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Finance 362 – Revision Questions: Topic 1

Multiple Choice Questions

1. Financial risk management can increase the value of the firm by:

(a) increasing the discount rate.

(b) ensuring that the firm has sufficient funds to fund profitable investment projects

(c) increasing the direct costs of financial distress

(d) increasing the indirect costs of financial distress.

2. A rise in jet fuel prices, all other things being equal, is likely to:

(a) have no effect on the value of an airline

(b) raise the value of an airline

(c) lower the value of an airline

(d) raise or lower the value of an airline.

3. Market participants who buy and sell risk management products to offset risk exposures in the spot market are referred to as:

(a) hedgers

(b) speculators

(c) arbitrageurs

(d) brokers.

4. Market participants who earn riskless profits from the mispricing of contracts are referred to as:

(a) speculators

(b) hedgers

(c) arbitrageurs

(d) brokers.

5. Which ONE of the following risk management products is traded solely on an organised exchange?

(a) swap contracts

(b) OTC currency options

(c) foreign exchange forward contracts

(d) futures contracts.

Practice Questions

1. Explain the difference between hedging and speculation.

2. An airline executive has argued: “There is no point in our using oil futures. There is as much chance that the price of oil in the future will be less than the futures price as there is that it will be greater than this price.” Discuss the executive’s viewpoint.

Finance 362 – Revision Questions: Topic 2

Multiple Choice Questions

1. Forward contracts are usually settled:

(a) on initiation

(b) one month after initiation

(c) one month prior to delivery date

(d) at delivery date.

2. An exporter anticipating receiving USD 10 million in two month’s time enters into a forward contract to sell the US dollar into New Zealand dollars at a forward rate of NZD1 = USD0.8000. On the day the forward contract is settled the spot rate of the New Zealand dollar is NZD1 = USD0.8500. The New Zealand dollar proceeds from the forward transaction are:

(a) NZD11.765 million

(b) NZD8.500 million

(c) NZD12.500 million

(d) NZD8.000 million

3. The acronym “FRA” stands for:

(a) foreign rate arrangement

(b) foreign rate agreement

(c) forward rate agreement

(d) future rate agreement

4. Forward exchange and FRA contracts are a popular form of hedging with many companies because they:

(a) can be customised to suit the companies needs

(b) do not oblige companies to make delivery of the underlying asset

(c) do not involve any counterparty risk

(d) can be easily traded in a secondary market.

Use the following information to answer Questions 5 to 7.

A company plans to issue 90 day bank bills with a face value of $1 million in two month’s time. The treasurer enters into a 2X5FRA at a contract rate of 5.5% to hedge the interest rate risk. The bank bills are issued in two month’s time on the day the FRA is settled when the 90 day bank bill rate is 6.5%.

5. The settlement amount on a 2X5FRA on a face value of $1 million bought at a contract rate of 5.5% and settled at a market rate of 6.5% is:

(a) $2,394.38

(b) $10,985.81

(c) $13,380.19

(d) $15,774.57

6. The effective interest payment on the borrowing (i.e. the discount on the bills issued plus/minus the settlement amount of the FRA) is:

(a) $10,985.81

(b) $13,380.19

(c) $15,774.57

(d) $18,168.95

7. The effective interest rate on the borrowing is:

(a) 7.50%

(b) 6.50%

(c) 5.50%

(d) 4.50%

8. The margin payment cash flow that arises from the daily mark-to-market is referred to as the:

(a) maintenance margin

(b) variation margin

(c) mark-to-market margin

(d) performance margin.

9. What organisational feature of futures trading reassures the buyer and seller of a futures contract that the obligations of the other party will be fulfilled?

(a) standardisation of contracts

(b) a defined contract maturity date

(c) the margining system

(d) restricted membership of the exchange

10. “Open interest” is measured as:

(a) total long or total short positions

(b) total short positions minus total long positions

(c) total long positions minus total short positions

(d) total long plus total short positions.

11. In general, what proportion of futures positions result in the trader making or taking delivery of the underlying commodity?

(a) 100%

(b) more than 90%

(c) about 50%

(d) less than 10%

12. Which ONE of the following statements is true?

(a) The futures prices approaches zero as expiration date approaches.

(b) Futures and spot prices converge as futures expiration date approaches.

(c) The basis approaches unity as futures expiration date approaches.

(d) Futures contracts have non-linear payoffs.

13. What is the duration of a 90-day bank bill with a face value of $1 million when 90-day bank bill yields are 4.0% p.a.?

(a) 0.2565 years

(b) 0.2500 years

(c) 0.2367 years

(d) 0.2466 years.

14. A one-year treasury bond with a face value of $100 carrys a 6% coupon, paid semi-annually. What is the price of the bond under zero coupon valuation when the six-month and one-year zero coupon rates are 2.5% and 3.0% respectively on a continuously compounded basis?

(a) $102.92

(b) $106.00

(c) $102.89

(d) $100.00.

15. What is the theoretical 2X5 FRA rate if two-month and five-month bank bills are yielding 2.50% and 2.75% respectively on a continuously compounded basis?

(a) 2.33%

(b) 2.92%

(c) 2.65%

(d) 2.60%.

Practice Questions

1. How do forward and futures contracts differ with respect to “delivery”?

2. Demonstrate how a 1X4FRA at 5.4% on a planned issue of bills with a face value of $5 million in one month’s time serves to hedge a borrower given that the 90-day bill rate on the day the bills are issued in one month’s time is 6%.

3. Explain how margins protect futures traders against the possibility of default.

4. The CMX gold futures contract is written on 100 troy ounces of gold. The initial margin is $1,000 per contract and the maintenance margin is $750 per contract.

Assume the following transactions occur between 6 July and 8 July in the September gold futures contract:

6 July A (buyer) and B (seller) trade 5 contracts at a price of $294.50

C (buyer) and B (seller) trade 10 contracts at a price of $294.00

7 July D (buyer) and A (seller) trade 10 contracts at a price of $293.50

B (buyer) and D (seller) trade 5 contracts at a price of $293.80

8 July B (buyer) and A (seller) trade 7 contracts at a price of $293.70

The closing (settlement) prices are $294.00 on 6 July, $293.80 on 7 July and $299.50 on 8 July.

(a) Assume the open interest in the September contract is 10,000 at the close of trading on 5 July. Calculate the open interest at the end of trading on the following three days.

(b) Compute the overall profit/loss of Trader A.

5. What is the difference between a long and a short futures position?

6. “When a futures contract is traded, it may be the case that the open interest increases by one, stays the same or decreases by one.” Explain this statement.

7. Suppose we observe prices for the following maturities of government stock:

Term (Years)	Coupon (% p.a.)	Face value	Price
1	8%, semi-annual coupon	$100	$99.00
2	8%, annual	$100	$98.75

The six-month zero rate is 7.6% p.a. continuously compounded.

(a) Calculate the one-year and two-year zero rates.

(b) Calculate the one-year forward rate next year, i.e. ₁f₂.

Use continuous discounting for all calculations in this question.

Finance 362 – Revision Questions: Topic 3

Multiple Choice Questions

1. The difference between price of a futures contract written on an asset and the spot price of the asset represents the:

(a) futures spread

(b) net cost of carry

(c) initial margin

(d) convenience yield.

2. If the “net cost of carry’ for an investment asset is negative:

(a) the futures price will exceed the spot price

(b) the forward price will be below the futures price

(c) the futures price will exceed the forward price

(d) the forward price will be below the spot price.

3. A commodity incurs lump storage costs of $10 per month paid at month end. What is the present value of the storage costs incurred over a three-month interval if all risk-free rates are 5% p.a. on a continuously compounded basis?

(a) $40.00

(b) $30.00

(c) $29.88

(d) $29.76.

4. If the spot price of oil is $60 per barrel, the riskfree rate is 4% p.a. (continuously compounded), storage costs are 2% p.a. (continuously compounded) of the oil’s value, the theoretical price of an oil futures contract with four months to expiration will be:

(a) $60.00

(b) $63.60

(c) $61.21

(d) $63.71.

5. Assume the S&P500 index is currently 625 points, the riskfree rate is 5% p.a. (continuously compounded), the continuous dividend yield on the basket of stocks comprising the index is 2% p.a., and the price of a futures contract on the S&P500 index with three months to expiration is 632.47 points. Which ONE of the following statements is true?

(a) The S&P500 futures contract is overpriced.

(b) The S&P500 futures contract is correctly priced.

(c) The S&P500 futures contract is underpriced.

(d) There is not enough information to determine whether the futures contract is correctly priced or not.

6. Six-month interest rates (continuously compounded) are 1.5% in the US and 4.5% in New Zealand and the current spot rate of the New Zealand dollar is NZD1 = USD0.8135. The theoretical six-month forward rate on the New Zealand dollar should be:

(a) USD0.8383

(b) USD0.8258

(c) USD0.8014

(d) USD0.7895

7. Three-month interest rates (continuously compounded) are 4.5% in the US and 6.75% in New Zealand and the three-month forward rate on the New Zealand dollar is NZD1 = USD0.6835. If the forward rate is correctly priced, then the current spot rate of the New Zealand dollar must be:

(a) USD0.6683

(b) USD0.6874

(c) USD0.6797

(d) USD0.6891

8. Under “cash and carry” arbitrage, the arbitrageur simultaneously:

(a) buys the commodity for immediate delivery in the spot market and sells the same commodity for delivery at a later date in the futures market

(b) buys the commodity for delivery at a later date in the forward market and sells the commodity for delivery at the same date in the futures market

(c) sells the commodity for immediate delivery in the spot market and buys the same commodity for delivery at a later date in the futures market

(d) sells the commodity for delivery at a later date in the futures market and buys the commodity for delivery at an earlier date in the futures market

9. Under “reverse cash and carry” arbitrage, the arbitrageur simultaneously:

(a) sells the commodity for immediate delivery in the spot market and buys the same commodity for delivery at a later date in the futures market

(b) buys the commodity for delivery at a later date in the forward market and sells the commodity for delivery at the same date in the futures market

(c) buys the commodity for immediate delivery in the spot market and sells the same commodity for delivery at a later date in the futures market

(d) sells the commodity for delivery at a later date in the futures market and sells the commodity for delivery at an earlier date in the futures market

10. If the price of the NZSX15 index futures contract exceeds its theoretical level an arbitrageur should be able to earn a riskless profit by:

(a) selling NZSX15 index futures and buying all the stocks in the NZSX15 index

(b) selling NZSX15 index futures contracts

(c) selling short all the stocks in the NZSX15 index and investing in treasury bills

(d) selling short all the stocks in the NZSX15 index and buying NZSX15 index futures

11. Which of the following “commodities” is most likely to provide a convenience yield to the holder?

(a) stocks

(b) wheat

(c) foreign exchange

(d) bonds

12. What is the theoretical price of a three-month futures contract written on a commodity selling in the spot market for $50 when the three-month risk-free rate is 3% p.a.(c.c.), storage costs are 5% p.a. (c.c.) and the commodity has a convenience yield to the holder valued at 12% p.a. (c.c.)?

(a) $48.52

(b) $48.77

(c) $49.50

(d) $61.07.

13. At the time a forward contract is entered into, the value of the contract is:

(a) the forward price

(b) the spot price

(c) the difference between the spot price and the forward price

(d) zero.

(a) -$1,487.55

(b) -$1,500

(c) -$1,518.87

(d) -$2,000

15. A hedger sells a three-month forward contract on 1,000 barrels of oil at $70 per barrel. One month later, the forward price is $73.50, the spot price is $75.00 and the risk-free rate (continuously compounded) is 4% p.a. What is the value of the forward contract?

(a) $3,500

(b) $3,476.90

(c) -$3,476.90

(d) -$3,500

Practice Questions

1. What is the difference between the price of a forward contract and the value of a forward contract?

2. What is the difference between an investment asset and a consumption asset? What implications does this have for the pricing of futures contracts on these assets?

3. A one-year forward contract on a non-dividend-paying stock is bought when the stock price is $40 and the risk-free rate of interest is 10% p.a. (continuously compounded).

(a) What are the theoretical forward price and initial value of the forward contract?

(b) Six months later, the price of the stock is $45 and the risk-free rate is still 10% (continuously compounded). What are the theoretical forward price and the value of the forward contract?

4. A two-year short forward contract on a non-dividend-paying stock is sold when the stock price is $25 and the risk-free rate is 12% (continuously compounded).

(a) What is the theoretical forward price and initial value of the contract?

(b) Fourteen months later, the price of the stock is $33 and the risk-free rate is still 12%. What are the theoretical forward price and the value of the forward contract?

5. Contact Energy is expected to pay a dividend of 15 cents per share in two months and 20 cents per share in eight months. The current stock price is $5.10 and the risk-free rate of interest is 8% p.a. (continuously compounded) for all maturities. An investor who holds the stock has just taken a short position in a twelve-month forward contract on the stock.

(a) What are the theoretical forward price and initial value of the forward contract?

(b) Six months later the price of the stock is $4.40 and the risk-free rate of interest is 9.00% p.a. (continuously compounded). What are the forward price and value of the short position in the forward contract?

6. Consider two silver forward contracts. Each contract is based on 5,000 ounces of silver. The first silver contract expires in exactly three months, and the forward price is quoted at $4.70 per ounce. The second silver contract expires in exactly six months, and the forward price is quoted at $4.90. The riskfree rate is 8% p.a. (continuously compounded) for all maturities. Assume that this riskfree rate will not change over the next six months and that storage costs and convenience yields are both zero.

(a) Suppose the quoted three-month futures is correctly priced. Calculate the theoretical price for the six-month futures contract.

(b) Given the quoted prices, describe how you could form an arbitrage portfolio using only the two futures contracts (You cannot buy or sell silver in the initial formation of your arbitrage portfolio). What is your arbitrage profit?

7. A crude oil futures contract has a size of 42,000 gallons. The spot price of crude oil is $30 per barrel and the risk-free rate is 6% p.a. (continuously compounded). Assume that there is a $1.00 per barrel per six-month storage cost that is payable in advance, and that the convenience yield is 4% p.a. (continuously compounded). Calculate the theoretical price for the six-month crude oil futures.

Finance 362 – Revision Questions: Topic 4

Multiple Choice Questions

Use the following information to answer Questions 1 to 3.

A copper producer plans to sell 1,000 tonnes of copper next month in the spot market. The treasurer is worried that the spot price might decline before the sale is made and is considering using copper futures to hedge this price risk. The current spot price of copper is $7,500 per tonne and the price of the futures contract expiring next month is $7,550 per tonne. Each futures contract is written on 100 tonnes of copper.

1. If the treasurer follows a naïve hedging strategy, what position should she establish in the nearby futures contract?

(a) a long position of 1,000 contracts

(b) a short position of 1,000 contracts

(c) a short position of 10 contracts

(d) a long position of 10 contracts

2. If the treasurer establishes the correct position in the futures market today and closes out the position next month at futures expiration date when the futures price is $7,280 per tonne, the futures position will show:

(a) a profit of $270,000

(b)  a loss of $220,000

(c) a profit of $220,000

(d)  a loss of $270,000

3. The effective sale price (per tonne) under the hedging strategy is:

(a) $7,280

(b) $7, 415

(c) $7,500

(d) $7,550

4. The basis risk associated with a futures hedge is likely to be negligible when:

(a) the hedge is an own hedge and is held to futures expiration.

(b) the hedge is a cross hedge and is liquidated prior to futures expiration.

(c) the hedge is an own hedge and is rolled over after delivery is made or taken.

(d) the hedge is a cross hedge and is held to futures expiration.

5. An oil refinery must buy a shipment of light sweet crude oil in mid-June 200X. The refinery decides to hedge the price risk in the futures market. Which of the following hedges is likely to give the greatest protection against price risk?

(a) a long hedge in NYMEX’s May 200X light sweet crude oil futures contract liquidated just before futures expiration.

(b) a long hedge in NYMEX’s July 200X light sweet crude oil futures contract liquidated in mid-June.

(c) a long hedge in NYMEX’s December 200X light sweet crude oil futures contract liquidated in mid-June.

(d) a long hedge in NYMEX’s July 200X Brent crude oil futures contract liquidated in mid-June.

Use the following information to answer Questions 6 and 7.

A copper producer plans to sell 800 tonnes of copper next month in the spot market. The treasurer is worried that the spot price might decline before the sale is made and is considering using copper futures to hedge this price risk. Each futures contract is written on 100 tonnes of copper. The standard deviations of the daily change in the spot price and nearby futures price are $22 and $31 respectively and the correlation between daily changes in spot and futures prices is 0.85.

6. The minimum variance hedge ratio is:

(a) 0.71

(b) 0.60

(c) 1.41

(d) 1.20

7. The optimal number of futures contracts the treasurer should sell (to 1 decimal place) is:

(a) 5.7

(b) 9.6

(c) 11.3

(d) 4.8

Contract	a	b	R2
X	0.01	0.03	0.84
Y	-0.02	1.11	0.81
Z	0.03	0.97	0.86

Which contract is likely to offer the greatest “hedging effectiveness”?

(a) contract X

(b) contract Y

(c) contract Z

(d) Impossible to tell. Not enough information is provided.

Use the following information to answer Questions 9 and 10.

A fund manager has a stock portfolio with a beta of 1.2 currently valued at $10 million. The fund manager is worried that stock prices might decline over the next six months and seeks to hedge the price risk in the STX100 futures contract. The current level of the STX100 index is 620 points, the continuous dividend yield on the index is estimated at 2% p.a. and the riskfree rate is 5% p.a. (continuously compounded). The price of the STX100 index futures contract with six months to expiration is 629.37 points and the point value of the contract is $1,000.

9. To implement the “minimum variance” hedge the fund manager must:

(a) sell 15.9 STX100 futures contracts

(b) buy 13.4 STX100 futures contracts

(c) buy 19.1 STX100 futures contracts

(d) sell 19.1 STX100 futures contracts.

10. How many index futures contracts must the fund manager trade is she wishes to reduce the portfolio beta to 1?

(a) sell 3.2 STX100 futures contracts

(b) buy 16.1 STX100 futures contracts

(c) buy 6.2 STX100 futures contracts

(d) sell 15.9 STX100 futures contracts.

11. In general, selling index futures contracts will:

(a) raise the beta of a stock portfolio

(b) have no impact on the beta of a stock portfolio

(c) reduce the beta of a stock portfolio

(d) only raise the beta of stock portfolios with an initial beta below 1.

(a) a long position of two contracts

(b) a short position of ten contracts

(c) a short position of fifteen contracts

(d) a long position of five contracts.

Use the following information to answer Questions 13 and 14.

A fund manager plans to buy $2 million of two-year government stock in the bond tender scheduled for next month. The stock will carry a 7% coupon (paid semi-annually) and have a face value of $10,000. Government stock with maturities of five years or less are currently trading at a yield of 7%. The fund manager decides to hedge the price risk using the three-year government stock futures contract. This contract is based on a three-year government stock with $100,000 face value and 8% coupon (paid semi-annually). This contract is currently trading at a yield of 7%.

13. The duration of the two-year government stock planned for issue is:

(a) 1.9 years

(b) 2.0 years

(c) 2.8 years

(d) 3.0 years.

14. If the fund manager uses a duration-based hedging strategy, the number of three-year government stock futures contracts he should trade (to one decimal place) is:

(a) sell 29.5 three-year government stock futures contracts

(b) buy 295 three-year government stock futures contracts

(c) sell 300 three-year government stock futures contracts

(d) buy 13.6 three-year government stock futures contracts.