Fixed Income Securities
Mock Exam
Course Introduction
This course provides a comprehensive overview of fixed income securities, including their structures, valuation, and risk characteristics. Students will explore various types of debt instruments such as bonds, mortgage-backed securities, and government and corporate obligations. The curriculum covers fundamental topics such as yield curves, interest rate risk, credit risk analysis, and pricing models. Additionally, the course examines methods for managing fixed income portfolios and the impact of macroeconomic factors on fixed income markets. Practical applications and case studies are integrated to prepare students for real-world investment and risk management decisions in the fixed income arena.
Recommended Textbook
Options Futures and Other Derivatives 10th Edition by John C. Hull
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Chapter 1: Introduction
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Q1) A company knows it will have to pay a certain amount of a foreign currency to one of its suppliers in the future.Which of the following is true
A) A forward contract can be used to lock in the exchange rate
B) A forward contract will always give a better outcome than an option
C) An option will always give a better outcome than a forward contract
D) An option can be used to lock in the exchange rate
Answer: A
Q2) The price of a stock on February 1 is $84.A trader buys 200 put options on the stock with a strike price of $90 when the option price is $10.The options are exercised when the stock price is $85.The trader's net profit or loss is
A) Loss of $1,000
B) Loss of $2,000
C) Gain of $200
D) Gain of $1000
Answer: A
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3
Chapter 2: Futures Markets and Central Counterparties
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Q1) A speculator takes a long position in a futures contract on a commodity on November 1,2012 to hedge an exposure on March 1,2013.The initial futures price is $60.On December 31,2012 the futures price is $61.On March 1,2013 it is $64.The contract is closed out on March 1,2013.What gain is recognized in the accounting year January 1 to December 31,2013? Each contract is on 1000 units of the commodity.
A) $0
B) $3,000
C) $1,000
D) $4,000
Answer: C
Q2) Clearing houses are
A) Never used in futures markets and sometimes used in OTC markets
B) Used in OTC markets, but not in futures markets
C) Always used in futures markets and sometimes used in OTC markets
D) Always used in both futures markets and OTC markets
Answer: C
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Chapter 3: Hedging Strategies Using Futures
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Q1) Which of the following is true?
A) Gold producers should always hedge the price they will receive for their production of gold over the next three years
B) Gold producers should always hedge the price they will receive for their production of gold over the next one year
C) The hedging strategies of a gold producer should depend on whether it shareholders want exposure to the price of gold
D) Gold producers can hedge by buying gold in the forward market
Answer: C
Q2) Futures contracts trade with every month as a delivery month.A company is hedging the purchase of the underlying asset on June 15.Which futures contract should it use?
A) The June contract
B) The July contract
C) The May contract
D) The August contract
Answer: B
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Chapter 4: Interest Rates
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Q1) The two-year zero rate is 6% and the three year zero rate is 6.5%.What is the forward rate for the third year? All rates are continuously compounded.
A) 6.75%
B) 7.0%
C) 7.25%
D) 7.5%
Q2) Bootstrapping involves
A) Calculating the yield on a bond
B) Working from short maturity instruments to longer maturity instruments determining zero rates at each step
C) Working from long maturity instruments to shorter maturity instruments determining zero rates at each step
D) The calculation of par yields
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) An exchange rate is 0.7000 and the six-month domestic and foreign risk-free interest rates are 5% and 7% (both expressed with continuous compounding).What is the six-month forward rate?
A) 0.7070
B) 0.7177
C) 0.7249
D) 0.6930
Q2) The spot price of an investment asset is $30 and the risk-free rate for all maturities is 10% with continuous compounding.The asset provides an income of $2 at the end of the first year and at the end of the second year.What is the three-year forward price?
A) $19.67
B) $35.84
C) $45.15
D) $40.50
Q3) As inventories of a commodity decline,which of the following is true?
A) The one-year futures price as a percentage of the spot price increases
B) The one-year futures price as a percentage of the spot price decreases
C) The one-year futures price as a percentage of the spot price stays the same
D) Any of the above can happen
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Page 7
Chapter 6: Interest Rate Futures
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Q1) 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.
Q2) The conversion factor for a bond is approximately
A) The price it would have if all cash flows were discounted at 6% per annum
B) The price it would have if it paid coupons at 6% per annum
C) The price it would have if all cash flows were discounted at 8% per annum
D) The price it would have if it paid coupons at 8% per annum
Q3) How much is a basis point?
A) 1.0%
B) 0.1%
C) 0.01%
D) 0.001%
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Chapter 7: Swaps
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Q1) Which of the following is a way of valuing interest rate swaps where LIBOR is exchanged for a fixed rate of interest?
A) Assume that floating payments will equal forward LIBOR rates and discount net cash flows at the risk-free rate
B) Assume that floating payments will equal forward OIS rates and discount net cash flows at the risk-free rate
C) Assume that floating payments will equal forward LIBOR rates and discount net cash flows at the swap rate
D) Assume that floating payments will equal forward OIS rates and discount net cash flows at the swap rate
Q2) Since the 2008 credit crisis
A) LIBOR has replaced OIS as the discount rate for non-collateralized swaps
B) OIS has replaced LIBOR as the discount rate, but only for non-collateralized swaps
C) LIBOR has replaced OIS as the discount rate for collateralized swaps
D) OIS has replaced LIBOR as the discount rate for swaps
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) Which of the following describes regulatory arbitrage?
A) Finding a way of reducing capital requirements without changing the risks being taken
B) Buying products that are not subject to regulation
C) Shorting products that are not subject to regulation
D) Trading with the government
Q2) Suppose that ABSs are created from portfolios of subprime mortgages with the following allocation of the principal to tranches: senior 94.5% (rated AAA),mezzanine 0.1% (rated BBB),and equity 5% (rated C).The portfolios of subprime mortgages have the same default rates.An ABS CDO is then created from the mezzanine tranches.Which of the following is true?
A) The ABS CDO tranches should have ratings ranging from AAA to C
B) The ABS CDO tranches should all be rated BBB
C) The ABS CDO tranches should all be rated C
D) The ABS CDO tranches are almost worthless because the mezzanine tranches are so thin
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Chapter 9: Xvas
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Q1) Which of the following is true
A) FVA is always positive
B) FVA is always negative
C) FVA for a transaction is initially zero
D) None of the above
Q2) FVA is concerned with
A) The cost of funding initial margin
B) The cost of funding variation margin
C) The cost of regulatory capital
D) None of the above
Q3) Prior to the credit crisis that started in 2007 which of the following was used by derivatives traders for the discount rate when derivatives were valued
A) The Treasury rate
B) The LIBOR rate
C) The repo rate
D) The overnight indexed swap rate
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11
Chapter 10: Mechanics of Options Markets
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Q1) 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
Q2) An investor has exchange-traded put options to sell 100 shares for $20.There is a $1 cash dividend.Which of the following is then the position of the investor?
A) The investor has put options to sell 100 shares for $20
B) The investor has put options to sell 100 shares for $19
C) The investor has put options to sell 105 shares for $19
D) The investor has put options to sell 105 shares for $19.05
Q3) A trader buys a call and sells a put with the same strike price and maturity date.What is the position equivalent to?
A) A long forward
B) A short forward
C) Buying the asset
D) None of the above
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Page 12
Chapter 11: Properties of Stock Options
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Q1) Which of the following describes a situation where an American put option on a stock becomes more likely to be exercised early?
A) Expected dividends increase
B) Interest rates decrease
C) The stock price volatility decreases
D) All of the above
Q2) 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
Q3) 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
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13
Chapter 12: Trading Strategies Involving Options
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Q1) What is a description of the trading strategy where an investor sells a 3-month call option and buys a one-year call option,where both options have a strike price of $100 and the underlying stock price is $75?
A) Neutral Calendar Spread
B) Bullish Calendar Spread
C) Bearish Calendar Spread
D) None of the above
Q2) A stock price is currently $23.A reverse (i.e short)butterfly spread is created from options with strike prices of $20,$25,and $30.Which of the following is true?
A) The gain when the stock price is greater than $30 is less than the gain when the stock price is less than $20
B) The gain when the stock price is greater than $30 is greater than the gain when the stock price is less than $20
C) The gain when the stock price is greater than $30 is the same as the gain when the stock price is less than $20
D) It is incorrect to assume that there is always a gain when the stock price is greater than $30 or less than $20
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Page 14
Chapter 13: Binomial Trees
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Q1) The current price of a non-dividend-paying stock is $30.Over the next six months it is expected to rise to $36 or fall to $26.Assume the risk-free rate is zero.An investor sells call options with a strike price of $32.What is the value of each call option?
A) $1.6
B) $2.0
C) $2.4
D) $3.0
Q2) The current price of a non-dividend paying stock is $50.Use a two-step tree to value an American put option on the stock with a strike price of $48 that expires in 12 months.Each step is 6 months,the risk free rate is 5% per annum,and the volatility is 20%.Which of the following is the option price?
A) $1.95
B) $2.00
C) $2.05
D) $2.10
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Chapter 14: Wiener Processes and Itos Lemma
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Q1) A variable x starts at zero and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.During the first two years a=3 and b=4.During the following three years a=6 and b=3.What is the expected value of the variable at the end of 5 years
A) 16
B) 20
C) 24
D) 30
Q2) If a stock price follows a Markov process which of the following could be true
A) Whenever the stock price has gone up for four successive days it has a 70% chance of going up on the fifth day.
B) Whenever the stock price has gone up for four successive days there is almost certain to be a correction on the fifth day.
C) The way the stock price moves on a day is unaffected by how it moved on the previous four days.
D) Bad years for stock price returns are usually followed by good years.
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16
Chapter 15: The Black-Scholes-Merton Model
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Q1) The risk-free rate is 5% and the expected return on a non-dividend-paying stock is 12%.Which of the following is a way of valuing a derivative?
A) Assume that the expected growth rate for the stock price is 17% and discount the expected payoff at 12%
B) Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 12%
C) Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 5%
D) Assuming that the expected growth rate for the stock price is 12% and discounting the expected payoff at 5%
Q2) The volatility of a stock is 18% per year.Which is closest to the volatility per month?
A) 1.5%
B) 3.0%
C) 5.2%
D) 6.3%
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Chapter 16: Employee Stock Options
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Q1) 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.
Q2) Employee stock options are particularly popular with start ups because
A) They encourage employees to work hard
B) The start up cannot afford to pay high salaries
C) The risk associated with the company's success is shared with employees.
D) All of the above
Q3) Which of the following is NOT usually true about employee stock options?
A) There is a vesting period
B) They can be sold to other employees
C) They are often at-the-money when issued
D) Their value is currently a charge to the income statement
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Chapter 17: Options on Stock Indices and Currencies
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Q1) Which of the following is NOT true about a range forward contract?
A) It ensures that the exchange rate for a future transaction will lie between two values
B) It can be structured so that it costs nothing to set up
C) It requires a forward contract as well as two options
D) It can be used to hedge either a future inflow or a future outflow of a foreign currency
Q2) For a European put option on an index,the index level is 1,000,the strike price is 1050,the time to maturity is six months,the risk-free rate is 4% per annum,and the dividend yield on the index is 2% per annum.How low can the option price be without there being an arbitrage opportunity?
A) $50.00
B) $43.11
C) $29.21
D) $39.16
Q3) What is the size of one option contract on the S&P 500?
A) 250 times the index
B) 100 times the index
C) 50 times the index
D) 25 times the index
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Chapter 18: Futures Options and Blacks Model
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Q1) The risk-free rate is 5% and the dividend yield on the S&P 500 index is 2%.Which of the following is correct when a futures option on the index is being valued?
A) The futures price of the S&P 500 is treated like a stock paying a dividend yield of 5%.
B) The futures price of the S&P 500 is treated like a stock paying a dividend yield of 2%.
C) The futures price of the S&P 500 is treated like a stock paying a dividend yield of 3%.
D) The futures price of the S&P 500 is treated like a non-dividend-paying stock.
Q2) What is the cash settlement if a put futures option on 50 units of the underlying asset is exercised?
A) (Current Futures Price - Strike Price) times 50
B) (Strike Price - Current Futures Price) times 50
C) (Most Recent Futures Settlement Price - Strike Price) times 50
D) (Strike Price - Most Recent Futures Settlement Price) times 50
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20
Chapter 19: The Greek Letters
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Q1) 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
Q2) A call option on a stock has a delta of 0.3.A trader has sold 1,000 options.What position should the trader take to hedge the position?
A) Sell 300 shares
B) Buy 300 shares
C) Sell 700 shares
D) Buy 700 shares
Q3) What does theta 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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21
Chapter 20: Volatility Smiles
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Q1) If the volatility implied from an at-the-money put stock option were used to price other put options on the stock,which of the following would be true?
A) Out-of-the money and in-the-money prices would be too high
B) Out-of-the money and in-the-money prices would be too low
C) Out-of-the-money option prices would be too high and in-the-money option prices would be too low
D) Out-of-the-money option prices would be too low and in-the-money option prices would be too high
Q2) Which of the following is true when the tails of a future stock price distribution are compared with those of a lognormal distribution with the same mean and standard deviation?
A) The left tail and right tail are thinner
B) The left tail is thinner and the right tail is fatter
C) The right tail is thinner and the left tail is fatter
D) Both tails are fatter
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22
Chapter 21: Basic Numerical Procedures
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Q1) Which of the following cannot be valued by Monte Carlo simulation
A) European options
B) American options
C) Asian options (i.e., options on the average stock price)
D) An option which provides a payoff of $100 if the stock price is greater than the strike price at maturity
Q2) A binomial tree prices an American option at $3.12 and the corresponding European option at $3.04.The Black-Scholes-Merton price of the European option is $2.98.What is the control variate price of the American option?
A) $3.06
B) $3.18
C) $2.90
D) $3.08
Q3) What is the recommended way of making volatility a function of time in a Cox,Ross,Rubinstein tree?
A) Make u a function of time
B) Make p a function of time
C) Make u and p a function of time
D) Make the lengths of the time steps unequal
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Page 23
Chapter 22: Value at Risk and Expected Shortfall
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Q1) Which of the following is true?
A) The quadratic model approximates daily changes using delta and gamma
B) The quadratic model approximates daily changes using delta, but not gamma
C) The quadratic model approximates daily changes using gamma, but not delta
D) None of the above
Q2) The 10-day VaR is often assumed to be which of the following
A) The 1-day VaR multiplied by 10
B) The 1-day VaR multiplied by the square root of10
C) The 1-day VaR divided by 10
D) The 1-day VaR divided by the square root of 10
Q3) Which of the following is true of the 99.9% value at risk?
A) There is 1 chance in 10 that the loss will be greater than the value of risk
B) There is 1 chance in 100 that the loss will be greater than the value of risk
C) There is 1 chance in 1000 that the loss will be greater than the value of risk
D) None of the above
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24
Chapter 23: Estimating Volatilities and Correlations
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Q1) At the end of Thursday,the estimated covariance between assets A and B is 0.0001.During Friday asset A produces a return of 3% and asset B produces a return of zero.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the covariance at the end of Friday?
A) 0.000090
B) 0.000081
C) 0.000100
D) 0.000095
Q2) How many parameters are necessary to define a GARCH (1,1)model
A) 1
B) 2
C) 3
D) 4
Q3) Which of the following is true
A) Volatilities and correlations decreased in the second half of 2008
B) Volatilities and correlations increased in the second half of 2008
C) Volatilities decreased and correlations increased in the second half of 2008
D) Volatilities increased and correlations decreased in the second half of 2008
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25
Chapter 24: Credit Risk
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Q1) Which of the following is usually used to define the recovery rate of a bond?
A) The value of the bond immediately after default as a percent of its face value
B) The value of the bond immediately after default as a percent of the sum of the bond's face value and accrued interest
C) The amount finally realized by a bondholder as a percent of face value
D) The amount finally realized by a bondholder as a percent of the sum of the bond's face value and accrued interest
Q2) Which of the following is true
A) The Gaussian copula model assumes that the defaults of different companies are independent.
B) The Gaussian copula model assumes that defaults, conditional on the value of a factor , are independent.
C) The Gaussian copula model assumes that the number of defaults is normally distributed.
D) None of the above.
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Chapter 25: Credit Derivatives
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Q1) Which of the following describes "base correlation"
A) The most basic correlation measure possible
B) A correlation used to value all tranches
C) The correlation implied from market data
D) The correlation for valuing a tranche with an attachment point of 0%
Q2) Which of the following happens when the default correlation of the companies underlying a CDO increases?
A) The value of the senior tranche and the equity tranche to the protection buyer both increase
B) The value of the senior tranche and the equity tranche to the protection buyer both decrease
C) The value of the senior tranche to the protection buyer decreases and the value of the equity tranche to the protection buyer increases
D) The value of the senior tranche to the protection buyer increases and the value of the equity tranche to the protection buyer decreases
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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) When can Bermudan options be exercised?
A) Any time during the life of the options
B) Any time after a certain date up to the end of the life of the life
C) Any time before a certain date or at the end of the option's life
D) On dates specified at the start of the option
Q3) Which of the following is the payoff from an average strike call option?
A) The excess of the strike price over the average stock price, if positive
B) The excess of the final stock price over the average stock price, if positive
C) The excess of the average stock price over the strike price, if positive
D) The excess of the average stock price over the final stock price, if positive
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