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Fair value measurements - Rollforward of level 3 fair value measurements (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Sep. 30, 2020
Sep. 30, 2019
Sep. 30, 2020
Sep. 30, 2019
Dec. 31, 2019
Rollforward of Level 3, Derivative instruments assets & (liabilities)          
Balance at beginning of the period $ 1.5 $ (3.6) $ 0.8 $ (0.5)  
Total realized and unrealized gains (losses) (1.7) (2.0) (20.7) (7.7)  
Purchases 0.0 0.0 0.0 0.0  
Sales/Settlements(2) (2.2) 3.4 17.5 6.0  
Balance at end of the period (2.4) (2.2) (2.4) (2.2)  
Rollforward of Level 3, (liabilities)          
Payment of contingent consideration     28.4 0.0  
IMG          
Rollforward of Level 3, (liabilities)          
Payment of contingent consideration 18.4 6.9 18.4 6.9  
Armada          
Rollforward of Level 3, (liabilities)          
Payment of contingent consideration 4.5   10.0    
Hedge funds and private equity funds          
Rollforward of Level 3, (liabilities)          
Fair value of hedges 301.1 287.7 301.1 287.7 $ 269.0
Fixed maturity investments          
Rollforward of Level 3 Fair Value Measurements          
Balance at beginning of the period 2.6 0.0 17.0 5.4  
Total realized and unrealized gains (losses) 0.0 0.0 2.6 0.0  
Purchases 0.0 17.0 0.0 17.0  
Sales/Settlements(2) 0.0 0.0 (17.0) (5.4)  
Balance at end of the period 2.6 17.0 2.6 17.0  
Other Long-term Investments          
Rollforward of Level 3 Fair Value Measurements          
Balance at beginning of the period 78.2 88.0 77.8 63.6  
Total realized and unrealized gains (losses) 8.2 (0.3) 3.1 10.6  
Purchases 0.0 0.0 5.5 15.8  
Sales/Settlements(2) 0.0 (6.0) 0.0 (7.8)  
Balance at end of the period 86.9 80.7 86.9 80.7  
Loan participation          
Rollforward of Level 3 Fair Value Measurements          
Balance at beginning of the period 27.3 0.0 20.0 0.0  
Total realized and unrealized gains (losses) 0.0 0.0 0.0 0.0  
Purchases 2.5 0.0 9.9 0.0  
Sales/Settlements(2) (1.3) 0.0 (1.4) 0.0  
Balance at end of the period 28.5 0.0 28.5 0.0  
Contingent consideration (liabilities)          
Rollforward of Level 3, (liabilities)          
Balance at beginning of the period (22.9) (30.8) (28.2) (28.8)  
Total realized and unrealized gains (losses) (0.3) (2.1) (0.5) (4.1)  
Foreign currency gains (losses) through Other Comprehensive Income 0.0 0.0 0.0 0.0  
Purchases 0.0 0.0 0.0 0.0  
Sales/Settlements 22.9 6.9 28.4 6.9  
Balance at end of the period (0.3) (26.0) (0.3) (26.0)  
Foreign currency gains through Other Comprehensive Income          
Rollforward of Level 3, Derivative instruments assets & (liabilities)          
Foreign currency gains through Other Comprehensive Income 0.0 0.0 0.0 0.0  
Foreign currency gains through Other Comprehensive Income | Fixed maturity investments          
Rollforward of Level 3 Fair Value Measurements          
Foreign currency gains through Other Comprehensive Income 0.0 0.0 0.0 0.0  
Foreign currency gains through Other Comprehensive Income | Other Long-term Investments          
Rollforward of Level 3 Fair Value Measurements          
Foreign currency gains through Other Comprehensive Income 0.5 (1.0) 0.5 (1.5)  
Foreign currency gains through Other Comprehensive Income | Loan participation          
Rollforward of Level 3 Fair Value Measurements          
Foreign currency gains through Other Comprehensive Income $ 0.0 $ 0.0 $ 0.0 $ 0.0