Fixed Income Securities
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Course Introduction
Fixed Income Securities explores the fundamental concepts, instruments, and analytical tools used in the valuation and management of fixed income investments such as bonds, treasury securities, mortgage-backed securities, and other debt instruments. The course covers the structure of fixed income markets, interest rate risk, yield curves, pricing methodologies, and credit risk analysis. Students learn to evaluate the risk-return characteristics of various fixed income products, understand the impact of changing economic conditions on bond prices, and apply quantitative techniques for portfolio management, asset allocation, and hedging strategies. Special attention is given to current market practices, regulatory frameworks, and the role of fixed income securities in diversifying investment portfolios.
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Options Futures and Other Derivatives 10th Edition by John C. Hull
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Page 2
Chapter 1: Introduction
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Q1) The price of a stock on February 1 is $48.A trader sells 200 put options on the stock with a strike price of $40 when the option price is $2.The options are exercised when the stock price is $39.The trader's net profit or loss is
A) Loss of $800
B) Loss of $200
C) Gain of $200
D) Loss of $900
Answer: C
Q2) The price of a stock on February 1 is $124.A trader sells 200 put options on the stock with a strike price of $120 when the option price is $5.The options are exercised when the stock price is $110.The trader's net profit or loss is
A) Gain of $1,000
B) Loss of $2,000
C) Loss of $2,800
D) Loss of $1,000
Answer: D
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3
Chapter 2: Futures Markets and Central Counterparties
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Q1) A company enters into a short futures contract to sell 50,000 units of a commodity for 70 cents per unit.The initial margin is $4,000 and the maintenance margin is $3,000.What is the futures price per unit above which there will be a margin call?
A) 78 cents
B) 76 cents
C) 74 cents
D) 72 cents
Answer: D
Q2) The frequency with which futures margin accounts are adjusted for gains and losses is
A) Daily
B) Weekly
C) Monthly
D) Quarterly
Answer: A
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Chapter 3: Hedging Strategies Using Futures
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Q1) 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
Q2) Which of the following describes tailing the hedge?
A) A strategy where the hedge position is increased at the end of the life of the hedge
B) A strategy where the hedge position is increased at the end of the life of the futures contract
C) A more exact calculation of the hedge ratio when forward contracts are used for hedging
D) None of the above
Answer: D
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Chapter 4: Interest Rates
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Q1) Under liquidity preference theory,which of the following is always true?
A) The forward rate is higher than the spot rate when both have the same maturity.
B) Forward rates are unbiased predictors of expected future spot rates.
C) The spot rate for a certain maturity is higher than the par yield for that maturity.
D) Forward rates are higher than expected future spot rates.
Q2) Which of the following is true?
A) When interest rates in the economy increase, all bond prices increase
B) As its coupon increases, a bond's price decreases
C) Longer maturity bonds are always worth more that shorter maturity bonds when the coupon rates are the same
D) None of the above
Q3) An interest rate is 5% per annum with continuous compounding.What is the equivalent rate with semiannual compounding?
A) 5.06%
B) 5.03%
C) 4.97%
D) 4.94%
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Chapter 5: Determination of Forward and Futures Prices
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Q1) The spot price of an investment asset that provides no income is $30 and the risk-free rate for all maturities (with continuous compounding)is 10%.What is the three-year forward price?
A) $40.50
B) $22.22
C) $33.00
D) $33.16
Q2) Which of the following describes contango?
A) The futures price is below the expected future spot price
B) The futures price is below today's spot price
C) The futures price is a declining function of the time to maturity
D) The futures price is above the expected future spot price
Q3) Which of the following is NOT a reason why a short position in a stock is closed out?
A) The investor with the short position chooses to close out the position
B) The lender of the shares issues instructions to close out the position
C) The broker is no longer able to borrow shares from other clients
D) The investor does not maintain margins required on his/her margin account
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Chapter 6: Interest Rate Futures
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Q1) Which of the following is true?
A) The futures rates calculated from a Eurodollar futures quote are always less than the corresponding forward rate
B) The futures rates calculated from a Eurodollar futures quote are always greater than the corresponding forward rate
C) The futures rates calculated from a Eurodollar futures quote should equal the corresponding forward rate
D) The futures rates calculated from a Eurodollar futures quote are sometimes greater than and sometimes less than the corresponding forward rate
Q2) An ultra T-bond futures contract is one where
A) Bonds with maturities less than 3 years can be delivered
B) Bonds with maturities less than 10 years can be delivered
C) Bonds with maturities greater than 15 years can be delivered
D) Bonds with maturities greater than 25 year can be delivered
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Chapter 7: Swaps
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Q1) A company can invest funds for five years at LIBOR minus 30 basis points.The five-year swap rate is 3%.What fixed rate of interest can the company earn by using the swap?
A) 2.4%
B) 2.7%
C) 3.0%
D) 3.3%
Q2) Which of the following is a use of a currency swap?
A) To exchange an investment in one currency for an investment in another currency
B) To exchange borrowing in one currency for borrowings in another currency
C) To take advantage situations where the tax rates in two countries are different
D) All of the above
Q3) Which of the following is usually true
A) OIS rates are less than the corresponding LIBOR rates
B) OIS rates are greater than corresponding LIBOR rates
C) OIS rates are sometimes greater and sometimes less than LIBOR rates
D) OIS rates are equivalent to one-day LIBOR rates
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) 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%
Q2) Which of the following describes the S&P/Case-Shiller index?
A) A stock market index
B) An index of interest rates on mortgages
C) An index of house prices
D) An index showing the dollar amount of mortgages granted each month
Q3) What are teaser rates
A) Interest rates that appear lower than they are
B) Interest rates that depend on LIBOR
C) Interest rates on mortgages with a very long amortization period
D) Interest rates that apply only for the first two or three years
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Chapter 9: Xvas
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Q1) CVA stands for
A) Collateral valuation adjustment
B) Credit valuation adjustment
C) Credit valuation agreement
D) Collateral valuation agreement
Q2) When a bank's borrowing rate goes up,which of the following is true
A) DVA increases so that the bank's profit goes down
B) DVA increases so that the bank's profit goes up
C) DVA declines so that the bank's profit goes down
D) DVA declines so that the bank's profit goes up
Q3) 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
Q4) 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
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Chapter 10: Mechanics of Options Markets
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Q1) Which of the following is true?
A) A long call is the same as a short put
B) A short call is the same as a long put
C) A call on a stock plus a stock is the same as a put
D) None of the above
Q2) Consider a put option and a call option with the same strike price and time to maturity.Which of the following is true?
A) It is possible for both options to be in the money
B) It is possible for both options to be out of the money
C) One of the options must be in the money
D) One of the options must be either in the money or at the money
Q3) The price of a stock is $67.A trader sells 5 put option contracts on the stock with a strike price of $70 when the option price is $4.The options are exercised when the stock price is $69.What is the trader's net profit or loss?
A) Loss of $1,500
B) Loss of $500
C) Gain of $1,500
D) Loss of $1,000
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Page 12
Chapter 11: Properties of Stock Options
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Q1) The price of a European call option on a stock with a strike price of $50 is $6.The stock price is $51,the continuously compounded risk-free rate (all maturities)is 6% and the time to maturity is one year.A dividend of $1 is expected in six months.What is the price of a one-year European put option on the stock with a strike price of $50?
A) $8.97
B) $6.97
C) $3.06
D) $1.12
Q2) Which of the following is true when dividends are expected?
A) Put-call parity does not hold
B) The basic put-call parity formula can be adjusted by subtracting the present value of expected dividends from the stock price
C) The basic put-call parity formula can be adjusted by adding the present value of expected dividends to the stock price
D) The basic put-call parity formula can be adjusted by subtracting the dividend yield from the interest rate
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13
Chapter 12: Trading Strategies Involving Options
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Q1) 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
Q2) Which of the following is correct?
A) A calendar spread can be created by buying a call and selling a put when the strike prices are the same and the times to maturity are different
B) A calendar spread can be created by buying a put and selling a call when the strike prices are the same and the times to maturity are different
C) A calendar spread can be created by buying a call and selling a call when the strike prices are different and the times to maturity are different
D) A calendar spread can be created by buying a call and selling a call when the strike prices are the same and the times to maturity are different
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Chapter 13: Binomial Trees
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Q1) Which of the following describes how American options can be valued using a binomial tree?
A) Check whether early exercise is optimal at all nodes where the option is in-the-money
B) Check whether early exercise is optimal at the final nodes
C) Check whether early exercise is optimal at the penultimate nodes and the final nodes
D) None of the above
Q2) 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 six-month call options with a strike price of $32.Which of the following hedges the position?
A) Buy 0.6 shares for each call option sold
B) Buy 0.4 shares for each call option sold
C) Short 0.6 shares for each call option sold
D) Short 0.4 shares for each call option sold
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15
Chapter 14: Wiener Processes and Itos Lemma
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Q1) The process followed by a variable X is dX = mX dt+sX dz What is the coefficient of dt in the process for the square of X.
A) 2mX2+s2X2
B) 2mX2
C) mX2+2s2X2
D) mX2+s2X2
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.
Q3) The variance of a Wiener process in time t is
A) t
B) t squared
C) the square root of t
D) t to the power of 4
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Page 16
Chapter 15: The Black-Scholes-Merton Model
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Q1) When the non-dividend paying stock price is $20,the strike price is $20,the risk-free rate is 6%,the volatility is 20% and the time to maturity is 3 months which of the following is the price of a European put option on the stock
A) 19.7N(-0.1)-20N(-0.2)
B) 20N(-0.1)-20N(-0.2)
C) 19.7N(-0.2)-20N(-0.1)
D) 20N(-0.2)-20N(-0.1)
Q2) Which of the following is NOT true?
A) Risk-neutral valuation provides prices that are only correct in a world where investors are risk-neutral
B) Options can be valued based on the assumption that investors are risk neutral
C) In risk-neutral valuation the expected return on all investment assets is set equal to the risk-free rate
D) In risk-neutral valuation the risk-free rate is used to discount expected cash flows
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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) Which of the following was true after 2005?
A) The options never had any affect on a company's financial statements
B) The value of options which were at-the-money when issued had to be expensed on the income statement
C) The value of options which were at-the-money when issued had to be reported in the notes to the financial statements
D) Options which were at-the-money when issued did not affect a company's financial statements
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18
Chapter 17: Options on Stock Indices and Currencies
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Q1) 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
Q2) 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
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Chapter 18: Futures Options and Blacks Model
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Q1) Which of the following is true for a September futures option?
A) The expiration month of option is September
B) The option was first traded in September
C) The delivery month of the underlying futures contract is September
D) September is the first month when the option can be exercised
Q2) A futures price is currently 40 cents.It is expected to move up to 44 cents or down to 34 cents in the next six months.The risk-free interest rate is 6%.What is the probability of an up movement in a risk-neutral world?
A) 0.4
B) 0.5
C) 0.72
D) 0.6
Q3) Which of the following is acquired (in addition to a cash payoff)when the holder of a call futures exercises?
A) A long position in a futures contract
B) A short position in a futures contract
C) A long position in the underlying asset
D) A short position in the underlying asset
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Chapter 19: The Greek Letters
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Q1) What does rho 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) Vega tends to be high for which of the following
A) At-the money options
B) Out-of-the money options
C) In-the-money options
D) Options with a short time to maturity
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) Gamma tends to be high for which of the following
A) At-the money options
B) Out-of-the money options
C) In-the-money options
D) Options with a long time to maturity
21
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Chapter 20: Volatility Smiles
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Q1) Which of the following is NOT true?
A) A volatility surface provides more information than a single volatility smile
B) A volatility surface is used to determine the implied volatility of an option that does not trade actively
C) A volatility surface can be determined from a single volatility smile using interpolation
D) A volatility surface incorporates information about options with different maturity dates
Q2) A volatility surface is a table showing the relationship between which of the following
A) Implied volatility, time to maturity, and strike price
B) Implied volatility, historical volatility, and time to maturity
C) Historical volatility, strike price, and time to maturity
D) None of the above
Q3) Which of the following could cause the volatility smile typically seen for foreign currency options?
A) Currencies are traded in different countries at different times of the day
B) Currencies tend to have low volatilities
C) The activities of central banks causes occasional jumps in the exchange rate
D) Interest rates may be different in the two countries
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22
Chapter 21: Basic Numerical Procedures
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Q1) What is the difference between valuing an American and a European option using a tree?
A) The value of u is higher for American options
B) The value of u is lower for American options
C) The time steps for American options are not equal
D) It is necessary to do two calculations at nodes where the option is in the money
Q2) Which of the following is true for u in a Cox-Ross-Rubinstein binomial tree?
A) It depends on the interest rate and the volatility
B) It depends on the volatility but not the interest rate
C) It depends on the interest rate but not the volatility
D) It depends on neither the interest rate nor the volatility
Q3) Which of the following can be valued without using a numerical procedure such as a binomial tree?
A) American put options on a non-dividend paying stock
B) American call options on a non-dividend paying tock
C) American call options on a currency
D) American put options on futures
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Chapter 22: Value at Risk and Expected Shortfall
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Q1) Consider a position in options on a particular stock.The position has a delta of 12 and the stock price is 10.Which of the following is the approximate relation between the change in the portfolio value in one day,dP,and the return on the stock during the day,dx
A) dP=12dx
B) dP=1.2dx
C) dP=120dx
D) dP=22dx
Q2) In the case of interest rate movements the most important factor corresponds to A) A parallel shift
B) A slope change
C) A bowing
D) An increase in short rates
Q3) Which of the following is true of a covariance matrix?
A) The numbers on the diagonal are variances
B) The numbers on the diagonal are standard deviations
C) The numbers on the diagonal are all one.
D) The numbers on the diagonal are all zero
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Chapter 23: Estimating Volatilities and Correlations
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Q1) At the end of Thursday,the estimated volatility of asset A is 2% per day.During Friday asset A produces a return of 3%.An EWMA model with lambda equal to 0.9 is used.What is an estimate of the volatility of asset A at the end of Friday?
A) 2.08%
B) 2.10%
C) 2.12%
D) 2.14%
Q2) Which of the following is true
A) GARCH (1,1) will always give a maximum likelihood at least as high as EWMA
B) EWMA will always give a maximum likelihood at least as high as GARCH (1,1)
C) The maximum likelihood is the same for GARCH (1,1) and EWMA
D) Sometimes A is true and sometimes B is true.
Q3) How many parameters are necessary to define a GARCH (1,1)model
A) 1
B) 2
C) 3
D) 4
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Chapter 24: Credit Risk
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Q1) Suppose that the cumulative probability of a company defaulting by years one,two,three and four are 3%,6.5%,10%,and 14.5%,respectively.What is the probability of default in the fourth year conditional on no earlier default?
A) 4.5%
B) 5.0%
C) 5.5%
D) 6.0%
Q2) 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
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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Chapter 25: Credit Derivatives
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Q1) 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
Q2) What is the rating of the companies underlying the iTraxx index?
A) A or above
B) BBB or above
C) BB or below
D) BBB or below
Q3) A portfolio of ten companies is formed.In a third-to-default swap (Circle one)
A) There is a payoff when the third default on the portfolio happens
B) There is a payoff when the first, second and third companies defaults happen
C) There is a payoff when the third, fourth, fifth tenth companies defaults happen
D) None of the above
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Chapter 26: Exotic Options
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Q1) Which of the following describes a cliquet option
A) An option to exchange one asset for another
B) An instrument when the holder can choose between several alternative options
C) An option on an option with predetermined strike prices for the two options
D) A series of options with rules for determining strike prices
Q2) Static options replication for a portfolio of American options on a stock involves
A) Finding a hedge portfolio to match daily changes
B) Finding a hedge portfolio to match values on a boundary that is certain to be reached
C) Finding a hedge portfolio to match values at one particular time
D) Constructing a hedge taking both gamma and delta into account
Q3) In a shout call option the strike price is $30.The holder shouts when the asset price is $40.What is the payoff from the option if the final asset price is $35?
A) $0
B) $5
C) $10
D) $15
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