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Investments (Details) - USD ($)
$ in Thousands
3 Months Ended 6 Months Ended
Mar. 31, 2021
Mar. 31, 2020
Mar. 31, 2021
Mar. 31, 2020
Sep. 30, 2020
Schedule of Equity Method Investments [Line Items]          
Equity in earnings of investees $ 303 $ 324 $ 727 $ 579  
Distributions from equity method investment     864 705  
Equity method investment accounted for under the fair value option 16,872   16,872   $ 12,152
Unrealized (loss) gain on equity method investment accounted for under the fair value option $ (3,402) (2,200) $ 4,720 (762)  
TA          
Schedule of Equity Method Investments [Line Items]          
Equity interest percentage 4.50%   4.50%    
TRMT          
Schedule of Equity Method Investments [Line Items]          
Equity in earnings of investees     $ 727    
Distributions from equity method investment $ 847 $ 353 $ 864 $ 705  
Tremont Advisors | TRMT          
Schedule of Equity Method Investments [Line Items]          
Number of shares owned (in shares) 1,600,100   1,600,100    
Ownership percentage 19.30%   19.30%    
RMR LLC | TA          
Schedule of Equity Method Investments [Line Items]          
Equity interest percentage 4.30%   4.30%    
RMR LLC | TA          
Schedule of Equity Method Investments [Line Items]          
Number of shares owned (in shares) 621,853   621,853