All of the positions listed will benefit from a price decline, except:
A) Short put
B) Long put
C) Short call
D) Short stock
Techie, Inc. may invest $5 million in a new Star Communicator project. Annual
production costs and revenues are projected to be $2 million and $1.5 million, with
each growing at 2.0% and 4.0%, respectively. At an interest rate of 5.5%, what is the
approximate investment year that will maximize value? (Use static analysis.)
A) Year 20
B) Year 15
C) Year 10
D) Year 5
Assume S = $60, K = $60, r = 0.07, σ = 0.24, div = 0.02, and 90 days until expiration.
What is the premium on an Asian average price put where N = 4?
A) $1.74
B) $1.84
C) $1.94
D) $2.04
A strategy consists of buying a market index product at $830 and longing a put on the
index with a strike of $830. If the put premium is $18.00 and interest rates are 0.5% per
month, what is the estimated price of a call option with an exercise price of $830?
A) $42.47
B) $45.26
C) $47.67
D) $49.55
Assume a = 0.25, b = 0.13, r = 0.06, and σ = 0.25. Using the CIR model, calculate the
gamma of a zero coupon bond maturing in 3 years.
A) 2.14
B) 2.34
C) 2.54
D) 2.74
Daniels, Inc. has assets valued at $2 million and 50,000 outstanding shares. A 5-year
zero-coupon bond exists, which pays $400,000 at maturity. The bond is convertible into
10,000 shares. Assume σ = 0.30, r = 0.055, and no dividend is paid. What is the value of
the bond?
A) $402,672
B) $452,172
C) $415,022
D) $385,172
What is the expected return on equity using the Black-Scholes formula, given a
zero-coupon bond that pays $250 at maturity in 4 years? Assume assets are worth $200,
r = 0.05, σ = 0.30, and no dividend is paid. The return on assets is 11.5%.
A) 10.27%
B) 14.27%
C) 18.27%
D) 22.27%
For purposes of option pricing, when the movement of a stock price follows a
geometric Brownian motion, the stock price is said to follow which type of
distribution?
A) Bimodal
B) Latin hypercube
C) Lognormal
D) Normal
A critical assumption in Monte Carlo simulations is that valuation is based on:
A) Random variables
B) True probabilities
C) Risk-neutral probabilities
D) None of the above
A farmer sells 4 million bushels of corn at a spot price of $2.10 per bushel. The total
cost of production was $9.2 million. The farmer has an effective tax rate of 25%. If the
farmer entered into a futures contract at a price of $2.40 per bushel on 4 million
bushels, what is the farmer’s net loss or gain?
A) $100,000 loss
B) $800,000 loss
C) $300,000 gain
D) $400,000 gain
Willco, Inc. issues compensation options with the following terms. Strike = $45,
price = $42.00, σ = 0.48, r = 0.05, div = 0.02. What is the value of the option if it will
be
repriced at $30? Assume 10 years to expiration.
A) $22.78
B) $24.65
C) $26.22
D) $30.46
Which of the following statements does NOT accurately reflect the relationship
between securities and synthetic forward contracts?
A) Forward = stock – zero coupon bond
B) Zero coupon bond = stock – forward
C) Prepaid forward = forward – zero coupon bond
D) Stock = forward + zero coupon bond
A stock price is $85.00. Assume r = 0.07 and there is no dividend. What is the 6-month
forward price?
A) $88.03
B) $89.16
C) $90.26
D) $92.33
For an option trading in the money, what is the likely impact on the binomial option
price as the number of binomial steps is increased?
A) The price will fall
B) The price will increase
C) The price will remain constant
D) The impact cannot be determined
The price of a 3-year zero coupon government bond is 85.16. The price of a similar
4-year bond is 78.81. What is the yield to maturity (effective annual yield) on the 3-year
bond?
A) 4.6%
B) 5.5%
C) 5.8%
D) 6.7%
When defining a change in measure, a redefining of the units in which a payoff is
measured is called:
A) Brownian motion
B) Change of numeraire
C) Stochastic discount factor
D) Utility function
Use Cox-Ross-Rubenstein to construct a 2-year binomial tree for the evolution of cash
flows with a binomial period of 1. Assume the initial cash flow (CF1) is $20 million, σ
= 0.45, r = 0.13, g = 0.02, and the project lasts 2 years. What is the value of the project
on the up node in year 1?
A) $85 million
B) $185 million
C) $285 million
D) $385 million
Lapel Inc. stock price is $32.00. Joe bets Sarah that the price will be above $35.00 in 6
months (180 days). The standard deviation of the stock is 0.25 and the risk free interest
rate is 5.0%. If Joe wins the bet, he wishes to be paid with one share of stock. If Sarah
agrees to the bet, what is the value of her wager?
A) $3.00
B) $9.65
C) $12.44
D) $19.58
Oil is selling at a spot price of $42.00 per barrel. Oil can be stored at a cost of $0.42 per
barrel per month. The opportunity cost of capital is 7.2% per year (or 0.6% per month).
What is the gain or loss realized by an oil refinery that floats its exposure and purchases
oil on the spot market in 2 months at a price of $43.00 per barrel, instead of hedging
with a forward contract?
A) $0.35 gain
B) $0.35 loss
C) $1.00 gain
D) $1.00 loss
Assume that a $50 strike put pays a 2.0% continuous dividend, r = 0.07, σ = 0.25, and
the stock price is $48.00. What is the profit or loss, per share, for a short put position if
the option expires in 60 days and the price rises to $50.00 after 5 days?
A) $1.05 loss
B) $1.05 gain
C) $1.12 gain
D) $1.12 loss
The current price per cord of lumber is $26.00. The effective annual lease rate is 2.0%
and the risk free rate is 4.0%. The cost to harvest one cord is $20.00 and constant. What
is the trigger price at which we will harvest the lumber?
A) $27.61
B) $31.61
C) $35.61
D) $39.61
Use Cox-Ross-Rubenstein to construct a 2-year binomial tree for the evolution of cash
flows with a binomial period of 1. Assume the initial cash flow is (CF1) = $62 million,
σ = 0.20,
rp = 0.14, and g = 0.03. What is the highest possible value of the project?
A) $222 million
B) $314 million
C) $622 million
D) $841 million
A forward contract that pays ln(ST/S0) and can be used to hedge or speculate on
variance is called a ________ contract.
A) Growth
B) Log
C) Variance
D) Volatility
Zero-coupon bonds maturing in 1, 2, and 3 years have prices of 0.9345, 0.8766, and
0.8212, respectively. What is the forward price for a 1-year bond purchased in year 2?
A) 0.6866
B) 0.7234
C) 0.8787
D) 0.9368
The spot price of gasoline is 258 cents per gallon and the annualized risk free interest
rate is 4.0%. Given a lease rate of 1.0%, a continuously paid storage rate of 0.5%, and a
convenience yield of 0.75%, what is the no-arbitrage price range of a 1-year forward
contract (in cents)?
A) 265.19 to 267.19
B) 258 to 265.19
C) 258 to 267.19
D) 247.16 to 265.19
A farmer expects to harvest 800,000 bushels of corn. To eliminate price risk, the farmer
elects to short corn futures. What would cause the farmer to short only 720,000 bushels
of corn?
A) Basis risk
B) Illiquid futures markets
C) Margin requirements
D) Quantity uncertain
The monthly standard deviation for a stock is 4.2%. What is the 6 month standard
deviation for the security?
A) 4.2 %
B) 10.3 %
C) 25.2 %
D) 50.4 %
The ratio of the future uncertain martingale utility to the present known martingale
utility is called:
A) Brownian motion
B) Change of measure
C) Stochastic discount factor
D) Utility function
What is the price of a 2-year equity-linked CD under the following terms? No coupon is
paid. At maturity the CD pays 80.0% of the S&P 500 index appreciation. The S&P 500
price = 900, div = 0.02, σ = 0.20, and interest rates are 5.0%.
A) $890.22
B) $990.23
C) $1064.20
D) $1110.55
You own $4 million of Jacko Corp. The expected return is 14.0% and σ = 0.20. What is
the value at risk over 4 weeks at a 99% confidence level?
A) $383,000
B) $413,000
C) $453,000
D) $473,000
A series of 1-year interest rate caplets for 4 years have values of $0.05, $0.07, $0.08,
and $0.10, respectively. What is the value of a 3-year interest rate cap?
A) $0.08
B) $0.12
C) $0.20
D) $0.30
How is VaR used in credit risk scenarios?
What is implied volatility?
Why is Brownian motion the foundation for modern derivatives pricing models?
Why might a variable rate mortgage be considered a “derivative” and a fixed rate
mortgage not?
What is meant by the phrase “tranche” when referring to collateralized debt obligations?
All else being equal, explain why American options are at least as valuable as European
options.
What feature of reload options prevents the use of a Black-Scholes valuation?
When is it possible for the lease rate to fall below zero?
Why do we care about Greeks?
How does a quanto hedge the currency risk a U.S. investor encounters when investing
in foreign indexes?
Explain a “diff swap” as it relates to currency swaps.
What would cause the spread between the market rate of interest and the repo rate to be
small?
What is the difference between implied volatility and historical volatility?
For a long put position, what benefit is provided by a gap option should prices rise?