Risk Management Final Exam
Course Introduction
Risk Management is a comprehensive course that introduces students to the fundamental concepts and practices involved in identifying, assessing, and mitigating risks within organizations. The course covers various types of risks including financial, operational, strategic, and compliance risks and explores the processes of risk analysis, measurement, and control. Students learn how to develop risk management frameworks, employ quantitative and qualitative tools, and implement effective risk response strategies. Through case studies and real-world examples, the course emphasizes the importance of integrating risk management into decision-making to enhance organizational resilience and achieve objectives.
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Options Futures and Other Derivatives 10th Edition by
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Page 2
John C. Hull
Chapter 1: Introduction
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Q1) Which of the following is NOT true
A) A call option gives the holder the right to buy an asset by a certain date for a certain price
B) A put option gives the holder the right to sell an asset by a certain date for a certain price
C) The holder of a call or put option must exercise the right to sell or buy an asset
D) The holder of a forward contract is obligated to buy or sell an asset
Answer: C
Q2) An investor sells a futures contract an asset when the futures price is $1,500.Each contract is on 100 units of the asset.The contract is closed out when the futures price is $1,540.Which of the following is true
A) The investor has made a gain of $4,000
B) The investor has made a loss of $4,000
C) The investor has made a gain of $2,000
D) The investor has made a loss of $2,000
Answer: B
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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) A haircut of 20% means that
A) A bond with a market value of $100 is considered to be worth $80 when used to satisfy a collateral request
B) A bond with a face value of $100 is considered to be worth $80 when used to satisfy a collateral request
C) A bond with a market value of $100 is considered to be worth $83.3 when used to satisfy a collateral request
D) A bond with a face value of $100 is considered to be worth $83.3 when used to satisfy a collateral request
Answer: A
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Chapter 3: Hedging Strategies Using Futures
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Q1) A company will buy 1000 units of a certain commodity in one year.It decides to hedge 80% of its exposure using futures contracts.The spot price and the futures price are currently $100 and $90,respectively.The spot price and the futures price in one year turn out to be $112 and $110,respectively.What is the average price paid for the commodity?
A) $92
B) $96
C) $102
D) $106
Answer: B
Q2) Which of the following increases basis risk?
A) A large difference between the futures prices when the hedge is put in place and when it is closed out
B) Dissimilarity between the underlying asset of the futures contract and the hedger's exposure
C) A reduction in the time between the date when the futures contract is closed and its delivery month
D) None of the above
Answer: B
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5
Chapter 4: Interest Rates
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Q1) 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%
Q2) The zero curve is upward sloping.Define X as the 1-year par yield,Y as the 1-year zero rate and Z as the forward rate for the period between 1 and 1.5 year.Which of the following is true?
A) X is less than Y which is less than Z
B) Y is less than X which is less than Z
C) X is less than Z which is less than Y
D) Z is less than Y which is less than X
Q3) Which of the following is true of the fed funds rate
A) It is the same as the Treasury rate
B) It is an overnight interbank rate
C) It is a rate for which collateral is posted
D) It is a type of repo rate
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6
Chapter 5: Determination of Forward and Futures Prices
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Q1) As the convenience yield increases,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
Q2) 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.
Q3) Which of the following is a consumption asset?
A) The S&P 500 index
B) The Canadian dollar
C) Copper
D) IBM stock
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Chapter 6: Interest Rate Futures
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Q1) A trader uses 3-month Eurodollar futures to lock in a rate on $5 million for six months.How many contracts are required?
A) 5
B) 10
C) 15
D) 20
Q2) Which of the following is NOT true about duration?
A) It equals the years-to-maturity for a zero coupon bond
B) It equals the weighted average of payment times for a bond, where weights are proportional to the present value of payments
C) Equals the weighted average of individual bond durations for a portfolio, where weights are proportional to the present value of bond prices
D) The prices of two bonds with the same duration change by the same percentage amount when interest rate moves up by 100 basis points
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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 company enters into an interest rate swap where it is paying fixed and receiving LIBOR.When interest rates increase,which of the following is true?
A) The value of the swap to the company increases
B) The value of the swap to the company decreases
C) The value of the swap can either increase or decrease
D) The value of the swap does not change providing the swap rate remains the same
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9
Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) Which of the following is NOT true
A) The bonus structure at banks can lead to short-term horizons for decision making
B) Securitization involves the transfer of risk
C) The term "agency costs" describes the situation where the incentives of two parties in a business relationship are not perfectly aligned
D) Correlations decrease in stressed market conditions
Q2) In 2008 the TED spread reached a high of
A) About 150 basis points
B) About 250 basis points
C) About 450 basis points
D) About 550 basis points
Q3) Which of the following is true as the correlation between mortgage defaults increases?
A) Equity tranches are almost certain to incur losses
B) Senior tranches become more likely to incur losses
C) The expected number of defaults increases
D) Equity tranches are unaffected
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Chapter 9: Xvas
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Q1) CVA 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
Q2) Which of the following is NOT a valuation adjustment
A) CVA
B) MVA
C) ZVA
D) KVA
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) DVA stands for
A) Debt valuation adjustment
B) Debt valuation agreement
C) Debt variation adjustment
D) Debit valuation agreement
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Chapter 10: Mechanics of Options Markets
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Q1) Which of the following describes LEAPS?
A) Options which are partly American and partly European
B) Options where the strike price changes through time
C) Exchange-traded stock options with longer lives than regular exchange-traded stock options
D) Options on the average stock price during a period of time
Q2) The price of a stock is $64.A trader buys 1 put option contract on the stock with a strike price of $60 when the option price is $10.When does the trader make a profit?
A) When the stock price is below $60
B) When the stock price is below $64
C) When the stock price is below $54
D) When the stock price is below $50
Q3) 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
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Page 12
Chapter 11: Properties of Stock Options
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Q1) A European call and a European put on a stock have the same strike price and time to maturity.At 10:00am on a certain day,the price of the call is $3 and the price of the put is $4.At 10:01am news reaches the market that has no effect on the stock price or interest rates,but increases volatilities.As a result the price of the call changes to $4.50.Which of the following is correct?
A) The put price increases to $6.00
B) The put price decreases to $2.00
C) The put price increases to $5.50
D) It is possible that there is no effect on the put price
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
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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) How can a strap trading strategy be created?
A) Buy one call and one put with the same strike price and same expiration date
B) Buy one call and one put with different strike prices and same expiration date
C) Buy one call and two puts with the same strike price and expiration date
D) Buy two calls and one put with the same strike price and expiration date
Q3) 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
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Page 14
Chapter 13: Binomial Trees
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Q1) A tree is constructed to value an option on an index which is currently worth 100 and has a volatility of 25%.The index provides a dividend yield of 2%.Another tree is constructed to value an option on a non-dividend-paying stock which is currently worth 100 and has a volatility of 25%.Which of the following are true?
A) The parameters p and u are the same for both trees
B) The parameter p is the same for both trees but u is not
C) The parameter u is the same for both trees but p is not
D) None of the above
Q2) The current price of a non-dividend paying stock is $30.Use a two-step tree to value a European call option on the stock with a strike price of $32 that expires in 6 months.Each step is 3 months,the risk free rate is 8% per annum with continuous compounding.What is the option price when u = 1.1 and d = 0.9?
A) $1.29
B) $1.49
C) $1.69
D) $1.89
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Page 15
Chapter 14: Wiener Processes and Itos Lemma
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Q1) Which of the following gives a random sample from a standard normal distribution in Excel?
A) =NORMSINV()
B) =NORMSINV(RAND())
C) =RND(NORMSINV())
D) =RAND()
Q2) 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
Q3) A variable x starts at 10 and follows the generalized Wiener process dx = a dt + b dz Where time is measured in years.If a = 3 and b =4 what is the standard deviation of the value in 4 years?
A) 4
B) 8
C) 12
D) 16
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Page 16
Chapter 15: The Black-Scholes-Merton Model
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Q1) Which of the following is measured by the VIX index
A) Implied volatilities for stock options trading on the CBOE
B) Historical volatilities for stock options trading on CBOE
C) Implied volatilities for options trading on the S&P 500 index
D) Historical volatilities for options trading on the S&P 500 index
Q2) When there are two dividends on a stock,Black's approximation sets the value of an American call option equal to which of the following
A) The value of a European option maturing just before the first dividend
B) The value of a European option maturing just before the second (final) dividend
C) The greater of the values in A and B
D) The greater of the value in B and the value assuming no early exercise
Q3) What was the original Black-Scholes-Merton model designed to value?
A) A European option on a stock providing no dividends
B) A European or American option on a stock providing no dividends
C) A European option on any stock
D) A European or American option on any stock
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Chapter 16: Employee Stock Options
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Q1) Which of the following ensures that managers are rewarded only when a company performs better than its competitors?
A) A constant strike price for executive stock options
B) A strike price that increases with time
C) A strike price that changes in line with an index of stock prices
D) A strike price that is tied to reported profit
Q2) Which of the following defines the vesting period?
A) The period during which employee stock options can be exercised
B) The period during which the options are issued
C) The period during which the strike price of the options equals the stock price
D) The period during which employee stock options cannot be exercised
Q3) 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
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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 0.5? Assume that the risk-free rate is 10% per annum and there are no dividends.
A) 400
B) 410
C) 420
D) 425
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
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Page 19
Chapter 18: Futures Options and Blacks Model
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Q1) What is the value of a European call futures option where the futures price is 50,the strike price is 50,the risk-free rate is 5%,the volatility is 20% and the time to maturity is three months?
A) 49.38N(0.05)-49.38N(-0.05)
B) 50N(0.05)-50N(-0.05)
C) 49.38N(0.1)-49.38N(-0.1)
D) 50N(0.1)-49.38N(-0.1)
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 are true?
A) Futures options are usually European
B) Futures options are usually American
C) Both American and European futures options trade actively in exchanges
D) Both American and European futures options trade actively in the OTC market
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Page 20
Chapter 19: The Greek Letters
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Q1) Which of the following could NOT be a delta-neutral portfolio?
A) A long position in call options plus a short position in the underlying stock
B) A short position in call options plus a short position in the underlying stock
C) A long position in put options and a long position in the underlying stock
D) A long position in a put option and a long position in a call option
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
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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?
A) Volatility smile for European puts is the same as for European calls
B) Volatility smile for European puts is the same as for American puts
C) Volatility smile for European calls is the same as for American calls
D) Volatility smile for American puts is the same as for American calls
Q3) What does the shape of the volatility smile reveal about put options on equity?
A) Options close-to-the-money have the lowest implied volatility
B) Options deep-in-the-money have a relatively high implied volatility
C) Options deep-out-of-the-money have a relatively high implied volatility
D) All of the above
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22
Chapter 21: Basic Numerical Procedures
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Q1) When the stock price is 20 and the present value of dividends is 2,which of the following is the recommended way of constructing a tree?
A) Draw a tree for an initial stock price of 20 and subtract the present value of future dividends at each node
B) Draw a tree for an initial stock price of 22 and subtract the present value of future dividends at each node
C) Draw a tree with an initial stock price of 18 and add the present value of future dividends at each node
D) Draw a tree with an initial stock price of 18 and add 2 at each node
Q2) 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
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23
Chapter 22: Value at Risk and Expected Shortfall
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Q1) An investor has $2,000 invested in stock A and $5,000 in stock B. The daily volatilities of A and B are 1.5% and 1% respectively and the coefficient of correlation is 0.8. What is the one day 99% VaR? Assume that returns are multivariate normal (Note that N(-2.326)=0.01)
A) $177
B) $135
C) $215
D) $331
Q2) 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
Q3) The gain from a project is equally likely to have any value between -$0.15 million and +$0.85 million.What is the 99% value at risk?
A) $0.145 million
B) $0.14 million
C) $0.13 million
D) $0.10 million
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Page 24
Chapter 23: Estimating Volatilities and Correlations
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Q1) Which of the following is true
A) EWMA is a particular case of GARCH (1,1) where the reversion rate is zero
B) EWMA has a lower reversion rate than GARCH (1,1), but it is not zero
C) EWMA has a higher reversion rate than GARCH (1,1)
D) Sometimes EWMA has a higher reversion rate than GARCH (1,1) and sometimes it has a lower reversion rate than GARCH (1,1).
Q2) If the volatility for a portfolio is 20% per year,what is the volatility per quarter?
A) 20%
B) 10%
C) 5%
D) 2%
Q3) The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.What is the reversion rate for the variance rate implied by the model
A) 0.5% per day
B) 1.0% per day
C) 1.5% per day
D) 2.0% per day
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Chapter 24: Credit Risk
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Q1) 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
Q2) To be investment grade,a company has to have a credit rating of
A) AA or better
B) A or better
C) BBB or better
D) BB or better
Q3) Which of the following is true?
A) Risk neutral default probabilities are usually much lower than real world default probabilities
B) Risk neutral default probabilities are usually much higher than real world default probabilities
C) Risk neutral and real world probabilities must be close to each other if there are to be no arbitrage opportunities
D) Risk-neutral default probabilities cannot be calculated from CDS spreads
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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) 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) 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
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) As the barrier is observed more frequently,which of the following is true of a knock-out option
A) It becomes more valuable
B) It becomes less valuable
C) There is no effect on value
D) It may become more valuable or less valuable
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