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Chapter 6

Chapter 6. Market Making by Financial Engineering. Market Making by Financial Innovation. Conversion arbitrage ： The investment bank takes one (or more) financial instruments and, through a process of composition or decomposition, creates one (or more) very different financial instruments.

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Chapter 6

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  1. Chapter 6 Market Making by Financial Engineering

  2. Market Making by Financial Innovation • Conversion arbitrage：The investment bank takes one (or more) financial instruments and, through a process of composition or decomposition, creates one (or more) very different financial instruments. • Mortgage Pass-through • Zero coupon bonds • Interest rate swaps • Financial Innovations

  3. Zero Coupon Securities • Definition A zero coupon bond is a debt instrument that is sold at a deep discount from face value. • No periodic coupons • Accrual interest • Redeem for full face value at maturity • TIGRs (Treasury Investment Growth Receipts) • Merrill Lynch, 1982 • Separated cash flows • A created irrevocable trust with a custodial bank • Trust units • Fully collateralized by Treasury obligations

  4. Risk of fixed income securities • Interest rate risk • Definition The value of a securities will change after its purchased in response to changes in interest rates and its yield. • Measurement Duration vs. interest rate risk • Managing the interest rate risk • Maturity/Horizon Matching method： To match the maturity of the instrument to the investor’s investment horizon • Short-term Rollovers method： To invest shorter maturity instrument and roll over, with the final rollover having a maturity date identical to the investor’s horizon. • Hedging method： To invest a maturity greater than the investor’s horizon, but then to hedge the interest rate risk in futures, forwards, or other derivatives.

  5. Default risk • Definition Default risk is the risk that the issuer of the security will default on its financial obligations so that the holder of the instrument does not receive full payment of interest and/or principal in a timely fashion. • Measurement Debt rating • Managing the default risk • Low risk method • Diversification method • Default swap • Reinvestment risk • Definition The periodic coupons received will be reinvested at rates which differ from the yield prevailing on the bond at the time of its purchase. • Measurement Fluctuations of the reinvestment rate • Managing the reinvestment risk No periodic coupons

  6. Call risk • Definition The risk that the investor is prepaid the loan principal prior to the security’s maturity date. • Measurement Fluctuations of the reinvestment rate • Managing the call risk Call protection • Purchase power risk • Definition The risk of unexpected purchasing power due to the unexpected inflation rate • Measurement unexpected inflation rate • Managing the purchasing power Inflation-indexed bonds

  7. Security 1 Security 1 • Zeros and Conversion Arbitrage • Conversion arbitrage model Input Output Securities Securities Combine or Decompose •Input Cash Flows• •• •• • Zeros generation from conventional bonds Output Securities Input Security Decompose (Separate) Cash Flows • • • Security 2 Security 2 Security n Security m ½ year zero 1 year zero N-year Conventional bond n year zero

  8. Yield curves • Conventional yield curve • Spot yield curve (Zero coupon yield curve) • Implied zero coupon yield curve • Bootstrapping • Zeros in Financial Engineering • Replicate the cash flow pattern of a great many conventional and nonconventional forms of debt • Taking position of the mispricing between conventional debts and synthetic forms

  9. Mortgage-Backed Securities • Definition The securities issued by mortgage pools of loans which are secured by real property, such as buildings or land. • Ginnie mae, Government National Mortgage Associate (GNMA), FNMA, Federal National Mortgage associate, FHLMC, Federal Home Loan Mortgage Corporation • Pass-through certificates • Embedded call option：The right of the mortgagor to prepay the mortgage principal • Option-adjusted spread • Option-adjusted duration • Conventional mortgage amortization schedule • Cash flow patterns of mortgage debt

  10. Pass-through certificates StepⅠ： GNMA specifies mortgage standards Ⅱ： Pool the mortgage and purchase a performance guarantee from GNMA Ⅲ： Issue pass-through certificates in the pools Ⅳ： Distribute by an investment bank syndicate Example p.214 Figure 8.4 The Structure of the Passthrough Market 6basis guarantee points 10.75﹪ 10.25﹪ Mortgagors Investors (homeowners) (pass-through holders) GNMA Mortgage Originator Owns Servicing rights 44 basis points Pool

  11. Collateralized Mortgage Obligation (CMO) • The First Boston Corporation and Salomon Brothers, 1983 • Purchase mortgage pass-through (or whole mortgage) and then issue special bonds that are collateralized by the mortgages. • Multiclass mortgage back securities • Reduce reinvestment risk • Primary market making, SEC • Due diligence • Shelf registration • Secondary market making, bid ask spread • Variation of CMO • PACs, Planned amortization classes • TACs, Targeted amortization classes • IOs, Interest only • POs, Principal-only • FRCMOs, Floating rate CMOs

  12. Tranche 1 Master servicer Tranche 2 (fastest-pay) • The structure of the CMO Interest Principal • CMO with accrual bond tranches • Accrual bond, accretion bond, Z-bond A deferred interest obligation resembling a zero coupon bond. • The accrual bond does not receive any interest or principal until the preceding tranches are fully retired. Tranche 3 Tranche4

  13. Swap • Definition A Contractual agreement in which two parties, call counterparties, agree to exchange a series of payments over a period of time. • Currency swap, London, 1979 • Interest rate swap, London, 1981 • Commodity swap, Chase Manhattan Bank, 1986 • Equity swap, Bankers trust, 1989 • The structure of a generic swap • Atypical swap Figure 9.2 Swap：Periodic Service Payments (required) Figure 9.3 Swap：Reexchange of Notionals notionals Swap Dealer notionals Counterparty A Counterparty B notionals notionals fixed price fixed price Swap Dealer Counterparty A Counterparty B Floating price Floating price notionals notionals Swap Dealer Counterparty A Counterparty B notionals notionals

  14. Cash Market A Cash Market B • A swap with cash market transactions actuals and/or payments actuals and/or payments • Currency swap • Case：one counterparty has comparatively cheaper access to one currency than it does to another • Counterparty A can borrow DM for 7 years at a fixed rate of 9﹪ US＄ for 7year at a floating rate of 1 year LIBOR (floating rate dollar financing) • Counterparty B can borrow DM for 7years at a fixed rate of 10.1﹪ US＄ for 7year at a floating rate of 1 year LIBOR (fixed rate DM financing) Counterparty A Counterparty B

  15. Process：Investment bank’s financial engineering for DM-US＄ currency swap Dealer pays a fixed rate of 9.45﹪on DM against dollar LIBOR Dealer pays dollar LIBOR against a fixed rate of 9.55﹪on DM. Figure 9.8 Currency Swap with Cash Market Transactions (initial borrowings and exchanges of notional principal) CASH MARKET TRANSACTIONS deutschemark principal dollar principal deutschermark deutschemark principal principal dollar dollar principal principal SWAP Debt Market Deutschemarks Debt Market Dollars Swap Dealer Counterparty A Counterparty B

  16. Debt Market Deutschemarks 9﹪ DEM Debt Market Dollars USD LIBOR Figure 9.9 Currency Swap with Cash Market Transactions (debt service with swap payments) CASH MARKET TRANSACTIONS Swap Dealer 9.45﹪ DEM 9.55﹪ DEM Counterparty A Counterparty B USD LIBOR USD LIBOR Figure 9.10 Currency Swap with Cash Market Transactions (repayment of actuals and reexchanges of notional principal) CASH MARKET TRANSACTIONS SWAP Debt Market Deutschemarks deutschemark principal Debt Market Dollars dollar principal deutschermark deutschemark Swap Dealer principal principal Counterparty A Counterparty B dollar dollar principal principal SWAP

  17. Results Counterparty A： Borrows DM, swap to dollars, floating rate, net cost of LIBOR -45 basis points, net saving of 45 basis point. Counterparty B： Borrows dollar, swap to DM, net cost of 9.55﹪, net saving of 55 basis points. • Interest rate swap • Case：one party has access to comparatively cheap fixed- rate funding but desires floating rate funding. Another party has access to comparatively cheap floating rate funding but desires fixed rate funding. Counterparty A： Borrows a floating rate of 6M LIBOR＋50 bps, or at a semiannual fixed rate of 11.25﹪, desires a fixed rate obligation. Counterparty B： Borrows a floating rate of 6M LIBOR, or at a semiannual fixed rate of 10.25﹪, desires a floating rate obligation.

  18. Process：The swap dealer enter a swap as either fixed-rate payer or floating rate payer. • Fixed rate payer --- 10.40﹪ s.a. • Fixed rate receiver --- 10.50﹪s.a. Figure 9.5 interest Rate Swap with Cash Market Transactions (initial borrowing of principals) CASH MARKET TRANSACTIONS Debt Market (floating rate) principal Debt Market (fixed rate) principal Swap Dealer Counterparty A Counterparty B SWAP

  19. Debt Market (floating rate) 6－M LIBOR＋50 bps Debt Market (fixed rate) 10.25﹪ (sa) Figure 9.6 Interest Rate Swap with Cash Market Transactions (debt service payments with swap service payments) CASH MARKET TRANSACTIONS Swap Dealer 10.50﹪ (sa) 10.40﹪ (sa) Counterparty A Counterparty B 6－M LIBOR 6－M LIBOR Figure 9.7 Interest Rate Swap with Cash Market Transactions (repayment of principals) CASH MARKET TRANSACTIONS Debt Market (floating rate) principal Debt Market (fixed rate) principal Counterparty A Swap Dealer Counterparty B

  20. Results Counterparty A： Pays LIBOR＋50bps, receives LIBOR, net payment 10.50﹪ s.a., adjusted net cost 11.01﹪, net benefit 24 basis points. Counterparty B： Pays fixed 10.25﹪, receives 10.40﹪, net ahead 15 basis points, net benefit 15 basis points. Swap dealer： Pays 10.40﹪, receive 10.50﹪, net benefit 10 basis points, bid-ask spread. • Commodity Swaps • Case： One counterparty make periodic payments to the other at a fixed price for a given quantity of notional commodity, while the second counterparty pays the first counterparty a floating price for the same quantity of notional commodity. Counterpaty A --- A crude oil producer want to fix the price of 8,000 barrels oil received for 5 years. Counterpaty B --- An oil refiner Want to fix the price of 12,000 barrels oil paid for 5 years.

  21. Process： The swap dealer sets the fixed price on ＄18.25 a barrel. Pays ＄18.20 per barrel to counterparty A； Receives ＄18.30 a barrel from counterparty B. Figure 9.11 Commodity Swap with Cash Market Transactions CASH MARKET TRANSACTIONS Spot Oil Market actuals actuals Spot price Spot price ＄18.20 (per barrel) Swap Dealer ＄18.30 (per barrel) Counterparty B Counterparty A Spot price (average) Spot price (average) (refiner) (Oil producer)

  22. Results： Counterparty A set a fixed price of oil received. Counterparty B set a fixed price of oil paid. Swap dealer enjoys a bid ask spread of ＄.10 per barrel. • Equity Swaps • Case： One leg is pegged to the return on a stock index. The other leg can be pegged to a floating rate of interest, can be fixed, or a different stock index. • Process： • Converting a fixed income return to an equity return Fixed Income portfolio Equity Swap Dealer Investment bank Fixed income return Fixed income return Fixed Income Portfolio Owner S＆P return

  23. equity portfolio Equity Swap Dealer Investment bank S＆P return S＆P return • Converting an equity return to a fixed income return • Converting a foreign equity return to a domestic equity return Equity Portfolio Owner Fixed income return Japanese equity portfolio Equity Swap Dealer Investment bank Nikkei return Nikkei return Japanese Equity Portfolio Owner S＆P return

  24. Swap Variants --- The Circus Swap • Case： Converting a fixed-rate DM obligation to a fixed rate dollar obligation. • Process： Pay floating rate dollar by entering a fixed-for-floating DM/US ＄ currency swap； Receive floating rate dollar by entering a dollar based interest rate swap. Figure 9.15 The Circus Swap German lenders fixed rate DEM Currency Swap Dealer fixed rate DEM Counterparty A USD libor Circus swap USD libor Interest Rate Swap Dealer Counterparty A Fixed rate USD

  25. Interest Rate Caps • Case： The writer of a cap pays the cap holder each time the contract’s reference rate of interest is above the contract’s “cap rate” of interest on a settlement date. • Process： The cap dealer and the customer enter a cap agreement. Dealer pays ＝ D*MAX[RR－CR , 0]*NP*LP D：cap seller, ＋1；cap purchaser, －1, RR：reference rate of interest, CR：cap rate, NP：notional payment, LP：length of payment, Profit MAX[RR – CR, 0] × NP× LP - premium Cap rate 0 Reference rate Per-period premium (amortized)

  26. Cap Dealer MAX[LIBOR - 10﹪, 0] LIBOR＋ 80 bps Firm 3rd party lender 5-year FRN 5-year rate cap • Applications： • Capped floating rate debt Figure 9.18 Capped Floating Rate Debt Note：This cash flow diagram depicts only interest flows. It does not show the principal flows between the firm and the third party lenders or the up-front fee for the cap paid to the cap dealer. • A rate-capped swap Figure 9.19 A Rate-Capped Swap Firm Fixed rate Swap Dealer Fixed rate Fixed rate lender Floating rate Cap Dealer Cap on floating rate Investment bank

  27. Interest Rate Floors • Case： The writer of a floor pays the floor holder each time the contract’s reference rate of interest is below the contract’s “floor rate” of interest on a settlement date. • Process： The floor dealer and the customer enter a floor agreement. Dealer pays ＝ D*MAX[FR－RR , 0]*NP*LP D：cap seller, ＋1；cap purchaser, －1, RR：reference rate of interest, FR：floor rate, NP：notional payment, LP：length of payment, Figure 9.20 Payoff Profile for a Floor Purchaser (Per Settlement Period) MAX[FR – RR, 0] × NP × LP - premium Per-period premium (amortized) Profit Floor rate 0 Reference rate

  28. Treasury Bills 6-M T-bill rate Annuity Holders Floor Dealer MAX[7﹪ - T-bill rate, 0] 7.00 percent Firm • Return protection by interest rate floor • Achieve a minimum return by floor 10-year rate floor 10-year policy Note：This cash flow diagram only depicts interest flows. It does not show the principal flows between the firm and the annuity holders or the up-front fee for the floor paid to the floor dealer. Fixed Rate asset Fixed return Fixed rate Firm Swap Dealer Floating rate floor Dealer Max[FR-CR, 0] Investment bank

  29. Interest Rate Collars • Definition： A combination of a cap and a floor. The purchaser of a collar buy a cap and simultaneously sell a floor. • Payoff file： Figure 9.23 Payoff Profile for a Collar Purchaser (Per Settlement Period) Cap settlement received less Settlement paid and net premium Profit Floor rate Cap rate . 0 Reference rate Difference between premium paid On the cap and premium received on The floor (per-period equivalents).

  30. Assets 10 percent Cap Dealer Max[prime – 9.5﹪, 0] Firm Lender Prime rate • An interest rate collar • A collar swap Figure 9.25 A Collar Swap at Work floor Dealer Max[7﹪ - prime , 0] Note：This cash flow diagram ignores the cost of the collar and the exchanges of principals on both assets and liabilities. Firm Swap Dealer Fixed rate Fixed rate Lender LIBOR Cap Dealer Max[LIBOR – cap, 0] floor Dealer Max[floor – LIBOR, 0]

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