Quiz 1:
1. What is the primary use of derivatives for corporations?
a. Reducing risk
2. What is a potential explanation for backwardation and inverted markets?
a. High convenience yield
3. If the risk-free rate is 6%, and the repo rate is 5%, then how could an arbitrageur use this
information to make profits?
a. The arbitrageur would short the asset, invest the proceeds at the risk-free rate, and
enter into a long forward contract to buy the asset in the future at the forward price
4. How are options different from forwards?
a. There is a cost associated with buying an option, but not with entering a forward
contract.
Options have a "hockey stick" payoff profile, whereas forwards have a "linear" payoff
profile.
Options are a right to trade in the future, whereas forwards are an obligation to trade in
the future.
5. You entered a forward contract to buy stock for 110 in two months. At maturity the stock price is
100. Assume each forward contract is for 1000 shares. What is your total payoff?
a. -10,000
100 – 110 = -10
-10 * 1000 = -10,000
6. The forward price for buying the underlying asset in 6 months is 100 and the spot price is 95.
What is the implied repo rate? Ignore holding costs.
a. 10.26%
1
100
ln
6
95
12
7. The spot price of an underlying asset is 120 and the interest rate is 4%. Ignore holding costs.
What will the forward price be for a contract that matures in 5 months?
a. 122.02
𝑒 0.04×0.5 × 120 = 122.42
Don’t know where 0.5 is coming from.
8. You enter a long forward contract that matures in 7 months and has a delivery price of 110 per
barrel. 4 months have elapsed since inception and the spot price is now 110. The risk-free rate is
5%. Ignore holding costs. What is the value of the forward contract that you have taken a long
position in? Assume the contract is for 1000 barrels.
a. 1366.44
e^-0.05*(3/12) = 0.987 * 110 = 108 – 110 = -1.3664 * 1000 = -1366.44
The value of the forward contract is PV(F-K). F = exp(rT) x S = exp(0.05 x (5 – 4)/12) x S = 112.47. K = 110.
PV(F-K) = exp(-rT) x (F-K) = exp(-0.05 x (5-4)/12) x (112.47-110) = 2,457.
9. You make an initial investment of 100 dollars and the risk-free rate of return is 6%. How many
years 6 does it take for your investment to grow to 2 times the original investment under
continuous compounding?
a. 11.6
1
ln 2
×
12 ln (1 + 0.06)
12
10. You purchased a call option on ABC's stock with a strike price of 120 and a maturity date of 3
months. At maturity, ABC's stock price is 134. What is your return from buying the option, given
that the option premium (the cost of the option) was $3?
a. 367%
14-3 / 3 = 3.66 * 100 = 367
Quiz 2:
1. In the presence of basis risk, is a hedge ratio equal to 1 always better than a hedge ratio of equal
to 0?
a. No, because there are scenarios where having a hedge ratio of 1 can increase cash flow
risk more than having a hedge ratio of 0.
2. The correlation between changes in the price of the underlying and futures contract A is 80%.
The underlying has a correlation of -85% with another futures contract B. Which of the two
contracts would you prefer for the minimum variance hedge?
a. B
The minimum variance hedge depends on the size of the correlation, and it doesn't matter whether the
correlation is negative or positive, so the correct answer would be -85%.
3. What factors affect basis risk (the cash flow risk of entering the futures/forward contract)?
a. The underlying associated with the futures contract versus the underlying that you are
trying to hedge.
The delivery date of the futures contract versus the time you actually need the spot
asset.
4. The standard Treasury Bond futures contract has a face value of $100,000, at least 15 years to
maturity and a coupon of 6%, payable semi-annually. The quoted price of the futures contract is
based on this standard bond. Instead of the standard bond, the short position chooses to deliver
a treasury bond with a remaining maturity of 19 years and a 7% coupon, payable semi-annually.
What conversion factor will be applied to the quoted price?
a. 1.112
N = 38 (19 * 2)
I/Y = 6
PMT = 3.5 (7 /2)
FV = 100
P/Y = 2
C/Y = 2
CPT PV = 111.25  1.112
You need to compute the value of the bond using a discount rate of 6% and a coupon rate of 7%. The
value of the bond would be based on the following inputs in Excel: rate = 0.06/2 = 0.03, nper = 19 x 2 =
38, pmt = 0.07 x 100000 / 2 = 3500, fv = 1000,000. Based on this you compute the PV and then divide
(111,246) and divide by the face value to get a rate of 1.112.
5. The current price of gold futures is $1000 per ounce. Each futures contract is for 100 ounces.
Assume that you initiate a long position in 1 COMEX gold futures contract at this price. The initial
margin is 5% of the initial contract value, and the maintenance margin is 4% of the initial
contract value. Assume the following evolution of gold prices over the next few days.
Day 1: 990
Day 2: 993
Assuming you meet all margin calls, what is the margin account's closing balance on day 2?
a. 4300
1000 * 100 * 1 = 100,000
Initial margin = 5% = 5000
After one day price from to 990 from 1000
5000 – 10 * 100 = 4000
Second day price jumps to 993
4000 + 3 * 100 = 4300
6. The standard deviation of daily price changes is observed to be 41. Assuming that daily price
changes are independent and identically distributed, what is the 6-month standard deviation of
price changes?
a. 455
The answer would be sqrt(6 months x 22 trading days per month) x 41 = 471.
SQRT(6*22)*41
(use excel)
7. You use silver wire in manufacturing. You are looking to buy 100,000 ounces of silver in three
months' time. One COMEX silver futures contract is for 5000 ounces. You have the following
information:
Standard deviation of daily silver spot price change = 32
Standard deviation of daily silver futures price change = 31
Correlation between spot price change and futures price change = 0.70
Based on this information, what should the size (number of contracts) of your optimal futures position
be?
a. 18
The answer would be minimum variance hedge h = rho x stdev(dS) / stdev(dF) = 0.84 x 31 /29 =
0.89973. Units required in the futures contract H = rho x S = 0.89973 x 100,000=89,973. Contracts = total
units in futures / units per contract = 89,973 / 5000 = 18.
8. If the correlation between spot and futures price changes is -0.8, what fraction of cash-flow
uncertainty is removed by minimum-variance hedging?
a. 64%