Expected loss, risk-weighted assets and capital of a portfolio

Runs scr_irb_rw() on every exposure, aggregates by segment, compares the IRB result with the standardized approach for the output floor, reconciles regulatory expected loss with the provision stock (shortfall deducted from capital; excess eligible as tier 2 up to 0.6 % of the IRB risk-weighted assets), measures the impact of each input floor, runs a fixed sensitivity grid and reports the name concentration of the book. The parameter tables come from params; the object records whether they were edited.

Usage

scr_capital(
  x,
  pd = "pd",
  lgd = "lgd",
  ead = "ead",
  segment = NULL,
  asset_class = config$asset_class,
  m = NULL,
  defaulted = NULL,
  elbe = NULL,
  provisions = NULL,
  ltv = NULL,
  rating = NULL,
  sales = NULL,
  fi = NULL,
  transactor = NULL,
  grade = NULL,
  id = NULL,
  claim = NULL,
  granular = TRUE,
  params = scr_irb_params(config$framework),
  config = scr_config(),
  keep_rows = FALSE
)

Arguments

x: A table of exposures (data.frame or data.table) or the list form described above.
pd, lgd, ead: Column names of the probability of default, loss given default and exposure at default.
segment: Optional column name of the reporting segment.
asset_class: A column name or a single asset class (see scr_irb_rw()).
m, defaulted, elbe, provisions, ltv, rating, sales, fi, transactor, grade, id: Optional column names: effective maturity, default flag, best estimate of expected loss, provision stock, loan-to-value, external rating, annual sales, financial-institution flag, transactor flag, PD grade (defines the SQL pools together with segment) and exposure identifier.
claim: Optional column name: the claim type of each exposure under the foundation approach (a row of params$lgd_firb); the supervisory LGD then replaces lgd.
granular: TRUE, FALSE or a column name: whether the retail exposures belong to a granular regulatory retail pool (the standardized comparison uses the non-granular weight otherwise).
params: An scr_irb_params() object; defaults to the preset of config$framework.
config: An scr_config() object (capital_approach, capital_target_ratio, capital_output_floor, capital_sensitivity, nthread, verbose).
keep_rows: Keep the per-exposure table in the object.

Value

An object of class scr_capital: a list with exposures (per-exposure table, only with keep_rows = TRUE), segments (the reconciliation table: segment, n, ead, pd_mean, lgd_mean, m, r_mean, k_mean, rw, rwa_irb, rwa_sa, irb_sa_ratio, el, provisions, shortfall_excess), pools (one row per segment and grade with the constants the SQL emits), totals (n, ead, el, rwa_irb, rwa_sa, irb_sa_ratio, output_floor, rwa_floor, rwa_reported, floor_binding, headroom, density, target_ratio, capital, provisions, shortfall, excess, tier2_addback, tier2_cap, hhi, n_eff, max_share, granular), floors (floor, n_hit, ead_hit, delta_rwa), sensitivity (shock, rwa, delta, delta_pct), concentration (share of EAD and RWA by segment), framework, approach, params, config, ledger, model_card and, after scr_export(), files. segments and totals also carry n_defaulted; totals also el_rate and rwa_irb_no_floors; concentration has segment, n, ead, rwa, ead_share, rwa_share and hhi_contribution; columns records the column names the SQL reads.

Inputs

x is either a table of exposures, the remaining arguments naming its columns, or a list list(pd = , lgd = , ead = , data = ) whose elements are fitted models with an scr_apply() method (the PD, LGD and EAD objects of the IRB modules) and data the table to apply them to. In the list form each model present fills the corresponding vector from the columns pd_final, lgd_final and ead_predicted of its scr_apply() output, and the provenance is written to the ledger; elements that are NULL fall back to the named columns of data.

asset_class is a column name of x or a single class applied to every row. Segment means are weighted by EAD. The sensitivity grid shocks the PD (x1.10, x1.25, x1.50), the LGD (+5 percentage points), the EAD (+10 %), removes the input floors, scales the correlation (x1.25) and stresses the PD with the one-factor model at q = 0.95 and 0.99 (scr_pd_stress(), the stressed PD then re-entering the function so that the correlation follows it).

References

Basel Committee on Banking Supervision (2023). The Basel Framework, CRE31, CRE35 (treatment of expected losses and provisions), RBC20 (output floor).

Examples

cfg <- scr_config(verbose = FALSE)
cap <- scr_capital(scr_demo_portfolio, segment = "segment", asset_class = "asset_class",
                   m = "m", defaulted = "defaulted", elbe = "elbe", provisions = "provision",
                   ltv = "ltv", rating = "rating", sales = "sales", transactor = "transactor",
                   grade = "grade", id = "id", config = cfg)
cap
#> <scr_capital> bcb | airb | 5,000 exposures in 6 segments
#>   EAD 1,940,402,792 | EL 31,028,477 (1.60%) | RWA IRB 1,214,315,257 | density 62.6% | capital (8.0%) 97,145,221
#>   standardized RWA 1,553,528,212 | IRB/SA 0.782 | output floor 72.5%: not binding (headroom 88,007,303)
#>   provisions 43,425,571 vs EL: shortfall 0 | excess 12,397,094 | tier 2 add-back 7,285,892 (cap 7,285,892)
#>   floors: pd 194 rows, RWA 5,221,058 | lgd 0 rows, RWA         0 | m 0 rows, RWA         0 | HHI 0.00231 (n_eff 433, max share 1.19%)
#>   top segments by RWA:
#>     corporate_large        n 500     EAD 1,451,911,238  RW  65.1%  RWA 944,938,904     IRB/SA 0.77
#>     corporate_sme          n 700     EAD 302,516,540    RW  79.2%  RWA 239,492,431     IRB/SA 0.92
#>     mortgages              n 1,000   EAD 165,305,905    RW  12.6%  RWA 20,764,980      IRB/SA 0.37
#>     retail_loans           n 1,500   EAD 15,592,011     RW  44.5%  RWA 6,935,236       IRB/SA 0.59
#>     cards_revolver         n 800     EAD 3,282,347      RW  54.2%  RWA 1,777,936       IRB/SA 0.71
#>   sensitivity: vasicek_q0.99 +95.8% | vasicek_q0.95 +55.7% | r_x1.25 +26.8%
cap$segments[, c("segment", "n", "rw", "irb_sa_ratio")]
#>             segment     n        rw irb_sa_ratio
#>              <char> <int>     <num>        <num>
#> 1:  corporate_large   500 0.6508242    0.7729808
#> 2:    corporate_sme   700 0.7916672    0.9233544
#> 3:        mortgages  1000 0.1256155    0.3672066
#> 4:     retail_loans  1500 0.4447942    0.5866356
#> 5:   cards_revolver   800 0.5416660    0.7118514
#> 6: cards_transactor   500 0.2260868    0.4907211
cap$floors
#>        floor n_hit   ead_hit delta_rwa
#>       <char> <int>     <num>     <num>
#> 1:  pd_floor   194 110745561   5221058
#> 2: lgd_floor     0         0         0
#> 3:   m_floor     0         0         0