Commercial Banking & Prudential Risk
Basel CET1 Ratio, RWA Density & Texas Ratio Formula
Audit bank solvency from three angles: Basel III Common Equity Tier 1 Ratio CET1 / RWA, Risk-Weight Density RWA / Total_Assets, and Gerard Cassidy’s Non-Performing Asset Texas Ratio.
Cross-check risk-weighted CET1 % with RWA Density and Gerard Cassidy’s Texas Ratio!
During banking crises, institutions with seemingly comfortable Basel Common Equity Tier 1 Ratios CET1_Ratio = CET1_Capital / Risk_Weighted_Assets (Basel minimum 4.5% + 2.5% Capital Conservation Buffer = 7.0%) can still fail if aggressive internal models compress RWA Density = RWA / Total_Assets or unreserved sour loans overwhelm tangible equity! Prudential credit analysts pair three complementary solvency checks: (1) CET1 Ratio = (Common_Equity - Goodwill_Intangibles_DTA_Deductions) / RWA, (2) Tier-1 / Tangible Leverage & RWA Density = RWA / Total_Assets, and (3) Gerard Cassidy’s (RBC) Texas Ratio = (NonPerforming_Loans + Foreclosed_OREO) / (Tangible_Common_Equity + Loan_Loss_Reserves) — coined during the 1980s Texas bank failures, where Texas Ratio >= 1.00 (100%) warns that problem assets exceed the bank’s entire loss-absorbing cushion!
Verify on Total_Assets = 20,000 ($M, B2), Risk_Weighted_Assets RWA = 12,500 ($M, B3), Tangible_CET1_Capital = 1,500 ($M, B4), Allowance_For_Credit_Losses LLR = 300 ($M, B5), and NonPerforming_Assets_Plus_OREO NPA = 450 ($M, B6): Basel CET1 Ratio is 1,500 / 12,500 = 0.1200 (12.00% >= 7.0% buffer); RWA Density is 12,500 / 20,000 = 0.6250 (62.50%); Unweighted Tangible Equity-to-Assets is 1,500 / 20,000 = 0.0750 (7.50%); and Texas Ratio is 450 / (1,500 + 300) = 450 / 1,800 = 0.2500 (25.00% — healthy < 50%, whereas NPA spiking to 1,980 $M pushes Texas Ratio to 1.1000 = 110.0% insolvency warning!)!
| Bank Solvency Metric (Assets=$20B, RWA=$12.5B, CET1=$1.5B, LLR=$0.3B, NPA=$0.45B) | Formula | Verified Output |
|---|---|---|
| Basel III CET1 Capital Ratio | CET1_Capital / RWA | 0.1200 (12.00%) |
| Risk-Weighted Asset Density | RWA / Total_Assets | 0.6250 (62.50%) |
| Unweighted Tangible Leverage Ratio | CET1_Capital / Total_Assets | 0.0750 (7.50%) |
| Cassidy Texas Ratio (NPA Coverage) | NPA / (CET1_Capital + LLR) | 0.2500 (25.0% < 100% Safe) |
Basel III Common Equity Tier 1 (CET1) Ratio & RWA Density Formula
Notice the exact identity: Unweighted_Leverage_Ratio = CET1_Ratio * RWA_Density (0.1200 * 0.6250 = 0.0750)!
=IF(OR(B2 <= 0, B3 <= 0, B3 > 2 * B2, B4 < 0), "Invalid Solvency Input", ROUND(B4 / B3, 4))Gerard Cassidy Non-Performing Asset Texas Ratio Formula
Guard exhausted loss-absorbing capital CET1 + LLR <= 0 ("Capital Exhausted: Insolvent").
=LET(cet_1, B4, llr_r, B5, npa_s, B6, IF(OR(llr_r < 0, npa_s < 0), "Invalid Solvency Input", IF(cet_1 + llr_r <= 0, "Capital Exhausted", ROUND(npa_s / (cet_1 + llr_r), 4))))Try the example
Use the original values or change them to test your understanding.