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Notice of Proposed Rulemaking Implementing    New Risk-Based Capital Framework in the United States

 Figure 1 is titled "Probability Distribution of Potential Losses."       The vertical axis is labeled "Probability" and the horizontal       axis is labeled "Losses." The probability distribution shown       in the chart begins at zero, increases steeply to a peak, than decreases       asymptotically toward the horizontal axis. The mean and the 99.9th percentile       of the probability distribution are labeled. The horizontal axis from zero       to the mean is labeled expected losses and the horizontal axis from the       mean to the 99.9th percentile of losses is labeled unexpected       losses. The text that follows discusses this chart in more depth.

Table A is titled "QIS-4 Results: Changes in Minimum Required Capital."       The table shows the changes in Minimum Required Capital or MRC by portfolio,       aggregated across all QIS-4 participants. Entries in parentheses denote       negative numbers. The term "portfolio" is used here to identify       discrete segments of capital requirements. For example, operational risk       is listed as a separate line item in this table, which means that all risk-based       capital requirements associated with operational risk have been captured       within this line item. It is important to note that operational risk has       been segregated in this way when considering the changes in MRC for the       various credit portfolios. For most institutions, at least some portion       of the operational risk charge would be associated with various credit-related       activities. However, Table A makes no attempt to allocate operational       risk to the various portfolios, as any such allocation would require arbitrary       assumptions. There are no percentage change numbers for operational risk       because it is not separated out as a specific charge under current rules.

Column 1 shows the dollar-weighted (Each institution's contribution to       the aggregate is equal to the dollar amount of its MRC.) average percentage       change in MRC by portfolio. Some of the largest changes in MRC occur for       mortgages – both home equity lines of credit (HELOCs) and all other       residential mortgages – and for qualifying revolving exposures (QREs),       which mostly consist of credit card exposures. However, it is important       to consider the relative size of portfolios as well as the percentage change       when attempting to understand the drivers of the 12.5 percent aggregate       decrease in MRC. Columns 5 and 6 show the share each portfolio contributes       to MRC, under the current framework (Column 5) and the QIS-4 interpretation       of Basel II as defined in the QIS-4 instructions (Column 6).       Column 2 shows the percentage point contribution of each portfolio to the       overall average percentage change (of 12.5%). From this column, we       can see that operational risk, Corporate-Bank-Sovereign, HELOCs, Residential       Mortgages, and QREs were key drivers of the aggregate change in MRC.

Column 3 shows that risk-based capital requirements declined by more than       26 percent in half the institutions in the study. Most portfolios       showed double-digit declines in minimum risk-based capital requirements       for over half the banking organizations, with the exception of credit cards.       It should be noted that Column 3 gives every participating institution       equal weight. Column 4 shows the analogous weighted median change,       using total exposures as weights.

Table B is titled "Transitional Floors,"       and shows the transitional floor percent for each of the three transitional       floor periods. During the first transitional floor period, the transitional       floor percentage will be 95 percent; the second period will have a       floor of 90 percent; and the third period will have a floor of 85 percent.

Table C is titled "IRB Risk-Based Capital       Formulas for Wholesale Exposures to Non-Defaulted Obligors and Segments       of Non-Defaulted Retail Exposures" and outlines the supervisory formulas       necessary to calculate the capital requirement for non-defaulted retail       and wholesale exposures.

Within the Retail section, the formula for the Capital Requirement (K)       for Non-Defaulted Exposures reads as follows:

Also within the Retail section, the formulas for Correlation (R) include       residential mortgages, qualifying revolving exposures and other retail       exposures. For residential mortgage exposures: R = 0.15. For       qualifying revolving exposures: R = 0.04. For other retail exposures:       R = 0.03 x e−35×PD.

Within the Wholesale section, the formula for the Capital Requirement (K)       for Non-Defaulted Exposures reads as follows:

Also within the Wholesale section, the formulas for Correlation (R)       include HVCRE exposures and wholesale exposures other than HVCRE exposures.       For HVCRE exposures:

For wholesale exposures other than HVCRE exposures:

Also within the Wholesale section, there is a formula for Maturity Adjustment (b)       which reads as follows:

Table D illustrates which EAD estimation methodologies may be applied to       particular types of exposure. OTC Derivatives may apply the Current exposure       methodology or Internal models methodology. Collateralized OTC derivatives       may apply the collateral haircut methodology (in conjunction with the current       exposure methodology) or internal models methodology. Both repo-style transactions       and eligible margin loans may apply the collateral haircut methodology,       simple VaR methodology or the internal models methodology. Cross-product       netting sets can apply only the internal models methodology. Footnote 56       is applicable to the Simple VaR methodology and states "... (o)nly       repo-style transactions and eligible margin loans subject to a single-product       qualifying master netting agreement are eligible for the simple VaR methodology."

 Figure 2 is titled "EAD and LGD for Eligible Margin Loans and Repo-Style       Transactions." It is a flow chart with several potential paths. All       paths begin with "Eligible Margin Loans and Repo-Style Transactions"       with two options. The first is "Notional Exposure with Adjusted LGD"       which concludes with "Plug PD, Adjusted LGD, and Notional EAD into       wholesale function." The other path is "Adjusted Exposure at       Default Approach" and can flow in two directions. The first, "Models       Approach," then asks the question, "Is there a Master Netting       Agreement?" If "no," then the path flows to "Internal       Models Methodology" and concludes with "Plug PD, Unsecured LGD,       and Adjusted EAD into wholesale function." If "yes," the       path can flow the same as the "no" answer, or it can flow to       "Simple VaR Methodology." Heading back to "Adjusted Exposure       at Default Approach," the path can also flow to "Haircut Approach"       with again two options, "Standardized" and "Own Estimates,"       both of which lead to "Repo-Style Transaction?" Simple "VaR"       Methodology from the "Master Netting Agreement" question also       has a dotted connection to "Repo-Style Transaction") From "Repo-Style       Transaction?," if "yes," the path leads to "5 day       holding period," and then concludes with "Plug PD, Unsecured       LGD, and Adjusted EAD into wholesale function." If "no,"       the path leads to "10 day holding period" and again concludes       with "Plug PD, Unsecured LGD, and Adjusted EAD into wholesale function."

Table E is titled "Standard Supervisory Market Price Volatility Haircuts"       and allows the bank to locate the appropriate haircut to be used for a       security based on its rating and residual maturity. There are four primary       columns titled "External rating grade category for debt securities,"       "Residual maturity for debt securities," "Issuers exempt       from the 3 basis point floor," and "Other Issuers." The       rows contain various ranges of ratings and the first two of these rows       also have 3 sub-rows within each to account for the varying residual maturities       within each rating category.

Following these first primary rows, the table gives specific haircuts for       four other assets that may not be rated. These include main index equities,       other publicly traded equities, mutual funds, and cash on deposit with       the bank.   

H subscript m equals H subscript n multiplied by the square root of (T subscript       M divided by T subscript N).

Figure 3 is titled "EAD and LGD for OTC Derivative Contracts." It       is a flow chart with several potential paths. All paths begin with "EAD       for OTC Derivatives" with two potential methods to choose from: "Current       Exposure Methodology" or "Internal Models Methodology."       If the Current Exposure Methodology is chosen, the path then leads to "Master       Netting Agreement." From here, the path follows either "yes"       or "no." If yes, the path follows to "Net Replacement Cost       + Adjusted Potential Future Exposure." If no, the path follows to       "Transaction Replacement Cost + Potential Future Exposure." Both       of these paths then lead to the question, "Is Collateral Posted?"       and if "yes," there are two options. The first option is "Adjust       LGD" leading to "Plug PD, Adjusted LGD, and EAD into Wholesale       Function." The second option for "yes" is "Haircut       Collateral to Adjust EAD" with again two options, "Standardized       Haircuts" and "Own Estimates," both of which conclude to       "Plug PD, Unsecured LGD, and Adjusted EAD into Wholesale Function."       Going back to "Is Collateral Posted?," if "no" is selected,       the path concludes with "Plug PD, Unsecured LGD, and EAD into Wholesale       Function." Heading all the way back to the first box, "EAD for       OTC Derivatives," the second option is "Internal Models Methodology,"       which flows to "Collateral Considered in Internal Models Methodology"       and concludes with "Plug PD, Unsecured LGD, and Adjusted EAD into       Wholesale Function."

The maturity of the expected positive exposure equals 1 plus the ratio       of A over B, where:

A equals the summation of the quantities (effective expected exposure for       future time periods t subscript k multiplied by delta for future time periods       t subscript k multiplied by the risk-free discount factor for future time       periods t subscript k) over all values of k for which t subscript k is       greater than one year; and 

B equals the summation of the quantities (effective expected exposure for       future time periods t subscript k multiplied by delta for future time periods       t subscript k multiplied by the risk-free discount factor for future time       periods t subscript k) over all values of k for which t subscript k is       one year or less.   

Table F is titled "Risk Weights for Unsettled DvP and PvP Transactions"       and shows the risk weight to be applied to positive current exposure for       various ranges of the number of business days after contractual settlement       date for DvP and PvP transactions. For business days from 5 to 15,       the risk weight is 100 percent; for business days from 16 to 30,       the risk weight is 625 percent; for business days 31 to 45, the risk       weight is 937.5 percent; and for business days 46 or more, the       risk weight is 1,250 percent.

Table G is titled "Long-Term Credit Rating Risk Weights under RBA       and IAA." It consists of 4 primary columns with headings of "Applicable       Rating (Illustrative rating example)," "Column 1: Risk weights       for senior securitization exposures backed by granular pools," "Column 2:       Risk weights for non-senior securitization exposures backed by granular       pools," and "Column 3: Risk weights for securitization exposures       backed by non-granular pools." Overall, this table allows banks to       apply the correct risk weight for different types of securitization exposures       based on the applicable long-term credit rating.

Table H is titled "Short-Term Credit Rating Risk Weights under RBA       and IAA" and consists of 4 primary columns with headings of "Applicable       Rating (Illustrative rating example)," "Column 1: Risk weights       for senior securitization exposures backed by granular pools," "Column 2:       Risk weights for non-senior securitization exposures backed by granular       pools," and "Column 3: Risk weights for securitization exposures       backed by non-granular pools." Overall, this table allows banks to       apply the correct risk weight for different types of securitization exposures       based on the applicable short-term credit rating. 

When Y is less than K subscript IRB, the function S[Y] is equal to Y, where       K subscript IRB is defined as the ratio of the risk-based capital requirement       for the underlying exposures plus the expected credit loss of the underlying       exposures (all as determined as if the underlying exposures were directly       held by the bank) to the amount of the underlying exposures

When Y is greater than K subscript IRB, the function S[Y] is equal to K       subscript IRB plus the function K[Y] minus the function K[K subscript IRB]       plus the product of ((d multiplied by K subscript IRB) divided by 20) multiplied       by (1 minus e) raised to the power of (20 minus (K subscript IRB minus       Y) divided by K subscript IRB))

The function K[Y] is equal to (1 minus       h) multiplied by [(1 minus the cumulative beta distribution with parameters       [a and b evaluated at Y]) multiplied by Y, plus the cumulative beta distribution       with parameters [a plus 1 and b evaluated at Y] multiplied by c]

h equals (1 minus the quantity (K       subscript IRB divided by the securitization's exposure-weighted average       loss given default)) raised to the power of N

a equals g multiplied by c

b equals g multiplied by (1 minus c)

c equals K subscript IRB divided by (1 minus h)

g equals ((1 minus c) multiplied by c) divided by f) minus 1

f equals the quantity ((v plus K subscript IRB raised to the second power)       divided by (1 minus h)) minus c to the second power plus (1 minus K subscript       IRB) multiplied by K subscript IRB minus v) divided by ((1 minus h) multiplied       by 1000))

v equals K subscript IRB multiplied by ((the securitization's exposure-weighted       average loss given default minus K subscript IRB) plus 0.25 multiplied       by (1 minus the securitization's exposure-weighted average loss given default))       divided by N))

 d equals 1 minus (1 minus h) multiplied by (1 minus the cumulative beta distribution       with parameters a and b evaluated at K subscript IRB)

N equals (the summation of exposure at       default subscript i for all values of i) raised to the power of two divided       by (the summation of exposure at default subscript i raised to the power       of two) for all values of i

N equals ((100 plus 1 plus 1 plus 1)       raised to the power of 2) divided by (100 raised to the power of 2 plus       1 raised to the power of two plus 1 raised to the power of two plus one       raised to the power of 2) equals 10,609 divided by 10,003 equals 1.06

The securitization's exposure-weighted       average loss given default equals the summation of the loss given default       subscript i multiplied by the exposure at default subscript i for all values       of i.

N equals 1 divided by C subscript 1 multiplied       by C subscript m plus ((C subscript m minus C subscript 1) divided by m       minus 1)) multiplied by the greater of {1 minus m multiplied by C subscript       1 and zero}

H equals the summation of (a subscript       i multiplied by H subscript i) for all values of i 

Table I is titled "Controlled Early Amortization       Provisions" and consists of two main sections, "Retail Credit       Lines" and "Non-retail Credit Lines." Within both sections,       there are two columns, "Uncommitted" and "Committed."       This table allows banks to determine the appropriate 3-month average excess       spread conversion factor (CF) for both uncommitted and committed,       retail and non-retail credit lines.

Table J is titled "Non-Controlled Early       Amortization Provisions" and consists of two main sections, "Retail       Credit Lines" and "Non-retail Credit Lines." Within both       sections, there are two columns, "Uncommitted" and "Committed."       This table allows banks to determine the appropriate 3-month average excess       spread conversion factor (CF) for both uncommitted and committed,       retail and non-retail credit lines. 

E equals 1 minus (the summation of t       from t equals 1 to T of the quantity (X subscript t minus X subscript t       minus 1) raised to the power of two), divided by (the summation of t from       t equals 1 to T of the quantity (A subscript t minus A subscript t minus       1) raised to the power of two) 

Table 1 is titled "Transitional       Floors," and shows the transitional floor percent for each of the       three transitional floor periods. During the first transitional floor period,       the transitional floor percentage will be 95 percent; the second period       will have a floor of 90 percent; and the third period will have a       floor of 85 percent.

Table 2 is titled "IRB Risk-Based       Capital Formulas for Wholesale Exposures to Non-Defaulted Obligors and       Segments of Non-Defaulted Retail Exposures" and outlines the supervisory       formulas necessary to calculate the capital requirement for non-defaulted       retail and wholesale exposures.

Within the Retail section, the formula for the Capital Requirement (K)       for Non-Defaulted Exposures reads as follows:

Also within the Retail section, the formulas for Correlation (R) include       residential mortgages, qualifying revolving exposures and other retail       exposures. For residential mortgage exposures: R = 0.15. For       qualifying revolving exposures: R = 0.04. For other retail exposures:       R = 0.03 x e−35×PD.

Within the Wholesale section, the formula for the Capital Requirement (K)       for Non-Defaulted Exposures reads as follows:

Also within the Wholesale section, the formulas for Correlation (R)       include HVCRE exposures and wholesale exposures other than HVCRE exposures.       For HVCRE exposures:

For wholesale exposures other than HVCRE exposures:

Also within the Wholesale section, there is a formula for Maturity Adjustment (b)       which reads as follows:

Table 3 is titled "Standard Supervisory Market Price Volatility Haircuts"       and allows the bank to locate the appropriate haircut to be used for a       security based on its rating and residual maturity. There are four primary       columns titled "External rating grade category for debt securities,"       "Residual maturity for debt securities," "Issuers exempt       from the 3 basis point floor," and "Other Issuers." The       rows contain various ranges of ratings and the first two of these rows       also have 3 sub-rows within each to account for the varying residual maturities       within each rating category.

Following these first primary rows, the table gives specific haircuts for       four other assets that may not be rated. These include main index equities,       other publicly traded equities, mutual funds, and cash on deposit with       the bank.

H subscript m equals H subscript n multiplied by the square root of (T subscript       M divided by T subscript N). 

The maturity of the expected positive exposure equals 1 plus the ratio       of A over B, where:

A equals the summation of the quantities (effective expected exposure for       future time periods t subscript k multiplied by delta for future time periods       t subscript k multiplied by the risk-free discount factor for future time       periods t subscript k) over all values of k for which t subscript k is       greater than one year; and 

B equals the summation of the quantities (effective expected exposure for       future time periods t subscript k multiplied by delta for future time periods       t subscript k multiplied by the risk-free discount factor for future time       periods t subscript k) over all values of k for which t subscript k is       one year or less.

K subscript o equals [the Loss Given       Default subscript g multiplied by N multiplied by ((N raised to the negative       1 power multiplied by (the Probability of Default subscript o) plus N raised       to the negative 1 power multiplied by (0.999) times the square root of       the asset value correlation of the obligor) divided by (the square root       of 1 minus the asset value correlation of the obligor)) minus (the Expected       Loss Given Default subscript g multiplied by the Probability of Default       subscript o)] multiplied by [(1 plus (M minus 2.5) multiplied by b) divided       by 1 minus 1.5 multiplied by b] 

Table 5 is titled "Risk Weights       for Unsettled DvP and PvP Transactions" and shows the risk weight       to be applied to positive current exposure for various ranges of the number       of business days after contractual settlement date for DvP and PvP transactions.       For business days from 5 to 15, the risk weight is 100 percent;       for business days from 16 to 30, the risk weight is 625 percent;       for business days 31 to 45, the risk weight is 937.5 percent; and       for business days 46 or more, the risk weight is 1,250 percent.

Table 6 is titled "Long-Term Credit       Rating Risk Weights under RBA and IAA." It consists of 4 primary columns       with headings of "Applicable Rating (Illustrative rating example),"       "Column 1: Risk weights for senior securitization exposures backed       by granular pools," "Column 2: Risk weights for non-senior       securitization exposures backed by granular pools," and "Column 3:       Risk weights for securitization exposures backed by non-granular pools."       Overall, this table allows banks to apply the correct risk weight for different       types of securitization exposures based on the applicable long-term credit       rating.

Table 7 is titled "Short-Term Credit       Rating Risk Weights under RBA and IAA" and consists of 4 primary       columns with headings of "Applicable Rating (Illustrative rating example),"       "Column 1: Risk weights for senior securitization exposures backed       by granular pools," "Column 2: Risk weights for non-senior       securitization exposures backed by granular pools," and "Column       3: Risk weights for securitization exposures backed by non-granular pools."       Overall, this table allows banks to apply the correct risk weight for different       types of securitization exposures based on the applicable short-term credit       rating. 

When Y is less than K subscript IRB, the function S[Y] is equal to Y, where       K subscript IRB is defined as the ratio of the risk-based capital requirement       for the underlying exposures plus the expected credit loss of the underlying       exposures (all as determined as if the underlying exposures were directly       held by the bank) to the amount of the underlying exposures

When Y is greater than K subscript IRB, the function S[Y] is equal to K       subscript IRB plus the function K[Y] minus the function K[K subscript IRB]       plus the product of ((d multiplied by K subscript IRB) divided by 20) multiplied       by (1 minus e) raised to the power of (20 minus (K subscript IRB minus       Y) divided by K subscript IRB))

The function K[Y] is equal to (1 minus       h) multiplied by [(1 minus the cumulative beta distribution with parameters       [a and b evaluated at Y]) multiplied by Y, plus the cumulative beta distribution       with parameters [a plus 1 and b evaluated at Y] multiplied by c]

h equals (1 minus the quantity (K       subscript IRB divided by the securitization's exposure-weighted average       loss given default)) raised to the power of N

a equals g multiplied by c

b equals g multiplied by (1 minus c)

c equals K subscript IRB divided by (1 minus h)

g equals ((1 minus c) multiplied by c) divided by f) minus 1

f equals the quantity ((v plus K subscript IRB raised to the second power)       divided by (1 minus h)) minus c to the second power plus (1 minus K subscript       IRB) multiplied by K subscript IRB minus v) divided by ((1 minus h) multiplied       by 1000))

v equals K subscript IRB multiplied by ((the securitization's exposure-weighted       average loss given default minus K subscript IRB) plus 0.25 multiplied       by (1 minus the securitization's exposure-weighted average loss given default))       divided by N))

 d equals 1 minus (1 minus h) multiplied by (1 minus the cumulative beta distribution       with parameters a and b evaluated at K subscript IRB)

N equals (the summation of exposure at       default subscript i for all values of i) raised to the power of two divided       by (the summation of exposure at default subscript i raised to the power       of two) for all values of i

The securitization's exposure-weighted       average loss given default equals the summation of the loss given default       subscript i multiplied by the exposure at default subscript i for all values       of i.

N equals 1 divided by C subscript 1 multiplied       by C subscript m plus ((C subscript m minus C subscript 1) divided by m       minus 1)) multiplied by the greater of {1 minus m multiplied by C subscript       1 and zero}

H equals the summation of (a subscript       i multiplied by H subscript i) for all values of i 

Table 8 is titled "Controlled Early Amortization       Provisions" and consists of two main sections, "Retail Credit       Lines" and "Non-retail Credit Lines." Within both sections,       there are two columns, "Uncommitted" and "Committed."       This table allows banks to determine the appropriate 3-month average excess       spread conversion factor (CF) for both uncommitted and committed,       retail and non-retail credit lines.

Table 9 is titled "Non-Controlled Early       Amortization Provisions" and consists of two main sections, "Retail       Credit Lines" and "Non-retail Credit Lines." Within both       sections, there are two columns, "Uncommitted" and "Committed."       This table allows banks to determine the appropriate 3-month average excess       spread conversion factor (CF) for both uncommitted and committed,       retail and non-retail credit lines. 

E equals 1 minus (the summation of t       from t equals 1 to T of the quantity (X subscript t minus X subscript t       minus 1) raised to the power of two), divided by (the summation of t from       t equals 1 to T of the quantity (A subscript t minus A subscript t minus       1) raised to the power of two) 

Basel II Capital AccordNotice of Proposed Rulemaking (NPR) and Supporting Board Documents

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