Fixed Income Securities and Derivatives
Final Test Solutions
Course Introduction
This course provides an in-depth exploration of fixed income securities and their associated derivatives, focusing on valuation, risk analysis, and practical applications in investment management. Topics include the structure and features of bonds, pricing and yield calculations, term structure of interest rates, credit risk, and portfolio strategies. The course also covers interest rate derivatives such as swaps, futures, and options, emphasizing their role in hedging and speculation. Through a combination of theoretical frameworks and real-world case studies, students will develop the analytical skills necessary to navigate the complexities of the fixed income markets and effectively use derivative instruments.
Recommended Textbook
Options Futures and Other Derivatives 10th Edition by John C. Hull
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2
Chapter 1: Introduction
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Q1) Which of the following is true about a long forward contract
A) The contract becomes more valuable as the price of the asset declines
B) The contract becomes more valuable as the price of the asset rises
C) The contract is worth zero if the price of the asset declines after the contract has been entered into
D) The contract is worth zero if the price of the asset rises after the contract has been entered into
Answer: B
Q2) A trader has a portfolio worth $5 million that mirrors the performance of a stock index.The stock index is currently 1,250.Futures contracts trade on the index with one contract being on 250 times the index.To remove market risk from the portfolio the trader should
A) Buy 16 contracts
B) Sell 16 contracts
C) Buy 20 contracts
D) Sell 20 contracts
Answer: B
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Chapter 2: Futures Markets and Central Counterparties
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Q1) Which of the following is NOT true
A) Futures contracts nearly always last longer than forward contracts
B) Futures contracts are standardized; forward contracts are not.
C) Delivery or final cash settlement usually takes place with forward contracts; the same is not true of futures contracts.
D) Forward contracts usually have one specified delivery date; futures contract often have a range of delivery dates.
Answer: A
Q2) Which of the following are cash settled
A) All futures contracts
B) All option contracts
C) Futures on commodities
D) Futures on stock indices
Answer: D
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4
Chapter 3: Hedging Strategies Using Futures
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Q1) Which of the following is true?
A) The optimal hedge ratio is the slope of the best fit line when the spot price (on the y-axis) is regressed against the futures price (on the x-axis).
B) The optimal hedge ratio is the slope of the best fit line when the futures price (on the y-axis) is regressed against the spot price (on the x-axis).
C) The optimal hedge ratio is the slope of the best fit line when the change in the spot price (on the y-axis) is regressed against the change in the futures price (on the x-axis).
D) The optimal hedge ratio is the slope of the best fit line when the change in the futures price (on the y-axis) is regressed against the change in the spot price (on the x-axis).
Answer: C
Q2) Which of the following best describes the capital asset pricing model?
A) Determines the amount of capital that is needed in particular situations
B) Is used to determine the price of futures contracts
C) Relates the return on an asset to the return on a stock index
D) Is used to determine the volatility of a stock index
Answer: C
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Chapter 4: Interest Rates
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Q1) Which of the following is NOT a theory of the term structure
A) Expectations theory
B) Market segmentation theory
C) Liquidity preference theory
D) Maturity preference theory
Q2) The compounding frequency for an interest rate defines
A) The frequency with which interest is paid
B) A unit of measurement for the interest rate
C) The relationship between the annual interest rate and the monthly interest rate
D) None of the above
Q3) Which of the following is true of LIBOR
A) The LIBOR rate is free of credit risk
B) A LIBOR rate is lower than the Treasury rate when the two have the same maturity
C) It is a rate used when borrowing and lending takes place between banks
D) It is subject to favorable tax treatment in the U.S.
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Chapter 5: Determination of Forward and Futures Prices
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Q1) The spot price of an asset is positively correlated with the market.Which of the following would you expect to be true?
A) The forward price equals the expected future spot price.
B) The forward price is greater than the expected future spot price.
C) The forward price is less than the expected future spot price.
D) The forward price is sometimes greater and sometimes less than the expected future spot price.
Q2) Which of the following is true for a consumption commodity?
A) There is no limit to how high or low the futures price can be, except that the futures price cannot be negative
B) There is a lower limit to the futures price but no upper limit
C) There is an upper limit to the futures price but no lower limit, except that the futures price cannot be negative
D) The futures price can be determined with reasonable accuracy from the spot price and interest rates
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Chapter 6: Interest Rate Futures
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Q1) Which of the following is closest to the duration of a 2-year bond that pays a coupon of 8% per annum semiannually? The yield on the bond is 10% per annum with continuous compounding.
A) 1.82
B) 1.85
C) 1.88
D) 1.92
Q2) The most recent settlement bond futures price is 103.5.Which of the following four bonds is cheapest to deliver?
A) Quoted bond price = 110; conversion factor = 1.0400.
B) Quoted bond price = 160; conversion factor = 1.5200.
C) Quoted bond price = 131; conversion factor = 1.2500.
D) Quoted bond price = 143; conversion factor = 1.3500.
Q3) In the U.S.what is the longest maturity for 3-month Eurodollar futures contracts?
A) 2 years
B) 5 years
C) 10 years
D) 20 years
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8
Chapter 7: Swaps
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Q1) Which of the following describes the way a LIBOR-in-arrears swap differs from a plain vanilla interest rate swap?
A) Interest is paid at the beginning of the accrual period in a LIBOR-in-arrears swap
B) Interest is paid at the end of the accrual period in a LIBOR-in-arrears swap
C) No floating interest is paid until the end of the life of the swap in a LIBOR-in-arrears swap, but fixed payments are made throughout the life of the swap
D) Neither floating nor fixed payments are made until the end of the life of the swap
Q2) A floating-for-fixed currency swap is equivalent to
A) Two interest rate swaps, one in each currency
B) A fixed-for-fixed currency swap and one interest rate swap
C) A fixed-for-fixed currency swap and two interest rate swaps, one in each currency
D) None of the above
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) Which of the following tends to lead to an increase in house prices?
A) An increase in interest rates
B) Regulators specifying a maximum level for the loan-to-value ratio on mortgages
C) Banks reducing the minimum FICO score that borrowers are required to have
D) An increase in foreclosures
Q2) Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 85%,mezzanine 10%,and equity 5%.(The portfolios of subprime mortgages have the same default rates.)An ABS CDO is then created from the mezzanine tranches with the same allocation of principal.How high can losses on the mortgages be before the mezzanine tranche of the ABD CDO bears losses?
A) 5.0%
B) 5.5%
C) 6.0%
D) 6.5%
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Chapter 9: Xvas
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Q1) Which of the following is true
A) CVA and DVA can be calculated deal by deal
B) CVA and DVA must both be calculated for the whole portfolio a bank has with a counterparty
C) CVA can be calculated deal by deal but DVA must be calculated for a portfolio
D) DVA can be calculated deal by deal but CVA must be calculated for a portfolio
Q2) CVA stands for
A) Collateral valuation adjustment
B) Credit valuation adjustment
C) Credit valuation agreement
D) Collateral valuation agreement
Q3) Financial economics argues that
A) All investments by a company should earn the company's weighted average cost of capital
B) The required expected return on an investment is the average cost of debt
C) The required expected return on an investment increases with the riskiness of the investment
D) The required expected return on an investment decreases with the riskiness of the investment
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Page 11
Chapter 10: Mechanics of Options Markets
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Q1) In which of the following cases is an asset NOT considered constructively sold?
A) The owner shorts the asset
B) The owner buys an in-the-money put option on the asset
C) The owner shorts a forward contract on the asset
D) The owner shorts a futures contract on the stock
Q2) Which of the following describes a difference between a warrant and an exchange-traded stock option?
A) In a warrant issue, someone has guaranteed the performance of the option seller in the event that the option is exercised
B) The number of warrants is fixed whereas the number of exchange-traded options in existence depends on trading
C) Exchange-traded stock options have a strike price
D) Warrants cannot be traded after they have been purchased
Q3) Which of the following must post margin?
A) The seller of an option
B) The buyer of an option
C) The seller and the buyer of an option
D) Neither the seller nor the buyer of an option
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Chapter 11: Properties of Stock Options
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Q1) When dividends increase with all else remaining the same,which of the following is true?
A) Both calls and puts increase in value
B) Both calls and puts decrease in value
C) Calls increase in value while puts decrease in value
D) Puts increase in value while calls decrease in value
Q2) When the strike price increases with all else remaining the same,which of the following is true?
A) Both calls and puts increase in value
B) Both calls and puts decrease in value
C) Calls increase in value while puts decrease in value
D) Puts increase in value while calls decrease in value
Q3) Which of the following can be used to create a long position in a European put option on a stock?
A) Buy a call option on the stock and buy the stock
B) Buy a call on the stock and short the stock
C) Sell a call option on the stock and buy the stock
D) Sell a call option on the stock and sell the stock
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13
Chapter 12: Trading Strategies Involving Options
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Q1) A trader creates a long butterfly spread from options with strike prices
$60,$65,and $70 by trading a total of 400 options.The options are worth $11,$14,and $18.What is the maximum net gain (after the cost of the options is taken into account)?
A) $100
B) $200
C) $300
D) $400
Q2) Which of the following describes a covered call?
A) A long call option on a stock plus a long position in the stock
B) A long call option on a stock plus a short put option on the stock
C) A short call option on a stock plus a short position in the stock
D) A short call option on a stock plus a long position in the stock
Q3) Six-month call options with strike prices of $35 and $40 cost $6 and $4,respectively.What is the maximum gain when a bull spread is created by trading a total of 200 options?
A) $100
B) $200
C) $300
D) $400
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Page 14
Chapter 13: Binomial Trees
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Q1) Which of the following are NOT true
A) Risk-neutral valuation and no-arbitrage arguments give the same option prices
B) Risk-neutral valuation involves assuming that the expected return is the risk-free rate and then discounting expected payoffs at the risk-free rate
C) A hedge set up to value an option does not need to be changed
D) All of the above
Q2) The current price of a non-dividend-paying stock is $40.Over the next year it is expected to rise to $42 or fall to $37.An investor buys put options with a strike price of $41.What is the value of each option? The risk-free interest rate is 2% per annum with continuous compounding.
A) $3.93
B) $2.93
C) $1.93
D) $0.93
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15
Chapter 14: Wiener Processes and Itos Lemma
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Q1) A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz
If a = 3 and b =4 what is the standard deviation of the value in three months?
A) 1
B) 2
C) 3
D) 4
Q2) Which of the following defines an Ito process?
A) A process where the drift is non-constant and can be stochastic
B) A process where the coefficient of dz is non-constant and can be stochastic
C) A process where either the drift or the coefficient of dz or both are non-constant and can be stochastic
D) A process where proportional changes follow a generalized Wiener process
Q3) For what value of the correlation between two Wiener processes is the sum of the processes also a Wiener process?
A) 0.5
B) 0.5
C) 0
D) 1
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16
Chapter 15: The Black-Scholes-Merton Model
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Q1) The original Black-Scholes and Merton papers on stock option pricing were published in which year?
A) 1983
B) 1984
C) 1974
D) 1973
Q2) A stock provides an expected return of 10% per year and has a volatility of 20% per year.What is the expected value of the continuously compounded return in one year?
A) 6%
B) 8%
C) 10%
D) 12%
Q3) Which of the following is assumed by the Black-Scholes-Merton model?
A) The return from the stock in a short period of time is lognormal
B) The stock price at a future time is lognormal
C) The stock price at a future time is normal
D) None of the above
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Chapter 16: Employee Stock Options
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Q1) What term is used to describe losses shareholders experience because the interests of managers are not aligned with their own?
A) Agency costs
B) Backdating scandals
C) Dilution
D) Income statement expense
Q2) Which of the following are true of employee stock options?
A) They are commonly valued as though they are regular American options
B) They are commonly valued as though they are regular American options, but with a reduced life.
C) They are commonly valued as though they are regular European option
D) They are commonly valued as though they are regular European options but with a reduced life.
Q3) When an employee leaves the company which of the following is usually true?
A) All outstanding employee stock options are forfeited
B) Out-of the money employee stock options are forfeited
C) All options which have vested are forfeited
D) All options are retained
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18
Chapter 17: Options on Stock Indices and Currencies
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Q1) Suppose that the domestic risk free rate is r and dividend yield on an index is q.How should the put-call parity formula for options on a non-dividend-paying stock be changed to provide a put-call parity formula for options on a stock index? Assume the options last T years.
A) The stock price is replaced by the value of the index multiplied by exp(qT)
B) The stock price is replaced by the value of the index multiplied by exp(rT)
C) The stock price is replaced by the value of the index multiplied by exp(-qT)
D) The stock price is replaced by the value of the index multiplied by exp(-rT)
Q2) A portfolio manager in charge of a portfolio worth $10 million is concerned that the market might decline rapidly during the next six months and would like to use put options on an index to provide protection against the portfolio falling below $9.5 million.The index is currently standing at 500 and each contract is on 100 times the index.What should the strike price of options on the index be the portfolio has a beta of 1?
A) 425
B) 450
C) 475
D) 500
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Chapter 18: Futures Options and Blacks Model
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Q1) One-year European call and put options on an asset are worth $3 and $4 respectively when the strike price is $20 and the one-year risk-free rate is 5%.What is the one-year futures price of the asset if there are no arbitrage opportunities? (Use put-call parity.)
A) $19.55
B) $18.95
C) $20.95
D) $20.45
Q2) Consider a European one-year call futures option and a European one-year put futures options when the futures price equals the strike price.Which of the following is true?
A) The call futures option is worth more than the put futures option
B) The put futures option is worth more than the call futures option
C) The call futures option is sometimes worth more and sometimes worth less than the put futures option
D) The call futures option is worth the same as the put futures option
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Chapter 19: The Greek Letters
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Q1) What does gamma measure?
A) The rate of change of delta with the asset price
B) The rate of change of the portfolio value with the passage of time
C) The sensitivity of a portfolio value to interest rate changes
D) None of the above
Q2) Which of the following is true?
A) The delta of a European put equals minus the delta of a European call
B) The delta of a European put equals the delta of a European call
C) The gamma of a European put equals minus the gamma of a European call
D) The gamma of a European put equals the gamma of a European call
Q3) Which of the following is true for a long position in an option
A) Both gamma and vega are negative
B) Gamma is negative and vega is positive
C) Gamma is positive and vega is negative
D) Both gamma and vega are positive
Q4) What does vega measure?
A) The rate of change of delta with the asset price
B) The rate of change of the portfolio value with the passage of time
C) The sensitivity of a portfolio value to interest rate changes
D) None of the above
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Chapter 20: Volatility Smiles
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Q1) Which of the following is true of a volatility smile?
A) Implied volatility is on the horizontal axis and strike price is on the vertical axis
B) Historical volatility is on the horizontal axis and strike price is on the vertical axis
C) Implied volatility is on the vertical axis and strike price is on the horizontal axis
D) Historical volatility is on the vertical axis and strike price is on the horizontal axis
Q2) Which of the following causes a volatility smile that is a ``frown``?
A) There is a small probability of a large stock price decrease in one week
B) There is a small probability of a large stock price increase in one week
C) The outcome of a lawsuit (roughly equal chance of being favorable or unfavorable) will create a large movement up or down in one week
D) None of the above
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22
Chapter 21: Basic Numerical Procedures
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Q1) The values of a stock price at the end of the second time step are $80,$100,$125.The corresponding values of an option are $0,$5,and $20 respectively.What is an estimate of gamma?
A) 0.136
B) 0.146
C) 0.156
D) 0.166
Q2) How many different paths are there through a Cox-Ross-Rubinstein tree with four-steps?
A) 5
B) 9
C) 12
D) 16
Q3) How many nodes are there at the end of a Cox-Ross-Rubinstein five-step binomial tree?
A) 4
B) 5
C) 6
D) 7
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Page 23
Chapter 22: Value at Risk and Expected Shortfall
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Q1) In the case of interest rate movements the second most important factor corresponds to
A) A parallel shift
B) A slope change
C) A bowing
D) An increase in short rates
Q2) A German bank has exposure to the S&P500.Which of the following is true
A) The S&P 500 index should be always be measured in U.S. dollars when VaR is calculated
B) The S&P 500 index should be always be measured in euros when VaR is calculated
C) Either A or B can be done
D) The S&P 500 index should be measured in euros only if the bank has not got a U.S. subsidiary.
Q3) Which was the minimum capital requirement for market risk in the 1996 BIS Amendment?
A) At least 3 times the 10-day VaR with a 99% confidence level
B) At least 3 times 7-day VaR with a 97% confidence level
C) At least 2 times 5-day VaR with a 95% confidence level
D) 1-day VaR with a 99% confidence level
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Page 24
Chapter 23: Estimating Volatilities and Correlations
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Q1) How many parameters are necessary to define a GARCH (1,1)model
A) 1
B) 2
C) 3
D) 4
Q2) Which of the following is true
A) All option implied volatilities tend to move by the same amount from one day to the next
B) The implied volatilities of long-dated options tend to move by more than the implied volatilities of short-dated options
C) The implied volatilities of short-dated options tend to move by more than the implied volatilities of long-dated options
D) Sometimes B is true and sometimes C is true
Q3) Which of the following is true of a positive semi-definite variance-covariance matrix
A) All elements of the matrix are positive
B) The determinant of the matrix is positive
C) The matrix has ones on the diagonal
D) The matrix is internally consistent
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Chapter 24: Credit Risk
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Q1) In the Gaussian copula model which of the following is true
A) The time to default for a company is assumed to be normally distributed.
B) The time to default for a company is assumed to be lognormally distributed
C) The time to default for a company is transformed to a normal distribution
D) The time to default for a company is transformed to a lognormal distribution
Q2) Which of the following is true
A) Downgrade triggers are particularly valuable if they are widely used by a company's counterparties
B) Downgrade triggers become less valuable if they are widely used by a company's counterparties
C) Downgrade triggers are useless because their impact is always anticipated by the market
D) Downgrade triggers are a two-edged sword. If company A has a downgrade trigger for company B then company B has a downgrade trigger for company A
Q3) Which of the following is true of Merton's model:
A) The equity is a call option on the assets
B) The assets are a call option on the debt
C) The debt is a call option on the equity
D) The equity is a call option on the debt
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Page 26
Chapter 25: Credit Derivatives
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Q1) Which of the following best describes a total return swap?
A) It exchanges the realized return on an asset, including both income and capital gains/losses, for a return, equal to LIBOR plus a spread on the initial value of the asset
B) It exchanges the promised return on an asset, including both income and capital gains/losses, for a return equal to LIBOR plus a spread on the initial value of the asset
C) It exchanges the realized return on an asset, including income but not capital gains/losses, for a return equal to LIBOR plus a spread on the initial value of the asset
D) It exchanges the promised return on an asset, including income but not capital gains/losses, for a return equal to LIBOR plus a spread on the initial value of the asset
Q2) Which of the following is true about a CDS?
A) Restructuring is never a credit event
B) Restructuring is always a credit event
C) Certain types of restructuring qualify as credit events but others do not
D) Sometimes a CDS is defined so that restructuring is a credit event and sometimes it is not
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27
Chapter 26: Exotic Options
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Q1) A volatility swap is
A) An instrument that swaps the change in the value of a market variable for a fixed amount
B) A swap involving an asset whose volatility is greater than a certain level
C) An exchange of the implied volatility of an option at a future time for a fixed volatility
D) An exchange of the realized volatility of an asset for a fixed volatility
Q2) There are two types of regular options (calls and puts).How many types of barrier options are there?
A) Two
B) Four
C) Six
D) Eight
Q3) A floating lookback call option pays off which of the following
A) The amount by which the final stock price exceeds the minimum stock price
B) The amount by which the maximum stock price exceeds the final stock price
C) The amount by which the strike price exceeds the minimum stock price
D) The amount by which the maximum stock price exceeds the strike price
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