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Quarterly Financial Data - Summary of Quarterly Financial Data (Detail) (USD $)
In Millions, except Per Share data, unless otherwise specified
3 Months Ended 12 Months Ended
Dec. 31, 2014
Sep. 30, 2014
Jun. 30, 2014
Mar. 31, 2014
Dec. 31, 2013
Sep. 30, 2013
Jun. 30, 2013
Mar. 31, 2013
Dec. 31, 2014
Dec. 31, 2013
Dec. 31, 2012
Quarterly Financial Information Disclosure [Abstract]                      
Revenues $ 3,476us-gaap_Revenues $ 3,574us-gaap_Revenues $ 3,542us-gaap_Revenues $ 3,506us-gaap_Revenues $ 3,476us-gaap_Revenues $ 3,403us-gaap_Revenues $ 3,551us-gaap_Revenues $ 3,517us-gaap_Revenues $ 14,098us-gaap_Revenues $ 13,947us-gaap_Revenues $ 13,595us-gaap_Revenues
Losses and expenses 2,714cb_LossesAndExpenses 2,756cb_LossesAndExpenses 2,864cb_LossesAndExpenses 2,903cb_LossesAndExpenses 2,690cb_LossesAndExpenses 2,664cb_LossesAndExpenses 2,755cb_LossesAndExpenses 2,601cb_LossesAndExpenses      
Federal and Foreign Income Tax 204us-gaap_IncomeTaxExpenseBenefit 224us-gaap_IncomeTaxExpenseBenefit 179us-gaap_IncomeTaxExpenseBenefit 154us-gaap_IncomeTaxExpenseBenefit 217us-gaap_IncomeTaxExpenseBenefit 198us-gaap_IncomeTaxExpenseBenefit 217us-gaap_IncomeTaxExpenseBenefit 260us-gaap_IncomeTaxExpenseBenefit 761us-gaap_IncomeTaxExpenseBenefit 892us-gaap_IncomeTaxExpenseBenefit 451us-gaap_IncomeTaxExpenseBenefit
NET INCOME $ 558us-gaap_NetIncomeLoss $ 594us-gaap_NetIncomeLoss $ 499us-gaap_NetIncomeLoss $ 449us-gaap_NetIncomeLoss $ 569us-gaap_NetIncomeLoss $ 541us-gaap_NetIncomeLoss $ 579us-gaap_NetIncomeLoss $ 656us-gaap_NetIncomeLoss $ 2,100us-gaap_NetIncomeLoss $ 2,345us-gaap_NetIncomeLoss $ 1,545us-gaap_NetIncomeLoss
Basic earnings per share $ 2.35us-gaap_EarningsPerShareBasic $ 2.47us-gaap_EarningsPerShareBasic $ 2.03us-gaap_EarningsPerShareBasic $ 1.81us-gaap_EarningsPerShareBasic $ 2.25us-gaap_EarningsPerShareBasic $ 2.11us-gaap_EarningsPerShareBasic $ 2.22us-gaap_EarningsPerShareBasic $ 2.49us-gaap_EarningsPerShareBasic $ 8.65us-gaap_EarningsPerShareBasic $ 9.08us-gaap_EarningsPerShareBasic $ 5.73us-gaap_EarningsPerShareBasic
Diluted earnings per share $ 2.35us-gaap_EarningsPerShareDiluted $ 2.47us-gaap_EarningsPerShareDiluted $ 2.03us-gaap_EarningsPerShareDiluted $ 1.80us-gaap_EarningsPerShareDiluted $ 2.24us-gaap_EarningsPerShareDiluted $ 2.10us-gaap_EarningsPerShareDiluted $ 2.21us-gaap_EarningsPerShareDiluted $ 2.48us-gaap_EarningsPerShareDiluted $ 8.62us-gaap_EarningsPerShareDiluted $ 9.04us-gaap_EarningsPerShareDiluted $ 5.69us-gaap_EarningsPerShareDiluted
Underwriting ratios                      
Losses to premiums earned 53.8cb_LossesToPremiumsEarned 54.0cb_LossesToPremiumsEarned 58.7cb_LossesToPremiumsEarned 61.1cb_LossesToPremiumsEarned 54.7cb_LossesToPremiumsEarned 53.0cb_LossesToPremiumsEarned 56.7cb_LossesToPremiumsEarned 52.3cb_LossesToPremiumsEarned      
Expenses to premiums written 30.5cb_ExpensesToPremiumsWritten 31.8cb_ExpensesToPremiumsWritten 31.3cb_ExpensesToPremiumsWritten 32.1cb_ExpensesToPremiumsWritten 30.8cb_ExpensesToPremiumsWritten 32.7cb_ExpensesToPremiumsWritten 32.1cb_ExpensesToPremiumsWritten 32.3cb_ExpensesToPremiumsWritten      
Combined 84.3cb_CombinedLossAndExpenseRatio 85.8cb_CombinedLossAndExpenseRatio 90.0cb_CombinedLossAndExpenseRatio 93.2cb_CombinedLossAndExpenseRatio 85.5cb_CombinedLossAndExpenseRatio 85.7cb_CombinedLossAndExpenseRatio 88.8cb_CombinedLossAndExpenseRatio 84.6cb_CombinedLossAndExpenseRatio