Risk Management

Question 1

Fratton Plc trades extensively in Europe.

The firm is due to receive 2,960,00 (Euro) in three months’ time. The following information is available:

1) The spot exchange rate is currently €1.1845 - 1.1856/£
2) The three-month forward rate of exchange is currently at 0.79-0.59 cent premium
3) The prices of three-month sterling traded option contracts (premiums in cents per £ are payable up front, with a standard contract size of £10,000) are as follows:

Exercise Price: €1.18

Calls: 2.40
Puts: 1.20

4) Annual Interest rates at the present time are as follows:

Uk:
- Deposit 1.15%
- Borrowing: 2.40%

Eurozone:
- Deposit 0.75%
- Borrowing: 1.60%

a) Calculate the net sterling receipt that Fratton can expect in three months’ time if it hedges its foreign exchange exposure using:
- the forward market

Answer 1

Forward Market

Bank sells £ at €1.1856/£

Forward rate = €1.797 (1.1856 - 0.0059)

So €2,960,000/1.797 = £2,509,112.49

Question 2

Fratton Plc trades extensively in Europe.

The firm is due to receive 2,960,00 (Euro) in three months’ time. The following information is available:

1) The spot exchange rate is currently €1.1845 - 1.1856/£
2) The three-month forward rate of exchange is currently at 0.79-0.59 cent premium
3) The prices of three-month sterling traded option contracts (premiums in cents per £ are payable up front, with a standard contract size of £10,000) are as follows:

Exercise Price: €1.18

Calls: 2.40
Puts: 1.20

4) Annual Interest rates at the present time are as follows:

Uk:
- Deposit 1.15%
- Borrowing: 2.40%

Eurozone:
- Deposit 0.75%
- Borrowing: 1.60%

a) Calculate the net sterling receipt that Fratton can expect in three months’ time if it hedges its foreign exchange exposure using:
- The money market

Answer 2

To hedge a euro receivable, Fratton needs to create a euro liability which, with interest, will exactly equal the receivable in three months’ time:

€2,960,000/1.004 = £2,948,207.17

Convert to £ at spot (1.1856) to give £2,486,679.46

Which with three months’ interest at 0.2875% gives £2,493,828.66 (1.15% x 3/12)

Question 3

Fratton Plc trades extensively in Europe.

The firm is due to receive 2,960,000 (Euro) in three months’ time. The following information is available:

1) The spot exchange rate is currently €1.1845 - 1.1856/£
2) The three-month forward rate of exchange is currently at 0.79-0.59 cent premium
3) The prices of three-month sterling traded option contracts (premiums in cents per £ are payable up front, with a standard contract size of £10,000) are as follows:

Exercise Price: €1.18

Calls: 2.40
Puts: 1.20

4) Annual Interest rates at the present time are as follows:

Uk:
- Deposit 1.15%
- Borrowing: 2.40%

Eurozone:
- Deposit 0.75%
- Borrowing: 1.60%

a) Calculate the net sterling receipt that Fratton can expect in three months’ time if it hedges its foreign exchange exposure using:
- the options market, assuming the spot exchange rate in three months is:
- €1.1185 - 1.1200/£
- €1.1985 - 1.2000/£

Answer 3

Fratton should enter into a call option to buy £ at €1,18/£

Number of contracts = €2,960,000/1.18 = £2,508,475
£2,508,475/10,000 = 250.85 = 250 contracts

The premium would be €60,000 (0.024 x 10,000 x 250) - Calls UK percentage

Which at spot would cost £50,654.28 (60,000/1.1845)

Scenario 1:
Spot on expiry €1.12/£ - Exercise price €1.18/£ - intrinsic value: 0 - do we exercise? No
£ receipt at spot = 2,960,000/1.12 = £2,642,857.14 (net £2,592,202.860

Scenario 2:
Spot on expiry = Euro1.20/£ - Exercise price = 1.18 - intrinsic value = 0.02 per £ - exercise? Yes

Gain on option of €50,000 (0.02 x 10,000 x 250)

Sell €3,010,000/1.20 = £2,508,333.22 (net £2,457,679.05)

Question 4

One of Fratton’s customers is suggesting the use of Bitcoin to make a payment in two months’ time and has proposed a payment of 50 Bitcoins on 31st March 20X1

The directors are worried about the volatility of the Bitcoin price and are considering using a forward contract to hedge the risk

The following rates are relevant:

Spot rate: 1 Bitcoin = £7,500 - £7,600
Forward rate: 1 Bitcoin = £7,550 - £7,650

A) Calculate the sterling receipt that Fratton can expect in two months’ time if it hedges its Bitcoin exposure using the forward market

Answer 4

50 Bitcoins x £7,550 = £377,500

The spot rate is irrelevant if a forward hedge is used

£7,550 is the correct forward rate to use for selling Bitcoin in three months’ time

Question 5

Discuss the key problems associated with using cryptocurrencies to settle international transactions

Answer 5

Two key problems:
- Exchangeability: Cryptocurrency exchanges are only likely to exchange Bitcoins for a narrow range of major currencies eg., sterling, US dollars, and euros. This appears to be less of a problem for Fratton given that it is a UK company and will be receiving sterling
- Price volatility: Cryptocurrency exchange rates are extremely volatile, with prices moving significantly each day.
However, Fratton can choose to hedge this risk using OTC agreements such as forward contracts (if these are available) and also using derivative agreements such as futures. In both cases there is the possibility that the rate quoted by the markets is unattractive.

Question 6

In addition, in three months’ time Fratton will be drawing down a three-month £2.5 million loan facility which is granted each year by its bank to see the firm through its peak borrowing period. The following info is available:
1) The quotation for a ‘3-6’ forward rate agreement is currently 2.60 - 1.35
2) The spot rate of interest today is 2.40% pa and the relevant three-month sterling interest rate futures contract (standard contract size £500,000) is currently trading at 97.20

a) Explain how Fratton could use a forward rate agreement to resolve the uncertainty surrounding its future borrowing costs and show the effect if, in three months’ time, the spot rate of interest is 3% pa.

Answer 6

As a borrower Fratton should BUY a 3-6 FRA and can thereby fix a borrowing rate of 2.60%

At 3.00% rates have risen, so the bank will pay Fratton £2,500 (2.5m x (3%-2.6%) x 3/12). Payment on the underlying loan will be 3% x 2,500,000 x 3/12 = £18,750

Net payment on the loan: £16,250 (18,750 - 2,500) - an effective rate of 2.60%

Question 7

In addition, in three months’ time Fratton will be drawing down a three-month £2.5 million loan facility which is granted each year by its bank to see the firm through its peak borrowing period. The following info is available:
1) The quotation for a ‘3-6’ forward rate agreement is currently 2.60 - 1.35
2) The spot rate of interest today is 2.40% pa and the relevant three-month sterling interest rate futures contract (standard contract size £500,000) is currently trading at 97.20

b) Explain how Fratton could use sterling interest rate futures to hedge its exposure to interest rate risk and show the effect if, in three months’ time, the spot rate of interest is 3% pa and the price of the interest rate futures contract has fallen to 97

Answer 7

Fratton will need to sell three-month £ interest rate futures contracts

Fratton will need to sell five contracts (2,500,000/500,000 x 3/3)

Sell at 97.20 and buy at 97.00 for a gain of 0.20%

Futures outcome: 0.20% x 500,000 x 3/12 x 5 = £1,250

Payment in the spot market: 2,500,000 x 3% x 3/12 = £18,750 - £1,250 = £17,500 (=2.80%)

Question 8

The finance director of Sunwin Plc is a trustee of the firm’s employee pension fund.
The vast majority of the fund’s assets are currently invested in a portfolio of FTSE 100 shares.
It is 1 December 20X2 and the trustees are concerned that FTSE 100 share prices will fall over the next month and they wish to hedge against this possibility by using FTSE index options.

The current market value of the pension fund’s portfolio of shares is £5.6 million.
The FTSE 100 index stands at 5,000 on 1 December 20X2 and the directors wish to protect the current value of the portfolio.
The trustees have obtained the following information as at 1 December 20X2:
FTSE 100 INDEX OPTIONS: £10 per full index point (points per contract)

4,900:
Call
- Dec: 139, - Jan: 214, - Feb: 275
Put
- Dec: 34, - Jan: 94, - Feb: 135

4,950
Call
- Dec: 104, - Jan: 184, - Feb: 245
Put
- Dec: 48, - Jan: 114, - Feb: 155

5,000
Call
- Dec: 74, - Jan: 154, - Feb: 220
Put
- Dec: 70, - Jan: 134, - Feb: 180

5,050
Call
- Dec: 49, - Jan: 124, - Feb: 190
Put
- Dec: 99, - Jan: 159, - Feb: 200

5,100
Call
- Dec: 34, - Jan: 104, - Feb: 165
Put
- Dec: 134, - Jan: 189, - Feb: 225

Demonstrate how FTSE 100 index options can be used by the trustees to hedge the pension fund’s exposure to falling share prices and show the outcome if, on 31 December 20X2, the portfolio’s value:
a) rises to £6.608 million and the FTSE index rises to 5,900

Answer 8

Sunwin requires an option to sell - a December put option with an exercise price of 5,000

Portfolio value = £5.6m
Exercise price = 5,000

Value of one contract = 5,000 x £10 = £50,000

Number of contracts required = £5.6m/50,000 = 112 contracts

Premium: 70 points x £10 per point x 112 contracts = £78,400

a) If the index rises to 5,900, the put option gives Sunwin the right to sell @ 5,000, so the option would be abandoned (with zero value)
Overall position:
Value of portfolio = £6,608,000
Gain on option = 0
Less premium = (78,400)
—
6,529,600

Question 9

The finance director of Sunwin Plc is a trustee of the firm’s employee pension fund.
The vast majority of the fund’s assets are currently invested in a portfolio of FTSE 100 shares.
It is 1 December 20X2 and the trustees are concerned that FTSE 100 share prices will fall over the next month and they wish to hedge against this possibility by using FTSE index options.

The current market value of the pension fund’s portfolio of shares is £5.6 million.
The FTSE 100 index stands at 5,000 on 1 December 20X2 and the directors wish to protect the current value of the portfolio.
The trustees have obtained the following information as at 1 December 20X2:
FTSE 100 INDEX OPTIONS: £10 per full index point (points per contract)

4,900:
Call
- Dec: 139, - Jan: 214, - Feb: 275
Put
- Dec: 34, - Jan: 94, - Feb: 135

4,950
Call
- Dec: 104, - Jan: 184, - Feb: 245
Put
- Dec: 48, - Jan: 114, - Feb: 155

5,000
Call
- Dec: 74, - Jan: 154, - Feb: 220
Put
- Dec: 70, - Jan: 134, - Feb: 180

5,050
Call
- Dec: 49, - Jan: 124, - Feb: 190
Put
- Dec: 99, - Jan: 159, - Feb: 200

5,100
Call
- Dec: 34, - Jan: 104, - Feb: 165
Put
- Dec: 134, - Jan: 189, - Feb: 225

Demonstrate how FTSE 100 index options can be used by the trustees to hedge the pension fund’s exposure to falling share prices and show the outcome if, on 31 December 20X2, the portfolio’s value:
b) Falls to £4.592 million and the FTSE index falls to 4,100

Answer 9

Sunwin requires an option to sell - a December put option with an exercise price of 5,000

Portfolio value = £5.6m
Exercise price = 5,000

Value of one contract = 5,000 x £10 = £50,000

Number of contracts required = £5.6m/50,000 = 112 contracts

Premium: 70 points x £10 per point x 112 contracts = £78,400

b) If the index falls to 4,100, the put option gives Sunwin the right to sell @ 5,000, so the option would be exercised.
(value = £9,000 (900 x £10) x 112 contracts = £1,008,000) - 900 is the difference between 5,000 and 4,100

Overall position:
Value of portfolio = 4,592,000
Gain on option = 1,008,000
Less premium = (78,400)
—-
5,521,600

Question 10

It is 1 December 20X2 and Sunwin’s board of directors has recently agreed to purchase machinery from a UK supplier on 28 February 20X3.
The firm’s cash flows reveal that the firm will need to borrow £4 million on 28 February 20X3 for a period of nine months.

The directors are considering the use of either sterling short-term interest rate futures or traded interest rate options on futures to hedge against the firm’s exposure to interest rate rises.

The spot rate of interest on 1 December is 3% pa. and March three-month sterling interest rate futures with a contract size of £500,000 are trading at 96. Information regarding traded interest options on futures on 1 December 20X2 is as follows:

Strike price: 96.25
Calls: March = 0.20, June = 0.23, Sept = 0.25
Puts: March = 0.18, June = 0.96, Sept = 1.66

Strike price: 96.50
Calls: March = 0.09, June = 0.10, Sept = 0.11
Puts: March = 0.32, June = 1.19, Sept = 1.89

Strike price: 96.75
Calls: March = 0.05, June = 0.06, Sept = 0.07
Puts: March = 0.53, June = 1.43, Sept = 2.14

Demonstrate how sterling short-term interest rate futures can be used by Sunwin to hedge against interest rate rises, and show the effective loan rate achieved and the hedge efficiency if, on 28 February 20X3, the spot rate of interest is 4.5% pa and the March interest rate futures price has fallen to 95

Answer 10

Sunwin needs to sell a three-month contract

Number of contracts = 4m/0.5 x 9/3 = 24 contracts

Futures outcome:
Selling at the opening rate of 96 and buying at the closing rate of 95 yields a gain of 1%

Therefore 1% x 0.5m x 3/12 x 24 = £30,000

Net outcome:

Spot market £4m x 4.5% x 9/12 = (£135,000) plus the futures receipt of £30,000 = (£105,000)

Effective interest rate 105,000/4,000,000 x 12/9 = 3.5%

Hedge efficiency:

Increase in spot rate = 1.5% so increase in interest = £60,000 (1.5% x 4m) x 9/12 = £45,000

So the hedge efficiency = 30,000/45,000 x 100 = 66.7%

Question 11

It is 1 December 20X2 and Sunwin’s board of directors has recently agreed to purchase machinery from a UK supplier on 28 February 20X3.
The firm’s cash flows reveal that the firm will need to borrow £4 million on 28 February 20X3 for a period of nine months.

The directors are considering the use of either sterling short-term interest rate futures or traded interest rate options on futures to hedge against the firm’s exposure to interest rate rises.

The spot rate of interest on 1 December is 3% pa. and March three-month sterling interest rate futures with a contract size of £500,000 are trading at 96. Information regarding traded interest options on futures on 1 December 20X2 is as follows:

Strike price: 96.25
Calls: March = 0.20, June = 0.23, Sept = 0.25
Puts: March = 0.18, June = 0.96, Sept = 1.66

Strike price: 96.50
Calls: March = 0.09, June = 0.10, Sept = 0.11
Puts: March = 0.32, June = 1.19, Sept = 1.89

Strike price: 96.75
Calls: March = 0.05, June = 0.06, Sept = 0.07
Puts: March = 0.53, June = 1.43, Sept = 2.14

Demonstrate how traded interest rate options on futures can be used by Sunwin to hedge against the interest rate rising above 3.75% pa and show the effective loan rate achieved if, on 28 February 20X3:
1) The spot price is 4.4% pa and the futures price is 95.31

Answer 11

Traded interest options on futures:
Sunwin requires a March put option with a strike price of 96.25 (100 - 3.75)

The number of contracts required = 4m/0.5m x 9/3 = 24 contracts @0.18% (Put)

So the premium = 24 x 0.18% x 0.5m x 3/12 = £5,400

Spot price = 4.4%

Futures price = 95.31

Strike price = 96.25

Exercise? Yes

Gain on future = 0.94% therefore 0.94% x 0.5m x 3/12 x 24 = £28,200

Borrowing cost at spot: £132,000 (4m x (4.4% x 9/12))
Option (28,200)
Premium 5,400
Effective interest rate £109,200/4m x 12/9 = 3.64%

Question 12

It is 1 December 20X2 and Sunwin’s board of directors has recently agreed to purchase machinery from a UK supplier on 28 February 20X3.
The firm’s cash flows reveal that the firm will need to borrow £4 million on 28 February 20X3 for a period of nine months.

The directors are considering the use of either sterling short-term interest rate futures or traded interest rate options on futures to hedge against the firm’s exposure to interest rate rises.

The spot rate of interest on 1 December is 3% pa. and March three-month sterling interest rate futures with a contract size of £500,000 are trading at 96. Information regarding traded interest options on futures on 1 December 20X2 is as follows:

Strike price: 96.25
Calls: March = 0.20, June = 0.23, Sept = 0.25
Puts: March = 0.18, June = 0.96, Sept = 1.66

Strike price: 96.50
Calls: March = 0.09, June = 0.10, Sept = 0.11
Puts: March = 0.32, June = 1.19, Sept = 1.89

Strike price: 96.75
Calls: March = 0.05, June = 0.06, Sept = 0.07
Puts: March = 0.53, June = 1.43, Sept = 2.14

Demonstrate how traded interest rate options on futures can be used by Sunwin to hedge against the interest rate rising above 3.75% pa and show the effective loan rate achieved if, on 28 February 20X3:
2) The spot price is 2.1% pa and the futures price is 97.75

Answer 12

Traded interest options on futures:
Sunwin requires a March put option with a strike price of 96.25 (100 - 3.75)

The number of contracts required = 4m/0.5m x 9/3 = 24 contracts @0.18% (Put)

So the premium = 24 x 0.18% x 0.5m x 3/12 = £5,400

Spot price = 2.1%

Futures price = 97.75

Strike price = 96.25

Exercise? No

Gain on future = 0

Borrowing cost at spot: £63,000
Option = 0
Premium 5,400
Effective interest rate £68,400/4m x 12/9 = 2.28%

Question 13

Padd will send a large consignment of footwear to DS for sale in its shops across India. The price for this consignment is 200 million Indian rupees (INR), which will be payable by DS on 30 June 20X4.

You have been asked to prepare advice for the board and have obtained the following information at the close of business on 31 March 20X4:

Spot rate (INR/£) = 94.0625 - 95.4930
Sterling interest rate (lending) = 3.2% pa
Sterling interest rate (borrowing) = 4.0% pa
INR interest rate (lending) = 4.2% pa
INR interest rate (borrowing) = 4.8% pa

Three-month OTC currency call option on INR - exercise price = INR 94.7500/£
Three-month OTC currency put option on INR - exercise price = INR 95.5500/£

Three-month forward rate discount (INR/£) = 0.0195 - 0.2265

Cost of relevant OTC currency option = £8,000
Cost of forward contract = £4,500

Calculate Padd’s sterling receipt from the sale to DS if it:
a) does not hedge the receipt and the Indian rupee weakens by 1% by 30 June 20X4

Answer 13

Sterling receipt at spot rate = INR200,000,000/95.4930 = £2,094,394

A) INR200,000,000/(95.4930 x 1.01) = INR200,000,000/96.4479 = £2,073,658

Question 14

Padd will send a large consignment of footwear to DS for sale in its shops across India. The price for this consignment is 200 million Indian rupees (INR), which will be payable by DS on 30 June 20X4.

You have been asked to prepare advice for the board and have obtained the following information at the close of business on 31 March 20X4:

Spot rate (INR/£) = 94.0625 - 95.4930
Sterling interest rate (lending) = 3.2% pa
Sterling interest rate (borrowing) = 4.0% pa
INR interest rate (lending) = 4.2% pa
INR interest rate (borrowing) = 4.8% pa

Three-month OTC currency call option on INR - exercise price = INR 94.7500/£
Three-month OTC currency put option on INR - exercise price = INR 95.5500/£

Three-month forward rate discount (INR/£) = 0.0195 - 0.2265

Cost of relevant OTC currency option = £8,000
Cost of forward contract = £4,500

Calculate Padd’s sterling receipt from the sale to DS if it:
b) Uses an OTC Currency Option

Answer 14

Option (@ exercise price)

INR200,000,000/95,5500 = £2,093,145
Less cost: (8,000)
—–
£2,085,145

Question 15

Padd will send a large consignment of footwear to DS for sale in its shops across India. The price for this consignment is 200 million Indian rupees (INR), which will be payable by DS on 30 June 20X4.

You have been asked to prepare advice for the board and have obtained the following information at the close of business on 31 March 20X4:

Spot rate (INR/£) = 94.0625 - 95.4930
Sterling interest rate (lending) = 3.2% pa
Sterling interest rate (borrowing) = 4.0% pa
INR interest rate (lending) = 4.2% pa
INR interest rate (borrowing) = 4.8% pa

Three-month OTC currency call option on INR - exercise price = INR 94.7500/£
Three-month OTC currency put option on INR - exercise price = INR 95.5500/£

Three-month forward rate discount (INR/£) = 0.0195 - 0.2265

Cost of relevant OTC currency option = £8,000
Cost of forward contract = £4,500

Calculate Padd’s sterling receipt from the sale to DS if it:
c) Uses a forward contract

Answer 15

INR200,000,000/(95,4930 + 0.2265) = INR200,000,000/95.7195 = £2,089,438
Less cost: (4,500)
—-
£2,084,938

Question 16

Padd will send a large consignment of footwear to DS for sale in its shops across India. The price for this consignment is 200 million Indian rupees (INR), which will be payable by DS on 30 June 20X4.

You have been asked to prepare advice for the board and have obtained the following information at the close of business on 31 March 20X4:

Spot rate (INR/£) = 94.0625 - 95.4930
Sterling interest rate (lending) = 3.2% pa
Sterling interest rate (borrowing) = 4.0% pa
INR interest rate (lending) = 4.2% pa
INR interest rate (borrowing) = 4.8% pa

Three-month OTC currency call option on INR - exercise price = INR 94.7500/£
Three-month OTC currency put option on INR - exercise price = INR 95.5500/£

Three-month forward rate discount (INR/£) = 0.0195 - 0.2265

Cost of relevant OTC currency option = £8,000
Cost of forward contract = £4,500

Calculate Padd’s sterling receipt from the sale to DS if it:
d) Uses a Money Market Hedge

Answer 16

Borrow in rupees: INR200,000,000/1.012 = INR 197,628,450

Convert @ spot rate = 95.4930
197,628,450 / 95.4930 = £2,069,560

Lend in sterling = 2,069,560 x 1.008
= £2,086,116

Question 17

Advise Padd’s board whether it is worth hedging the DS receipt (ideas)

Answer 17

• Padd’s directors’ attitude to risk is important
• The interest rates and the forward rate discount suggest that the rupee will weaken. A weaker rupee will produce less sterling on conversion, so hedging may be worthwhile
• The worst-case scenario from 28.1 is if the rupee weakens by 1% over the next three months
• The MMH (which would give a fixed sterling amount) gives the highest sterling figure, followed closely by the OTC option, with which there is some flexibility for the directors
• The forward contract (which would also give a fixed sterling amount) produces a comparatively poor sterling remittance, It has a high arrangement fee,
• Were sterling to remain at spot rate, then this would give the best outcome and a strengthening of the rupee would enhance the sterling receipt even more

Question 18

On 1 April 20X3 Padd borrowed £8.5 million over a four-year period at SONIA + 1% pa to finance an expansion of its production capacity and the refurbishment of a number of its larger stores.

Padd’s board is now investigating whether it should hedge against adverse interest rate movements over the next 12 months. Its bank has offered either (a) an option at 4% pa plus a premium of 0.75% of the sum borrowed or (b) a Forward Rate Agreement (FRA) at 4.5% pa.

By preparing suitable interest payment calculations, recommend to Padd’s board whether it is worth hedging against interest rate movements over the next 12 months if SONIA is either (a) 3% or (b) 6%

Answer 18

SONIA + 1
Option
4%
Exercise? - Indifferent
Rate (4%)
Premium (0.75%)
–
4.75%
Annual interest payment (£8.5m) = £403,750

7%
Exercise? Yes
4%
Exercise? - Indifferent
Rate (4%)
Premium (0.75%)
–
4.75%
Annual interest payment (£8.5m) = £403,750

FRA

Pay at SONIA+1 (4%)
(Payment to)/receipt from bank (0.5%)
(4.5%)
—
Annual interest payment (on £8.5m) = (382,500)

Pay at SONIA+1 (7%)
(Payment to)/receipt from bank 2.5%
(4.5%)
—
Annual interest payment (on £8.5m) = (382,500)

No hedge:
Pay at SONIA+1 on £8.5m
4% = (340,000) pa
7% = (595,000) pa

If SONIA is 3% then it’s better not to hedge and at 6% the FRA seems to be the cheapest option
It also depends on the board’s attitude to risk

The FRA eliminates down side risk (rates rising) as well as upside risk (rates falling)

Question 19

Due to increases in the level of trade conducted in the USA, Lambourn’s finance director is now considering the use of a variety of hedging instruments

Receipts and payments in respect of the following exports and imports (designated in the currencies shown) are due in six months’ time:

Receipts due from exports to:
- Biotron Inc : $600,000
- Hope Inc: £400,000
- USMed Inc: $200,000

Payments due on imports from:
- Biotron Inc: $1,100,000
- Hope Inc: £900,000
- USMed Inc: $1,250,000

Exchange rates at the present time are as follows:
- Spot: $1.6666 - 1.6720/£
- 3-month forward premium: 0.90c - 0.98c
- 6-month forward premium: 2.49c - 2.65c

Sterling currency options (standard contract size £10,000) are currently priced as follows (with premiums, payable up front, quoted in cents per £)

Strike Price: $1.63
Calls: September = 3.67, December = 4.59
Puts: September = 0.06, December = 1.69

Strike Price: $1.65
Calls: September = 2.35, December = 3.07
Puts: September = 1.63, December = 3.43

Strike Price: $1.67
Calls: September = 1.82, December = 2.65
Puts: September = 2.04, December = 5.55

Sterling currency futures (standard contract size £62,500) are currently priced as follows:
September: $1.6555/£
December: $1.6496/£

Annual borrowing and deposit interest rates at the present time are as follows:
- Sterling: 3.00% - 1.70%
- Dollar: 1.50% - 0.50%

Requirements:
Assuming the spot rate in six months’ time will be $1.6400 - 1.6454/£, calculate Lambourn’s net foreign currency exposure, and the outcome achieved, using:
A) A forward market hedge

Answer 19

Lambourn’s net foreign currency exposure is the net $ payment due = $1,550,000

The sterling payments and receipts can be ignored

The forward rate would be 1.6666 - 0.0249 = $1.6417/£

The cost of the payment would therefore be 1,550,000/1.6417 = £944,143

Question 20

Due to increases in the level of trade conducted in the USA, Lambourn’s finance director is now considering the use of a variety of hedging instruments

Receipts and payments in respect of the following exports and imports (designated in the currencies shown) are due in six months’ time:

Receipts due from exports to:
- Biotron Inc : $600,000
- Hope Inc: £400,000
- USMed Inc: $200,000

Payments due on imports from:
- Biotron Inc: $1,100,000
- Hope Inc: £900,000
- USMed Inc: $1,250,000

Exchange rates at the present time are as follows:
- Spot: $1.6666 - 1.6720/£
- 3-month forward premium: 0.90c - 0.98c
- 6-month forward premium: 2.49c - 2.65c

Sterling currency options (standard contract size £10,000) are currently priced as follows (with premiums, payable up front, quoted in cents per £)

Strike Price: $1.63
Calls: September = 3.67, December = 4.59
Puts: September = 0.06, December = 1.69

Strike Price: $1.65
Calls: September = 2.35, December = 3.07
Puts: September = 1.63, December = 3.43

Strike Price: $1.67
Calls: September = 1.82, December = 2.65
Puts: September = 2.04, December = 5.55

Sterling currency futures (standard contract size £62,500) are currently priced as follows:
September: $1.6555/£
December: $1.6496/£

Annual borrowing and deposit interest rates at the present time are as follows:
- Sterling: 3.00% - 1.70%
- Dollar: 1.50% - 0.50%

Requirements:
Assuming the spot rate in six months’ time will be $1.6400 - 1.6454/£, calculate Lambourn’s net foreign currency exposure, and the outcome achieved, using:
b) Exchange-traded currency options (hedging to the nearest whole number of contracts) so as to guarantee no worse an exchange rate than the current spot rate

Answer 20

The current spot rate is $1.6666/£ so Lambourn should buy December put options on £ with a strike price of $1.67 as $1.65/£ and $1.63/£ are worse than the current spot rate.

Number of contracts = $1,550,000/1.67/10,000 = 92.8 = 93 contracts

Premium = 93 x 10,000 x 0.0555 = $51,615 at spot ($1.6666) would cost £30,970

Outcome if the spot rate is $1.6400/£: Exercise the option

Option $1.67 Spot $1.64 so profit of ($0.03 x 93 x 10,000) = $27,900

Convert $1,550,000- - $27,900 = $1,522,100/1.64 = £928,110 + £30,970 = £959,080

Question 21

Due to increases in the level of trade conducted in the USA, Lambourn’s finance director is now considering the use of a variety of hedging instruments

Receipts and payments in respect of the following exports and imports (designated in the currencies shown) are due in six months’ time:

Receipts due from exports to:
- Biotron Inc : $600,000
- Hope Inc: £400,000
- USMed Inc: $200,000

Payments due on imports from:
- Biotron Inc: $1,100,000
- Hope Inc: £900,000
- USMed Inc: $1,250,000

Exchange rates at the present time are as follows:
- Spot: $1.6666 - 1.6720/£
- 3-month forward premium: 0.90c - 0.98c
- 6-month forward premium: 2.49c - 2.65c

Sterling currency options (standard contract size £10,000) are currently priced as follows (with premiums, payable up front, quoted in cents per £)

Strike Price: $1.63
Calls: September = 3.67, December = 4.59
Puts: September = 0.06, December = 1.69

Strike Price: $1.65
Calls: September = 2.35, December = 3.07
Puts: September = 1.63, December = 3.43

Strike Price: $1.67
Calls: September = 1.82, December = 2.65
Puts: September = 2.04, December = 5.55

Sterling currency futures (standard contract size £62,500) are currently priced as follows:
September: $1.6555/£
December: $1.6496/£

Annual borrowing and deposit interest rates at the present time are as follows:
- Sterling: 3.00% - 1.70%
- Dollar: 1.50% - 0.50%

Requirements:
Assuming the spot rate in six months’ time will be $1.6400 - 1.6454/£, calculate Lambourn’s net foreign currency exposure, and the outcome achieved, using:
c) Currency futures contracts (hedging to the nearest whole number of contracts) and assuming the relevant futures contract is trading at $1.6400 in six months’ time

Answer 21

Sell December futures @ 1.6496

$1,550,000/1.6496 = £939,622

Therefore 939,622/62,500 = 15.03 = 15 contracts

Futures market outcome:
Sell at 1.6496
Buy at 1.6400
—
Profit: 0.0096 x 15 x 62,500 = $9,000

Spot market outcome: Buy $1,541,000 @ $1.6400/£ = £939,634

Question 22

Due to increases in the level of trade conducted in the USA, Lambourn’s finance director is now considering the use of a variety of hedging instruments

Receipts and payments in respect of the following exports and imports (designated in the currencies shown) are due in six months’ time:

Receipts due from exports to:
- Biotron Inc : $600,000
- Hope Inc: £400,000
- USMed Inc: $200,000

Payments due on imports from:
- Biotron Inc: $1,100,000
- Hope Inc: £900,000
- USMed Inc: $1,250,000

Exchange rates at the present time are as follows:
- Spot: $1.6666 - 1.6720/£
- 3-month forward premium: 0.90c - 0.98c
- 6-month forward premium: 2.49c - 2.65c

Sterling currency options (standard contract size £10,000) are currently priced as follows (with premiums, payable up front, quoted in cents per £)

Strike Price: $1.63
Calls: September = 3.67, December = 4.59
Puts: September = 0.06, December = 1.69

Strike Price: $1.65
Calls: September = 2.35, December = 3.07
Puts: September = 1.63, December = 3.43

Strike Price: $1.67
Calls: September = 1.82, December = 2.65
Puts: September = 2.04, December = 5.55

Sterling currency futures (standard contract size £62,500) are currently priced as follows:
September: $1.6555/£
December: $1.6496/£

Annual borrowing and deposit interest rates at the present time are as follows:
- Sterling: 3.00% - 1.70%
- Dollar: 1.50% - 0.50%

Requirements:
Assuming the spot rate in six months’ time will be $1.6400 - 1.6454/£, calculate Lambourn’s net foreign currency exposure, and the outcome achieved, using:
d) A money market hedge

Answer 22

Lambourn requires $1,550,000 in six months’ time - the company therefore needs to deposit $1,546,135 now (1,550,000/1.0025)

To buy $1,546,135 now will cost £927,718 (1,546,135/1.6666)

The cost of this payment with six months’ interest is £941,634 (927,718 x 1.015)

Question 23

Lambourn has sold a new range of pharmaceutical products to US Med Inc and is expecting to receive payment in two months’ time.

US Med Inc has stated that it will be making the payment using Bitcoin and has agreed to pay 50 Bitcoins on 30 August 20X2.

The directors are worried about the volatility of the Bitcoin price and are considering using the futures market to hedge the risk.

The current (spot) value of a Bitcoin is £8,500 and Bitcoin futures (standard contract size 5 Bitcoins) are currently priced as follows:

• July £8,450
• August £8,344
• September £8,100

Assuming that the market value (and futures value) for Bitcoin on 30 August is £6,500 explain how Bitcoin futures could be used to manage the price risk of Bitcoins nd calculate the outcome from the Bitcoin futures hedge.

Answer 23

Given that Lambourn are due to receive Bitcoin they should sell futures to protect the value of the transaction

Number of contracts = 50 (transaction size) / 5 (standard contract size) = 10 contracts

Lambourn should use August futures to cover the transaction date of 30 August

Step 1: Position in spot market

Loss on transaction = 50 bitcoin x (8,500 - 6,500) = £100,000

Step 2: Calculate gain or loss on futures

Buy futures at lower price than we sold them for (closing out).
The price to close out the position is £6,500

Initially committed to sell futures for £8,344
Now buy futures for £6,500
——–
Gain on closing out futures £1,844 x 5 Bitcoin x 10 contracts = £92,200

Step 3: Calculate net position

Net position = £92,200 gain on futures - £100,000 loss on spot = £7,800 loss overall

The final outcome is that 50 Bitcoin are received and sold at the spot rate of £6,500 per Bitcoin (50 x market price of £6,500 = £325,000) and compensation is received from the futures market (£92,200) so total revenue is £325,000 + £92,200 = £417,200

Question 24

In 6 months’ time (December 20X2), Lambourn will need to borrow £1.5million for a period of six months at a fixed rate of interest.
The company’s finance director is keen to ensure that the interest rate on the loan does not exceed 3.75% pa.
The spot rate of interest is currently 3% pa.
The finance director intends to use three-month sterling traded interest rate options on futures to hedge the company’s interest rate exposure.

The current schedule of prices (premiums are in annual % terms) for these contracts (standard contract size £500,000) is as follows:

Strike Price: 96.25
Calls: Sept = 0.20, Dec = 0.23, Mar = 0.25
Puts: Sept = 0.19, Dec = 0.96, Mar = 1.66

Strike Price: 96.50
Calls: Sept = 0.09, Dec = 0.10, Mar = 0.11
Puts: Sept = 0.32, Dec = 1.19, Mar = 1.89

Strike Price: 96.75
Calls: Sept = 0.05, Dec = 0.06, Mar = 0.07
Puts: Sept = 0.53, Dec = 1.43, Mar = 2.14

Calculate the outcome of the hedge and the effective annual rate of interest achieved if prices in December 20X2, when Lambourne negotiates the six-month fixed rate loan with its bank, are:
- A spot interest rate of 4.4% pa and a futures price of 95.31
- A spot interest rate of 2.1% pa and a futures price of 97.75

Answer 24

Contract: December
Contract type: Put option
Strike price: 96.25 (to cap the interest rate at 3.75% pa)
Number of contracts: £1.5m/£0.5m x 6/3 = 6 contracts
Premium = December put options at 96.25 = 0.96%

Therefore 6 x 0.96% x £500,000 x 3/12 = £7,200

Closing prices:
Case 1:
- Spot Price: 4.4%
- Futures price: 95.31

Outcome:
Options market:
Strike Price (sell) = 96.25
Closing price (buy) = 95.31
Exercise? Yes.
Gain on future = 0.94%
0.94% x £500,000 x 3/12 x 6 = £7,050

Net position:
Borrow at spot rate = 33,000
Gain from option = (7,050)
Option premium = 7,200
—-
£33,150

Interest rate = 33,150/1,500,000 x 12/6 = 4.42%pa

Case 2:
- Spot Price: 2.1%
- Futures price: 97.75

Outcome:
Options market:
Strike Price (sell) = 96.25
Closing price (buy) = 97.75
Exercise? No.
Gain on future = 0

Net position:
Borrow at spot rate = 15,750
Gain from option = (0)
Option premium = 7,200
—-
£22,950

Interest rate = 22,950/1,500,000 x 12/6 = 3.06%pa

Question 25

1) BE has been expanding in recent years by acquisition. David would like to know how his company might use traded options to protect itself against a fall in the value of the small shareholdings that it holds in potential acquisitions.

One such potential acquisition is Sickle Plc in which BE has a holding on 31 December 20X5

The following information is available:
On 31 December 20X5 the share price of Stickle is 287 pence (ex div) and traded options on its shares are available as follows (all figures in pence):

Exercise price; 2.80
Calls: Jan = 8.5, March = 16
Puts: Jan = 1.5, March = 10.5

Question 25

1) BE has been expanding in recent years by acquisition. David would like to know how his company might use traded options to protect itself against a fall in the value of the small shareholdings that it holds in potential acquisitions.

One such potential acquisition is Sickle Plc in which BE has a holding on 31 December 20X5

The following information is available:
On 31 December 20X5 the share price of Stickle is 287 pence (ex div) and traded options on its shares are available as follows (all figures in pence):

Exercise price; 2.80
Calls: Jan = 8.5, March = 16
Puts: Jan = 1.5, March = 10.5