q's Flashcards
Suppose that the continously compounded interest rate is 4% per year and the 6 month forward price of TSLA is $360. What is today’s spot price of TSLA? A. $345.88 B. $374.69 C. $367.27 D. $352.87
D (Lecture 2) F = S0e^(rT) => S0 = F e^−rT S0 = 360e= ^−.04×.5 = $352.87
The GSCI Commodity Index is computed from returns of holding a diversified index of commodities. Compute the six month forward price for this index if the spot price is $1,000 and the continously compounded annual rates for the various costs and benefits of carrying the underlying are 6% for interest rates, 3% for storage costs, and 10% for convenience yield. A. $990.05 B. $995.01 C. $1,005.01 D. $1,072.51 E. $1,116.28
B: Lecture 2 F = 1000e^[(.06+.03)−(.10)]0.5 = 995.01
An investor purchases a European call option and a risk free zero coupon bond with a face value equal to the strike price of the call. This portfolio is equivalent to a: A. covered call B. protective put C. straddle D. strangle E. none of the above F. more than one of the above
B: Lecture 15, either look at put-call parity c + Ke−rT = p + S0. The left hand side of put-call parity is the portfolio described in the question and the right hand side is the protective put (buy put, buy underlying stock). Alternatively, you could draw the payoffs of each choice to see which matches the portfolio of interest.
How could you replicate the payoff to buying a stock that doesn’t pay dividends? A. Buy a put option with a strike price of K , write a call option with a strike price of K, and buy a zero coupon bond with a face value of K. B. Buy a put option with a strike price of K, write a call option with a strike price of K, and short sell a zero coupon bond with a face value of K. C. Write a put option with a strike price of K, buy a call option with a strike price of K, and buy a zero coupon bond with a face value of K. D. Write a put option with a strike price of K, buy a call option with a strike price of K, and short sell a zero coupon bond with a face value of K.
C: Either work with put-call parity =⇒ S0 = c + K−rT − p, or you could have drawn the payoffs of each choice to see which one matches that of buying a stock.
If a call option on BAC had a strike of $30, a time value of $8, and BAC’s current share price was $35 per share. What is the call option’s premium? A. $3 B. $5 C. $8 D. $13
D: Time Value=Premium-Intrinsic Value, Premium = max(35-30,0) + 8 = 13.
What is the maximum and minimum potential payoff of a trading strategy consisting of buying a put with a strike price of $50 and writing a call with a strike price of $50? A. max: $0, min: Unlimited B. max: $50, min: $0 C. max: $50, min: Unlimited D. max: Unlimited, min: -$50 E. max: $50, min: -$50
The price of a non-dividend paying stock is $100 and the price of a two year European put on the stock with a strike price of $90 is $10. The risk-free rate is 5%. What is the price of a two year European call with a strike price of $90? A. $9.52 B. $16.39 C. $24.39 D. $28.56
D: By put-call parity, we know that:
c + K e^−r T = p + S0
Solve for the price of the European call, c, and plug in the values we are given to obtain:
c = −K e^−r T + p + S0 = −$90 e ^−0.05×2 + $10 + $100 = $28.56
We need to buy $1,000,000 of a commodity in three months. We’ve found a futures contract that has a strong negative historical price correlation of -.90 with the spot price of the commodity that we’re trying to hedge. The standard deviation of our spot asset is .075, the standard deviation of the futures contract price is .080. The size of each futures contract in dollars notional is $10,000 a. What is our hedge ratio? b. Should we buy or sell futures contracts to hedge? c. How many contracts should we buy or sell in order to hedge?
oday’s share price of MRK is
$
82.91/Share and the continuously com-
pounded interest rate is 5%. A dealer in the over the counter market for forwards quotes
you a forward contract for 100 shares of MRK with one year to maturity and a quoted
Forward price of
$
95.00/share.
a.
What is the no-arbitrage price of this forward contract?
b.
Go into detail, explaining all legs of a trading strategy to arbitrage this quote (for example, tell me exactly how much you will borrow or lend).
c.
What would your arbitrage profits be from this trading strategy? You can construct a strategy that either earns profits now or profits later.
lcoa will sell 2000 metric tons of aluminum in nine months. Alcoa finds that the standard deviation of the spot price of aluminum is .075, the standard deviation of the futures price of aluminum is .080, and the coefficient of correlation between the spot and futures price changes is 0.75. Each futures contract is for 25 metric tons.
a.
What is Alcoa’s hedge ratio?
b.
Should Alcoa buy or sell contracts to hedge?
c.
How many contracts should they buy or sell in order to hedge?
Today’s share price of TSLA is $306.50/Share and the continuously compounded interest rate is 4%. A dealer in the over the counter market for forwards quotes you a forward contract for 100 shares of TSLA with nine months to maturity and a quoted Forward price of $308.00/share.
a.
What is the no-arbitrage price of this forward contract?
b.
Go into detail, explaining all legs of a trading strategy to arbitrage this quote (for example, tell me exactly how much you will borrow or lend).
c.
What would your arbitrage profits be from this trading strategy? You can construct a strategy that either earns profits now or profits later.
Consider the exotic security with the following payoff function:
[IMG]
a.
Draw the payoff diagram of this exotic security.
b.
Go into detail, listing a set a trades that you could use to replicate this exotic security.
