Sample Examination Paper

Notes on the Sample Final Examination Script 

The final exam for the course will take the form illustrated in the sample exam following this page.



Examinable material includes everything that has been covered in either the lectures or tutorials during the whole semester.



Many of the questions are discussed and included in the class activities and so you should have access to most of the answers.

Sample Examination Paper OPTIONS FUTURES AND RISK MANAGEMENT Official Reading Time: Writing Time: Total Duration

10 mins 180 mins 190 mins

Instructions to Candidate: 1. Answer ALL questions. 2. You should answer all questions in the answer book(s). No attachments will be considered. If you used an additional book, please incorporate it within the first book. 3. Please allocate your time according to the percentage contribution of the questions. 4. You should answer Section A questions (multiple-choice) on the first writing page of the answer book and start each Section B question on a new page in the answer book. Please label your answers appropriately and show sufficient workings for all Section B questions. 5. Please submit this examination question paper with your answer book at the end of the examination. Examination materials must NOT be removed from the examination room. Materials: 

This is a Closed Book examination. No textbook is allowed.



A calculator incapable of storing text is permitted.

Special Instructions: 1. Unless otherwise instructed, assume continuous compounding/discounting for all calculations 2. Unless otherwise stated, contract multipliers for options and futures are assumed to be on a 1:1 ratio.

PLEASE DO NOT COMMENCE WRITING UNTIL INSTRUCTED TO DO SO

PLEASE SEE NEXT PAGE

SECTION A Answer all questions. Where appropriate, be sure to show your solutions in the answer booklet. 15 Multiple Choice Questions

[30 Marks] – 2 Marks Each

1. The following diagram shows the value of a put option at expiration:

4 Long Put Exercise price of both Options

Option Value

0 Short Put -4 76

80 Stock Price ($)

Ignoring transaction costs, which of the following statements about the value of the put option at expiration is TRUE? A. B. C. D.

The value of the short position in the put is $4 if the stock price is $76. The value of the long position in the put is –$4 if the stock price is $76. The long put has value when the stock price is below the $80 exercise price. The value of the short position in the put is zero for stock prices equalling or exceeding $76.

2. Which of the following statements about the value of a call option at expiration is FALSE? A. The short position in the same call option can result in a loss if the stock price exceeds the exercise price. B. The value of the long position equals zero or the stock price minus the exercise price, whichever is higher. C. The value of the long position equals zero or the exercise price minus the stock price, whichever is higher. D. The short position in the same call option has a zero value for all stock prices equal to or less than the exercise price.

3. Which of the following statements about “short selling” is TRUE? A. B. C. D.

A short position may be hedged by writing call options. A short position may be hedged by purchasing call options. Short sellers may be subject to margin calls if the stock price increases. Stocks that pay large dividends should be sold short before the ex-dividend date and bought afterward to take advantage of the large price decline in a short time period.

4. The current price of an asset is 75. A three-month, at-the-money American call option on the asset has a current value of 5. At what value of the asset will a covered call writer break even at expiration? A. B. C. D.

70. 75. 80. 85.

5. A silver futures contract requires the seller to deliver 5,000 Troy ounces of silver. An investor sells one July silver futures contract at a price of $8 per ounce, posting a $2,025 initial margin. If the required maintenance margin is $1,500, the price per ounce at which the investor would first receive a maintenance margin call is closest to: A. B. C. D.

$5.92. $7.89. $8.11. $10.80.

6. Which of the following statements about an American call is not true? A. B. C. D. E.

Its time value decreases as expiration approaches Its maximum value is the stock price It can be exercised prior to expiration It pays dividends none of the above

7. When puts are priced with the binomial model, which of the following is true? A. B. C. D. E.

the puts must be American the puts cannot be properly hedged the puts will violate put-call parity the hedge ratio is one throughout the tree none of the above

8. When the number of time periods in a binomial model is large, what happens to the binomial probability of an up move? A. B. C. D. E.

it approaches 1.0 it approaches zero it fluctuates without pattern it converges to .5 none of the above

9. If the stock price is 44, the exercise price is 40, the put price is 1.54, and the BlackScholes price using .28 as the volatility is 1.11, the implied volatility will be A. B. C. D. E.

higher than .28 lower than .28 .28 lower than the risk-free rate none of the above

10. What would be the spot price if a stock index futures price were $75, the risk-free rate were 10 percent, the dividend yield 3 percent, and the futures expires in three months? A. B. C. D. E.

$73.70 $77.48 $72.60 $76.32 none of the above

11. Find the profit if the investor buys a July futures at 75, sells an October futures at 78 and then reverses the July futures at 72 and the October futures at 77. A. B. C. D. E.

-3 -2 2 1 none of the above

12. Find the price of an American call option on a futures if the current spot price is 30, the exercise price is 25, the futures price is 33.70, the risk-free interest rate is 6 percent, the spot asset can go up by 10 percent or down by 8 percent per period and the call expires in two periods, which is also when the futures expires. A. B. C. D. E.

9.98 8.70 7.73 8.22 none of the above

13. A firm that has a sum of money denominated in a foreign currency that plans to later convert it to dollars could hedge by which of the following methods. A. B. C. D. E.

a call on the foreign currency a long futures or forward on the foreign currency a short put on the foreign currency futures all of the above none of the above

14. What is the lower bound of a European call on a futures contract where f0 is the futures price and X is the exercise price? A. B. C. D. E.

the difference between f0 and X zero the present value of the difference between f0 and X the ratio of f0 to X none of the above

15. When referring to futures markets, a short hedge is one in which A. B. C. D. E.

the margin requirement is waived the hedger is short futures the hedger is short in the spot market the futures price is lower than the spot price none of the above

SECTION B Answer all questions. Show your worked-out solutions in the answer booklet. 4 Long-Answer questions [35 marks] QUESTION 1

[7 MARKS]

You are a portfolio manager holding the following Australian stocks on 1st October. The number of shares, and the betas are as follows:

Stock

Shares

Price

Beta

Goodday Inc. Goodnight Ltd. Hello Ltd. The End Inc.

4000 8310 4300 7500

$62.625 $24.5 $47.875 $32.125

1.2 1.05 0.95 1.15

The portfolio is to be liquidated on 30 November. However, you believe that the Australian market will rally during October and November and would like to increase the beta to 1.3. A. Construct transactions that will increase the beta of the portfolio to 1.3 using one or more of these December futures contracts: S&P 500 futures, which are currently trading at 151. SPI 200 futures, which are currently trading at 373. Goodday Inc. futures, which are currently trading a 394. All prices are in Australian dollars and assume all futures contracts have a contract multiplier of $250 per index point. [4 marks] B. Identify two alternative methods (other than selling securities from the portfolio or using futures) that replicates the feature strategy in Part a. Contrast each of these methods with the futures strategy. [3 marks]

QUESTION 2

[7 MARKS]

The current December SPI 200 futures contract is at 3301. The ASX 200 is at 3305.4. The current 30-day bank bill is at 4.492%. A. If there are 45 days remaining until December 2001 futures contracts expire, determine whether put-call parity is maintained for the December call & put options on SPI 200 futures with the exercise price closest to the current SPI 200 price. [4 marks]

B. If put-call parity is not maintained, explain the possible reasons why it might not be. [3 marks]

QUESTION 3 [12 MARKS] You are a fund manager for high net-wealth clients. One of your clients expects short-term interest rates to remain low over the coming year and expects equities to offer a significantly higher return. The investor wants to shift some funds from cash to equities. The investor currently holds a portfolio of money market assets. A. Detail 3 possible solutions available to the client to achieve her aims, along with the advantages/disadvantages associated with each method. One of these solutions should be a swap contract. [4.5 marks] B. The client decides to enter into a one-year equity swap where the counterparty agrees to pay the investor the total return to the stock index in exchange for dollardenominated Libor on a quarterly basis. The Exhibit below summarizes the mechanics of the swap assuming that on settlement date the stock index is at 640, dividends are 3.30 index points each quarter, and current 90-day Libor is 3.25% and the notional amount of the contract is $1,000,000. Each quarter contains 91 days.

Fill in the missing values from the cash flow schedule below:

[4 marks] C. What is the total incremental return for the above swap?

[1.5 marks]

D. Swaps can be viewed as an amalgamation of a number of alternate financial instruments. What type of portfolio of financial instruments is the above swap replicating? What benefits are there from using the swap over the alternative? [2 marks]

QUESTION 4 [9 MARKS] A. The current price of gold is $300 per ounce. Carrying costs in total are 0.5% (not including interest) of the gold value payable in 6 months time. If the interest rate is 8%, is there an arbitrage opportunity if the gold futures price for delivery in six months is $310 per ounce? [3 marks]

B. If an arbitrage opportunity exists, explain how you would conduct it and calculate the arbitrage profit. [2 marks] C. Why is it not possible in reality to perfectly hedge a portfolio using Options and/or futures Instruments? [2 marks] D. Explain the shortcomings of LTCM’s financial strategy that led to its eventual downfall. [2 marks]

END OF EXAMINATION QUESTIONS.