hedging risk and exposure

Hedging risk and exposure

May 2, 2023 ASHOK PATIL 2

MANAGEMENT OF TRANSACTION EXPOSURE


MANAGEMENT OF OPERATING (ECONOMIC) EXPOSURE


INTEREST RATE AND CURRENCY SWAPS


HEDGING INTEREST RATE


• When money is lent (borrowed) to earn (pay) interest and interest rate is volatile, then this risk can be hedged using futures contract.

• It is hedged in such a way that whenever there is a loss due to interest rate, the same is recovered in the futures market.


Hedging interest rate with futures contract

• There are two main interest rate futures contract– Eurodollar futures (Chicago Merchantile Exchange-

CME)– US treasury bond (T-bill) futures (CBOT)

• The eurodollar futures is most popular and active contract. Open interest is in excess of $4 trillion at any point in time.


T-bill Futures• These futures are listed using the IMM (International Monetary

Market) index• IMM = 100 – Annualized forward discount yield (DY)• For example, if the Price of a $100, 90 Day Treasury were $98.

• IMM price of futures =100 – 8 =92 • Note that forward discount yield is not rate of return.• You can observe that futures prices are inversely related to

interest rates (in this case DY).

%810090360

10098$100$

10090

360

DY

FVPFVDY

©David Dubofsky and 10-9 Thomas W. Miller, Jr.

T-bill Futures, II.

• Note that the discount yield is not a rate of return. • If the day count method is actual/365, the

annualized rate of return, r, with simple interest, is

• This is called the bond equivalent yield (if t < 182 days)

t365

PPFr


T-bill Futures, III.• The futures discount yield is the forward yield on a 3-month T-bill,

beginning on the delivery date of the contract. Example:– Suppose today is October 8, the delivery day for the Dec contract is Dec.

18th, and the futures price is 97.22. – Then, someone who goes long a T-bill futures contract has “essentially”

agreed to buy $1 million face value of 3-month T-bills on Dec. 18th, at a forward discount yield of 2.78%, which is a forward price of $992,972.78.

• One tick = $12.50 = 1/2 basis point change in the yield.• The contract is cash-settled.• To speculate, go long T-bill futures if you think that 3-month T-bill

prices will rise (yields on 3-month T-bills will fall). Sell T-bill futures to bet on falling prices (rising yields).


Eurodollar Futures, I.• When foreign banks receive dollar deposits, those dollars are called

Eurodollars.• Underlying asset is the 90-day $1,000,000 Eurodollar time deposit

interest rate; LIBOR• Cash settled• IMM Index = 100 – aoy = 100 - LIBOR

• aoy = add on yield on a 90-day forward Eurodollar time deposit (LIBOR).

• If the IMM Index is 95.19, then the futures LIBOR is 4.81%. (100 – 95.19 = 4.81)

• LIBOR rises => IMM index falls.

t360

PPFLIBOR aoy


Eurodollar Futures

• The futures price is quoted in terms of LIBOR rate. Since LIBOR rate is decided by transactions between banks and is floating, the futures price is also floating.

• IMM Futures price = 100 – LIBOR (at the time)• If LIBOR is 4.14% at maturity, then futures price is 95.86• Let’s say if futures price today is 94.86, how much is

the implied LIBOR?• = 100 – 94.86 = 5.14• Futures price negatively related to LIBOR.


Eurodollar futures hedge example(lending or depositing)

• An MNC expects to receive $20,000,000 in cash from a large sale of merchandise on June 15, 2005. The money will not be needed for a period of 90 days after receipt. Thus the treasurer of this MNC should invest the excess funds for this period in a money market instrument such as Eurodollar deposit.

• He notes that three-month LIBOR is currently 2.91 percent. The implied three-month LIBOR rate in the June 2005 contract is at 3.44 percent.

• Treasurer would like to lock in this interest rate of 3.44 percent by taking a position in futures contract.


• Recall futures price is inversely related to LIBOR i.e. futures price will increase if LIBOR decreases.

• Therefore, to hedge against the downside risk in the interest rate, treasurer will have to take short position in the interest rate. But there is no futures contract on the interest rate. However, the futures contract based 100 – LIBOR is available.

• Therefore, treasurer would take a long position in 20 such futures contract.


Case 1• Assume that on the last day of trading in the June 2005

contract three-month LIBOR is 3.10 percent.• At 3.10 percent, when the MNC deposits in a 90-day

Eurodollar, deposit of $20,000,000 will generate only $155,000 of interest income, or $17,000 less than that at a rate of 3.44 percent.

• But the shortfall will be made up by profits from the long futures contract. At a rate of 3.10 percent, the final settlement price on the June 2005 contract is 96.90 (=100-3.10). The profit earned on the futures position is

• [96.90 – 96.56]/4*10000*20 contracts = $17,000.


Or alternatively,

• Hedging profit/loss from futures = $25*no of basis points*no of contracts

• Hedging profit = $25*34*20=$17,000


Money market

Futures market

2.91

96.56Implied LIBOR = 3.44

3.10

96.90LIBOR =3.10

MNC receives moneyNow and invests at 3.10%For 3 months from here.

Settlement in futures[96.90 – 96.56]/4*10,000*20 contracts = $17,000


Case 2

• Assume that on the last day of trading in the June 2005 contract three-month LIBOR is 3.60 percent.

• At 3.60 percent, a 90-day Eurodollar deposit of $20,000,000 will generate $180,000 of interest income, or $8000 more than that at a rate of 3.44 percent.

• But the surplus will be offsetted by losses from the long futures contract. At a rate of 3.60 percent, the final settlement price on the June 2005 contract is 96.40 (=100-3.60). The profit earned on the futures position is

• [96.40 – 96.56]/4*10000*20 contracts = -$8,000.


Money market

Futures market

2.91

96.56Implied LIBOR = 3.44

3.60

96.40LIBOR =3.60

MNC receives moneyNow and invests at 3.60%For 3 months from here.

Settlement in futures[96.40 – 96.56]/4*10,000*20 contracts = -$8,000


Eurodollar Futures Example

• Suppose in February you buy a March Eurodollar futures contract. The quoted futures price at the time you enter into the contract is 94.86.

• If the 90-day LIBOR rate at the end of March turns out to be 4.14% p.a., what is the payoff on your futures contract?– The price at the time the contract is purchased is 94.86.– The LIBOR rate at the time the contract expires is 4.14%. – This means that the futures price at maturity is 100 -

4.14 = 95.86.


The payoff of contract?

• LIBOR has decreased from 5.14 to 4.14 indicating the futures price must have increased.

• Payoff = (95.86-94.86)/4*10000 = 2500– The increase in the futures price is multiplied by

$10,000 because the futures price is per $100 and the contract is for $1,000,000.

– We divide the increase in the futures price by 4 because the contract is a 90-day (90/360) contract.


Using Eurodollar futures contract to hedge interest rate risk (borrowing)

• Suppose a firm knows in February that it will be required to borrow $1 million in March for a period of 90 days.

• The rate that the firm will pay for its borrowing is LIBOR + 50 basis points.

• The firm is concerned that interest rates may rise before March and would like to hedge this risk.

• Assume that the March Eurodollar futures price is 94.86.


Using Eurodollar futures contract to hedge interest rate risk…continued

• Step 1: Specify the risk.– Your company will lose if interest rates rise. That is, if the

interest rate is higher, your firm will have to pay more interest on the loan.

• Step 2: Determine an appropriate futures position.– You want a futures position that gives a positive return if interest

rates rise. That is, you want a futures position that gives a positive return if (100-LIBOR) falls. Hence, you want a futures position that gives a positive return if the futures price falls. Therefore you sell Eurodollar futures.

• Step 3: Determine the amount.– $1 mm amounts to one contract.


Continued…

• The LIBOR rate implied by the current futures price is: 100-94.86 = 5.14%.

• If the LIBOR rate increases, the futures price will fall. Therefore, to hedge the interest rate risk, the firm should sell one March Eurodollar futures contract.

• The gain (loss) on the futures contract should exactly offset any increase (decrease) in the firm’s interest expense.


Case I: LIBOR rises to 6.14%

• Suppose LIBOR increases to 6.14% at the maturity date of the futures contract.

• The interest expense on the firm’s $1 million loan commencing in March will be:

• The payoff on the Eurodollar futures contract is– As (94.86-93.86)*10000/4=2500

• Therefore total payoff = payment of loan + gain in futures• = -16600+2500= -14100 • This is equivalent to interest payment of 5.14% at which

futures was signed plus 0.5 = 5.64%


Case II: LIBOR falls to 4.14%

• That is, the loan will be available at 4.14%+5 basis points. Therefore the interest expense will be

• The payoff on the Eurodollar futures contract is (94.86-95.86)*10000/4=-2500

• Therefore total payoff = payment of loan + loss in futures

• = -11600-2500= -14100• This is equivalent to interest payment of 5.14% at

which futures was signed plus 0.5 = 5.64%


• The net outlay is equal to $14,100 regardless of what happens to LIBOR.

• This is equivalent to paying 5.64% p.a. over 90 days on $1 million.

• The 5.64% borrowing rate is equal to the current implied LIBOR rate of 5.14%, plus the additional 50 basis points that the firm pays on its short-term borrowing.

• The firm’s futures position has locked in the current implied LIBOR rate.


Another example

• On July 28, 1999, a firm plans to borrow $50 million for 90 days, beginning on September 13, 1999.

• The firm will borrow at the Eurodollar spot market on September 13th.

• The current spot 3-month Eurodollar rate is 5.3125%.


• The firm will be borrowing in the spot market 47 days hence. Thus, on July 28th, the interest rate at which the firm will be borrowing on September 13th is unknown.

• The firm fears that when it comes time to borrow the funds in the Eurodollar spot market, interest rates will be higher (Eurodollar Index will be lower).

• Such a situation calls for a short hedge using Eurodollar futures contracts.

• On July 28, 1999, the closing price for September Eurodollar futures was 94.555. (IMM Index=futures price)

• Assuming transactions costs of zero, by shorting 50 Eurodollar futures contracts on July 28, 1999, the firm can lock in a 90-day borrowing rate of 5.445%.

• Rate: 100 – 94.555.


Case I. Spot 90-Day LIBOR on September 13th is 5.445%.

• The firm’s interest expense would be:

$680,625 = 50,000,000 * 0.05445 * (90/360) • Thus, in this case, there is no profit or loss on the

futures contracts because the firm went short at 94.555.


Case II. Spot 90-Day LIBOR on September 13th is 5.845%.

• Here, the bank’s actual interest expense would be higher than “anticipated” because interest rates rose above the original futures interest rate:

$730,625 = 50,000,000 * 0.05845 * (90/360)

• To calculate the futures profit on the 50 contracts, one must recall that each full point move in the IMM Index (i.e., 100 basis points) represents $2,500 for one futures contract. The delivery day futures price is 100-5.845 = 94.155. Thus,

(94.555 – 94.155) * 10000/4 * 50 = $50,000

• Here too, the net interest expense for the firm is -$730,625 +$50,000 = -$680,625.


Case III. Spot 90-Day LIBOR on September 13th is 5.045%.

• The bank’s actual interest expense would be:

$630,625 = 50,000,000 * 0.05045 * (90/360)

• However, because interest rates are lower, the bank loses on its short futures position. The delivery day futures price is 100-5.045 = 94.955. The futures loss is

(94.555 – 94.955) * 2500 * 50 = ($50,000)

• The net interest expense for the firm equals the interest expense with the 5.045% rate, plus the loss on the futures position. It is the same as the two previous cases: -$630,625 - $50,000 = -$680,625.


What is a Eurodollar Futures Contract?

• Contract: Eurodollar Time Deposit• Exchange: Chicago Merchantile Exchange• Quantity: $1 Million• Delivery Months: March, June, Sept., and Dec.• Delivery Specs: Cash Settlement Based on 3-Month

LIBOR• Min Price Move: $25 Per Contract (1 Basis Pt.)– 1% change = 100 basis points– Therefore, 1 basis point is 1/100 of 1%=0.0001– 1 basis point value = 0.0001/4*1,000,000=$25


• 1% change = 100 basis points (percentage terms)• This means that 1 basis point is 0.01 %

– Interest rate change from 3 to 4 % is change of 100 basis points.• 0.01 = 100 basis points (decimal terms)• This means that 1 basis point is 0.0001 in decimal terms.

– If 0.03 has become 0.0348, how many basis points have been changed?

• 48 basis points– 48 basis points is represented as 0.0048 in decimal terms– 48 basis points is represented as 0.48 in percent terms.


Note• Futures price is quoted per hundred value

basis. So if the futures price is quoted as 94.00 and the value of the contract is 1000, then the quote will be multiplied by 10.

• If the value is 1, 000,000, then the quoted price will be multiplied by 10,000

• Alternatively, use the formula

25$360

90*0001.0*000,000,1int____

360__int*_1*___int____

pobasisoneofValue

or

daysofnumberpobasiscontracttheofValuepobasisoneofValue


FORWARD-FORWARDS


Forward Forwards

• Suppose a company needs to borrow $10 million in six months for a three-month period.– It can wait or enter into forward forward with a bank.

• If bank fixes this rate at 8.4% per annum, then– Bank will loan the company $10 million in six months

from now for a period of 3 months @8.4/4=2.1.– The company will repay principal plus interest at the

maturity $10210000 (=10000000*1.021)


Forward Rate Agreement• Suppose a company needs to borrow $50 million in two

months for a six-month period. • Company buys (long) FRA (2x6) on LIBOR from the bank @

6.5% on a notional principal of $50 million– If LIBOR6 exceeds 6.5%, then bank will pay the difference in interest

expense– If LIBOR6 is less than 6.5%, then company will pay the bank.

• if LIBOR6 after two months is 7.2% then,

730,170$)360/180(072.01

)3601800.065)(-(0.072

50000000 position short for payment Interest

)360/(1

)360daysAR)(-(SR

principal notional position short for payment Interest

daysSR


PARTICIPATING FORWARDS


Participating Forward

• A PFC is an agreement with a bank that provides protection against unfavourable exchange rate movements by setting a contract rate at which you will exchange one currency for another.

• At the same time it provides you with some ability to participate in any favourable exchange rate movements on a pre-determined proportion of your contract amount.


Case of importer/payment of foreign currency/buying foreign currency: use of PFC

(Participating Forward Contract)• You are an Australian based importer due to

pay 100,000 United States dollars (USD) in 3 months’ time for goods bought overseas.

• Assume the current AUD/USD market foreign exchange rate is 1.265823 and the 3-month forward exchange rate is 1.275511


The contract: PFC

• You enter into a PFC to buy USD 100,000 with AUD in 3 months’ time and set the contract rate at 1.2903226 – In establishing a PFC, the contract rate must be set

at a rate above the current forward exchange rate.

• Based on a contract rate of 1.2903226 the bank determines the participation ratio to be 40 per cent.


Case I (PFC): If the market exchange rate is above AUD 1.2903226/USD

• You would exchange your AUD, on the full contract amount, at the contract rate. You will pay:

• USD 100,000*1.2903226 = AUD 129, 032.26


Case II: if the market foreign exchange rate is 1.219512

• You would exchange your AUD, on 60% (equal to 100 % - participation ratio of 40%) of the contract amount, at the contract rate of 1.2903226.

• You will buy USD 60,000 at contract rate of 1.2903226:

• USD 60,000*1.2903226 = AUD 77,419.35• AND (NEXT SLIDE)


• You may also choose to exchange the remaining 40% (the participation ratio) of your contract amount at the prevailing market rate. For example, if you choose to do this and as the AUD/USD market foreign exchange rate at the time is 1.2195122, you will require:

• USD 4 0,000 * 1.2195122 = AUD 48,780.49 • In this scenario the total amount of AUD you pay will be AUD

126,199.84 (equal to AUD 77,419.35 + AUD 48,780.49). • Your effective dealing rate will equate to: • AUD 126,199.84 /USD 100,000 = 1.2619984 (which is less

than current forward rate)


Case of exporter/receipt of foreign currency: use of PFC (Participating Forward Contract)

• You are an Australian based exporter due to receive 100,000 United States dollars (USD) in 3 months’ time for goods sold overseas.

• Assume the AUD/USD market foreign exchange rate is 1.2658228 and the 3-month forward exchange rate is 1.2755102.


The contract

• You enter into a PFC to sell USD 100,000 for AUD in 3 months’ time and set the contract rate at 1.2610340. – In establishing a PFC, the contract rate must be set

at a rate below the current forward exchange rate.

• Based on a contract rate the bank determines the participation ratio to be 40 per cent.


Case I: if the market foreign exchange rate is below the 1.2610340 contract rate

• You would exchange your USD, on the full contract amount, at the contract rate.

• You will receive: USD 100,000 *1.2610340 = AUD 126,103.40


Case II: if the market foreign exchange rate is above the 1.2610340 contract rate

• You would exchange your USD on 60 % (equal to 100 % - participation ratio of 40%) of the contract amount, at the contract rate. You will receive:

• USD 6 0,000*1.2610340 = AUD 75,662.04 • You may also choose to exchange the remaining 40 % (the

participation ratio) of your contract amount at the prevailing market rate.

• For example, if you choose to do this and as the AUD/USD market foreign exchange rate at the time is 1.3333333, you will receive:

• USD 4 0,000*1.3333333 = AUD 53,333.33


The result

• In this scenario the total amount of AUD you receive will be AUD 128,995.37 (equal to AUD 75,662.04 + AUD 53,333.33).

• Your effective dealing rate will equate to: • AUD 128,995.37 /USD 100,000 = 1.2899537

(which is more than current forward rate)


NON-DELIVERABLE FORWARDS


Non-deliverable Forwards• A Non Deliverable Forward Transaction (NDF) is an

agreement between you and Bank which protects you against unfavorable exchange rate movements. – It is a cash settled transaction, meaning that there is no

exchange of currencies at maturity as there is with a typical foreign exchange transaction.

– Rather, there is a single amount payable by either you or bank. • A contract rate is agreed up-front, together with the fixing

rate (spot rate on fixing date). The contract rate and fixing rate are used to calculate the amount payable on the nominated maturity date.


Hedging Foreign Currency Payables (importer) with NDF

• Suppose, you are an Australian based company importing goods from China. You are billed 1 million in Chinese Renminbi (CNY) but you are required to pay in US dollars (USD).

• Your supplier’s latest invoice requires you to pay the USD equivalent of CNY 1 million in 3 month’s time.

• Assume the current exchange rate for value spot is 1 CNY = 0.146199 USD


• It’s an importer’s case. If the firm were required to pay in CNY, it would have been short in CNY against AUD in spot market. i.e. if CNY appreciated against AUD it would make a loss.

• So you would take a LONG position in CNY against AUD in forward market.

• But it is required to pay in USD. So using cross rate formula

• You will be short in CNY against USD in spot market. i.e. if CNY appreciated (or dollar depreciated), it would make a loss.

• Therefore, it would take a LONG position in CNY against USD.

SELL

BUY

CNYAUD

SELL

BUY

SELL

BUY

SELL

BUY

CNYUSD

USDAUD

CNYAUD *


NDF with bank

• You wish to protect yourself against the USD depreciating against the CNY, in order to limit the amount of USD you will have to pay in 3 months’ time.

• You enter into an NDF and set a contract rate for 3 months’ time. – You set the notional principal amount of your trade to be

CNY 1,000,000. – At the same time you also agree the fixing date (two days

prior to the NDF’s maturity date). – Bank gives you a contract rate of 0.14556041 USD/CNY.


Case I: if the fixing rate for USD/CNY is 0.14814815 (rate on Fixing Date)

• The fixing settlement currency amount will be: USD 148,148.15 (= CNY 1,000,000 *0.14814815) while, the contract settlement currency amount will be: USD 145,560.41 (=CNY 1,000,000 *14556041)Accordingly, the difference (USD 2,587.74) will be payable by Bank to you on the maturity date.

If the fixing rate on the fixing date is less favorable to you than the contract rate Bank will pay you the cash settlement amount in USD on the maturity date.


How did the hedge work?

The cash settlement amount will compensate you for the higher USD amount you will need to pay for your goods. To purchase your goods, you would have had to pay USD 148,148.15.

With the benefit of the USD cash settlement amount you receive under the NDF (USD 2,587.74),

Your total USD outlay will be reduced to USD 145,560.41 This is equivalent to a USD/CNY exchange rate of 0.14556041, i.e. the NDF contract rate.


Case II: if the fixing rate for USD/CNY is 0.14265335

• The fixing settlement currency amount will be: USD 142,653.35 (= CNY 1,000,000 *0.14265335) while, the contract settlement currency amount will be: USD 145,560.41 (=CNY 1,000,000 *0.14556041)

If the fixing rate on the fixing date is more favorable to you than the contract rate you will pay the cash settlement amount in USD to Bank on the maturity date.


How did the hedge work?

• Accordingly, the difference (USD 2,907.06) will be payable by you to Bank on the maturity date.

• The cash settlement amount you pay Bank will diminish the extent to which you would have benefited through the lower USD amount when you pay for your goods.

• To purchase your goods, you pay USD 142,653.35. Adding the cash settlement amount (USD 2,907.06) your total USD outlay will now be USD 145,560.41.

• This is equivalent to a USD/CNY exchange rate of 0.14556041, i.e. the NDF contract rate.


Note this…• Entering into an NDF has effectively removed the

uncertainty of fluctuations in the USD/CNY exchange rate on the USD amount you will pay for your goods.

• However, you should also note that as an Australian company while you have effectively fixed your USD requirement with an NDF you will still need to obtain the required USD amount to pay for your goods.

• Accordingly, you will need to decide how you manage this risk to the AUD/USD exchange rate over the 3 months. NDFs can be denominated in AUD or alternatively the AUD/USD risk can be managed separately.

hedging risk and exposure

Economy & Finance

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