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Swaps and Parallel Loans

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Swaps and Parallel Loans

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    1. 8-1 Swaps and Parallel Loans

    2. Bank of Intl Settlements data 8-2

    3. 8-3 Introduction to Swaps A swap is a contract calling for an exchange of payments, on one or more dates, determined by the difference in two prices A swap provides a means to hedge a stream of risky payments A single-payment swap is the same thing as a cash-settled forward contract

    4. 8-4 Evolution of Swaps Increase in exchange rate volatility (1972) increase in earnings volatility fluctuation in asset value due to exchange rate volatility The first solution: Parallel Loans two firms simultaneously make financial loans to each other increasing use in the 1970s difficult to find partners Swaps start being written ~1981 by banks to help firms conduct parallel loan transactions

    5. 8-5 Parallel loans Two firms with opposite exposure to something Foreign exchange rates, interest rates, volatility of an asset (equity, commodity, foreign currency) structure a loan to eliminate risk Currency parallel loan Firm B lends dollars to firm C Firm C lends foreign currency to firm B Interest parallel loan Firm B lends $A to firm C, charges fixed rate Firm C lends $A to firm B, charges floating rate

    6. 8-6 Parallel Loan Example Suppose a US firm and a UK firm want to swap foreign currency exposure (US firm has UK exposure, and vice-versa). Suppose US firm is receiving 100,000 per year. Assume S=1.562 $/, rus = .08 and ruk = .10 US firms perspective: borrow 379,079 and repay 100,000 per year for 5 years lend 592,121 $ and receive $148,300 per year for 5 years Cash flow today = 379,079 (1.562 $/) - $592,121 = 0 Cash flow at date t=1 through t=5 Ct = $148,300 - 100,000(St $/) Ct = 100,000 (1.483$/ - St $/)

    7. 8-7 Parallel loan example continued What firm would enter such an agreement? A US exporter with 100,000 /year in revenue revenues at time period t + parallel loan payoff = hedged rev 100,000 (St$/) + 100,000 (1.483$/ - St $/) = $148,300 Problems with parallel loans default risk, impact on balance sheet, search costs Solution staple two loans/contracts together to form a currency swap netting the payments on each of the dates First swap created in 1979 for IBM Swap market was largely developed by Chase Manhattan in 1981-82

    8. 8-8 Swaps A swap is an agreement to exchange cash flows at a specified future times according to certain rules A swap may be viewed as a package of forward contracts Primary differences between swap and parallel loan:

    9. 8-9 A more formal treatment, linking swap prices (or rates) to forward prices (or rates)

    10. 8-10 An Example of a Commodity Swap An industrial producer, IP Inc., needs to buy 100,000 barrels of oil 1 year from today and 2 years from today The forward prices for deliver in 1 year and 2 years are $20 and $21/barrel The 1- and 2-year zero-coupon bond yields are 6% and 6.5%

    11. 8-11 An Example of a Commodity Swap (contd) IP can guarantee the cost of buying oil for the next 2 years by entering into two long forward contracts for 100,000 barrels in each of the next 2 years. The PV of this cost per barrel is Thus, IP could pay an oil supplier $37.383, and the supplier would commit to delivering one barrel in each of the next two years This arrangement is called a prepaid swap.

    12. 8-12 Example of a Commodity Swap (contd) With a prepaid swap, the buyer might worry about the resulting credit risk, and might prefer to not have a large cash exchange today. Therefore, a better solution is to defer payments until the oil is delivered, while still fixing the total price In theory, any payment stream with a PV of $37.383 is acceptable. Typically, however, a swap will call for equal payments in each year For example, the payment per year per barrel, x, will have to be $20.483 to satisfy the following equation We then say the 2-year swap price is $20.483

    13. 8-13 Physical Versus Financial Settlement Physical settlement of the swap

    14. 8-14 Physical Versus Financial Settlement (contd) Financial settlement of the swap The oil buyer, IP, pays the swap counterparty the difference between $20.483 and the spot price, and the oil buyer then buys oil at the spot price If the difference between $20.483 and the spot price is negative, then the swap counterparty pays the buyer

    15. 8-15 The Swap Counterparty The swap counterparty is typically a dealer, who is, in effect, a broker between buyer and seller The situation where the dealer matches the buyer and seller is called a back-to-back transaction or matched book transaction

    16. 8-16 Physical Versus Financial Settlement (contd) Whatever the market price of oil, the net cost to the buyer is the swap price, $20.483 Spot price 20.483 Spot price = 20.483 Swap Payment Spot Purchase of Oil Note that 100,000 barrels is the notional amount of the swap, meaning that 100,000 barrels is used to determine the magnitude of the payments when the swap is settled financially

    17. 8-17 Link to forward rates Swaps are forward contracts coupled with borrowing and lending money Consider the swap price of $20.483/barrel. Relative to the forward curve price of $20 in 1 year and $21 in 2 years, we are overpaying by $0.483 in the first year, and we are underpaying by $0.517 in the second year Thus, by entering into the swap, we are lending the counterparty money for 1 year. The interest rate on this loan is Given 1- and 2-year zero-coupon bond yields of 6% and 6.5%, 7% is exactly the 1-year implied forward yield from year 1 to year 2 R forward = 1.0652/1.06 1 = .07 If the deal is priced fairly, the interest rate implied inside the swap will equal the implied forward interest rate beautiful!

    18. 8-18 Market value of seasoned forward/swap Suppose at day t=0, you enter a 180-day forward to buy corn at F180= 220 per bushel. 90 days later, F90= 280 per bushel. How much would you pay or get paid to part with your contract if r=5% cc per annum? Since could enter to sell forward at 280, I can lock-in a gain of 60 per bushel, in 90 days. PV = 0.60e-.05(90/365) = 0.5926 per bushel. For swaps, just repeat this for each payment!

    19. 8-19 Interest and Currency Swaps

    20. 8-20 Example of interest rate swap Suppose we observe the following rates: r0(ti,tj) = todays forward rate from t=i, to t=j Rt = the swap rate covering through period t What is the 3-year swap rate? Or, what common rate gives the same 1 year interest payments implied by the term structure? R=.069548

    21. 8-21 Note the consistent logic The logic of finding the swap rate, was exactly the same as that we used to find the oil swap price The PV of the swap rate or price must equal the PV of the rates or prices found in the future strip. If not, arbs could buy the swap market and sell the futures market or vice-versa.

    22. 8-22 An Example of an Interest Rate Swap XYZ Corp. has $200M of floating-rate debt at LIBOR, i.e., every year it pays that years current LIBOR XYZ would prefer to have fixed-rate debt with 3 years to maturity XYZ could enter a swap, in which they receive a floating rate and pay the fixed rate, which is 6.9548%

    23. 8-23 An Example of an Interest Rate Swap (contd) On net, XYZ pays 6.9548% XYZ net payment = LIBOR + LIBOR 6.9548% = 6.9548% Floating Payment Swap Payment

    24. 8-24 Computing the Swap Rate This can be restated in general terms as: (8.1) And can be rearranged as: (8.2)

    25. 8-25 Computing the Swap Rate (contd) We can rewrite equation (8.2) to make it a little easier to interpret Therefore, the fixed swap rate is a weighted average of the implied forward rates, where zero-coupon bond prices are used to determine the weights We saw this with the oil swap example as well

    26. 8-26 Computing the Swap Rate (contd) Finally, we can rearrange again as: (8.3) This equation is exactly equivalent to the formula for the coupon on a par coupon bond Thus, the swap rate is the coupon rate on a par coupon bond

    27. 8-27 Swap rate calculation Recall Table 7.1 Then, using (8.3)

    28. 8-28 Commodity Swaps The fixed payment on a commodity swap is (8.11) This is same as equation 8.2 The commodity swap price is a weighted average of commodity forward prices

    29. 8-29 Commodity Swap Prices Suppose we observe the following oil strip and interest rates: Then, using (8.11):

    30. 8-30 Currency Swaps A currency swap entails an exchange of payments in different currencies A currency swap is equivalent to borrowing in one currency and lending in another As in our parallel loan example

    31. 8-31 Currency Swap Formulas Consider a swap in which a dollar annuity, R, is exchanged for an annuity in another currency, R* R is now a dollar quantity, not a rate It is a notional quantity There are n payments The time-0 forward price for a unit of foreign currency delivered at time ti is F0,ti The dollar-denominated zero-coupon bond price is P0,ti

    32. 8-32 Currency Swap Formulas (contd) Given R*, what is R? This equation is equivalent to equation (8.2), with the implied forward rate, r0(ti-1, ti), replaced by the foreign-currency-denominated annuity payment translated into dollars, R* F0,t Or, you can just use the forward rate stated as $/FC

    33. 8-33 Summary The swap formulas in different cases all take the same general form Let f0(ti) denote the forward price. Then the fixed swap is

    34. Enron swap use: 8-34

    35. Enron swap use: 8-35

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