column 6—to determine the general market risk charge of $66 for the whole fixed-
income portfolio.
(iii) Vertical Offsets. The BIS model assumes that long and short positions, in the
same maturity bucket but in different instruments, cannot perfectly offset each other.
Thus, the $66 general market risk charge tends to underestimate interest rate or price
risk exposure. For example, the FI is short $1,500 in 10–15 year U.S. Treasuries pro-
ducing a market risk charge of $67.50 and is long $1,000 in 10–15 year junk bonds
(with a risk charge of $45). However, because of basis risk—that is, the fact that the
rates on Treasuries and junk bonds do not fluctuate exactly together—we cannot as-
sume that a $45 short position in junk bonds is hedging an equivalent ($45) risk value
of U.S. Treasuries of the same maturity. Similarly, the FI is long $2,500 in three- to
four-year Treasuries (with a general market risk charge of $56.25) and short $2,000 in
three- to four-year quality corporate bonds (with a risk charge of $45). To account for
this, the BIS requires additional capital charges for basis risk, called vertical offsets or
disallowance factors. We show these calculations in part 2 of panel B in Exhibit 8.8
In panel B, column 1 lists the time bands for which the bank has both a long and
short position. Columns (2) and (3) list the general market risk charges—from col-
umn (7) of panel A—resulting from the positions, and column (4) lists the difference
(or residual) between the charges. Column (5) reports the smallest value of the risk
charges for each time band (or offset). As listed in column (6), the BIS disallows
10%^36 of the $45 position in corporate bonds in hedging $45 of the Treasury bond
position. This results in an additional capital charge of $4.50 ($45 ×10%).^37 The total
charge for all vertical offsets is $9.
8.6 REGULATORY MODELS: THE BIS STANDARDIZED FRAMEWORK 8 • 21Time Band Longs Shorts Residual* Offset Disallowance Charge- Horizontal Offsets between Time Zones
Zones 1 and 2 23.75 (26.50) (2.75) 23.75 40.00% 9.50
Zones 1 and 3 68.75 (2.75) 66.00 2.75 150.00% 4.12 - Total Capital Charge
Specific risk 229.00
Vertical disallowances 9.00
Horizontal disallowances
Offsets within same time zones 53.16
Offsets between time zones 13.62
Residual general market risk after all offsets __66.00
Total 370.78
*Residual amount carried forward for additional offsetting as appropriate.
Note: Qual Corp is an investment grade debt issue (e.g., rated BBB and above). Non Qual is
a below investment grade debt issue (e.g., rated BB and below), that is, a “junk bond.”
Exhibit 8.8. (Continued)
(^36) Note again that the disallowance factors were set subjectively by regulators.
(^37) Intuitively, this implies that long-term U.S. Treasury rates and long-term junk bond rates are ap-
proximately 90% correlated. However, in the final plan, it was decided to cut vertical disallowance fac-
tors in half. Thus, a 10% disallowance factor becomes a 5% disallowance factor, and so on.