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Assets and Liabilities, at Fair Value - Narrative (Details) - USD ($)
$ in Millions
Sep. 30, 2025
Sep. 30, 2024
Mar. 01, 2024
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments owned $ 8,604.4 $ 6,767.1  
Financial instruments sold, not yet purchased, at fair value 2,919.8 2,853.3  
Senior Secured Notes due 2031      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Senior notes $ 544.1 543.1  
Senior Secured Notes due 2031 | Senior Notes      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Stated interest rate (as a percent) 7.875%   7.875%
Senior Secured Notes due 2032      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Senior notes $ 614.9 0.0  
Senior Secured Notes due 2032 | Senior Notes      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Stated interest rate (as a percent) 6.875%    
Fair Value, Measurements, Recurring      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments owned $ 8,604.4 6,767.1  
Financial instruments sold, not yet purchased, at fair value 2,919.8 2,853.3  
Fair Value, Measurements, Recurring | Mutual funds and other      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments owned 27.4 25.7  
Fair Value, Measurements, Recurring | Other      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments sold, not yet purchased, at fair value 0.1 0.9  
Level 2 | Senior Secured Notes due 2031 | Senior Notes      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Long-term debt, fair value 578.5    
Level 2 | Senior Secured Notes due 2032 | Senior Notes      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Long-term debt, fair value 643.6    
Level 2 | Fair Value, Measurements, Recurring      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments owned 7,618.6 5,541.6  
Financial instruments sold, not yet purchased, at fair value 954.5 758.5  
Level 2 | Fair Value, Measurements, Recurring | Mutual funds and other      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments owned 0.0 0.0  
Level 2 | Fair Value, Measurements, Recurring | Other      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments sold, not yet purchased, at fair value 0.0 0.0  
Level 3 | Fair Value, Measurements, Recurring      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments owned 2.3 2.1  
Financial instruments sold, not yet purchased, at fair value 0.1 0.9  
Level 3 | Fair Value, Measurements, Recurring | Mutual funds and other      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments owned 2.3 2.1  
Level 3 | Fair Value, Measurements, Recurring | Other      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Financial instruments sold, not yet purchased, at fair value 0.1 $ 0.9  
Benchmark      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Fair value of contingent consideration 26.5    
Right Corporation      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Fair value of contingent consideration 2.6    
JBR      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Fair value of contingent consideration 1.5    
Trust Advisory Group, Ltd      
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]      
Fair value of contingent consideration $ 1.7