Financial Instruments
Exam Solutions
Course Introduction
This course offers a comprehensive overview of financial instruments, including their types, structures, and functions within global financial markets. Students will explore traditional instruments such as stocks, bonds, and money market securities, as well as more complex derivatives like options, futures, and swaps. Emphasis is placed on understanding how these instruments are used for investment, risk management, and speculation. The course also covers valuation techniques, regulatory considerations, and the role of financial markets in economic growth and development. By the end of the course, students will have a solid foundation in the characteristics and applications of various financial instruments, preparing them for careers in finance and related fields.
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) Which of the following best describes the term "spot price"
A) The price for immediate delivery
B) The price for delivery at a future time
C) The price of an asset that has been damaged
D) The price of renting an asset
Answer: A
Q2) A one-year forward contract is an agreement where
A) One side has the right to buy an asset for a certain price in one year's time.
B) One side has the obligation to buy an asset for a certain price in one year's time.
C) One side has the obligation to buy an asset for a certain price at some time during the next year.
D) One side has the obligation to buy an asset for the market price in one year's time.
Answer: B
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3
Chapter 2: Futures Markets and Central Counterparties
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Q1) A limit order
A) Is an order to trade up to a certain number of futures contracts at a certain price
B) Is an order that can be executed at a specified price or one more favorable to the investor
C) Is an order that must be executed within a specified period of time
D) None of the above
Answer: B
Q2) With bilateral clearing,the number of agreements between four dealers,who trade with each other,is
A) 12
B) 1
C) 6
D) 2
Answer: C
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Chapter 3: Hedging Strategies Using Futures
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Q1) The basis is defined as spot minus futures.A trader is hedging the sale of an asset with a short futures position.The basis increases unexpectedly.Which of the following is true?
A) The hedger's position improves.
B) The hedger's position worsens.
C) The hedger's position sometimes worsens and sometimes improves.
D) The hedger's position stays the same.
Answer: A
Q2) 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
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Chapter 4: Interest Rates
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Q1) The modified duration of a bond portfolio worth $1 million is 5 years.By approximately how much does the value of the portfolio change if all yields increase by 5 basis points?
A) Increase of $2,500
B) Decrease of $2,500
C) Increase of $25,000
D) Decrease of $25,000
Q2) The compounding frequency for an interest rate defines
A) The frequency with which interest is paid
B) A unit of measurement for the interest rate
C) The relationship between the annual interest rate and the monthly interest rate
D) None of the above
Q3) 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
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6
Chapter 5: Determination of Forward and Futures Prices
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Q1) A short forward contract that was negotiated some time ago will expire in three months and has a delivery price of $40.The current forward price for three-month forward contract is $42.The three month risk-free interest rate (with continuous compounding)is 8%.What is the value of the short forward contract?
A) +$2.00
B) $2.00
C) +$1.96
D) $1.96
Q2) Which of the following describes a known dividend yield on a stock?
A) The size of the dividend payments each year is known
B) Dividends per year as a percentage of today's stock price are known
C) Dividends per year as a percentage of the stock price at the time when dividends are paid are known
D) Dividends will yield a certain return to a person buying the stock today
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) It is May 1.The quoted price of a bond with a 30/360 day count and 12% per annum coupon in the United States is 105.It has a face value of 100 and pays coupons on April 1 and October 1.What is the cash price? \
A) 106.00
B) 106.02
C) 105.98
D) 106.04
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) Which of following is applicable to corporate bonds in the United States?
A) Actual/360
B) Actual/Actual
C) 30/360
D) Actual/365
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Chapter 7: Swaps
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Q1) A semi-annual pay interest rate swap where the fixed rate is 5.00% (with semi-annual compounding)has a remaining life of nine months.The six-month LIBOR rate observed three months ago was 4.85% with semi-annual compounding.Today's three and nine month LIBOR rates are 5.3% and 5.8% (continuously compounded)respectively.From this it can be calculated that the forward LIBOR rate for the period between three- and nine-months is 6.14% with semi-annual compounding.If the swap has a principal value of $15,000,000,what is the value of the swap to the party receiving a fixed rate of interest? Assume OIS rates are the same as LIBOR rates.
A) $74,250
B) $70,933
C) $11,250
D) $103,790
Q2) A floating for floating currency swap is equivalent to
A) Two interest rate swaps, one in each currency
B) A fixed-for-fixed currency swap and one interest rate swap
C) A fixed-for-fixed currency swap and two interest rate swaps, one in each currency
D) None of the above
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Chapter 8: Securitization and the Credit Crisis of 2007
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Q1) Which of the following tends to lead to an increase in house prices?
A) An increase in interest rates
B) Regulators specifying a maximum level for the loan-to-value ratio on mortgages
C) Banks reducing the minimum FICO score that borrowers are required to have
D) An increase in foreclosures
Q2) 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) 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
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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) MVA 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) DVA for a bank is most dependent on
A) The default probabilities of the bank in future time periods
B) The default probabilities of the bank's counterparties in future times periods
C) Both A and B
D) Neither A nor B
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Chapter 10: Mechanics of Options Markets
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Q1) 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
Q2) When a six-month option is purchased
A) The price must be paid in full
B) Up to 25% of the option price can be borrowed using a margin account
C) Up to 50% of the option price can be borrowed using a margin account
D) Up to 75% of the option price can be borrowed using a margin account
Q3) An investor has exchange-traded put options to sell 100 shares for $20.There is a 2 for 1 stock split.Which of the following is the position of the investor after the stock split?
A) Put options to sell 100 shares for $20
B) Put options to sell 100 shares for $10
C) Put options to sell 200 shares for $10
D) Put options to sell 200 shares for $20
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Chapter 11: Properties of Stock Options
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Q1) Interest rates are zero.A European call with a strike price of $50 and a maturity of one year is worth $6.A European put with a strike price of $50 and a maturity of one year is worth $7.The current stock price is $49.Which of the following is true?
A) The call price is high relative to the put price
B) The put price is high relative to the call price
C) Both the call and put must be mispriced
D) None of the above
Q2) When the strike price increases with all else remaining the same,which of the following is true?
A) Both calls and puts increase in value
B) Both calls and puts decrease in value
C) Calls increase in value while puts decrease in value
D) Puts increase in value while calls decrease in value
Q3) Which of the following can be used to create a long position in a European put option on a stock?
A) Buy a call option on the stock and buy the stock
B) Buy a call on the stock and short the stock
C) Sell a call option on the stock and buy the stock
D) Sell a call option on the stock and sell the stock
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Page 13
Chapter 12: Trading Strategies Involving Options
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Q1) What is the number of different option series used in creating a butterfly spread?
A) 1
B) 2
C) 3
D) 4
Q2) 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
Q3) How can a strip 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
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14
Chapter 13: Binomial Trees
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Q1) Which of the following is true for a call option on a stock worth $50
A) As a stock's expected return increases the price of the option increases
B) As a stock's expected return increases the price of the option decreases
C) As a stock's expected return increases the price of the option might increase or decrease
D) As a stock's expected return increases the price of the option on the stock stays the same
Q2) 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
Q3) In a binomial tree created to value an option on a stock,the expected return on stock is
A) Zero
B) The return required by the market
C) The risk-free rate
D) It is impossible to know without more information
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Chapter 14: Wiener Processes and Itos Lemma
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Q1) If e is a random sample from a standard normal distribution,which of the following is the change in a Wiener process in time dt .
A) e times the square root of dt
B) e times dt
C) dt times the square root of e
D) The square root of e times the square root of dt
Q2) 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 the standard deviation of the value of the variable at the end of 5 years
A) 6.2
B) 6.7
C) 7.2
D) 7.7
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16
Chapter 15: The Black-Scholes-Merton Model
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Q1) 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
Q2) 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
Q3) A stock price is $100.Volatility is estimated to be 20% per year.What is an estimate of the standard deviation of the change in the stock price in one week?
A) $0.38
B) $2.77
C) $3.02
D) $0.76
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17
Chapter 16: Employee Stock Options
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Q1) Which of the following is true about the practice of backdating a stock options grant?
A) It is illegal
B) It is illegal in the majority of states in the U.S., but not all states
C) It is illegal in roughly half the states in the U.S.
D) It is unethical, but not illegal
Q2) 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
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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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) What should the continuous dividend yield be replaced by when options on an exchange rate are valued using the formula for an option on a stock paying a continuous dividend yield?
A) The domestic risk-free rate
B) The foreign risk-free rate
C) The foreign risk-free rate minus the domestic risk-free rate
D) None of the above
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Chapter 18: Futures Options and Blacks Model
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Q1) 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 value of a six-month put option with a strike price of 37 cents?
A) 3.00 cents
B) 2.91 cents
C) 1.16 cents
D) 1.20 cents
Q2) Consider a European one-year call futures option and a European one-year put futures options when the futures price equals the strike price.Which of the following is true?
A) The call futures option is worth more than the put futures option
B) The put futures option is worth more than the call futures option
C) The call futures option is sometimes worth more and sometimes worth less than the put futures option
D) The call futures option is worth the same as the put futures option
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Chapter 19: The Greek Letters
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Q1) A trader uses a stop-loss strategy to hedge a short position in a three-month call option with a strike price of 0.7000 on an exchange rate.The current exchange rate is 0.6950 and value of the option is 0.1.The trader covers the option when the exchange rate reaches 0.7005 and uncovers (i.e.,assumes a naked position)if the exchange rate falls to 0.6995.Which of the following is NOT true?
A) The exchange rate trading might cost nothing so that the trader gains 0.1 for each option sold
B) The exchange rate trading might cost considerably more than 0.1 for each option sold so that the trader loses money
C) The present value of the gain or loss from the exchange rate trading should be about 0.1 on average for each option sold
D) The hedge works reasonably well
Q2) What does vega measure?
A) The rate of change of delta with the asset price
B) The rate of change of the portfolio value with the passage of time
C) The sensitivity of a portfolio value to interest rate changes
D) None of the above
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Page 21
Chapter 20: Volatility Smiles
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Q1) Which of the following is true?
A) The volatility skew for equities is much more pronounced now than it was in 1985.
B) The volatility skew for equities has a positive gradient
C) The volatility skew for equities is consistent with the Black-Scholes-Merton model.
D) The volatility skew for equities is similar to that for foreign currencies.
Q2) Which of the following is true as time to maturity increases?
A) The volatility smile for currency options tends to become more pronounced
B) The volatility smile for currency options tends to become less pronounced
C) The volatility smile for currency options first becomes less pronounced and then becomes more pronounced
D) The volatility smile for currency options remains approximately the same
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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Page 22
Chapter 21: Basic Numerical Procedures
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Q1) How many different paths are there through a Cox-Ross-Rubinstein tree with four-steps?
A) 5
B) 9
C) 12
D) 16
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
Q3) How many nodes are there at the end of a Cox-Ross-Rubinstein five-step binomial tree?
A) 4
B) 5
C) 6
D) 7
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Chapter 22: Value at Risk and Expected Shortfall
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Q1) 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
Q2) A position in options on a particular stock has a delta of zero and a gamma of 4.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,dx
A) dP = 4 times the square of dx
B) dP = 2 times the square of dx
C) dP = 20 times the square of dx
D) dP = 200 times the square of dx
Q3) Which of the following is true
A) Expected shortfall is always less than VaR
B) Expected shortfall is always greater than VaR
C) Expected shortfall is sometimes greater than VaR and sometimes less than VaR
D) Expected shortfall is a measure of liquidity risk wheras VaR is a measure of market risk
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Chapter 23: Estimating Volatilities and Correlations
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Q1) 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
Q2) Which of the following is true when the parameter lambda equals 0.95?
A) The weight given to the most recent observation is 0.95
B) The weight given to the observation one day ago is 95% of the weight given to the observation two days ago
C) The weights given to observations add up to 0.95
D) The weights given to the observation two days ago is 95% of the weight given to the observation one day ago
Q3) The parameters in a GARCH (1,1)model are: omega =0.000002,alpha = 0.04,and beta = 0.95.The current estimate of the volatility level is 1% per day.What is the expected volatility in 20 days?
A) 1.09%
B) 1.10%
C) 1.11%
D) 1.12%
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Chapter 24: Credit Risk
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Q1) Which of the following is true
A) Recovery rates are lower for investment grade companies
B) Recovery rates are higher for non-investment grade companies
C) Recovery rates are negatively correlated with default rates
D) Recovery rates are positively correlated with default rates
Q2) 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
Q3) 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
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Chapter 25: Credit Derivatives
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Q1) If the CDS spread for a regular 5-year CDS is 120 basis points,what is the CDS spread for a 5-year binary CDS on the same underlying reference entity? Assume a recovery rate of 40%.
A) 48 basis points
B) 72 basis points
C) 200 basis points
D) 300 basis points
Q2) In a CDS with a notional principal of $100 million the reference entity defaults.What is the payoff to the buyer of protection when the recovery rate is 30%?
A) $100 million
B) $30 million
C) $130 million
D) $70 million
Q3) Which of the following is true of a synthetic CDO?
A) It is created from portfolios of bonds
B) It is created from portfolios of CDSs
C) It references a standard portfolio of bonds
D) None of the above
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Chapter 26: Exotic Options
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Q1) Which of the following is true of a gap option
A) The strike price determining whether a payoff is made is not the same as the strike price determining the size of the payoff
B) There is a straightforward valuation formula similar to Black-Scholes-Merton
C) It describes an option where there is a cost to exercising
D) All of the above
Q2) 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
Q3) 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
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