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Fair Value Measurements - Fair Value by Balance Sheet Grouping (Details) - USD ($)
$ in Thousands
Jun. 30, 2022
Sep. 30, 2021
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value $ 2,150,732 $ 2,138,259
FHLB and FRB stock 78,073 102,863
Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 2,150,732 2,138,259
Held-to-maturity securities 477,884 366,025
Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 2,150,732 2,138,259
Held-to-maturity securities 447,829 379,547
Level 1 | Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Cash and cash equivalents 607,421 2,090,809
Level 1 | Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Cash and cash equivalents 607,421 2,090,809
Level 2 | Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
FHLB and FRB stock 78,073 102,863
Time deposits 3,297,369 3,434,087
FHLB advances 1,700,000 1,720,000
Level 2 | Carrying Amount | Client swap program hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 43,219 10,983
Other liabilities 43,219 10,983
Level 2 | Carrying Amount | Commercial loan fair value hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 1,153 0
Other liabilities 0 2,177
Level 2 | Carrying Amount | Mortgage loan fair value hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 26,415 0
Other liabilities 0 1,641
Level 2 | Carrying Amount | Borrowings cash flow hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 136,436 42,442
Level 2 | Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
FHLB and FRB stock 78,073 102,863
Time deposits 3,212,617 3,382,206
FHLB advances 1,558,021 1,692,412
Level 2 | Estimated Fair Value | Client swap program hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 43,219 10,983
Other liabilities 43,219 10,983
Level 2 | Estimated Fair Value | Commercial loan fair value hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 1,153 0
Other liabilities 0 2,177
Level 2 | Estimated Fair Value | Mortgage loan fair value hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 26,415 0
Other liabilities 0 1,641
Level 2 | Estimated Fair Value | Borrowings cash flow hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 136,436 42,442
Level 3 | Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Loans receivable 15,565,165 13,833,570
Level 3 | Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Loans receivable 15,395,375 14,279,725
U.S. government and agency securities | Level 2 | Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 45,462 61,779
U.S. government and agency securities | Level 2 | Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 45,462 61,779
Asset-backed securities | Level 2 | Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 838,033 1,078,681
Asset-backed securities | Level 2 | Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 838,033 1,078,681
Municipal bonds | Level 2 | Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 37,231 39,984
Municipal bonds | Level 2 | Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 37,231 39,984
Corporate debt securities | Level 2 | Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 321,924 350,988
Corporate debt securities | Level 2 | Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 321,924 350,988
Agency pass-through certificates | Level 2 | Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 908,082 606,827
Held-to-maturity securities 477,884 366,025
Agency pass-through certificates | Level 2 | Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 908,082 606,827
Held-to-maturity securities $ 447,829 $ 379,547