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Fair Value Measurements - Fair Value by Balance Sheet Grouping (Details) - USD ($)
$ in Thousands
Mar. 31, 2024
Sep. 30, 2023
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value $ 2,438,114 $ 1,995,097
Held-to-maturity securities, at amortized cost 457,882 423,586
Loans held for sale 2,993,658 0
FHLB stock 160,817 126,820
Agency pass-through certificates    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Held-to-maturity securities, at amortized cost 457,882 423,586
Carrying Amount    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 2,438,114 1,995,097
Held-to-maturity securities, at amortized cost 457,882 423,586
Carrying Amount | Level 1    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Cash and cash equivalents 1,505,771 980,649
Carrying Amount | Level 2    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Loans held for sale 2,993,658 0
FHLB stock 160,817 126,820
Time deposits 9,000,911 5,305,016
Carrying Amount | Level 2 | Borrowings    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Debt 5,345,518 3,650,000
Carrying Amount | Level 2 | Senior Debt    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Debt 93,729 0
Carrying Amount | Level 2 | Client swap program hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 63,264 78,797
Other liabilities - client swap program hedges 64,020 79,668
Carrying Amount | Level 2 | Commercial loan fair value hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 2,509 3,405
Carrying Amount | Level 2 | Mortgage loan fair value hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 56,093 46,396
Carrying Amount | Level 2 | Borrowings cash flow hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 154,588 184,373
Carrying Amount | Level 2 | U.S. government and agency securities    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 312,199 217,053
Carrying Amount | Level 2 | Asset-backed securities    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 549,463 588,016
Carrying Amount | Level 2 | Municipal bonds    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 35,061 34,662
Carrying Amount | Level 2 | Corporate debt securities    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 249,743 242,522
Carrying Amount | Level 2 | Agency pass-through certificates    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 1,291,648 912,844
Held-to-maturity securities, at amortized cost 457,882 423,586
Carrying Amount | Level 3    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Loans receivable 20,795,259 17,476,550
Carrying Amount | Level 3 | Junior subordinated deferrable interest debentures    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Debt 50,254 0
Estimated Fair Value    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 2,438,114 1,995,097
Held-to-maturity securities, at amortized cost 407,461 355,188
Estimated Fair Value | Level 1    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Cash and cash equivalents 1,505,771 980,649
Estimated Fair Value | Level 2    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Loans held for sale 2,993,658 0
FHLB stock 160,817 126,820
Time deposits 9,037,254 5,232,689
Estimated Fair Value | Level 2 | Borrowings    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Debt 5,320,188 3,653,229
Estimated Fair Value | Level 2 | Senior Debt    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Debt 93,373 0
Estimated Fair Value | Level 2 | Client swap program hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 63,264 78,797
Other liabilities - client swap program hedges 64,020 79,668
Estimated Fair Value | Level 2 | Commercial loan fair value hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 2,509 3,405
Estimated Fair Value | Level 2 | Mortgage loan fair value hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 56,093 46,396
Estimated Fair Value | Level 2 | Borrowings cash flow hedges    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Other assets 154,588 184,373
Estimated Fair Value | Level 2 | U.S. government and agency securities    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 312,199 217,053
Estimated Fair Value | Level 2 | Asset-backed securities    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 549,463 588,016
Estimated Fair Value | Level 2 | Municipal bonds    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 35,061 34,662
Estimated Fair Value | Level 2 | Corporate debt securities    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 249,743 242,522
Estimated Fair Value | Level 2 | Agency pass-through certificates    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Available-for-sale securities, at fair value 1,291,648 912,844
Held-to-maturity securities, at amortized cost 407,461 355,188
Estimated Fair Value | Level 3    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Loans receivable 20,245,348 16,559,758
Estimated Fair Value | Level 3 | Junior subordinated deferrable interest debentures    
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items]    
Debt $ 50,320 $ 0