Techniques of asset/liability management: Futures, options, and swaps Outline –Financial futures –Options –Interest rate swaps

–Futures contract: Standardized agreement to buy or sell a specified quantity of an asset on a specified date at a set price. Pricing and delivery occur at two points in time. Buyer is in a long position, and seller is in a short position. The buyer of the contract is to receive delivery of the good and pay for it, while the seller of the contract promises to deliver the good and receive payment. The payment price is determined at the initial time of the contract.

Suppose you know that you will need 5,000 bushels of corn in one year and want to lock in the price of corn today. You (long position trader) find a seller (short position trader) who agrees to sell at $4/bushel (strike price) in one year(settlement or expiration date). On expiration date, corn is selling for $5/bushel. You would pay the previously agreed-upon $4/bushel for 5,000 bushels, $20,000, to the seller and the seller has to deliver the 5,000 bushels of corn. Your gain is $5,000, which is equal to the seller’s loss.

Standardization tells traders exactly what is being traded and the conditions of the transactions Uniformity promotes market liquidity. Exchange clearinghouse is a counterparty to each contract. Default risk on futures (but not forward) contracts is minimized by the role of the exchange clearinghouse in all futures contracts. The exchange clearinghouse is, in effect, the counterparty in each transaction. Marked-to-market at the end of each day. Futures contracts are evaluated daily at their market values and gains or losses are added to or subtracted from the margin balance each day.

Margin Account (Stocks) Margin Account: A brokerage account in which, subject to limits, securities can be bought and sold on credit. –Margin = Equity in account / Value of securities the portion of the value of an investment that is not borrowed. –Initial Margin: the minimum margin that must be supplied on a security purchase. Initial margin of 50% has been set by the Fed.

–Maintenance Margin: the minimum margin that must be present at all times in a margin account. Typically 30%. –When the margin in account drops below the maintenance margin, the broker issue a margin call. –Investors receiving this margin call should add new cash or securities to the margin account. Otherwise, your securities are sold and the margin loan will be repaid.

You have $10,000 Initial margin is 50%; maintenance is 30% The maximum margin loan is $10,000. You buy 1,000 shares at $18 Margin = $10,000/$18,000 = 55.56% Price falls to $10 Total value of stock is $10,000; You borrowed $8,000, so your equity is $2,000. Margin = $2,000 / $10,000 = 20%

You have $5,000 and buy 400 WMT at $25 each. Initial margin is 50%; maintenance is 30% Your account balance sheet is as follows: Assets Liabilities 400 WMT$10,000Margin $25/share ______Equity$5,000 Total$10,000Total $10,000 Your margin is $5,000/$10,000 = 50%

Margin call occurs at what price? Value of your stock = Margin loan + Equity Value = 400 x P Equity = Value of stock – margin loan = 400 x P - $5,000 Maintenance margin = Equity / Value of stock =.3 (400 x P - $5,000) / (400 x P) = 0.3 P = $ At any price below $17.86, you will be subject to a margin call.

Margin account (Futures) Bob buys one futures contract of corn at $2/bushel (1 contract =5,000 bushels). The initial margin was $1,000. The next day the price of corn falls by 3 cent a bushel. So, Bob has just lost $( ). At the end of the day, the daily settlement process marks Bob’s margin account to market by taking $150 out of his account leaving a balance of 850. Now, assume the maintenance margin level is 75%. If Bob’s margin balance falls to or below $750, he will get a ( ) and have to bring his account back up to the initial $1,000. Suppose during the next day, corn again falls 3 cent per bushel. Bob’s margin account balance now falls to $ ( ), and he gets a margin call to deposit $300 in variation margin. The deposit of $300 will bring his account back up to the initial level of $1,000.

Marking to market (Financial futures) Suppose on day 1 the seller entered into a 90-day contract to deliver 20-year T-Bonds at $97. The next day, because of a rise in interest rates, the futures contract, which now has 89 days to maturity, is trading at $96 when the market closes. Marking to market requires the prices of all contracts to be marked to market at each night’s closing price. As a result, the price of the contract is lowered to $96 per $100 of face value, but in turn for this lowering of the price from $97 to $96, the buyer has to compensate the seller $1 per $100 of face value. Thus, given a $100,000 contract, there is a cash flow payment of $1,000 on that day from the buyer to the seller. Note that if the price had risen to $98, the seller would have had to compensate the buyer $1,000.

Q: What is meant by a short position in financial futures? A long position? How is each affected by changes in interest rates? A financial futures contract is a standardized agreement to buy or sell a specified quantity of a financial instrument at a set price. A short position represents the sale of a futures contract. A long position represents the purchase of a futures contract. Since interest rates and the prices of fixed income instruments move inversely, a short position will benefit if interest rates increase but will be harmed by falling interest rates. Conversely, a long position will benefit from falling rates and will be harmed by rising rates.

Using interest rate futures to hedge a dollar gap position Q: How would a bank use interest rate futures to hedge a positive dollar gap? A negative dollar gap? ANSWER: A bank with a positive dollar gap would benefit on-balance-sheet from rising interest rates but would lose from falling interest rates. It would hedge this risk by taking a long or buy position in the financial futures market. If, conversely, the bank has a negative dollar gap it would take a short position in the futures market.

Q: How would a bank use interest rate futures to hedge a positive duration gap? A negative duration gap? ANSWER: With a positive duration gap, a bank would experience a decline in the market value of equity if interest rates increased (because the market value of assets would fall more than the market value of liabilities). It could help this exposure by taking a short position in financial futures. With such a position, increases in interest rates would produce gains in the futures market position that could be used to offset the losses in the cash market position. In contrast, a bank with a negative duration gap would hedge with a long position in the futures market.

–Number of contracts to purchase in a hedge: [(V/F) x (M C / M F )] b V = value of cash flow to be hedged F = face value of futures contract M C = maturity of cash assets M F = maturity of futures contacts b = variability of cash market to futures market. Example: A bank wishes to use 3-month futures to hedge a $48 million positive dollar gap over the next 6 months. Assume the correlation coefficient of cash and futures positions as interest rates change is 1.0. N = [(48/1) x (6/3)] 1 = 96 contracts.

Balance sheet hedging example Consider the problem of a bank with a negative dollar gap facing an expected increase interest rates in the near future. Assume that bank has assets comprised of only one-year loans earning 10% and liabilities comprised of only 90-day CDs paying 6%. If interest rates do not change:

Day Loans: Inflows $1, Outflows $ CDs: Inflow $ $ $ $ Outflows $ $ $ $ Net cash flows $ Notice that for loans $1,000/(1.10) = $ Also notice that CDs are rolled over every 90 days at the constant interest rate of 6% [e.g., $ = $909.09(1.06) 0.25, where 0.25 = 90 days/360 days].

As a hedge against this possibility, the bank may sell 90-day financial futures with a par of $1,000. To simplify matters, we will assume only one T-bill futures contract is needed. In this situation the following entries on its balance sheet would occur over time.

Balance sheet hedging example As a hedge against this possibility, the bank may sell 90-day financial futures with a par of $1,000. To simplify matters, we will assume only one T-bill futures contract is needed. In this situation the following entries on its balance sheet would occur over time. Day T-bill futures (sold) Receipts $ $ $ T-bill (spot market purchase) Payments $ $ $ Net cash flows It is assumed here that the T-bills pay 6% and interest rates will not change (i.e., $1,000/(1.06) 0.25 = $985.54).

If interest rates increase by 2% in the next year (after the initial issue of CDs), the bank’s net cash flows will be affected as follows:

Balance sheet hedging example If interest rates increase by 2% in the next year (after the initial issue of CDs), the bank’s net cash flows will be affected as follows: Day Loans: Inflows $1, Outflows $ CDs: Inflow $ $ $ $ Outflows $ $ $ $ Net cash flows $ Thus, the net cash flows would decline by $ In terms of present value, this loss equals $13.59/1.10 = $12.35.

Balance sheet hedging example We next show the effect of this interest rate increase on net cash flows from the short T-bill futures position : Day T-bill futures (sold) Receipts $ $ $ T-bill (spot market Purchase) Payments $ $ $ Net cash flows $4.60 $4.60 $4.60 The total gain in net cash flows is $ In present value terms, this equals 4.60/(1.10) /(1.10) /(1.10).75 = $ Thus, the gain on T-bill futures exceeds the loss on spot bank loans and CDs.

Options Definition: Right but not obligation to buy or sell at a specified price (“striking price”) on or before a specified date (“expiration date”). Call option: Right to buy -- pay “premium” to seller for this right. A July call option on Motorola stock with exercise price of $50 gives the owner of the call option to buy this stock for a price of $50 before expiration in July. The holder of the call is not required to exercise the option. Only when the stock price exceeds the exercise price of $50, the holder will exercise the call option.

Put Option: Right to sell -- pay “premium” to seller for this right. An October put option on Motorola stock with exercise price of $50 gives the owner of the put option to sell this stock for a price of $50 at any time before expiration in October. A put option will be exercised only if the stock price is less than the exercise price of $50. –Note: Seller of option must sell or buy as arranged in the option, so the seller gets a premium for this risk. The premium is the price of the option.

Option Payoffs to Buyers Payoff Premium = $4 Gross payoff Net payoff Price of security Call Option $100$104 Buy for $4 with exercise price $100 “ In the money ” NOTE: Sellers earn premium if option not exercised by buyers. -4

Option Payoffs to Buyers Gross profit Net payoff Price of security Put Option Premium = $5 NOTE: Sellers earn premium if option not exercised by buyers. $40 $35 Buy put for $5 with exercise price of $40. Payoff “ In the money ” 0 -4

Options on futures contracts (futures options) Give the holder the right, but not the obligation to enter into a futures contract on an underlying security or commodity at a later date and at a predetermined price. Purchasing a call on a futures allows for the acquisition of a long position in the futures market, while exercising a put would create a short futures position. The writer of the call would be obligated to enter into the short side of the futures contract if the option holder decided to exercise the contract, while the seller of the put might be forced into a long futures contract.

When the bank hedges by buying put options on futures, if interest rates rise and bond prices fall, the exercise of the put results in the bank delivering a futures contract to the writer at an exercise price higher than the cost of the bond future currently trading on the futures exchange. If interest rates fall while bond and futures prices rise, the buyer of the futures put option will not exercise the put, and the losses on the futures put option are limited to the put premium.

Q) What is a futures options contract? Compare and contrast a futures options contract with a futures contract. ANSWER: A futures options contract is an option contract in which the deliverable is a futures contract, such as the Treasury bill futures contract. As with all options contracts, the holder has the right but not the obligation to take delivery (call option) or make delivery (put option).

Q) Suppose that your bank has a commitment to make a fixed rate loan in three months at the existing rate. In order to hedge against the prospect of rising interest rates, the bank takes a position in the futures options markets. What position should it take? The relevant information is as follows: T-bill futures prices 89 Put option 90 Premium $2500 What will be the net gain to the bank if T-bill futures prices fall to 85? Increase to 93?

If T-bill futures prices fall to 85, the put option could be exercised at 90 for a gain of 5, or $50,000. After paying the premium, the net gain would be $47,500. If T-bill futures prices rise to 93, the put option would not be exercised. The loss would equal the premium paid for the option, or $2,500.

Q) Explain how futures options contracts can be used to hedge interest rate risk. ANSWER: A bank that would be harmed if interest rates increased could hedge this risk by selling call options on futures or buying put option on futures. In contrast, if the bank was in a position in its portfolio where it would lose if interest rates fell it could hedge by buying a call option on futures or selling a put option.

Caps Buying a cap means buying a call option on interest rates. If interest rates rise above the cap rate, the seller of the cap compensates the buyer in return of an up-front premium. The seller of the cap is obliged to pay the difference between LIBOR and the exercise or cap rate (times the fraction of the year, times the notional principal). As a result, buying an interest cap is like buying insurance against an increase in interest rates.

Suppose a bank buys a 9 % cap at t=0 with exercise dates at the end of the first year and end of the second year. Face value is $100M. If the actual interest rate at the end of year 1 is 10%, the cap holder is entitled to receive the difference between the current market interest rate and the strike price multiplied by the principal value of the contract. (10%-9%)(100M)= $1M If the interest rate is below the cap, the cap seller makes no payments to the buyer.

Floors a put option on interest rates. An interest rate floor is a contract that limits the exposure of the buyer to downward movements in interest rates. The seller of a floor makes settlement payments only when LIBOR is below the floor rate

Your bank is liability sensitive. To protect itself against rising interest rates, management purchased 10 caps from a large investment bank firm. Each contract had a notional value of $1,000,000, a strike price (based on three-month Treasury bill rates) of 7% (rate was currently 6%), and a one-year maturity. Over the next year interest rates in Treasury bills fell, reaching 3% at the end of the year, the cap expired without benefit, and the bank lost the full premium of $46,000. Did management error in its decision to purchase the cap? ANSWER: No, the bank bought insurance against a negative event. The negative event did not occur.

Interest rate swaps An exchange of fixed interest payments for floating interest payments by two counterparties. The swap buyer agrees to make a number of fixed interest rate payments on periodic settlement dates to the swap seller. The seller agrees to make floating rate payments to the buyer on the same settlement dates.

Advantages of swap markets: swap markets are very private since only the counterparties know that the swap is taking place swap markets have virtually no government regulation swap markets allow for custom designed contracts (size and maturity)

Limitations of swap markets: it is difficult to find counterparites wanting to take the opposite side of a specific transaction swap agreements are difficult to alter and hard to terminate once they are initiated the counterparties are both exposed to default risk.

Consider two banks. Bank A has raised $100 million of its funds by issuing four-year medium-term notes with 10% annual fixed coupons. On the asset side of its portfolio, the bank makes C&I loans whose rates are indexed to LIBOR. Bank B has short-term CD with an average of duration of one year, and it has $100 million worth of fixed rate residential mortgages of long duration. Bank A has a positive dollar gap, while Bank B has a negative dollar gap. Bank A sells an IRS (makes floating-rate payments) and Bank B buys an IRS (makes fixed- rate payments)

Bank A sends annual payments indexed to one- year LIBOR+2% (assuming one-year LIBOR is 8%) to help the Bank B cover the cost of refinancing its one year CDs Bank B sends fixed annual payments of 10% for the notional principal of $100 M to the Bank A to allow the bank to cover fully the coupon interest payments on its note issue.

Bank A and Bank B have the following opportunities for borrowing in the short-term (floating rate) and long- term (fixed rate) markets. Bank ABank B Floating Rate T-Bill + 1.0%T Bill + 2.0% Fixed Rate 8%10.5% Bank A has a positive gap and Bank B has a negative gap. Show that both banks can benefit from a swap in the sense of lowering their interest rate risk. Can they also lower their cost of funds?

Bank A wants to receive fixed and pay floating. Bank B wants to receive floating and pay fixed. If Bank A and Bank B exchange flows in this manner it will reduce the interest rate risk of both parties. Since the relative credit quality spreads are different in the two markets (Bank A has a 1% advantage in the floating rate market and a 2.5% advantage in the fixed rate market), both parties can lower their cost of funds through the swap as well as reduce their interest rate risk. Pick swap terms and show this to be true. One such is the following (but there are others). Bank A pays T-Bill and receives 8%, and B receives T-Bill and pays 8%. In this case, the cost of funds to A is T- Bill with the swap (versus T Bill + 1.0% without the swap) and for B it is 10% with the swap (versus 10.5% without the swap).