1. Chapter 20
Swaps

2. Overview This chapter discusses the nature and concepts of swaps.
Swaps are over-the-counter (OTC) instruments.
We learn how these OTC instruments can hedge interest rate and foreign exchange risks over the long term.
We learn about the special credit risk exposures of swaps relative to other OTC instruments.
We discuss how each party to a swap manages its credit risk exposure.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

3. Major Swap Types
Generic types of swaps in order of quantitative importance:
Interest rate swaps,
Currency swaps,
Credit swaps,
Commodity swaps,
Equity swaps.
Swaps are used to restructure the cash flows of assets and/or liabilities by the transacting parties.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

4. Interest Rate Swaps
An exchange of fixed interest payments for floating interest payments by two counterparties.
By convention:
Swap buyer makes the fixed interest payment,
Swap seller makes the floating interest payment.
Plain vanilla: generic agreement.
Purpose of swap
Allows FIs to economically convert variable-rate instruments into fixed-rate (or vice versa) in order to better match the duration of assets and liabilities.
Off-balance-sheet transaction.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

5. Interest Rate Swaps Plain Vanilla Interest Rate Swap – Example:
First party: Bank A has raised $100 million by issuing 4-year notes with 10% fixed coupons. On asset side: C&I loans linked to LIBOR.
Duration gap is negative:
DA – kDL < 0
Second party: Bank B with $100 million in fixed-rate mortgages of long duration funded with CDs having duration of 1 year.
Duration gap is positive:
DA – kDL > 0
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

6. Interest Rate Swaps Plain Vanilla Interest Rate Swap – Example (cont):
Bank B can reduce duration gap by buying a swap (taking fixed-payment side).
Notional value of the swap is $100 million.
Maturity is 4 years with 10% fixed-payments.
Suppose that LIBOR currently equals 8% and bank agrees to pay LIBOR + 2%.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

7. Interest Rate Swaps Plain Vanilla Interest Rate Swap – Example (cont):
Suppose realised rates are as follows:
End of: LIBOR
Year %
Year %
Year %
Year %
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

8. Interest Rate Swaps Plain Vanilla Interest Rate Swap – Example (cont):
Swap payments:
LIBOR Bank A Bank B
End of : + 2% Net
Year 1 11% $11 $
Year
Year
Year
Total
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

9. Macrohedging with Swaps
Optimal notional value of swap contracts just offsets any on-balance sheet loss in net worth.
Example:
FI with positive duration gap:
∆E = – (DA – kDL) × A × [∆R / (1 + R)] > 0
Assume the FI chooses to hedge with 10-year swaps.
Fixed-rate payments are equivalent to payments on a 10-year T-bond.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

10. Macrohedging with Swaps
Example (continued):
Floating-rate payments repriced to LIBOR every year.
Changes in swap value DS, depend on duration difference (D10 – D1).
∆S = – (Dfixed – Dfloat) × NS × [∆R/(1 + R)]
Where:
∆S = change in the market value of the swap contract.
(Dfixed – Dfloat) = difference in duration of instruments.
NS = notional value of swap contracts.
[∆R/(1 + R)] = shock to interest rates.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

11. Macrohedging with Swaps
Example (continued):
Optimal notional value requires:
DS = DE
Substituting values for DS and DE:
–(Dfixed – Dfloat) × NS × [DR/(1 + R)]
= – (DA – kDL) × A × [DR/(1 + R)]
Solving for NS:
NS = [(DA – kDL) × A]/(Dfixed – Dfloat)
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

12. Pricing an Interest Rate Swap
No arbitrage conditions:
Expected fixed-payment PV = expected floating-payment PV
Fixed-rate payment priced off on-the-run yield curve.
Example:
Assume 4-year swap with fixed payments at year-end.
Expected one-year rates are derived from the on-the-run Treasury yield curve treating the individual payments as separate zero-coupon bonds and iterating forward.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

13. Pricing an Interest Rate Swap
Solving the Discount Yield Curve:
P1= 108/(1 + R1) = 100  R1 = 8%  d1 = 8%
P2 = 9/(1 + R2) + 109/(1 + R2)2 = 100  R2 = 9%
9/(1 + d1) + 109/(1 + d2)2 = 100  d2 = 9.045%
Similarly, d3 = 9.58% and d4 = %
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

14. Pricing an Interest Rate Swap
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

15. Pricing an Interest Rate Swap
Solving Implied Forward Rates:
d1 = 8%  E(r1) = 8%
1 + E(r2) = (1 + d2)2/(1 + d1)  E(r2) = 10.1%
1 + E(r3) = (1 + d3)3/(1 + d2)2  E(r3) = %
1 + E(r4) = (1 + d4)4/(1 + d3)3  E(r4) = %
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

16. Pricing an Interest Rate Swap
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

17. Currency Swaps
Swaps used to hedge against exchange rate risk from mismatched currencies on assets and liabilities.
Fixed–Fixed Currency Swaps:
Assume Australian bank with fixed-rate assets denominated in dollars.
Assets partially financed with €50 million in 3-year 10% (fixed) notes.
On the other hand, German bank partially funds its assets by $100 million 3-year 10%.
Both banks exposed to exchange rate risk.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

18. Currency Swaps Cash Flows from Fixed–Fixed Currency Swap:
Australian bank
German bank
Outflows (B/S)
-0.1 × €50
-0.1 × S100
Inflows (Swap)
0.1 × €50
0.1 × $100
Outflows (Swap)
-0.1 × $100
Net cash flows
Rates on notes:
$-denominated
€-denominated
-10.5%
10.5%
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

19. Currency Swaps Fixed–Floating Currency Swaps:
Allows simultaneous hedging of
interest rate, and
currency exposures.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

20. Currency Swaps
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

21. Credit Swaps Total Return Swaps:
Swaps involving an obligation to pay interest at a specified fixed or floating rate for payments representing the total return on a specified amount.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

22. Credit Swaps Pure Credit Swaps:
Swap in which an FI receives the face value of a loan in case of default in return for paying a periodic swap fee.
Periodic fee similar to insurance premium payments.
Pure credit swap similar to:
buying credit insurance,
multi-period credit option.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

23. Credit Swaps
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher

24. Credit Swaps Swaps and Credit Risk Concerns:
Credit risk on swaps generally lower than on loans.
Reasons:
Netting  netting by novation,
Payment flows: in case of default, only interest payments are affected,
Standby letters of credit.
Copyright  2007 McGraw-Hill Australia Pty Ltd PPTs t/a Financial Institutions Management 2e, by Lange, Saunders, Anderson, Thomson and Cornett
Slides prepared by Maike Sundmacher