Question: Assume the investor expects the share price of ABC on 19th June 2020 to equal 96p per share. Identify which of the following strategies a rational investor would prefer a) Butterfly b) Straddle c) Strangle d) Strip e) Strap

09 Oct 2022,10:10 PM

 

Section 1 – Futures and Forwards

 

Question 1: Which one of the following statements about futures and forwards is TRUE?

 

1. a) All futures are traded over the counter
2. b) All forwards are traded on exchanges
3. c) There are typically no margin requirements for futures trading
4. d) Forward contracts are most often held until physical delivery
5. e) Strategic defaults are more likely for futures than for forwards

 

Question 2: Which one of the following statements about futures is TRUE?

 

1. a) If futures prices are lower than the current spot price, opportunities for arbitrage exist
2. b) Futures prices converge to the spot prices as interest rates tend to zero
3. c) Futures prices converge to the spot price as holding costs tend to zero
4. d) Stock futures prices are lower when the expected dividend for underlying is higher
5. e) Commodity futures prices are lower when the risk-free interest rate is higher

 

Question 3: Which one of the following is NOT an underlying assumption of the futures valuation model?

 

1. a) Bid-ask spreads and brokerage fees are zero
2. b) The market provides unlimited long and short positions in futures and spot
3. c) There are no dividends, insurance, transportation, or storage costs
4. d) The market provides unlimited lending and borrowing at the risk-free rate
5. e) The underlying instrument can be liquidly traded on the market

 

Question 4: Which one of the following statements about futures trading is TRUE?

 

1. a) For a longing counterparty, a decrease in the futures price cannot lead to a margin call
2. b) For a shorting counterparty, an increase in the futures price can lead to a margin call
3. c) The current margin net of initial margin is always equal to the counterparty’s net payoff
4. d) The initial margin is always lower than the margin call threshold
5. e) A margin call is triggered when the value of current margin goes below zero

 

 

Questions 5 to 8 are based on the following scenario:

 

DEF PLC, a coffee manufacturer, wants to hedge its exposure to coffee prices. Therefore, on 17^th June 2021 it negotiates a short futures contract for 750,000 pounds of Arabica coffee deliverable December 2021. The exchange’s initial margin requirement is $60,000 and the margin call threshold is $36,000. The dynamics of the coffee futures prices shortly after the contract has been negotiated are the following:

 

Date	Futures price, $ per pound
17/06/2021	1.30
18/06/2021	1.29
21/06/2021	1.27
22/06/2021	1.30
23/06/2021	1.29
24/06/2021	1.34
25/06/2021	1.31
28/06/2021	1.32
29/06/2021	1.37
30/06/2021	1.32
01/07/2021	1.28

 

Question 5: Identify the total payoff of the futures contract on 1^st July 2021.

 

1. a) -$15,000
2. b) $15,000
3. c) -$30,000
4. d) $30,000
5. e) Impossible to calculate without knowing the wheat spot price on 1^st July 2021.

 

Question 6: Calculate the total margin payments payable to the exchange up to 1^st July 2021.

 

1. a) $30,000
2. b) $52,500
3. c) $60,000
4. d) $90,000
5. e) $112,500

 

On 1^st July 2021, the spot price is $1.26 per pound, the risk-free interest rate is 1.80% per annum, and the present value of rental payments for the warehouse sufficient to store 750,000 pounds of coffee over a 6-month period is $15,000.

 

Question 7: Calculate the value, if any, of the riskless profit that DEF can obtain from arbitraging on the futures market, assuming that all rent is payable at the beginning of the storage period and interest on loans and deposits is charged semi-annually.

 

1. a) $8,640
2. b) $15,000
3. b) $17,280
4. d) $38,775
5. e) No riskless profit can be obtained from arbitrage

 

Question 8: Calculate the spot price of coffee per pound at which DEF would be indifferent towards arbitrage, assuming no trading costs.

 

1. b) $1.260
2. a) $1.280
3. c) $1.237
4. d) $1.249
5. e) Arbitraging is not beneficial to DEF regardless of the coffee spot price

 

 

Section 2 – Options

 

 

Question 9: Which one of the following statements about options is TRUE?

 

1. a) Put options are exercised out-of-the-money
2. b) An investor is always able to buy a call option at the bid price
3. c) Writing an option leads to potentially unlimited downside
4. d) Holding an option leads to limited upside
5. e) Spreads in option trading refer to differences in premiums between calls and puts for the same strike price

 

Question 10: All other things held equal, identify which one of the following statements about vanilla option premiums is TRUE.

 

1. a) American options have lower premiums
2. b) The premiums on American and European options are equal
3. c) The premiums on American options are higher if volatility is low, the premiums on European options are higher if volatility is high
4. d) The premium of a European put increases with volatility
5. e) The premium of an American call increases with the strike price

 

Question 11: Which of the following statements about option strategies is FALSE?

 

1. a) The maximum downside of a strangle is lower than that of a straddle
2. b) The maximum upside of a condor is lower than that of a butterfly
3. c) The maximum downside of a strap is lower than that of a strangle
4. d) The maximum upside of a short straddle is limited
5. e) The maximum upside of a long strangle is unlimited

 

Question 12: Identify which forecast is consistent with a standard condor strategy.

 

1. a) Bullish on direction, bullish on volatility
2. b) Bearish on direction, bearish on volatility
3. c) Bullish on direction, bearish on volatility
4. d) Neutral on direction, bearish on volatility
5. e) Neutral on direction, bullish on volatility

 

Questions 13 to 16 are based on the following scenario:

 

The table below shows the option book for the European options tradable for the share of ABC PLC expiring on 18^th June 2021. On 1^st June 2021, an investor intends to develop an option trading strategy. The share price of ABC PLC on 1^st June 2021 is 49.8p per share.

 

Calls				Puts
Strike	Bid	Ask	Last	Strike	Bid	Ask	Last
48	2.3	2.4	2.4	48	0.5	0.7	0.6
50	1.1	1.3	1.2	50	1.0	1.2	1.1
52	0.6	0.7	0.6	52	2.2	2.5	2.3

 

Question 13: Identify the net payoff per share of a butterfly strategy using puts if the underlying price is 49p per share.

 

1. a) -0.2p
2. b) 0.3p
3. c) 0.7p
4. d) 0.8p
5. e) 2.0p

 

Question 14: Identify the maximal upside per share of an optimal butterfly strategy.

 

1. a) 0.8p
2. b) 1.1p
3. c) 1.7p
4. d) 2.2p
5. e) The optimal upside is unlimited

 

Question 15: Identify the net payoff per share of a bear call spread strategy if the underlying price is 49p per share.

 

1. a) 1.4p
2. b) 1.0p
3. c) 0.5p
4. d) 0.4p
5. e) -0.7p

 

Question 16: Identify the return of a strap strategy if the underlying price is 52p per share.

 

100. a) -100.00%
101. b) -45.95%
102. c) 5.26%
103. d) 54.05%
104. e) 105.26%

 

 

 

 

Section 3 – Swaps

 

 

Question 17: Which one of the following statements about swaps is FALSE?

 

1. a) The cash flows in the vanilla interest rate swap are denominated in the same currency for both counterparties
2. b) The net payoffs of the counterparties in an interest rate swap always add up to zero
3. c) A currency swap can only be motivated by absolute or comparative advantage of counterparties in terms of borrowing rates
4. d) In currency swaps, both principal and interest are exchanged
5. e) A collar is a combination of a cap and a floor

 

Question 18: Which one of the following statements about interest rate swaps is TRUE?

 

1. a) The replication strategy for an interest rate swap for the floating-receiving counterparty involves longing a fixed rate note and shorting a floating rate bond
2. b) If interest rates increase, the payoff of the counterparty receiving fixed in the swap increases
3. c) For interest rate swaps, setting a floor is equivalent to the fixed-receiving counterparty writing a put option for the floating-receiving counterparty
4. d) For interest rate swaps, setting a cap is equivalent to the fixed-receiving counterparty writing a call option for the floating-receiving counterparty
5. e) The notional principal is exchanged for interest rate swaps

 

Questions 19 and 20 are based on the following scenario:

 

ABC PLC is entering a four-year single name credit default swap with credit performance of DEF PLC as its underlying. The annual probability of default for DEF PLC is assessed at 2.24% and the recovery rate is estimated at 40%.

 

Question 19: Assuming all defaults occur mid-year and the annual cost of finance for ABC PLC is 6.72%, calculate the equilibrium swap rate for the credit default swap.

 

1. a) 94bps
2. b) 142bps
3. c) 140bps
4. d) 91bps
5. e) 136bps

 

Question 20: If the swap rate for the credit default swap is 167bps, calculate the implied annual probability of default for DEF PLC.

 

2. a) 2.62%
3. b) 2.66%
4. c) 2.56%
5. d) 1.60%
6. e) 3.96%

 

 

Section 1 - Futures and Forwards

 

Question 1: Which one of the following identifies the risk transformation achieved by a forward contract?

 

1. a) Business risk into credit risk
2. b) Business risk into systemic risk
3. c) Systemic risk into credit risk
4. d) Credit risk into market risk
5. e) Credit risk into liquidity risk

 

Question 2: Which one of the following is not an underlying assumption of the futures valuation model?

 

1. a) The market provides unlimited short-selling positions
2. b) The market provides unlimited lending and borrowing at the risk-free rate
3. c) The market enables liquid trading in the underlying instrument
4. d) There are no holding costs
5. e) There are no transaction costs

 

Question 3: Which one of the following statements about futures is true?

 

1. a) Equity futures prices are higher when the expected dividend for an underlying stock is higher
2. b) Commodity futures prices are lower when the risk-free interest rate is higher
3. c) If futures prices are higher than the current spot price, opportunities for arbitrage exist
4. d) Futures prices converge to the spot prices as interest rates tend to zero
5. e) Futures prices converge to the spot price as the maturity dates approach

 

Question 4: Which one of the following statements about futures and forwards is true?

 

1. a) All futures are traded over the counter
2. b) All forwards are traded on exchanges
3. c) Futures contracts are most often held until physical delivery
4. d) Strategic defaults are less likely for futures than for forwards
5. e) There are no margin requirements for futures trading

 

Questions 5 to 8 are based on the following scenario:

 

DEF PLC, a food manufacturing company, wants to hedge its exposure to wheat prices. Therefore, on 17^th June 2020 it negotiates a long futures contract for 100,000 bushels of wheat deliverable December 2020. The exchange’s initial margin requirement is $50,000 and the margin call threshold is $30,000. The dynamics of the wheat futures prices shortly after the contract has been negotiated are the following:

 

 

 

Date	Futures price, $ per bushel
17/06/2020	4.75
18/06/2020	4.61
19/06/2020	4.63
22/06/2020	4.53
23/06/2020	4.40
24/06/2020	4.44
25/06/2020	4.49
26/06/2020	4.12
29/06/2020	3.91
30/06/2020	3.80
01/07/2020	4.80

 

Question 5: Identify the total payoff of the futures contract at 1^st July 2020?

 

1. a) $100,000
2. b) -$100,000
3. c) $5,000
4. d) -$5,000
5. e) Impossible to calculate without knowing the wheat spot price on 1^st July 2020

 

Question 6: Calculate the total margin payments payable to the exchange up to 1^st July 2020?

 

1. a) $145,000
2. b) $84,000
3. c) $63,000
4. d) $113,000
5. e) $134,000

 

On 1^st July 2020 the spot price is $4.31 per bushel, the annual risk-free interest rate is 2.40% per annum and the present value of rental payments for the warehouse sufficient to store 100,000 bushels over a 6-month period is $40,000.

 

Question 7: Calculate the value, if any, of the riskless profit that DEF can obtain from arbitraging on the futures market, assuming that all rent is payable at the beginning of the storage period and interest on loans and deposits is charged semi-annually.

 

1. a) $9,000
2. b) $3,348
3. c) $3,828
4. d) $49,000
5. e) No riskless profit can be obtained from arbitrage

 

Question 8: Calculate the present value of rental payments at which DEF would be indifferent towards arbitrage, assuming no trading costs.

 

1. a) $43,308
2. b) $36,692
3. c) $0
4. d) $49,000
5. e) Arbitraging is not beneficial to DEF regardless of the present value of rental payments

 

Section 2 - Options

 

Question 9: Which one of the following statements about options is true?

 

1. a) An investor is always able to write a put option at the ask price
2. b) An investor is always able to buy a call option at the last price
3. c) The premium of a call option with a higher strike price, all other things held equal, should be higher
4. d) The premium of a put option with a lower strike price, all other things held equal, should be lower
5. e) The premium of a call option with a higher maturity, all other things held equal, should be lower

 

Question 10: All other things held equal, identify which one of the following statements about vanilla option premiums is true

 

1. a) American options have higher premiums
2. b) European options have higher premiums
3. c) The premiums on American and European options would be equal
4. d) Both American and European option premiums depend on the risk-free rate
5. e) The premiums on American calls would be higher, the premiums on European puts would be higher

 

Question 11: Identify which one of the following pairs of option strategies, at equilibrium, would be expected to deliver equivalent payoffs

 

1. a) Short straddle and butterfly
2. b) Short strangle and condor
3. c) Short call and long put
4. d) Protective put and short call
5. e) Covered call and short put

 

Question 12: Assume a current underlying share price is 99.5p and the implied volatility is 24% per annum. If an investor believes the volatility of the underlying share price will be 27% and the expected share price at the expiry date will be 92.5p per share, identify which one of the following strategies will be consistent with their forecast

 

1. a) Short call
2. b) Condor
3. c) Strangle
4. d) Strip
5. e) Strap

 

Questions 13 to 16 are based on the following scenario:

 

The table below shows the option book for the European options tradable for the share of ABC PLC expiring on 19^th June 2020. On 1^st June 2020, an investor intends to develop an option trading strategy. The share price of ABC PLC on 1^st June 2020 is 99.5p per share.

 

Calls				Puts
Strike	Bid	Ask	Last	Strike	Bid	Ask	Last
95	5.3	5.7	5.4	95	1.4	1.8	1.5
100	2.1	2.3	2.2	100	2.1	2.4	2.3
105	1.2	1.6	1.4	105	5.4	5.7	5.5

 

Question 13: Identify the net payoff per share of a butterfly strategy using puts if the underlying share price is 101p per share

 

2. a) 2.0p
3. b) 0.7p
4. c) 3.2p
5. d) -3.8p
6. e) 1.9p

 

Question 14: Identify the maximal downside per share of an optimal butterfly strategy

 

1. a) -1.9p
2. b) -2.0p
3. c) -3.1p
4. d) -3.3p
5. e) Unlimited downside

 

Question 15: Identify the net payoff per share of a strip strategy if the underlying share price is 103p per share

 

3. a) -3.3p
4. b) -0.3
5. c) -4.1p
6. d) -1.1p
7. e) -4.0p

 

Question 16: Assume the investor expects the share price of ABC on 19^th June 2020 to equal 104p per share. Identify which of the following strategies a rational investor would prefer

 

1. a) Butterfly
2. b) Straddle
3. c) Strangle
4. d) Strip
5. e) Strap

 

 

 

Section 3 - Swaps

 

Question 17: Which one of the following statements about swaps is true?

 

1. a) The terms “credit event” and “default” are synonymous
2. b) All other things held equal, the credit default swap rate is lower for longer-term swaps
3. c) All other things held equal, a higher recovery rate corresponds to a lower credit default swap rate
4. d) All other things held equal, a higher probability of default corresponds to a lower credit default swap rate
5. e) A higher cost of finance always leads to a decreased credit default swap rate due to time value of money considerations

 

Question 18: Which one of the following statements about swaps is true?

 

1. a) The notional principal is exchanged for both interest rate and currency swaps
2. b) The replication strategy for an interest rate swap for the fixed-receiving counterparty involves longing a floating rate bond and shorting a fixed rate note
3. c) If interest rates increase, the payoff of the counterparty receiving floating in the swap decreases
4. d) For interest rate swaps, setting a floor is equivalent to the floating-receiving counterparty writing a put option for the fixed-receiving counterparty
5. e) For interest rate swaps, setting a cap is equivalent to the floating-receiving counterparty writing a call option for the fixed-receiving counterparty

 

Questions 19 and 20 are based on the following scenario:

 

ABC PLC is entering a three-year single name credit default swap with credit performance of DEF PLC as its underlying. The annual probability of default for DEF PLC is assessed at 2.71% and the recovery rate is estimated at 30%.

 

Question 19: Assuming all defaults occur mid-year and the annual cost of finance for ABC PLC is 4.56%, calculate the equilibrium swap rate for the credit default swap

 

1. a) 202bps
2. b) 84bps
3. c) 192bps
4. d) 197bps
5. e) 199bps

 

Question 20: If the swap rate for the credit default swap is 252bps, calculate the implied annual probability of default for DEF PLC

 

3. a) 3.46%
4. b) 3.40%
5. c) 3.35%
6. d) 3.54%
7. e) 3.60%

 

 

Derivatives and Risk – Mock exam

 

Section 1 - Futures and Forwards

 

Question 1: Which one of the following identifies the risk transformation achieved by a forward contract?

 

1. a) Business risk into systemic risk
2. b) Business risk into credit risk
3. c) Credit risk into business risk
4. d) Credit risk into liquidity risk
5. e) Systemic risk into business risk

 

Question 2: Which one of the following is not an underlying assumption of the futures valuation model?

 

1. c) The underlying instrument is tradable on the spot market
2. a) A trader can open unlimited short-selling positions
3. b) A trader can lend and borrow indefinitely at the risk-free rate
4. e) Futures prices converge to the spot price as the maturity dates approach
5. d) Transaction costs are zero

 

Question 3: Which one of the following statements about futures trading is true?

 

1. a) For a longing counterparty, a decrease in the futures price cannot lead to a margin call
2. b) For a shorting counterparty, an increase in the futures price can lead to a margin call
3. c) The current margin net of initial margin is always equal to the counterparty’s net payoff
4. d) The initial margin is always lower than the margin call threshold
5. e) A margin call is triggered when the value of current margin goes below zero

 

Question 4: Which one of the following statements about futures is true?

 

1. a) Equity futures prices are lower when the expected dividend for an underlying stock is lower
2. b) Commodity futures prices are higher when storage costs are higher
3. c) If futures prices are lower than the current spot price, opportunities for arbitrage exist
4. d) There are future contracts available for trading with delivery specified at any trading day
5. e) Long futures contracts are primarily used to manage the supply chain

 

Question 5: Which one of the following statements about futures and forwards is true?

 

1. a) All futures are traded over the counter
2. b) All forwards are traded on exchanges
3. c) Forwards contracts are rarely held until physical delivery
4. d) Strategic defaults are more likely for futures than for forwards
5. e) There are typically no margin requirements for forwards trading

 

 

 

Questions 6 to 11 are based on the following scenario:

 

DEF PLC, an oil extraction company, wants to hedge its exposure to crude oil prices. Therefore, on 17^th June 2020 it negotiates a short futures contract for 50,000 barrels of Brent crude deliverable December 2020. The exchange’s initial margin requirement is $100,000 and the margin call threshold is $40,000. The dynamics of the Brent futures prices shortly after the contract has been negotiated are the following:

 

Date	Futures price, $ per barrel
17/06/2020	25.45
18/06/2020	25.41
19/06/2020	24.14
22/06/2020	26.62
23/06/2020	29.87
24/06/2020	31.12
25/06/2020	30.89
26/06/2020	32.34
29/06/2020	31.99
30/06/2020	31.68
01/07/2020	31.61

 

Question 6: Identify the total payoff of the futures contract at 1^st July 2020

 

1. a) $308,000
2. b) -$308,000
3. c) $3,500
4. d) -$3,500
5. e) $36,500

 

Question 7: Identify the number of margin calls triggered by 1st July 2020

 

1. a) 0
2. b) 1
3. c) 2
4. d) 3
5. e) 4

 

Question 8: Calculate the total margin payments payable to the exchange up to 1^st July 2020

 

1. a) $444,500
2. b) $344,500
3. c) $100,000
4. d) $65,500
5. e) $165,500

 

On 1^st July 2019 the spot price is $30.17 per bushel, the annual risk-free interest rate is 1.30% per annum and the present value of rental payments for the warehouse sufficient to store 50,000 barrels of oil over a 6-month period is $100,000.

 

Question 9: Calculate the value, if any, of the riskless profit that DEF can obtain from arbitraging on the futures market, assuming that all rent is payable at the beginning of the storage period and interest on loans and deposits is charged semi-annually.

 

1. a) $18,226
2. b) $28,000
3. c) $37,774
4. d) $182,240
5. e) No riskless profit can be obtained from arbitrage

 

Question 10: Calculate the present value of rental payments at which DEF would be indifferent towards arbitrage, assuming no trading costs

 

1. a) $62,226
2. b) $72,000
3. c) $81,774
4. d) $137,774
5. e) Arbitraging is not beneficial to DEF regardless of the present value of rental payments

 

Section 2 - Options

 

Question 11: Which one of the following statements about options is true?

 

1. a) Put options are exercised out-of-the-money
2. b) Call options are exercised in-the-money
3. c) Writing an option leads to potentially unlimited upside
4. d) Holding an option leads to limited downside
5. e) Spreads in option trading refer to differences in premiums between calls and puts for the same strike price

 

Question 12: Which one of the following statements about options is true?

 

1. a) An investor is always able to write a call option at the ask price
2. b) An investor is always able to buy a put option at the bid price
3. c) The premium of a call option with a lower strike price, all other things held equal, should be higher
4. d) The premium of a put option with a lower strike price, all other things held equal, should be higher
5. e) The premium of a put option with a lower maturity, all other things held equal, should be higher

 

Question 13: All other things held equal, identify which one of the following statements about vanilla option premiums is true

 

1. a) American options have lower premiums
2. b) European options have lower premiums
3. c) The premiums on American and European options would be equal
4. d) The premiums on American options would be higher if volatility is low, the premiums on European options would be higher if volatility is high
5. e) The premiums on American puts would be higher while the premiums on European calls would be higher

 

Question 14: Identify which one of the following pairs of option strategies, at equilibrium, would be expected to deliver equivalent payoffs

 

1. a) Short strangle and condor
2. b) Bullish spread with puts and bullish spread with calls
3. c) Short put and long call
4. d) Protective put and long call
5. e) Covered call and long put

 

Question 15: Which of the following statements about option strategies is false?

 

1. a) The maximum downside of a strangle is lower than that of a straddle
2. b) The maximum upside of a condor is lower than that of a butterfly
3. c) The maximum upside of a short straddle is limited
4. d) The maximum upside of a long strangle is unlimited
5. e) The maximum downside of a strap is lower than that of a strangle

 

Question 16: Which of the following statements about option strategies is true?

a) A butterfly is a net credit trade

1. b) A bearish call spread is a net debit trade
2. c) A short straddle is a net credit trade
3. d) A bullish put spread is a net debit trade
4. e) A strangle is a net credit trade

 

Question 17: Identify which forecast is consistent with a condor strategy

 

1. a) Bullish on direction, bullish on volatility
2. b) Bearish on direction, bearish on volatility
3. c) Bullish on direction, bearish on volatility
4. d) Neutral on direction, bearish on volatility
5. e) Neutral on direction, bullish on volatility

 

Question 18: Assume that current underlying share price is 104.9p and the implied volatility is 31% per annum. If an investor believes the annualised volatility of the underlying share price will be 36% and the share price at the expiry date will be 119.1p per share, identify which one of the following strategies will be consistent with their forecast

 

1. a) Long put
2. b) Butterfly
3. c) Strangle
4. d) Strip
5. e) Strap

Questions 19 to 24 are based on the following scenario:

 

The table below shows the option book for the European options tradable for the share of ABC PLC expiring on 19^th June 2020. On 1^st June 2020, an investor intends to develop an option trading strategy. The share price of ABC PLC on 1^st June 2020 is 104.9p per share.

 

Calls				Puts
Strike	Bid	Ask	Last	Strike	Bid	Ask	Last
100	5.8	6.3	6.1	100	1.0	1.1	1.0
105	2.7	2.9	2.8	105	2.8	3.0	2.9
110	1.1	1.3	1.2	110	5.7	6.6	6.0

 

Question 19: Identify the breakeven price for a long call strategy with a strike price of 110p per share

 

108. a) 108.9p
109. b) 108.7p
110. c) 110.0p
111. d) 111.1p
112. e) 111.3p

 

Question 20: Identify the maximal downside per share of a strangle strategy

 

2. a) -2.1p
3. b) -2.4p
4. c) -7.6p
5. d) -5.9p
6. e) -12.9p

 

Question 21: Identify the net payoff per share of a butterfly strategy using calls if the underlying share price is 104p per share

 

3. a) 3.3p
4. b) 2.9p
5. c) 2.3p
6. d) 1.8p
7. e) 1.9p

 

Question 22: Identify the maximal downside per share of an optimal butterfly strategy

 

1. a) -0.7p
2. b) -1.1p
3. c) -2.1p
4. d) -2.2p
5. e) Unlimited

 

 

Question 23: Identify the net payoff per share of a strap strategy if the underlying share price is 108p per share

 

2. a) -2.2p
3. b) -2.8p
4. c) -2.9p
5. d) -5.3p
6. e) -5.9p

 

Question 24: Assume the investor expects the share price of ABC on 19^th June 2020 to equal 96p per share. Identify which of the following strategies a rational investor would prefer

 

1. a) Butterfly
2. b) Straddle
3. c) Strangle
4. d) Strip
5. e) Strap

 

Section 3 - Swaps

 

Question 25: Which of the following statements about credit default swaps is true?

 

1. a) Credit default swaps can only be used for hedging
2. b) In case of default, the protection seller must always compensate the full par value of the underlying debt
3. c) All other things held equal, if the swap rate increases, the expected net payoff of the protection seller decreases
4. d) All other things held equal, if the recovery rate increases, the expected net payoff of the protection buyer decreases
5. e) Basket default swaps always protect against defaults of all underlying debts in the basket

 

Question 26: Which one of the following statements about credit default swap valuation is true?

 

1. a) All other things held equal, the swap rate is higher if defaults are assumed to occur at the start of the year instead of mid-year
2. b) All other things held equal, a higher cost of finance corresponds to a lower swap rate
3. c) All other things held equal, a longer-term swap corresponds to a higher swap rate
4. d) All other things held equal, a higher probability of default corresponds to a lower credit default swap rate
5. e) All other things held equal, a higher recovery rate corresponds to a higher credit default swap rate

 

Question 27: Which one of the following statements about swaps is false?

 

1. a) The cash flows in the vanilla interest rate swap are denominated in the same currency for both counterparties
2. b) The net payoffs of the counterparties in an interest rate swap always add up to zero
3. c) A currency swap can only be motivated by absolute or comparative advantage of counterparties in terms of borrowing rates
4. d) In currency swaps, both principal and interest are exchanged
5. e) A collar is a combination of a cap and a floor

 

Question 28: Which one of the following statements about interest rate swaps is true?

 

1. a) The replication strategy for an interest rate swap for the floating-receiving counterparty involves longing a fixed rate note and shorting a floating rate bond
2. b) If interest rates increase, the payoff of the counterparty receiving fixed in the swap increases
3. c) For interest rate swaps, setting a floor is equivalent to the fixed-receiving counterparty writing a put option for the floating-receiving counterparty
4. d) For interest rate swaps, setting a cap is equivalent to the fixed-receiving counterparty writing a call option for the floating-receiving counterparty
5. e) The notional principal is exchanged for interest rate swaps

 

Questions 29-30 are based on the following scenario:

 

ABC PLC is based in the UK and would like to borrow $120,000 for one year to expand to the US market. DEF PLC is based in the US and would like to borrow £100,000 for one year to expand to the UK market. The GBPUSD exchange rate is 1.20. The table below presents the annual rates the companies can borrow at:

 

	Borrow in $	Borrow in £
ABC PLC	4.5%	3.2%
DEF PLC	3.6%	4.7%

 

Question 29: Identify the total surplus that can be achieved by negotiating a currency swap, assuming the exchange rate remains unchanged

 

1. a) £0
2. b) £1,100
3. c) £1,300
4. d) £2,400
5. e) £6,800

 

Question 30: If the currency swap is intermediated by a financial institution, identify the maximum margin the institution can charge for the swap to be mutually beneficial

 

1. a) 0bps
2. b) 89bps
3. c) 109bps
4. d) 129bps
5. e) 149bps

 

 

 

Questions 31-36 are based on the following scenario:

 

ABC PLC is entering a four-year single name credit default swap with credit performance of DEF PLC as its underlying. The annual probability of default for DEF PLC is assessed at 2.24% and the recovery rate is estimated at 40%.

 

Question 31: Assuming all defaults occur mid-year and the annual cost of finance for ABC PLC is 6.72%, calculate the equilibrium swap rate for the credit default swap

 

1. a) 94bps
2. b) 142bps
3. c) 140bps
4. d) 91bps
5. e) 136bps

 

Question 32: Identify the present value of the net payoff for the protection seller in the swap if the par value is $100,000, the swap rate is 155bps, and DEF PLC defaults in the second year of the swap

 

52381. a) -$52381.04
52382. b) -$52970.61
52383. c) -$59070.00
52384. d) -$60000.00
52385. e) -$52267.64

 

Question 33: Identify the expected net payoff for the protection buyer in the swap if the par value is $100,000 and the swap rate is 155bps

 

2578. a) -$2578.26
2579. b) $729.58
2580. c) -$2006.27
2581. d) $418.87
2582. e) -$478.09

 

Question 34: Identify the equilibrium swap rate if the recovery rate increases to 60%

 

1. a) 94bps
2. b) 142bps
3. c) 140bps
4. d) 91bps
5. e) 136bps

 

Question 35: Identify the equilibrium swap rate if defaults are assumed to occur at the start of the year instead of mid-year

 

1. a) 145bps
2. b) 134bps
3. c) 137bps
4. d) 147bps
5. e) 142bps

 

Question 36: If the swap rate for the credit default swap is 167bps, calculate the implied annual probability of default for DEF PLC

 

2. a) 2.62%
3. b) 2.66%
4. c) 2.56%
5. d) 1.60%
6. e) 3.96%

 

 

 

Derivatives and Risk – Resit Exam

 

Section 1 - Futures and Forwards

 

Question 1: Identify which one of the following is not an underlying assumption of the futures valuation model

 

1. a) There are no bid-ask spreads on the futures market
2. b) The spot market provides unlimited short-selling opportunities
3. c) The market provides unlimited borrowing at the risk-free rate
4. d) The market provides unlimited lending at the risk-free rate
5. e) The underlying instrument pays no dividend

 

Question 2: Identify which one of the following statements about futures is true

 

1. a) Equity futures prices are lower when the expected dividend for an underlying stock is higher
2. b) Commodity futures prices are higher when the risk-free interest rate is lower
3. c) If futures prices are lower than the current spot price, opportunities for arbitrage exist
4. d) Futures prices converge to the spot prices as interest rates tend to zero
5. e) Futures prices converge to the spot price as holding costs tend to zero

 

Question 3: Identify which one of the following statements about futures and forwards is true

 

1. a) All futures are traded over the counter
2. b) All forwards are traded on exchanges
3. c) Forward contracts are most often held until physical delivery
4. d) Strategic defaults are more likely for futures than for forwards
5. e) There are typically high margin requirements for forwards trading

 

Question 4: Identify which of the following statements about margining is true

 

1. a) A margin call is triggered when the current margin goes below the initial margin
2. b) Margin requirements in futures trading are only imposed on shorting counterparties
3. c) A margin call threshold is typically higher than the initial margin
4. d) Margin requirements are typically higher on more volatile markets
5. e) A margin call cannot occur for a shorting counterparty when spot prices increase

 

Questions 5 to 8 are based on the following scenario:

 

DEF PLC, a copper mining company, wants to hedge its exposure to copper prices. Therefore, on 17^th September 2021 it negotiates a short futures contract for 100,000 pounds of copper deliverable December 2021. The exchange’s initial margin requirement is $30,000 and the margin call threshold is $20,000. The dynamics of the copper futures prices shortly after the contract has been negotiated are the following:

 

 

 

Date	Futures price, $ per pound
17/09/2021	4.31
20/09/2021	4.29
21/09/2021	4.26
22/09/2021	4.30
23/09/2021	4.34
24/09/2021	4.32
27/09/2021	4.39
28/09/2021	4.45
29/09/2021	4.41
30/09/2021	4.42
01/10/2021	4.47

 

Question 5: Identify the total payoff of the futures contract at 1^st October 2021

 

1. a) $5,000
2. b) -$5,000
3. c) $16,000
4. d) -$16,000
5. e) Impossible to calculate without knowing the copper spot price on 1^st October 2021

 

Question 6: Calculate the total margin payments payable to the exchange up to 1^st October 2021

 

1. a) $16,000
2. b) $46,000
3. c) $44,000
4. d) $14,000
5. e) $30,000

 

On 1^st October 2021 the spot price is $4.38 per pound, the annual risk-free interest rate is 2.20% per annum and the present value of rental payments for the warehouse sufficient to store 100,000 pounds of copper over a 3-month period is $28,000.

 

Question 7: Calculate the value, if any, of the riskless profit that DEF can obtain from arbitraging on the futures market, assuming that all rent is payable at the beginning of the storage period and interest on loans and deposits is charged quarterly

 

1. a) $19,000
2. b) $21,563
3. c) $24,126
4. d) $29,252
5. e) No riskless profit can be obtained from arbitrage

 

Question 8: Calculate the present value of rental payments at which DEF would be indifferent towards arbitrage, assuming no trading costs

 

1. a) $9,000
2. b) $4,137
3. c) $0
4. d) $6,555
5. e) Arbitraging is not beneficial to DEF regardless of the present value of rental payments

 

Section 2 - Options

 

Question 9: Identify which one of the following statements about options is true

 

1. a) An investor is always able to write a call option at the last price
2. b) An investor is always able to buy a put option at the bid price
3. c) The premium of a call option with a higher strike price, all other things held equal, should be lower
4. d) The premium of a put option with a lower strike price, all other things held equal, should be higher
5. e) The premium of a put option with a higher maturity, all other things held equal, should be lower

 

Question 10: Identify which of the following is NOT an assumption of the Black-Scholes model

 

1. a) The volatility of the underlying instrument is constant
2. b) The underlying instrument does not pay dividend
3. c) All investors are able to borrow and lend indefinitely at the risk-free rate
4. d) All investors have identical expectations and time horizons
5. e) The logarithmic return of the underlying instrument is normally distributed

 

Question 11: Identify which one of the following pairs of option strategies, at equilibrium, would be expected to deliver equivalent payoffs

 

1. a) Short straddle and condor with calls
2. b) Short strangle and butterfly with puts
3. c) Butterfly with puts and butterfly with calls
4. d) Protective put and long put
5. e) Covered call and short call

 

Question 12: Assume a current underlying share price is 200p and the implied volatility is 19% per annum. If an investor believes the volatility of the underlying share price will be 14% and the expected share price at the expiry date will be 198p per share, identify which one of the following strategies will be consistent with their forecast

 

1. a) Long put
2. b) Condor
3. c) Strangle
4. d) Strip
5. e) Strap

 

 

 

 

Questions 13 to 16 are based on the following scenario:

 

The table below shows the option book for the European options tradable for the share of ABC PLC expiring on 17^th September 2021. On 1^st September 2021, an investor intends to develop an option trading strategy. The share price of ABC PLC on 1^st September 2021 is 150p per share.

 

Calls				Puts
Strike	Bid	Ask	Last	Strike	Bid	Ask	Last
145	6.4	6.8	6.6	145	1.3	1.5	1.4
150	3.2	3.4	3.3	150	3.1	3.3	3.2
155	1.4	1.7	1.5	155	5.9	6.2	6.1

 

Question 13: Identify the net payoff per share of a butterfly strategy using calls if the underlying share price is 149p per share

 

1. a) 1.9p
2. b) 3.0p
3. c) 2.5p
4. d) 4.0p
5. e) 1.6p

 

Question 14: Identify the maximal downside per share of an optimal butterfly strategy

 

2. a) -2.1p
3. b) -1.5p
4. c) -1.0p
5. d) -0.6p
6. e) Unlimited

 

Question 15: Identify the net payoff per share of a bullish put spread if the underlying share price is 152p per share

 

2. a) -2.0p
3. b) -0.5p
4. c) -0.3p
5. d) 0.5p
6. e) 1.6p

 

Question 16: Assume the investor expects the share price of ABC on 17^th September 2021 to equal 151p per share. Identify which of the following strategies a rational investor would prefer

 

1. a) Bullish put spread
2. b) Bullish call spread
3. c) Bearish call spread
4. d) Butterfly
5. e) Straddle

 

 

 

Section 3 - Swaps

 

Question 17: Which one of the following statements about swaps is true?

 

1. a) All other things held equal, an earlier default results in lower net payoff for the protection buyer
2. b) All other things held equal, the credit default swap rate is lower for shorter-term swaps
3. c) All other things held equal, a lower recovery rate corresponds to a lower credit default swap rate
4. d) All other things held equal, a lower probability of default corresponds to a lower credit default swap rate
5. e) A lower cost of finance always leads to an increased credit default swap rate due to time value of money considerations

 

Question 18: Which one of the following statements about swaps is true?

 

1. a) The notional principal is not exchanged for currency swaps
2. b) The replication strategy for an interest rate swap for the floating-receiving counterparty involves shorting a variable rate bond and longing a fixed rate note
3. c) If interest rates decrease, the net payoff of the counterparty receiving fixed in the swap decreases
4. d) For interest rate swaps, setting a floor is equivalent to the fixed-receiving counterparty writing a put option for the floating-receiving counterparty
5. e) For interest rate swaps, setting a cap is equivalent to the fixed-receiving counterparty writing a call option for the floating-receiving counterparty

 

Questions 19 and 20 are based on the following scenario:

 

ABC PLC is entering a six-year single name credit default swap with credit performance of DEF PLC as its underlying. The annual probability of default for DEF PLC is assessed at 3.79% and the recovery rate is estimated at 40%.

 

Question 19: Assuming all defaults occur mid-year and the annual cost of finance for ABC PLC is 2.84%, calculate the equilibrium swap rate for the credit default swap

 

1. a) 392bps
2. b) 235bps
3. c) 232bps
4. d) 259bps
5. e) 157bps

 

Question 20: If the swap rate for the credit default swap is 200bps, calculate the implied annual probability of default for DEF PLC

 

3. a) 3.00%
4. b) 3.28%
5. c) 3.23%
6. d) 4.81%
7. e) 1.95%