C » Topics » Fair value hedges

This excerpt taken from the C 8-K filed Oct 13, 2009.

Fair value hedges

 

·          Hedging of benchmark interest rate risk—Citigroup hedges exposure to changes in the fair value of outstanding fixed-rate issued debt and borrowings. The fixed cash flows from those financing transactions are converted to benchmark variable-rate cash flows by entering into receive-fixed, pay-variable interest rate swaps. These fair-value hedge relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis.

 

Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale debt securities and loans. The hedging instruments used are receive-variable, pay-fixed interest rate swaps. Most of these fair-value hedging relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis, while certain others use regression analysis.

 

·          Hedging of foreign exchange risk—Citigroup hedges the change in fair value attributable to foreign-exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. Typically, the hedging instrument employed is a forward foreign-exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not Accumulated other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup typically considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is excluded from the assessment of hedge effectiveness and reflected directly in earnings. Dollar-offset method is typically used to assess hedge effectiveness. Since that assessment is based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged, the amount of hedge ineffectiveness is not significant.

 

This excerpt taken from the C 10-Q filed Aug 7, 2009.

Fair value hedges

Hedging of benchmark interest rate risk

        Citigroup hedges exposure to changes in the fair value of outstanding fixed-rate issued debt and borrowings. The fixed cash flows from those financing transactions are converted to benchmark variable-rate cash flows by entering into receive fixed, pay-variable interest rate swaps. These fair-value hedge relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis.

        Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale debt securities and loans. The hedging instruments used are receive-variable, pay-fixed interest rate swaps. Most of these fair-value hedging relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis, while certain others use regression analysis.

Hedging of foreign exchange risk

        Citigroup hedges the change in fair value attributable to foreign-exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. The hedging instrument employed is a forward foreign-exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not Accumulated other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is excluded from the assessment of hedge effectiveness and reflected directly in earnings. Dollar-offset method is used to assess hedge effectiveness. Since that assessment is based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged, the amount of hedge ineffectiveness is not significant.

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        The following table summarizes certain information related to the Company's fair value hedges for the three and six months ended June 30, 2009:

 
  Three months ended June 30, 2009   Six months ended June 30, 2009  
In millions of dollars   Principal
Transactions
  Other
Revenue
  Principal
Transactions
  Other
Revenue
 
Gain (loss) on fair value designated and qualifying hedges                          
  Interest rate contracts   $ 509   $ (3,687 ) $ 965   $ (5,886 )
  Foreign exchange contracts     1,186     467     1,303     322  
                   
Total gain (loss) on fair value designated and qualifying hedges   $ 1,695   $ (3,220 ) $ 2,268   $ (5,564 )
                   
Gain (loss) on the hedged item in designated and qualifying fair value hedges                          
  Interest rate hedges   $ (593 ) $ 3,546   $ (1,042 ) $ 5,990  
  Foreign exchange hedges     (1,306 )   (571 )   (1,151 )   (283 )
                   
Total gain (loss) on the hedged item in designated and qualifying fair value hedge   $ (1,899 ) $ 2,975   $ (2,193 ) $ 5,707  
                   
Hedge ineffectiveness recognized in earnings on designated and qualifying fair value hedges                          
  Interest rate hedges   $ 50   $ (170 ) $ 131   $ 85  
  Foreign exchange hedges     (3 )   (105 )   8     32  
                   
Total hedge ineffectiveness recognized in earnings on designated and qualifying fair value hedges   $ 47   $ (275 ) $ 139   $ 117  
                   
Net gain (loss) excluded from assessment of the effectiveness of fair value hedges                          
  Interest rate contracts   $ (134 ) $ 29   $ (208 ) $ 19  
  Foreign exchange contracts     (117 )   1     144     7  
                   
Total net gain / (loss) excluded from assessment of the effectiveness of fair value hedges   $ (251 ) $ 30   $ (64 ) $ 26  
                   
This excerpt taken from the C 10-Q filed May 11, 2009.

Fair value hedges

    Hedging of benchmark interest rate risk—Citigroup hedges exposure to changes in the fair value of outstanding fixed-rate issued debt and borrowings. The fixed cash flows from those financing transactions are converted to benchmark variable-rate cash flows by entering into receive fixed, pay-variable interest rate swaps. These fair-value hedge relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis.

        Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale debt securities and loans. The hedging instruments used are receive-variable, pay-fixed interest rate swaps. Most of these fair-value hedging relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis, while certain others use regression analysis.

    Hedging of foreign exchange risk—Citigroup hedges the change in fair value attributable to foreign-exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. The hedging instrument employed is a forward foreign-exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not Accumulated other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is excluded from the assessment of hedge effectiveness and reflected directly in earnings. Dollar-offset method is used to assess hedge effectiveness. Since that assessment is based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged, the amount of hedge ineffectiveness is not significant.

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        The following table summarizes certain information related to the Company's fair value hedges for the quarter ended March 31, 2009:

In millions of dollars for the three months ended March 31, 2009   Principal
Transactions
  Other
Revenue
 
Gain (loss) on fair value designated and qualifying hedges              
  Interest rate contracts   $ 456   $ (2,199 )
  Foreign exchange contracts     117     (145 )
           
Total gain (loss) on fair value designated and qualifying hedges   $ 573   $ (2,344 )
           
Gain (loss) on the hedged item in designated and qualifying fair value hedges              
  Interest rate hedges   $ (449 ) $ 2,444  
  Foreign exchange hedges     155     288  
           
Total gain (loss) on the hedged item in designated and qualifying fair value hedge   $ (294 ) $ 2,732  
           
Hedge ineffectiveness recognized in earnings on designated and qualifying fair value hedges              
  Interest rate hedges   $ 81   $ 255  
  Foreign exchange hedges     11     137  
           
Total hedge ineffectiveness recognized in earnings on designated and qualifying fair value hedges   $ 92   $ 392  
           
Net gain (loss) excluded from assessment of the effectiveness of fair value hedges              
  Interest rate contracts   $ (74 ) $ (10 )
  Foreign exchange contracts     261     6  
           
Total net gain/(loss) excluded from assessment of the effectiveness of fair value hedges   $ 187   $ (4 )
           
These excerpts taken from the C 10-K filed Feb 27, 2009.

Fair value hedges

 

Hedging of benchmark interest rate risk—Citigroup hedges exposure to changes in the fair value of outstanding fixed-rate issued debt and borrowings. The fixed cash flows from those financing transactions are converted to benchmark variable-rate cash flows by entering into receive-fixed, pay-variable interest rate swaps. These fair-value hedge relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis.

Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale debt securities and loans. The hedging instruments used are receive-variable, pay-fixed interest rate swaps. Most of these fair-value hedging relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis, while certain others use regression analysis.

 

 

Hedging of foreign exchange risk—Citigroup hedges the change in fair value attributable to foreign-exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. Typically, the hedging instrument employed is a forward foreign-exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not Accumulated other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup typically considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is excluded from the assessment of hedge effectiveness and reflected directly in earnings. Dollar-offset method is typically used to assess hedge effectiveness. Since that assessment is based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged, the amount of hedge ineffectiveness is not significant.

Fair value hedges

 

Hedging of benchmark interest rate risk—Citigroup hedges exposure to changes in the fair value of outstanding fixed-rate issued debt and borrowings. The fixed cash flows from those financing transactions are converted to benchmark variable-rate cash flows by entering into receive-fixed, pay-variable interest rate swaps. These fair-value hedge relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis.

Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale debt securities and loans. The hedging instruments used are receive-variable, pay-fixed interest rate swaps. Most of these fair-value hedging relationships use dollar-offset ratio analysis to determine whether the hedging relationships are highly effective at inception and on an ongoing basis, while certain others use regression analysis.

 

 

Hedging of foreign exchange risk—Citigroup hedges the change in fair value attributable to foreign-exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. Typically, the hedging instrument employed is a forward foreign-exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not Accumulated other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup typically considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is excluded from the assessment of hedge effectiveness and reflected directly in earnings. Dollar-offset method is typically used to assess hedge effectiveness. Since that assessment is based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged, the amount of hedge ineffectiveness is not significant.

This excerpt taken from the C 10-Q filed Nov 5, 2007.

Fair value hedges

    Hedging of benchmark interest rate risk—Citigroup hedges exposure to changes in the fair value of fixed-rate financing transactions, including liabilities related to outstanding debt, borrowings and time deposits. The fixed cash flows from those financing transactions are converted to benchmark-variable-rate cash flows by entering into receive-fixed, pay-variable interest rate swaps. Typically these fair value hedge relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis.

            Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale securities and inter-bank placements. The hedging instruments mainly used are receive-variable, pay-fixed interest rate swaps for the remaining hedged asset categories. Most of these fair value hedging relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis, while others use regression analysis.

            For a limited number of fair value hedges of benchmark interest rate risk, Citigroup uses the "shortcut" method as

75


      SFAS 133 allows the Company to assume no ineffectiveness if the hedging relationship involves an interest-bearing financial asset or liability and an interest rate swap. In order to assume no ineffectiveness, Citigroup ensures that all the shortcut method requirements of SFAS 133 for these types of hedging relationships are met.

    Hedging of foreign exchange risk—Citigroup hedges the change in fair value attributable to foreign exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be in or outside the U.S. Typically, the hedging instrument employed is a forward foreign exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not Accumulated other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup typically considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is generally excluded from the assessment of hedge effectiveness and reflected directly in earnings. Dollar-offset method is typically used to assess hedge effectiveness retrospectively and prospectively. Since that assessment is based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged, the amount of hedge ineffectiveness is not significant.

    Hedging the overall changes in fair value—Citigroup primarily hedges the change in the overall fair value of portfolios of similar held-for-sale mortgage loans. Derivatives used in these hedging relationships are mainly forward sales of mortgage-backed securities. Citigroup assesses effectiveness at inception and on an ongoing basis using regression analysis.
This excerpt taken from the C 10-Q filed May 4, 2007.

Fair value hedges

    Hedging of benchmark interest rate risk—Citigroup hedges exposure to changes in the fair value of fixed-rate financing transactions, including liabilities related to outstanding debt, borrowings and time deposits. The fixed cash flows from those financing transactions are converted to benchmark-variable-rate cash flows by entering into receive-fixed, pay-variable interest rate swaps. Typically these fair value hedge relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis.

        Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale securities, reverse repurchase agreements and inter-bank placements. The hedging instruments mainly used are receive-variable, pay-fixed interest rate swaps for the remaining hedged asset categories. Most of these fair value hedging relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis, while others use regression analysis.

        For a limited number of fair value hedges of benchmark interest rate risk, Citigroup uses the "shortcut" method as SFAS 133 allows the Company to assume no ineffectiveness if the hedging relationship involves an interest-bearing financial asset or liability and an interest rate swap. In order to assume no ineffectiveness, Citigroup ensures that all the shortcut method requirements of SFAS 133 for these types of hedging relationships are met.

    Hedging of foreign exchange risk—Citigroup hedges the change in fair value attributable to foreign exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. Typically, the hedging instrument employed is a short-term forward foreign exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup typically considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is generally excluded from the assessment of hedge effectiveness and reflected directly in earnings. Hedge effectiveness is typically assessed based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged. As a result, the amount of hedge ineffectiveness is not significant.

    Hedging the overall changes in fair value—Citigroup primarily hedges the change in the overall fair value of portfolios of similar held-for-sale mortgage loans. Derivatives used in these hedging relationships are mainly forward sales of mortgage-backed securities. Citigroup assesses effectiveness at inception and on an ongoing basis using regression analysis.
This excerpt taken from the C 10-K filed Feb 23, 2007.

Fair value hedges

 

Hedging of benchmark interest rate risk – Citigroup hedges exposure to changes in the fair value of fixed-rate financing transactions, including liabilities related to outstanding debt, borrowings and time deposits. The fixed cash flows from those financing transactions are converted to benchmark-variable-rate cash flows by entering into receive-fixed, pay-variable interest rate swaps. Typically these fair value hedge relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis.

Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale securities, reverse repurchase agreements and inter-bank placements. The hedging instruments mainly used are receive-variable, pay-fixed interest rate swaps for the remaining hedged asset categories. Most of these fair value hedging relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis, while others use regression analysis.

For a limited number of fair value hedges of benchmark interest rate risk, Citigroup uses the “shortcut” method as SFAS 133 allows the Company to assume no ineffectiveness if the hedging relationship involves an interest-bearing financial asset or liability and an interest rate swap. In order to assume no ineffectiveness, Citigroup ensures that all the shortcut method requirements of SFAS 133 for these types of hedging relationships are met.


 

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Table of Contents

 

 

Hedging of foreign exchange risk – Citigroup hedges the change in fair value attributable to foreign exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. Typically, the hedging instrument employed is a short-term forward foreign exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup typically considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is generally excluded from the assessment of hedge effectiveness and reflected directly in earnings. Hedge effectiveness is typically assessed based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged. As a result, the amount of hedge ineffectiveness is not significant.

 

Hedging the overall changes in fair value – Citigroup primarily hedges the change in the overall fair value of portfolios of similar held-for-sale mortgage loans. Derivatives used in these hedging relationships are mainly forward sales of mortgage-backed securities. Citigroup assesses effectiveness at inception and on an ongoing basis using regression analysis.

This excerpt taken from the C 10-Q filed Nov 3, 2006.

Fair value hedges

    Hedging of benchmark interest rate risk—Citigroup hedges exposure to changes in the fair value of fixed-rate financing transactions, including liabilities related to outstanding debt, borrowings and time deposits. The fixed cash flows from those financing transactions are converted to benchmark-variable-rate cash flows by entering into receive-fixed, pay-variable interest rate swaps. Typically these fair value hedge relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis.

115


        Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale securities, reverse repurchase agreements and inter-bank placements. The hedging instruments mainly used are receive-variable, pay-fixed interest rate swaps for the remaining hedged asset categories. Most of these fair value hedging relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis, while others use regression analysis.

        For a limited number of fair value hedges of benchmark interest rate risk, Citigroup uses the "shortcut" method as SFAS 133 allows the Company to assume no ineffectiveness if the hedging relationship involves an interest-bearing financial asset or liability and an interest rate swap. In order to assume no ineffectiveness, Citigroup ensures that all the shortcut method requirements of SFAS 133 for these types of hedging relationships are met.

    Hedging of foreign exchange risk—Citigroup hedges the change in fair value attributable to foreign exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. Typically, the hedging instrument employed is a short-term forward foreign exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup typically considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is generally excluded from the assessment of hedge effectiveness and reflected directly in earnings. Hedge effectiveness is typically measured based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged. As a result, the amount of hedge ineffectiveness is not significant.

    Hedging the overall changes in fair value—Citigroup primarily hedges the change in the overall fair value of portfolios of similar held-for-sale mortgage loans. Derivatives used in these hedging relationships are mainly forward sales of mortgage-backed securities. Citigroup assesses effectiveness at inception and on an ongoing basis using regression analysis.
This excerpt taken from the C 10-Q filed Aug 4, 2006.

Fair value hedges

    Hedging of benchmark interest rate risk—Citigroup hedges exposure to changes in the fair value of fixed-rate financing transactions, including liabilities related to outstanding debt, borrowings and time deposits. The fixed cash flows from those financing transactions are converted to benchmark-variable-rate cash flows by entering into receive-fixed, pay-variable interest rate swaps. Typically these fair value hedge relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis.

110


        Citigroup also hedges exposure to changes in the fair value of fixed-rate assets, including available-for-sale securities, reverse repurchase agreements and inter-bank placements. The hedging instruments mainly used are receive-variable, pay-fixed interest rate swaps for the remaining hedged asset categories. Most of these fair value hedging relationships use dollar-offset ratio analysis to assess whether the hedging relationships are highly effective at inception and on an ongoing basis, while others use regression analysis.

        For some fair value hedges of benchmark interest rate risk, Citigroup uses the "shortcut" method as SFAS 133 allows the Company to assume no ineffectiveness if the hedging relationship involves an interest-bearing financial asset or liability and an interest rate swap. In order to assume no ineffectiveness, Citigroup ensures that all the shortcut method requirements of SFAS 133 for these types of hedging relationships are met.

    Hedging of foreign exchange risk—Citigroup hedges the change in fair value attributable to foreign exchange rate movements in available-for-sale securities that are denominated in currencies other than the functional currency of the entity holding the securities, which may be within or outside the U.S. Typically, the hedging instrument employed is a short-term forward foreign exchange contract. In this type of hedge, the change in fair value of the hedged available-for-sale security attributable to the portion of foreign exchange risk hedged is reported in earnings and not other comprehensive income—a process that serves to offset substantially the change in fair value of the forward contract that is also reflected in earnings. Citigroup typically considers the premium associated with forward contracts (differential between spot and contractual forward rates) as the cost of hedging; this is generally excluded from the assessment of hedge effectiveness and reflected directly in earnings. Hedge effectiveness is typically measured based on changes in fair value attributable to changes in spot rates on both the available-for-sale securities and the forward contracts for the portion of the relationship hedged. As a result, the amount of hedge ineffectiveness is not significant.

    Hedging the overall changes in fair value—Citigroup primarily hedges the change in the overall fair value of portfolios of similar held-for-sale mortgage loans. Derivatives used in these hedging relationships are mainly forward sales of mortgage-backed securities. Citigroup assesses effectiveness at inception and on an ongoing basis using regression analysis.
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