1. Uses of Derivatives for Risk Management Charles Smithson Copyright 2004 Rutter Associates, LLC Assessing, Managing and Supervising Financial Risk The World Bank, Washington, DC May 19, 2004

2. 2 Rutter Associates Outline 1.Tool Box – Derivatives being used by financial institutions 2.Asset-Liability Management: Using interest rate derivatives to manage the ‘maturity gap’ and/or ‘duration and convexity’ 3.Managing Risks in the Investment Portfolio 4.Managing Credit Risk

3. 3 Rutter Associates 1. The Tool Box + + = = Forwards, Futures, Swaps Options Short Put/ “Floor” Short Call/ “Cap” Long Call/ “Cap” Long Put/ “Floor” Long Short

4. 4 Rutter Associates Managing Cash Flow Risk Managing Value Risk –Changing the “Duration” of the Portfolio –Changing the “Convexity” of the Portfolio 2, Asset Liability Management

5. 5 Rutter Associates “Maturity Gap” measures exposure on a net interest income basis r NII Gap =    (Net Interest Income) = (Gap) x  r Gap = RSA - RSL where RSA = Rate sensitive assets RSL = Rate sensitive liabilities

6. 6 Rutter Associates Gap = $600 - $900 = - $300 1 year ABC Bank ($ Millions) < 3 mo. 100 6 mo. 100 12 mo. 400 > 12 mo. 400 < 3 mo. 400 6 mo. 300 12 mo. 200 > 12 mo. 100 AssetsLiabilities 1,000 { RSA = $600 { RSL = $900 If interest rates rose by 100 basis points, NII would be expected to decline by $3 million

7. 7 Rutter Associates Gap = $600 - $800 = -$200 1 year ABC Bank ($ Millions) < 3 mo. 100 6 mo. 100 12 mo. 400 > 12 mo. 400 < 3 mo. 400 6 mo. 300 12 mo. 200 > 12 mo. 100 AssetsLiabilities 1,000 Suppose ABC enters into a 3-year, $100 million Interest Rate Swap in which it receives the 6-month rate and pays a 3-year rate. $100 million of the 6-month liabilities now have an effective maturity of 3 years 200

8. 8 Rutter Associates ~~~~~ NP = Notional Principal = $100 million R = 3-year Fixed Rate R = 6-month Rate _ ~ ABC Bank’s Interest Rate Swap PNR _ x PNR _ x PNR _ x PNR _ x PNR _ x PNR _ x ~ x N P R4R4 x N P R3R3 x N P R2R2 x N P R1R1 x N P R5R5 x N P R4R4 Month 0 6 12 18 24 30 36

9. 9 Rutter Associates Managing Cash Flow Risk Managing Value Risk –Changing the “Duration” of the Portfolio –Changing the “Convexity” of the Portfolio 2. Asset Liability Management

10. 10 Rutter Associates DURATION Shading represents the present value of the nominal cash flow at time t. Duration

11. 11 Rutter Associates Time t Cash Flow 0.5 1.0 1.5 2.0 2.5 90 Discount Rate 7.75% 8.00% 8.25% 8.35% 8.50% Calculation of Duration for Fixed Income Securities Present Value 86.70 83.33 79.91 76.66 73.40 400.00Price *Weight = PV(CF t )/Price Weight* 0.22 0.21 0.20 0.19 0.18 1.00 Duration (Weight x t) 0.11 0.21 0.31 0.38 0.45 1.46 years

12. 12 Rutter Associates Duration can also be expressed as an elasticity: Percent change in price Percent change in (1+ r) Duration can be used to estimate percentage change in price: Percent change in price  ~   r    r  1 D D  Duration as a Measure of Interest Rate Sensitivity

13. 13 Rutter Associates Bank holds a $50,000,000 loan with a duration of 13.183. Loan is funded with debt that has a duration of 9.38. The bank is not comfortable with a mismatch between the duration of the loan and the duration of the debt funding the loan. Bank wants duration of asset position to match that of the debt. - Bank could sell the existing asset and replace it with one that has a duration of 9.38 - Bank could use an interest rate swap to modify the duration of the existing asset. Changing the Duration of the Portfolio

14. 14 Rutter Associates PNR _ x PNR _ x PNR _ x PNR _ x PNR _ x ~~~~ x N P R4R4 x N P R3R3 x N P R2R2 x N P R1R1 x N P R5R5 ~ NP = Notional Principal R = Fixed Rate R = Floating Rate _ ~ Interest Rate Swap

15. 15 Rutter Associates R _ R _ R _ R _ R _ ~~~~ R4R4 R3R3 R2R2 R1R1 R5R5 ~ An interest rate swap can be viewed as equivalent to long and short positions in fixed- and floating- rate bonds. Lending Fixed Rate Borrowing Fixed Rate NP x Duration SWAP = Duration FIXED - Duration FLOATING - Fixed side of a 5-year swap paying 7% semi-annual has a duration of 4.3 - Floating side has a duration of 0.5. - Swap duration is 3.8

16. 16 Rutter Associates Duration of the $50,000,000 loan is 13.183 Duration of swap is 3.83 By paying the fixed rate on a $50,000,000 swap, the bank will reduce the duration of the asset position to 13.183 - 3.8 = 9.38 Changing the Duration of the Portfolio

17. 17 Rutter Associates Managing Cash Flow Risk Managing Value Risk –Changing the “Duration” of the Portfolio –Changing the “Convexity” of the Portfolio 2. Asset Liability Management

18. 18 Rutter Associates “True” Price Risk Duration provides a linear estimate of the change in value of a security given a change in the interest rate. Interest Rates Linear Approximation Estimation Error Price

19. 19 Rutter Associates Interest Rates “True” Value Profile Estimation Error-- after convexity adjustment Price Convexity adjusts the linear measure to compensate for the change in the slope of the price risk curve between two points

20. 20 Rutter Associates Interest Rate Value #1 Linear Profile #2 Positive Convexity V 0 r 0 #3 Negative Convexity The Impact of Positive and Negative Convexity Sources of Convexity Borrowers have prepayment and/or rate cap options Depositors have withdrawal options

21. Suppose the bank’s debt portfolio has a shorter duration than it’s assets VV rr Suppose the bank gave borrowers the right to prepay with no penalty VV rr The result would be NEGATIVE CONVEXITY VV rr Changing the Convexity of the Portfolio

22. A bank can reduce the effects of NEGATIVE CONVEXITY... VV rr... and buying out-of-the-money interest rate caps VV rr The net interest rate exposure would be reduced. VV rr VV rr and floors. VV rr... by entering into pay fixed- receive floating swaps... Changing the Convexity of the Portfolio

23. 23 Rutter Associates Assets in a Bank’s Investment Portfolio Government Bonds (Domestic and Foreign) Mortgage-Backed Securities Corporate Bonds (Domestic and Foreign) –Standard –Convertible –Asset-Backed Equity Structured Notes 3. Managing Risk in the Investment Portfolio Risks Interest Rate Risk Foreign Exchange Rate Risk Equity Price Risk Credit Risk Commodity Price Risk

24. 24 Rutter Associates A U.S. bank is considering investing in a GBP-denominated bond that matures in one year Face Value:GBP 1,000,000 Coupon:8.00% Price:100.3% The YTM in GBP is 7.67% The YTM to the U.S. bank would be 7.63%, after taking into account the bid/ask spread on the current USD/GBP spot rate, and assuming the FX rate does not change. The U.S. bank is concerned about the foreign exchange rate risk that is inherent in this investment. Managing FX Risk

25. 25 Rutter Associates If the U.S. bank wished to eliminate the foreign exchange risk, it could enter into a foreign exchange forward contract USD/GBPBidAsk Spot1.61751.6181 1-Year Forward1.58951.5904 By locking in the exchange rate at the one-year horizon, the U.S. bank has locked in a YTM of 5.77%. Data as of August 14, 1998 Managing FX Risk

26. 26 Rutter Associates Alternatively, the U.S. bank could protect against the GBP weakening against the USD by purchasing a foreign exchange option -- a put option on GBP. Suppose the U.S. bank elects to strike the option at the current spot rate. The premium for the option is USD 0.06132. Multiplying the premium with the GBP cash-flow at maturity, the cost to the U.S. bank for the option would be USD 66,226. Factoring the cost of the option into the investment, the U.S. bank has guaranteed itself a minimum YTM of 3.45%. But the U.S. bank’s YTM could rise if the GBP appreciates relative to 1.6181. Managing FX Risk

27. 27 Rutter Associates -10.00% -5.00% 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% 1.4001.4751.5501.6251.7001.7751.850 Spot USD/GBP at Maturity Yield-to-Maturity No Hedge FX Forward FX Option (Spot Strike) Managing FX Risk

28. 28 Rutter Associates Does your institution have a formal Credit Portfolio Management function? No 20% Yes 80% 4. Managing Credit Risk Source: 2002 Rutter Associates Survey of Credit Portfolio Management Practices, Sponsored by IACPM, ISDA, and RMA

29. 29 Rutter Associates Rank the following tools in order of their importance to the management of your credit portfolio. (“1” denotes the most important and “4” denotes the least important.) Management of new business and renewals of existing business Loan sales and trading Credit derivatives Securitizations 1.1 2.7 3.0 3.2 4. Managing Credit Risk Source: 2002 Rutter Associates Survey of Credit Portfolio Management Practices, Sponsored by IACPM, ISDA, and RMA

30. 30 Rutter Associates Credit Default Swap X basis points per year Protection Seller Protection Buyer Payment Credit event Zero No credit event or it could be bankruptcy, downgrade, failure to pay, repudiation or moratorium, acceleration, or restructuring Materiality conditions may be specified The credit event could be defined as default on a specific “reference” obligation, or an enumerated group of obligations, or all obligations in a specified class (e.g. “foreign currency bonds”) … Cash settlement: Payment of the post-default market value of the asset against receipt of the strike price (usually par) Physical delivery: Delivery of the reference bond or loan--or other acceptable instrument as agreed in the confirm--against receipt of the strike price (usually par)

31. 31 Rutter Associates BANK $20mm Exposure to XYZ Inc. Protection Seller $20mm x (x basis points) If credit event does not occur $20mm - Recovery $0 If credit event occurs Reducing the Portfolio’s Exposure to a Specific Obligor with a Credit Default Swap

32. 32 Rutter Associates Uses of Derivatives for Risk Management Charles Smithson Copyright 2004 Rutter Associates, LLC Assessing, Managing and Supervising Financial Risk The World Bank, Washington, DC May 19, 2004