Credit Risk & Corporate Banking
RAROC Risk-Adjusted Return on Capital Formula
Price commercial credit facilities via Risk-Adjusted Return on Capital RAROC = (Net_Interest_And_Fees - OpEx - EAD*PD*LGD + r_f*EC) / EC by separating Expected Loss (pricing reserve) from Unexpected Loss (Economic Capital).
Price Expected Loss into the spread and charge Economic Capital for Unexpected Tail Loss!
Pioneered by Charles Sanford at Bankers Trust in the late 1970s, Risk-Adjusted Return on Capital (RAROC) rests on a foundational credit principle: **Expected Loss EL = EAD * PD * LGD is a predictable cost of doing business** (deducted in the numerator just like operating expenses), whereas **Economic Capital EC** (the VaR/ES tail buffer beyond EL) sits in the denominator to absorb **Unexpected Loss**! For a facility with Exposure at Default EAD, Net Spread & Fee Revenue R_net, Direct Servicing Cost C_op, Probability of Default PD, Loss Given Default LGD, Economic Capital EC, and Risk-Free Return on Invested Equity Buffer r_f: Risk-Adjusted Net Income is RANI = R_net - C_op - (EAD * PD * LGD) + r_f * EC, and RAROC = RANI / EC (creating shareholder value iff RAROC > Cost_Of_Equity k_e)!
Verify on exact numbers for an EAD = 100.00 ($M, B2) corporate loan generating Net_Spread_And_Fees R_net = 2.80 ($M, B3), Servicing_OpEx C_op = 0.40 ($M, B4), Annual_PD = 0.015 (1.50%, B5), LGD = 0.40 (40.0%, B6 -> Expected Loss EL = 100 * 0.015 * 0.40 = 0.60 $M!), Economic_Capital EC = 8.00 ($M, B7), and Risk_Free_Yield_On_EC r_f = 0.03 (3.0%, B8 -> Capital Credit = 0.24 $M): Risk-Adjusted Net Income is 2.80 - 0.40 - 0.60 + 0.24 = 2.04 ($M), and RAROC is 2.04 / 8.00 = 0.2550 (25.50% — comfortably beating a 15.0% Cost-of-Equity hurdle by +10.50% = +0.84 $M Economic Profit)!
| RAROC Credit Facility Line (EAD = $100M, EC = $8M) | Formula | Verified Output |
|---|---|---|
| Expected Credit Loss Charge (EL) | EAD * PD * LGD = 100 * 0.015 * 0.40 | 0.6000 ($M / yr) |
| Risk-Free Return on Equity Buffer | r_f * EC = 0.03 * 8.00 | 0.2400 ($M / yr) |
| Risk-Adjusted Net Income (RANI) | Rev - OpEx - EL + r_f * EC | 2.0400 ($M / yr) |
| Pre-Tax Facility RAROC | RANI / Economic_Capital | 0.2550 (25.50% Return on EC) |
Expected Credit Loss EL = EAD * PD * LGD Formula
Validate EAD > 0, 0 <= PD <= 1, and 0 <= LGD <= 1.
=IF(OR(B2 <= 0, B5 < 0, B5 > 1, B6 < 0, B6 > 1), "Invalid Credit Input", ROUND(B2 * B5 * B6, 4))Full Bankers-Trust RAROC Ratio Formula
Validate strictly positive Economic Capital EC > 0.
=LET(ead_v, B2, rv_n, B3, op_c, B4, pd_a, B5, lgd_f, B6, ec_k, B7, rf_y, B8, IF(OR(ead_v <= 0, op_c < 0, pd_a < 0, pd_a > 1, lgd_f < 0, lgd_f > 1, ec_k <= 0), "Invalid Credit Input", LET(el_c, ead_v * pd_a * lgd_f, rani_v, rv_n - op_c - el_c + rf_y * ec_k, ROUND(rani_v / ec_k, 4))))Try the example
Use the original values or change them to test your understanding.