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Consolidated Statements of Cash Flows (USD $)
In Millions, unless otherwise specified
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Cash Flows from Operating Activities    
Net Income $ 375us-gaap_NetIncomeLoss $ 449us-gaap_NetIncomeLoss
Adjustments to Reconcile Net Income to Net Cash Provided by Operating Activities    
Increase in Unpaid Losses and Loss Expenses, Net 260us-gaap_IncreaseDecreaseInPropertyAndCasualtyInsuranceLiabilities 51us-gaap_IncreaseDecreaseInPropertyAndCasualtyInsuranceLiabilities
Increase in Unearned Premiums, Net 1us-gaap_IncreaseDecreaseInUnearnedPremiums 33us-gaap_IncreaseDecreaseInUnearnedPremiums
Amortization of Premiums and Discounts on Fixed Maturities 54us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments 46us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments
Depreciation 12us-gaap_Depreciation 14us-gaap_Depreciation
Realized Investment Gains, Net (11)us-gaap_GainLossOnInvestments (116)us-gaap_GainLossOnInvestments
Other, Net (161)us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet (105)us-gaap_IncreaseDecreaseInOtherOperatingCapitalNet
Net Cash Provided by Operating Activities 530us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations 372us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations
Cash Flows from Investing Activities    
Proceeds from Fixed Maturities - Sales 1,436us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt 379us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt
Proceeds from Fixed Maturities - Maturities, Calls and Redemptions 820us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities 957us-gaap_ProceedsFromMaturitiesPrepaymentsAndCallsOfAvailableForSaleSecurities
Proceeds from Sales of Equity Securities 29us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesEquity 101us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesEquity
Purchases of Fixed Maturities (2,421)us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt (1,810)us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt
Purchases of Equity Securities (24)us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesEquity (89)us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesEquity
Investments in Other Invested Assets, Net 17us-gaap_PaymentsForProceedsFromLimitedPartnership 98us-gaap_PaymentsForProceedsFromLimitedPartnership
Decrease in Short Term Investments, Net 82us-gaap_PaymentsForProceedsFromShortTermInvestments 417us-gaap_PaymentsForProceedsFromShortTermInvestments
Change in Receivable or Payable from Security Transactions Not Settled, Net 5cb_ChangeInNetPayableReceivableFromSecurityTransactionsNotSettled 105cb_ChangeInNetPayableReceivableFromSecurityTransactionsNotSettled
Purchases of Property and Equipment, Net (18)us-gaap_PaymentsToAcquirePropertyPlantAndEquipment (10)us-gaap_PaymentsToAcquirePropertyPlantAndEquipment
Other, Net   (3)us-gaap_PaymentsForProceedsFromOtherInvestingActivities
Net Cash Provided by (Used in) Investing Activities (74)us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations 145us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperations
Cash Flows from Financing Activities    
Decrease in Funds Held Under Deposit Contracts (1)us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements (1)us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements
Proceeds from Issuance of Common Stock Under Stock-Based Employee Compensation Plans 5us-gaap_ProceedsFromStockPlans 14us-gaap_ProceedsFromStockPlans
Repurchase of Shares (338)us-gaap_PaymentsForRepurchaseOfCommonStock (415)us-gaap_PaymentsForRepurchaseOfCommonStock
Dividends Paid to Shareholders (117)us-gaap_PaymentsOfDividendsCommonStock (110)us-gaap_PaymentsOfDividendsCommonStock
Net Cash Used in Financing Activities (451)us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperations (512)us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperations
Net Increase in Cash 5us-gaap_CashPeriodIncreaseDecrease 5us-gaap_CashPeriodIncreaseDecrease
Cash at Beginning of Year 47us-gaap_Cash 52us-gaap_Cash
Cash at End of Period $ 52us-gaap_Cash $ 57us-gaap_Cash