for Market Risk: The Internal Models
Approach,”Federal Reserve Bank of New York Economic Policy Review, December 1997. pp. 1–12, also
finds that the impact of the market risk capital charges on required capital ratios using internal models
are small. They calculate an increase in the level of required capital from the general market risk com-
ponent to range between 1.5 and 7.5% for the banks they examined. B. Hirtle, in “What Market Risk Cap-
ital Reporting Tells Us about Bank Risk,” Federal Reserve Bank of New York, Working Paper, July 2001,
finds that since the implementation of the market risk capital standards at the beginning of 1998, the bank
holding companies that were subject to the market capital requirements accounted for more than 98% of
the trading positions held by all U.S. banking organizations. For these banks, market risk capital repre-
sented just 1.9% of overall capital requirements of the median bank.