Financial Risk Analysis
Final Test Solutions
Course Introduction
Financial Risk Analysis focuses on the identification, measurement, and management of risks faced by financial institutions and investors. The course covers key concepts such as market risk, credit risk, operational risk, and liquidity risk, highlighting the tools and techniques used to quantify and mitigate these risks, including value-at-risk models, stress testing, scenario analysis, and credit scoring systems. Students will gain a comprehensive understanding of risk management strategies, regulatory frameworks, and the practical application of financial instruments like derivatives for hedging purposes. The course emphasizes both theoretical foundation and real-world case studies, preparing students to analyze and manage financial risk in dynamic market environments.
Recommended Textbook
Options Futures and Other Derivatives 9th Edition by John C. Hull
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Chapter 1: Introduction
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Q1) A speculator can choose between buying 100 shares of a stock for $40 per share and buying 1000 European call options on the stock with a strike price of $45 for $4 per option.For second alternative to give a better outcome at the option maturity,the stock price must be above
A)$45
B)$46
C)$55
D)$50
Answer: D
Q2) Which of the following is NOT true about call and put options:
A)An American option can be exercised at any time during its life
B)A European option can only be exercised only on the maturity date
C)Investors must pay an upfront price (the option premium) for an option contract
D)The price of a call option increases as the strike price increases
Answer: D
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Chapter 2: Mechanics of Futures Markets
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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
Q3) Which of the following is true
A)Both forward and futures contracts are traded on exchanges.
B)Forward contracts are traded on exchanges, but futures contracts are not.
C)Futures contracts are traded on exchanges, but forward contracts are not.
D)Neither futures contracts nor forward contracts are traded on exchanges.
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) Which of the following is necessary for tailing a hedge?
A)Comparing the size in units of the position being hedged with the size in units of the futures contract
B)Comparing the value of the position being hedged with the value of one futures contract
C)Comparing the futures price of the asset being hedged to its forward price
D)None of the above
Answer: B
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Chapter 4: Interest Rates
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Q1) A company invests $1,000 in a five-year zero-coupon bond and $4,000 in a ten-year zero-coupon bond.What is the duration of the portfolio?
A)6 years
B)7 years
C)8 years
D)9 years
Q2) 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
Q3) An interest rate is 6% per annum with annual compounding.What is the equivalent rate with continuous compounding?
A)5.79%
B)6.21%
C)5.83%
D)6.18%
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6
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 is NOT true?
A)Gold and silver are investment assets
B)Investment assets are held by significant numbers of investors for investment purposes
C)Investment assets are never held for consumption
D)The forward price of an investment asset can be obtained from the spot price, interest rates, and the income paid on the asset
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) Duration matching immunizes a portfolio against
A)Any parallel shift in the yield curve
B)All shifts in the yield curve
C)Changes in the steepness of the yield curve
D)Small parallel shifts in the yield curve
Q2) 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
Q3) A portfolio is worth $24,000,000.The futures price for a Treasury note futures contract is 110 and each contract is for the delivery of bonds with a face value of $100,000.On the delivery date the duration of the bond that is expected to be cheapest to deliver is 6 years and the duration of the portfolio will be 5.5 years.How many contracts are necessary for hedging the portfolio?
A)100
B)200
C)300
D)400
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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) In a fixed-for-fixed currency swap,3% on a US dollar principal of $150 million is received and 4% on a British pound principal of 100 million pounds is paid.The current exchange rate is 1.55 dollar per pound.Interest rates in both countries for all maturities are currently 5% (continuously compounded).Payments are exchanged every year.The swap has 2.5 years left in its life.What is the value of the swap?
A)-$7.15
B)-$8.15
C)-$9.15
D)-$10.15
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) Which of the following describes the waterfall typically used for mortgages pre-crisis?
A)A distribution of cash flows to tranches with priority given to tranche with the highest rating
B)A distribution of cash flows to tranches in proportion to their outstanding principals
C)A distribution of losses to tranches so that tranches bear losses in proportion to their outstanding principals
D)None of the above
Q2) 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
Q3) Which of the following describes a subprime mortgage?
A)The rate of interest is less than the prime rate of interest
B)The loan-to-value ratio is below average
C)The life of the mortgage is less than 25 years
D)The credit risk is high
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Chapter 9: OIS Discounting, Credit Issues, and Funding Costs
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Q1) Which of the following involves most credit risk
A)Exchange trading
B)OTC trading with a central clearing party being used
C)OTC trading with bilateral clearing and collateral being posted
D)OTC trading with bilateral clearing and no collateral being posted
Q2) Since the credit crisis that started in 2007 which of the following have derivatives traders used as the risk-free discount rate for collateralized transactions
A)The Treasury rate
B)The LIBOR rate
C)The repo rate
D)The overnight indexed swap rate
Q3) Which of the following is closest to the LIBOR forward rate for the second year when LIBOR discounting is used and the rate is expressed with annual compounding
A)7.199%
B)7.221%
C)7.223%
D)7.225%
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Page 11
Chapter 10: Mechanics of Options Markets
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Q1) 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
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
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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 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) Which of the following creates a bull spread?
A)Buy a low strike price put and sell a high strike price put
B)Buy a high strike price put and sell a low strike price put
C)Buy a high strike price call and sell a low strike price put
D)Buy a high strike price put and sell a low strike price call
Q2) Which of the following creates a bear spread?
A)Buy a low strike price call and sell a high strike price call
B)Buy a high strike price call and sell a low strike price call
C)Buy a low strike price call and sell a high strike price put
D)Buy a low strike price put and sell a high strike price call
Q3) Which of the following creates a bear spread?
A)Buy a low strike price put and sell a high strike price put
B)Buy a high strike price put and sell a low strike price put
C)Buy a high strike price call and sell a low strike price put
D)Buy a high strike price put and sell a low strike price call
Q4) Which of the following creates a bull spread?
A)Buy a low strike price call and sell a high strike price call
B)Buy a high strike price call and sell a low strike price call
C)Buy a low strike price call and sell a high strike price put
D)Buy a low strike price put and sell a high strike price call
Page 14
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Chapter 13: Binomial Trees
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Q1) Which of the following describes delta?
A)The ratio of the option price to the stock price
B)The ratio of the stock price to the option price
C)The ratio of a change in the option price to the corresponding change in the stock price
D)The ratio of a change in the stock price to the corresponding change in the option price
Q2) 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
Q3) 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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Page 15
Chapter 14: Wiener Processes and Itos Lemma
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Q1) 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.
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) What is the coefficient of dz in the process for the square of X.
A)sX
B)sX<sup>2</sup>
C)2sX<sup>2</sup>
D)msX
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Page 16
Chapter 15: The Black-Scholes-Merton Model
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Q1) 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%
Q2) Which of the following is a definition of volatility
A)The standard deviation of the return, measured with continuous compounding, in one year
B)The variance of the return, measured with continuous compounding, in one year
C)The standard deviation of the stock price in one year
D)The variance of the stock price in one year
Q3) An investor has earned 2%,12% and -10% on equity investments in successive years (annually compounded).This is equivalent to earning which of the following annually compounded rates for the three year period.
A)1.33%
B)1.23%
C)1.13%
D)0.93%
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Page 17
Chapter 16: Employee Stock Options
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Q1) Which of the following strategies makes no sense?
A)An employee exercises stock options early and sells the stock.No dividends are expected
B)An employee exercises stock options early and keeps the stock.No dividends are expected
C)An employee exercises stock options early and sells the stock.Dividends are expected
D)An employee exercises stock options early and keeps the stock.Dividends are expected.
Q2) Which of the following is true about employee stock options after they have been issued?
A)They have to be revalued every year
B)They have to be revalued every quarter
C)They have to be revalued every day like other derivatives
D)They never have to be revalued
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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Page 18
Chapter 17: Options on Stock Indices and Currencies
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Q1) What is the same as 100 call options to buy one unit of currency A with currency B at a strike price of 1.25?
A)100 call options to buy one unit of currency B with currency A at a strike price of 0.8
B)125 call options to buy one unit of currency B with currency A at a strike price of 0.8
C)100 put options to sell one unit of currency B for currency A at a strike price of 0.8
D)125 put options to sell one unit of currency B for currency A at a strike price of 0.8
Q2) Index put options are used to provide protection against the value of the portfolio falling below a certain level.Which of the following is true as the beta of the portfolio increases?
A)The cost of hedging increases
B)The required options have a higher strike price
C)The number of options required increases
D)All of the above
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Chapter 18: Futures Options
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Q1) 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
Q2) What is the cash component of the payoff if a call 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
Q3) Which of the following is true when the futures price exceeds the spot price?
A)Calls on futures should never be exercised early
B)Put on futures should never be exercised early
C)A call on futures is always worth at least as much as the corresponding call on spot
D)A call on spot is always worth at least as much as the corresponding call on futures
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Page 20
Chapter 19: The Greek Letters
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Q1) 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
Q2) Which of the following is NOT true about gamma?
A)A highly positive or highly negative value of gamma indicates that a portfolio needs frequent rebalancing to stay delta neutral
B)The magnitude of gamma is a measure of the curvature of the portfolio value as a function of the underlying asset price
C)A big positive value for gamma indicates that a big movement in the asset price in either direction will lead to a loss
D)A long position in either a call or a put has a positive gamma
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Chapter 20: Volatility Smiles
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Q1) Which of the following is true for European call and put options?
A)If they have the same strike price, they have the same implied volatility
B)If they have the same time to maturity, they have the same implied volatility
C)If they have the same strike price and time to maturity, they have the same implied volatility
D)None of the above
Q2) If the volatility implied from an at-the-money put currency option were used to price other put options on the currency,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
Q3) 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
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Page 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) A European option on a stock with a known dollar dividend is valued by setting the stock price variable equal to the stock price minus the present value of the dividend in the Black-Scholes-Merton formula.A second price can be obtained using the tree building procedure in the chapter.Which of the following is true when a very large number of time steps are used in the tree?
A)The first price is higher than the second price
B)The first price is lower than the second price
C)The first price is sometimes higher and sometimes lower than the second price
D)The two prices are almost exactly the same
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23
Chapter 22: Value at Risk
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Q1) In a principal components analysis which of the following is the quantity of a particular factor in an observation
A)Factor loading
B)Factor score
C)Factor size
D)Factor rating
Q2) An investor has $2,000 invested in stock A and $5,000 in stockB.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
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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Chapter 23: Estimating Volatilities and Correlations
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Q1) If the volatility for a portfolio is 20% per year,what is the volatility per quarter?
A)20%
B)10%
C)5%
D)2%
Q2) 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
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) 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
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
A)A derivative dealer's CVA is the counterparty's DVA and vice versa
B)Collateral posted by the counterparty reduces CVA
C)Collateral posted by the dealer reduces DVA
D)All of the above
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Page 26
Chapter 25: Credit Derivatives
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Q1) The yield on a company's five-year bonds is 5%.The five year swap rate is 4.5% and the five-year Treasury rate is 4%.What would be closest to your best estimate of the five-year CDS spread
A)200 basis points
B)150 basis points
C)100 basis points
D)50 basis points
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) 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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Chapter 26: Exotic Options
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Q1) There are two types of regular options (calls and puts).How many types of compound options are there?
A)Two
B)Four
C)Six
D)Eight
Q2) A fixed lookback put 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
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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