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					Using Derivatives for Hedging
Fixed Income Portfolios

                          Andrea Zager
                          May 13 2006
European Headquarters
30, St Mary Axe London
Environment of rising interest rates
EUR,USD 5Y last year
EUR, USD 5Y5Y Volatility
Are you long of bonds?
What can be done about it?

        You can sell the bonds and go home
  You can use Derivatives to protect against rising
                     interest rates
Which Derivatives?

• Futures
• Swaps
• Caps and Floors
What are Futures contracts?

• An agreement between two counterparties to exchange
  a cash amount at the expiry of the contract

• Cash amount: difference between the
     Forward Implied Interest Rate
     Actual Fixing of the same tenor Interest Rate
   at Expiry of the contract
Future Rates
How to use futures to hedge?

• To protect long bond portfolio you need to SELL Futures

                 If the interest rates go up

         The prices of both bonds and futures fall

            The bond portfolio losses its value
 The short futures position generates profit and therefore
               offsets the losses of the portfolio

• Agreement in which both parties agree to exchange a
  strip of interest payments (coupons) in the future where
  the amount each has to pay is calculated on a different

                        Pays Floating rate

       Counterparty A                        Counterparty B

                         Pays Fixed Rate
How to use Swaps to hedge?

• To protect a long bond portfolio against the parallel
  upward shift of the yield curve:
        Enter into Pay Fixed X Receive Float swap

              If the whole yield curve moves up

                        Bond prices fall

              The portfolio losses its value
    The swap hedge increases its value due to higher
           receivables from the floating side and
            offsets the losses of the portfolio
The spread     The spread
is currently   is currently
    0.6%           1.2%
How to use Swaps to hedge?

• To protect against the change in the shape of the yield
  curve (the yield curve steepens or flattens):
                  Enter into a CMS swap

                Steepening of the yield curve

        Bond positions with long maturity lose value

                   This is offset by CMS
  higher receivables of the long-term interest rate prevails
        lower payables of the short-term interest rate,
                  and profit is generated
CMS Swap, CMT Treasury

• Swap transactions where both of the counterparties
  agree to exchange strip of future payments both
  calculated on the basis of floating rates, e.g.:
      One based on the short term interest rate
      e.g. LIBOR 3M
      The other based on some long term interest rate
      e.g. CMSwap – the index is the 10 year Swap Rate
           CMTreasury – the index is a bond yield
CMS Swap, CMT Treasury

• Constant Maturity refers to the fact that one party pays in
  each period the 3M LIBOR and the other the 10Y Swap
• The maturity of the indexes is constant during the
  whole life of the swap.
CMS Swap, CMT Treasury
CMS Swap, CMT Treasury
How to price CMS?

• One the most sophisticated and complex instruments to

• Difficulties arise
       the non-linear function of yield
       the discrepancy in time between when the index is
       fixed         and
       the payment is made and the forward interest rate
       between those dates

• Price calculation requires volatility of the forward
  swap/bond and volatility of the forward short-term rate
Swaption ATF Rates Volatility Surface
Swaption Volatility Surface

• Are series of interest rate options called
  “Caplets” & “Floorlets”

• Each Caplet/Floorlet has
      the same strike
      the same underlying
   The difference: The expiry date

• The Cap/Floor buyer pays the seller an upfront premium

• Exercised automatically and cash settled

• CAP – the holder of the cap gains protection against
  rising interest rates

• FLOOR –the holder of the floor gains protection against
  falling interest rates
Cash Flow and Dates
Delta Risk Matrix
CAPs and FLOORs Volatility Surface
How to use Caps and Floors?

• In order to protect a long bond portfolio you need to BUY
  a CAP at a certain strike

                  If the interest rates increase

              The bond portfolio losses its value
           the CAP is automatically exercised and
 the profit arising from the difference between the strike of
            the CAP and the market rate is received
Thank you

 Andrea Zager
 Tel: + 44.20.7724.4167