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Managing Fixed-Income Positions with OTC Derivatives

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## Managing Fixed-Income Positions with OTC Derivatives

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**Managing Fixed-Income**Positions with OTC Derivatives 1**Hedging with OTC Derivatives**Hedging a Series of Cash Flows—OTC Caps and Floors Financing Caps and Floors: Collars and Corridors Other Interest Rate Derivatives Hedging Currency Positions with Currency Options 2**Forward Rate Agreements (FRA)**• A forward rate agreement, FRA, requires a cash payment or provides a cash receipt based on the difference between a realized spot rate such as the LIBOR and a pre-specified rate. • For example, the contract could be based on a specified rate of Rk = 6% (annual) and the 3-month LIBOR (annual) in 5 months and a notional principal, NP (principal used only for calculation purposes) of $10,000,000.**Forward Contracts and Forward Rate Agreements (FRA)**• In five months the payoff would be • If the LIBOR at the end of five months exceeds the specified rate of 6%, the buyer of the FRA (or long position holder) receives the payoff from the seller. • If the LIBOR is less than 6%, the seller (or short position holder) receives the payoff from the buyer.**Forward Contracts and Forward Rate Agreements (FRA)**• If the LIBOR were at 6.5%, the buyer would be entitled to a payoff of $12,267 from the seller; • If the LIBOR were at 5.5%, the buyer would be required to pay the seller $12,297.**Forward Contracts and Forward Rate Agreements (FRA)**• In general, a FRA that matures in T months and is written on a M-month LIBOR rate is referred to as a T x (T+M) agreement. • Thus, in this example the FRA is a 5 x 8 agreement. • At the maturity of the contract (T), the value of the contract, VT is**Forward Contracts and Forward Rate Agreements (FRA)**• FRAs originated in 1981 amongst large London Eurodollar banks that used these forward agreements to hedge their interest rate exposure. • Today, FRAs are offered by banks and financial institutions in major financial centers and are often written for the bank’s corporate customers. • They are customized contracts designed to meet the needs of the corporation or financial institution.**Forward Contracts and Forward Rate Agreements (FRA)**• FRAs are used by corporations and financial institutions to manage interest rate risk in the same way as financial futures are used. • Different from financial futures, FRAs are contracts between two parties and therefore are subject to the credit risk of either party defaulting. • The customized FRAs are also less liquid than standardized futures contracts. • The banks that write FRAs often takes a position in the futures market to hedge their position or a long and short position in spot money market securities to lock in a forward rate. • As a result, in writing the FRA, the specified rate Rk is often set equal to the rate implied on a futures contract.**Forward Contracts and Forward Rate Agreements (FRA)**Example: • Suppose Kendall Manufacturing forecast a cash inflow of $10,000,000 in 2 months that it is considering investing in a Sun National Bank CD for 90 days. • Sun National Bank’s jumbo CD pays a rate equal to the LIBOR. • Currently such rates are yielding 5.5%. • Kendall is concerned that short-term interest rates could decrease in the next 2 months and would like to lock in a rate now.**Forward Contracts and Forward Rate Agreements (FRA)**Example: • As an alternative to hedging its investment with Eurodollar futures, Sun National suggests that Kendall hedge with a Forward Rate Agreement with the following terms: • FRA would mature in 2 months (T) and would be written on a 90-day (3-month) LIBOR (T x (T+M) = 2 x 5 agreement • NP = $10,000,000 • Contract rate = Rk = 5.5% • Day count convention = 90/365 • Cagle would take the short position on the FRA, receiving the payoff from Sun National if the LIBOR were less than Rk = 5.5% • Sun National would take the long position on the FRA, receiving the payoff from Cagle if the LIBOR were greater than Rk = 5.5%**Forward Contracts and Forward Rate Agreements (FRA)**• The exhibit slide shows Kendall’s FRA receipts or payments and cash flows from investing the $10,000,000 cash inflow plus or minus the FRA receipts or payments at possible LIBORs of 5%, 5.25%, 5%, 5.75%, and 6%. • As shown, Kendall is able to earn a hedged rate of return of 5.5% from its $10,000,000 investment.**Interest Rate Call**• An interest rate call, also called a caplet, gives the buyer a payoff on a specified payoff date if a designated interest rate, R, such as the LIBOR, rises above a certain exercise rate, Rx. • On the payoff date: • If the designated rate is less than Rx, the interest rate call expires worthless. • If the rate exceeds Rx, the call pays off the difference between the actual rate and Rx, times a notional principal, NP, times the fraction of the year specified in the contract, θ.**Interest Rate Call**Example: • Given an interest rate call with a designated rate of LIBOR, Rx = 6%, NP = $1,000,000, time period of 180 days, and day-count convention of actual/360, the buyer would receive a $5,000 payoff on the payoff date if the LIBOR were 7%: Payoff = Max[.07−.06, 0](180/360)($1,000,000) Payoff = $5,000**Interest Rate Call**Hedging Use • Interest rate call options are often written by commercial banks in conjunction with futures loans they plan to provide to their customers. • The exercise rate on the option usually is set near the current spot rate, with that rate often being tied to the LIBOR.**Hedging a Future Loan Rate with an OTC Interest Rate Call**Example: • Suppose a construction company plans to finance one of its project with a $10,000,000 90-day loan from Sun Bank, with the loan rate to be set equal to the LIBOR + 100 BP when the project commences 60 day from now. • Furthermore, suppose that the company expects rates to decrease in the future, but is concerned that they could increase.**Hedging a Future Loan Rate with an OTC Interest Rate Call**Example: • To obtain protection against higher rates, suppose the company buys an interest rate call option from Sun Bank for $20,000 with the following terms: • Exercise rate = 7% • Reference rate = LIBOR • Time period applied to the payoff = 90/360 • Notional principal = $10,000,000 • Payoff made at the maturity date on the loan (90 days after the option’s expiration) • Interest rate call’s expiration = T = 60 days (time of the loan) • Interest rate call premium of $20,000 to be paid at the option’s expiration with a 7% interest: Cost = $20,000(1 + (.07)(60/360)) = $20,233**Hedging a Future Loan Rate with an OTC Interest Rate Call**Example: • The exhibit slide shows the company's cash flows from the call, interest paid on the loan, and effective interest costs that would result given different LIBORs at the starting date on the loan and the expiration date on the option. • As shown in Column 6 of the slide, the company is able to lock in a maximum interest cost of 8.016% if the LIBOR is 7% or greater at expiration, and still benefit with lower rates if the LIBOR is less than 7%.**Interest Rate Put**• An interest rate put, also called a floorlet, gives the buyer a payoff on a specified payoff date if a designated interest rate, R, is below the exercise rate, Rx. • On the payoff date: • If the designated rate (or reference rate) is more than Rx, the interest rate put expires worthless. • If the reference rate is less than Rx, the put pays the difference between Rx and the actual rate times a notional principal, NP, times the fraction of the year, θ, specified in the contract.**Interest Rate Put**Hedging Use • A financial or non-financial corporation that is planning to make an investment at some future date could hedge that investment against interest rate decreases by purchasing an interest rate put from a commercial bank, investment banking firm, or dealer.**Hedging a CD Rate with an OTC Interest Rate Put**Example: • Suppose the ABC manufacturing company was expecting a net cash inflow of $10,000,000 in 60 days from its operations and was planning to invest the excess funds in a 90-day CD from Sun Bank paying the LIBOR. • To hedge against interest rate decreases occurring 60 days from the now, suppose the company purchases an interest rate put (corresponding to the bank's CD it plans to buy) from Sun Bank for $10,000.**Hedging a CD Rate with an OTC Interest Rate Put**Example: • Suppose the put has the following terms: • Exercise rate = 7% • Reference rate = LIBOR • Time period applied to the payoff = θ = 90/360 • Day Count Convention = 30/360 • Notional principal = $10 million • Payoff made at the maturity date on the CD (90 days from the option’s expiration) • Interest rate put’s expiration = T = 60 days (time of CD purchase) • Interest rate put premium of $10,000 to be paid at the option’s expiration with a 7% interest: Cost = $10,000(1 + (.07)(60/360)) = $10,117**Hedging a CD Rate with an OTC Interest Rate Put**Example: • As shown in the exhibit slide, the purchase of the interest rate put makes it possible for the ABC company to earn higher rates if the LIBOR is greater than 7% and to lock in a minimum rate of 6.993% if the LIBOR is 7% or less.**Hedging a CD Rate with an OTC Interest Rate Put**Example: • If 60 days later the LIBOR is at 6.5%, then the company would receive a payoff (90 day later at the maturity of its CD) on the interest rate put of $12,500: • The $12,500 payoff would offset the lower (than 7%) interest paid on the company’s CD of $162,500: • At the maturity of the CD, the company would therefore receive CD interest and an interest rate put payoff equal to $175,000: $12,500 = ($10,000,000)[.07 − .065](90/360) $162,500 = ($10,000,000)(.065)(90/360) $175,000 = $162,500 + $12,500**Hedging a CD Rate with an OTC Interest Rate Put**Example: • With the interest-rate put’s payoffs increasing the lower the LIBOR, the company would be able to hedge any lower CD interest and lock in a hedged dollar return of $175,000. • Based on an investment of $10,000,000 plus the $10,117 costs of the put, the hedged return equates to an effective annualized yield of 6.993%: • On the other hand, if the LIBOR exceeds 7%, the company benefits from the higher CD rates. 6.993% = [(4)($175,000)]/[$10,000,000 + $10,117]**Cap**• A popular option offered by financial institutions in the OTC market is the cap. • A plain-vanilla cap is a series of European interest rate call options—a portfolio of caplets.**Cap**Example: • A 7%, 2-year cap on a 3-month LIBOR, with a NP of $100,000,000, provides, for the next 2 years, a payoff every 3 months of (LIBOR − .07)(.25)($100M) if the LIBOR on the reset date exceeds 7% and nothing if the LIBOR equals or is less than 7%. • Note: Typically, the payoff does not occur on the reset date, but rather on the next reset date.**Cap**Uses • Caps are often written by financial institutions in conjunction with a floating-rate loan and are used by buyers as a hedge against interest rate risk.**Cap**• A company with a floating-rate loan tied to the LIBOR could lock in a maximum rate on the loan by buying a cap corresponding to its loan. • At each reset date, the company would receive a payoff from the caplet if the LIBOR exceeded the cap rate, offsetting the higher interest paid on the floating-rate loan; on the other hand, if rates decrease, the company would pay a lower rate on its loan whereas its losses on the caplet would be limited to the cost of the option. • Thus, with a cap, the company is able to lock in a maximum rate each quarter, and yet still benefit with lower interest costs if rates decrease.**Floor**• A plain-vanilla floor is a series of European interest rate put options—a portfolio of floorlets.**Floor**Example: • A 7%, 2-year floor on a 3-month LIBOR, with a NP of $100,000,000, provides for the next 2 years a payoff every 3 months of (.07 − LIBOR)(.25)($100M) if the LIBOR on the reset date is less than 7% and nothing if the LIBOR equals or exceeds 7%.**Floor**Uses • Floors are often purchased by investors as a tool to hedge their floating-rate investment against interest rate declines. • Thus, with a floor, an investor with a floating-rate security is able to lock in a minimum rate each period, and yet still benefit with higher yields if rates increase.**Hedging a Series of Cash Flows: OTC Caps and Floors**• We have examined how a strip of Eurodollar futures puts can be used to cap the rate paid on a floating-rate loan, and how a strip of Eurodollar futures calls can be used to set a floor on a floating-rate investment. • Using such exchange-traded options to establish interest rate floors and ceiling on floating rate assets and liabilities, though, is subject to hedging risk. • As a result, many financial and non-financial companies looking for such interest rate insurance prefer to buy OTC caps or floors that can be customized to meet their specific needs.**Hedging a Series of Cash Flows: OTC Caps and Floors**• Financial institutions typically provide caps and floors with: • Terms that range from 1 to 5 years • Monthly, quarterly, or semiannual reset dates • LIBOR as the reference rate • Notional principal and the reset dates that often match the specific investment or loan • Settlement dates that usually come after the reset dates**Hedging a Series of Cash Flows:OTC Caps and Floors**• In cases where a floating-rate loan (or investment) and cap (or floor) come from the same financial institution, the loan and cap (or investment and floor) are usually treated as a single instrument so that when there is a payoff, it occurs at an interest payment (receipt) date, lowering (increasing) the payment (receipt). • The exercise rate is often set so that the cap or floor is initially out of the money, and the payments for these interest rate products are usually made up front, although some are amortized.**Floating Rate Loan Hedged with an OTC Cap**Example: • Suppose the Diamond Development Company borrows $50 million from Commerce Bank to finance a 2-year construction project. • Suppose: • The loan is for 2 years • The loan starts on March 1 at a known rate of 8% • The loan rate resets every three months—6/1, 9/1, 12/1, and 3/1—at the prevailing LIBOR plus 150 bp.**Floating Rate Loan Hedged with an OTC Cap**• In entering this loan agreement, suppose the company is uncertain of future interest rates and therefore would like to lock in a maximum rate, but still benefit from lower rates if the LIBOR decreases.**Floating Rate Loan Hedged with an OTC Cap**• To achieve this, suppose the company buys a cap corresponding to its loan from Commerce Bank for $150,000, with the following terms: • The cap consist of seven caplets with the first expiring on 6/1/Y1 and the others coinciding with the loan’s reset dates. • Exercise rate on each caplet = 8% • NP on each caplet = $50,000,000 • Reference Rate = LIBOR • Time period to apply to payoff on each caplet = 90/360. (Typically the day count convention is defined by the actual number of days between reset date.) • Payment date on each caplet is at the loan’s interest payment date, 90 days after the reset date. • The cost of the cap = $150,000; it is paid at beginning of the loan, 3/1/Y1.**Floating Rate Loan Hedged with an OTC Cap**• On each reset date, the payoff on the corresponding caplet would be • With the 8% exercise rate (sometimes called the cap rate), the Diamond Company would be able to lock in a maximum rate each quarter equal to the cap rate plus the basis points on the loan, 9.5%, but still benefit with lower interest costs if rates decrease. • This can be seen in the exhibit slide, where the quarterly interests on the loan, the cap payoffs, and the hedged and unhedged rates are shown for different assumed LIBORs at each reset date on the loan. Payoff = ($50,000,000) (Max[LIBOR − .08, 0])(90/360)**Floating Rate Loan Hedged with an OTC Cap**• For the 5 reset dates from 12/1/Y1 to the end of the loan, the LIBOR is at 8% or higher. • In each of these cases, the higher interest on the loan is offset by the payoff on the cap, yielding a hedged rate on the loan of 9.5% (the 9.5% rate excludes the $150,000 cost of the cap; the rate is 9.53% with the cost included). • For the first 2 reset dates on the loan, 6/1/Y1 and 9/1/Y1, the LIBOR is less than the cap rate. At these rates, there is no payoff on the cap, but the rates on the loan are lower with the lower LIBORs.**Floating Rate Asset Hedged with an OTC Floor**Example: • As noted, floors are purchased to create a minimum rate on a floating-rate asset. • As an example, suppose the Commerce Bank in the preceding example wanted to establish a minimum rate or floor on the rates it was to receive on the 2-year floating-rate loan it made to the Diamond Company.**Floating Rate Asset Hedged with an OTC Floor**• Suppose the bank purchased from another financial institution a floor for $100,000 with the following terms corresponding to its floating-rate asset: • The floor consist of 7 floorlets with the first expiring on 6/1/Y1 and the others coinciding with the reset dates on the bank’s floating-rate loan to the Diamond Company • Exercise rate on each floorlet = 8% • NP on each floorlet = $50,000,000 • Reference Rate = LIBOR • Time period to apply to payoff on each floorlet = 90/360 Payment date on each floorlet is at the loan’s interest payment date, 90 days after the reset date • The cost of the floor = $100,000; it is paid at beginning of the loan, 3/1/Y1**Floating Rate Asset Hedged with an OTC Floor**• On each reset date, the payoff on the corresponding floorlet would be • With the 8% exercise rate, Commerce Bank would be able to lock in a minimum rate each quarter equal to the floor rate plus the basis points on the floating-rate asset, 9.5%, but still benefit with higher returns if rates increase. Payoff = ($50,000,000) (Max[.08 − LIBOR, 0])(90/360)**Floating Rate Asset Hedged with an OTC Floor**• In the exhibit slide, Commerce Bank’s quarterly interests received on its loan to Diamond, its floor payoffs, and its hedged and unhedged yields on its loan are shown for different assumed LIBORs at each reset date.