Exam 2018, questions and answers PDF

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SAMPLE FINAL EXAM QUESTIONS 1.

Derivative instruments have the following advantage: (a) They help control risk. (b) They have lower transaction costs than most other financial assets. (c) They aid in keeping spot prices close to their true values. (d) All of the above are advantages of derivative instruments

2.

The following derivative instrument(s) usually trades on an organized exchange: (a) Swap contracts (b) Forward contracts (c) Option contracts (d) All of the above derivative instruments trade on organized exchanges

3.

The basis of a futures contract strengthens unexpectedly. Which one of the following statements is true? (a) A short hedger’s position improves. (b) A short hedger’s position worsens. (c) A short hedger’s position sometimes worsens and sometimes improves. (d) A short hedger’s position stays the same.

4.

A futures trader has a short position in a copper futures contract with an initial margin of $6,000 and a maintenance margin of $4,500. If the trader’s balance is $4,200, what is the size of the required deposit? (a) $300 (b) $1,500 (c) $1,800 (d) $4,500 (e) None of the above

5.

The following are always clearly defined as standard delivery specifications of a futures contract. (a) What can be delivered. (b) Where it can be delivered. (c) When it can be delivered. (d) All of the above.

6.

Who determines when physical delivery will take place in a futures contract? (a) The party with the short position. (b) The party with the long position. (c) The exchange specifies the exact delivery date. (d) Either party can specify a delivery date.

7.

An FRA is considered to be similar to which of the following derivative securities? (a) A long call option (b) An interest rate floor (c) A forward contract (d) An interest rate swap

8.

A long call option cannot be closed out by the following transaction: (a) Exercise of the option (b) Offsetting transaction (c) Expiration out-of-the-money (d) A long put

9.

A stock index is currently at 700 and the futures price for a contract on the index deliverable in five months is priced at 710. The continuously compounded risk-free interest rate is 6% per annum and the dividend yield on the index is 3% per annum. The arbitrage opportunity available is? (a) Short the futures, long the shares underlying the index. (b) Long the futures, short the shares underlying the index. (c) Long the futures, long the shares underlying the index. (d) Short the futures, short the shares underlying the index.

10.

When an index call option is exercised, the long party will ____________. (a) buy all the stocks in the index in their appropriate index proportions (b) buy a put option to offset the call option (c) receive the cash difference between the index and the exercise price (d) none of the above

11.

Using put-call parity, a trader finds a European call option trading lower than that implied in the formula. What should the trader do? (a) Buy the call and the stock and sell the put and the risk-free bond (b) Buy the put and the stock and sell the call and the risk-free bond (c) Buy the call and the put and sell the stock and the risk-free bond (d) Sell the put and the stock and buy the call and the risk-free bond

12.

A company has a $36 million equity portfolio with a beta of 0.9. The S&P index futures price is currently trading at 900. Futures contracts on $250 times the index can be traded. What trade is necessary to increase the beta to 1.2? (a) Long 48 futures contracts (b) Long 144 futures contracts (c) Long 192 futures contracts (d) Long 262 futures contracts (e) None of the above

13.

Which of the following strategies has the greatest potential profit? (a) A covered call (b) A protective put (c) A short put (d) A long put

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14.

Which of the following statements is true? (a) A short position in a futures contract can be closed out by going long in an identical contract. (b) The marking-to-market of exchange traded futures contracts reduces the counterparty credit risk. (c) It is easier to close out a derivative position before maturity if it involves exchangetraded instruments. (d) The terms of contracts traded on exchanges are less flexible than what can be negotiated in an over-the-counter trade. (e) All of the above are true.

15.

Which one of the following statements concerning currency swaps is true? (a) Principals are not usually exchanged. (b) The principal amounts usually flow in the opposite direction to interest payments at the beginning of the swap and in the same direction as interest payments at the end of the swap. (c) The principal amounts usually flow in the same direction as interest payments at the beginning of the swap and in the opposite direction to interest payments at the end of the swap. (d) Principals are not usually specified.

16.

The current price of a stock is $75. A put option with a strike price of $70 is purchased along with the stock. If the breakeven point for this hedge is at a stock price of $82, then the value of the put option at the time of purchase was ________. (a) $5 (b) $7 (c) $12 (d) $14 (e) None of the above

17.

A stock is currently trading at $62. Which of the following statements is NOT true (a) A call option on the stock with strike of $70 is out-of-the-money (b) A put option on the stock with strike of $70 is in-the-money (c) A put option on the stock with strike of $40 is in-the-money (d) A call option on the stock with strike of $55 is in-the-money (e) A put option on the stock with strike of $55 is out-of-the-money

18.

An investor purchases a stock for $80 and simultaneously sells a call option on the stock with a strike price of $88 and a premium of $6. What is the maximum profit that the writer of this position can earn at expiration? (a) $6 (b) $12 (c) $14 (d) $20 (e) None of the above

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19.

A futures contract requires the seller to deliver 1,000 ounces of gold. An investor sells a gold futures contract at a price of $400 per ounce, posting a $10,500 initial margin. If the maintenance margin is $5,500, the price per ounce at which the investor would first receive a margin call is closest to: (a) $395 (b) $400 (c) $405 (d) $410 (e) None of the above

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Question 1 (3 + 2 = 5 marks) Define delta and gamma of an option and briefly discuss the advantage in creating a portfolio which is simultaneously delta and gamma neutral. Delta () of an option measures the rate of change in the price of the option with respect to the price of the underlying asset and the Gamma () of an option measures the rate of change in the delta of the option with respect to the price of underlying asset. Creating a portfolio which is simultaneously delta and gamma neutral can hedge the risk of small or large price movement.

Question 2 (5 marks) Under the terms of a currency swap, a company has agreed to receive a fixed interest rate of 10% per annum on an American dollar loan with a notional principal of $5 million. In exchange, the company will pay a fixed interest rate of 8% per annum on a Dutch Euro loan with a notional principal of €2.5 million. Net interest payments are exchanged every six months. The swap has a remaining life of thirteen months. The current interest rates are 7% per annum in America and 6% per annum in Holland. Assume both rates are with continuous compounding for all maturities (assuming a flat term structure). The current exchange rate is €1 = $2. Calculate the current value of the currency swap for the company in American dollars. Value of American payments (receive) $5 million * 10% * ½ = $250,000 $250,000e -0.07 *1/12 + $250,000e -0.07 * 7/12 + $5,250,000e -0.07 * 13/12 = $248,546 + $239,997 + $4,866,596 = $5,355,139 Value of Dutch payments (pay) €2.5 million * 8% * ½ = €100,000 €100,000e -0.06 * 1/12 + €100,000e -0.06 * 7/12 + €2,600,000e -0.06 * 13/12 = €99,501 + €96,560 + €2,436,375 = €2,632,436 Value of swap Receive: $5,355,139 Pay: €2,632,436 * $2 = $5,264,872 Net: $90,267

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Question 3 (5 marks) As an options trader, you constantly analyse the share market, looking for profitable opportunities. Currently you are unsure of the general equity market direction, but you anticipate very high volatility over the next few months. Shares in Baobab Limited trade at $30 and has the following six-month European options available: Strike price $25 $25 $30 $30 $35 $35

Option class Call Put Call Put Call Put

Option premium $6.07 $0.09 $2.31 $1.14 $0.53 $4.16

Construct a long straddle combination from the options listed above. Construct a table showing the profit and loss from the strategy and indicate the straddle on a pay-off diagram, showing all the details of the straddle and the options included in the strategy including the maximum profit possible under this strategy. One long position in a call option with strike price of 30; One long position in a put option with strike price of 30; Premium = – $2.31 – $1.14 = – $3.45 Stock price S < 30 S > 30

(1.14)

1 x LC (30) 0 S – 30

26.55

1 x LP (30) 30 – S 0

30

Premium (3.45) (3.45)

Total payoff 26.55 – S S – 33.45

33.45

(2.31) (3.45)

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Question 4 (5 marks) The current futures price is $105 with an historical volatility of 10% per annum. The risk-free interest rate is 8% per annum with continuous compounding. Using a two-step binomial tree (the risk-neutral method) calculate the value of a six-month European call futures option with a strike price (exercise price) of $100. F0 = $105, K = $100, r = 8% & t = 0.25 per step u = e 0.10 √0.25 = 1.0513 d = e -0.10 √0.25 = 0.9512 $116.05 $110.39 $105

$105 $99.88 $95.01

p = (1 – d) / (u – d) p = (1 – 0.9512) / (1.0513 – 0.9512) p = 0.4875 $116.05f = max {FT – K, 0} = $116.05 – $100 = $16.05 (fu) $110.39 $105

f = max {FT – K; 0} = $105 – $100 = $5 (fd)

f = e –rT [pfu + (1 – p)fd] f = e –0.08 x 0.25 [(0.4875 x $16.05) + (0.5125 x $5] f = $10.18 $105

f = max {FT – K, 0} = $105 – $100 = $5 (fu)

$95.01

f = max {FT – K; 0} = $95.01 – $100 = $0 (fd)

$99.88

f = e –rT [pfu + (1 – p)fd] f = e –0.08 x 0.25 [(0.4875 x $5) + (0.5125 x $0] f = $2.39 $110.39f = $10.18 (fu) $105 $99.88

f = $2.39 (fd)

f = e –rT [pfu + (1 – p)fd] f = e –0.08 x 0.25 [(0.4875 x $10.18) + (0.5125 x $2.39] f = $6.07

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Question 5 (5 marks) The current level of the S&P250 market index is 950. Using the Black-Scholes option pricing model, calculate the price of a six-month European call option with a strike (exercise) price of 700. The dividend yield of the index is 2% per annum. The risk-free interest rate is 6% per annum with continuous compounding and the share price volatility is 15% per annum. S0 = 950; K = 700; T = 0.5; r = 6%; q = 2%; σ = 15%

d1 

ln(S 0 / K )  ( r  q   2 / 2)T  T

d1 

ln(950 / 700)  (0.06  0.02  0.152 / 2)0.50 0.15 0.50

d1 = 3.1199 N(d1) = 0.9991

d 2  d1   T d 2  3.1199  0.15 0.50 d2 = 3.0138 N(d2) = 0.9987 c = S0e-qT N(d1) – Ke-rT N(d2) c = (9500e-0.02 x 0.50 x 0.9991) – (700e-0.06 x 0.50 x 0.9987) c = 939.70 – 678.43 c = 261.27

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Question 6 (2 marks) Sketch the delta of a put option as a function of the underlying asset price. Be sure to indicate the behaviour of delta in the region of the exercise (strike) price.

K 0.0

Asset price

-1.0 Delta

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Question 7 (5 marks) A dividend paying stock is trading at $37 and the term structure of interest rates is flat at 6% with continuously compounded. Assume that a dividend of 0.50 is expected after six months. A European call option on this stock with strike $40 expiring in 18 months is trading at $2. A European put option with the same strike and maturity is trading at $1.25. How can you make a riskless profit?  Put-call parity: c + Ke -rT = 2 + 40 e -0.06 x 18/12 = $38.5573 p + S0 - D = 1.25 + 37 -0.4852 = $37.7648 $38.5573 (overvalued) < $37.7648 (undervalued) Difference = $0.7925 There is an arbitrage opportunity. A risk-less profit of $0.7925 can be made today. Today:  Borrow $36.25 (= 37 + 1.25 – 2) at 6% for 18 months to  Buy the stock at $37  Buy the put option for $1.25  short the call option for $2 After six months: Receives the dividend of $0.50 and invest it for 1 year at 6% After 18 months:  If S > $40, the short call is in-the-money, the long put is out-of-the-money, thus have the obligation to sell stock at $40. If S < $40, the long put is in-the-money, the short call is out-of-the-money, thus have the right to sell stock at $40.  Collect dividend investment of $0.50 e 0.06 x 1 = $0.5309  Repay the loan $36.25 e 0.06 x 18/12 = $39.6638  Thus: net profit = $0.8671 (40+0.5309-39.6638) (in T = 18 months) or $0.8671 e -0.06 x 18/12 = $0.7925 (today)

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