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FUTURES AND OPTIONS
Midterm Exam —Thursday, November 16, 2023 —1:20 p.m. —4:20 p.m.
Fall 2023 —Instructor Han-Hsing Lee
1. Multiple Choices (34%)
v
I .A company enters into sho
tures contract to sell 50,000 units of a commodity for 70
cents per unit. The initia mar in is $4,000 and the maintenance margin is $3,000. What is
the futures price per unit bove which there will be a margin call?
A.78 cents
(4,000
DOU
1,000
B.76 cents
C. 74 cents
1).72 cents
50,
0
2. Which of the following i
OT rue
A. Futures contracts nearl
ays last longer than forward contracts
Futures contracts are standardized; forward contracts are not.
. Delivery or final cash settlement usually takes place with forward contracts; the same
is not true of futures contracts.
A. Forward contracts usually have one specified delivery date; futures contract often have
a range of delivery dates.
v
(2 3.1n the corn futures contract a number of different types of corn can be delivered (with
price adjustments specified by the e
e) and there are a number of different delivery
locations. Which of the following i ru
A. This flexibility tends increase the tures price.
B. This flexibility tends decrease the futures price.
C. This flexibility may increase and may decrease the futures price.
D. This flexibility has no effect on the futures price
4.Margin accounts have the effect of
V/ A. Reducing the risk of one party regretting the deal and backing out
VB. Ensuring funds are available to pay traders when they make a profit
V C. Reducing systemic risk due to collapse of futures markets
D. All of the above
v
defined as spot min
es. A trader is hedging the sale of an asset with a
b i
tures position. The sis increa unexpectedly. Which of the following is true?
he hedger's position improves.
b b 70
B. The hedger's position worsens.
u The hedger's position sometimes worsens and sometimes improves.
x The hedger's position stays the same.
basb
b
1
=
s
-
hunt
f
bz > b |=> ST
af ↓
.
f
-
le
6.A silver mining c mpany has used futures markets to hedge the price it wi
eive for
everything it will produce over the next 5 years. Which of the following •s tru
A. It is liable to experience liquidity problems if the price of silver falls dramatically
B. It is liable to experience liquidity problems if the price of silver rises dramatically
C. It is liable to experience liquidity problems if the price of silver rises dramatically or
falls dramatically
. The operation of futures markets protects it from liquidity problems
7.A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract
on an index is 90 Futures contracts on $250 times the index can be traded. What trade is
necessaryto crease eta to 1.8?
A
A
A. Long 192
acts
Short 192 contracts
C. Long 96 contracts
Short 96 contracts
l)
(let-I.
. Define the cost of carry, c, is the storage cost plus the interest costs less the income
earned. Which of the following is true?
A. For a consumption asset, Fo SoecT
B. For a consumption asset, Fo 2 SoecT
C. For an investment asset, Fo SoecT
D. For an investment asset, Fo > SoecT
9. A In entor• of a commodity decline, which of the following i€
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
option with strike price $50 is priced at $6.50. If the current
10. A Europe—stock
has an intrinsic value of D and a time value of 5
this
call
$45,
stock price is
A. $6.50; $0
(45 _ 50 , o)
B. $5; $1.50
c. $1.50; $5
D. $0; $6.50
E. -$5; $6.50
t marg
11. Which of the following must
A. The seller of an option
B. The buyer of an option
C. The seller and the buyer of an option
D. Neither the seller nor the buyer of an option
2
C, 12. An investmr has exchange-traded put options to sell 100 shares for $20. There is 2 fo
l"tock spy. Which of the following is the position of the investor after the stock sp It?
A. Put opti6ns 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
with all else remaining the same, which of the following is
true.
A. 0th 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
14. Which of the following NO true? (Present values are calculated from the end of the
life of the option to the beginning.)
A. An American put option is always worth less than the present value of the strike price
B. A European put option is always worth less than the present value of the strike price PE
C. A European call option is always worth less than the stock price c %
y An American call option is always worth less than the stock price
C/ 15.Which of the following descr•
tion where an American ut
•sed earl ?
becomes more likely to b
A.Expected dividends increase
Xlnterest rates decrease
C.The stock price volatility decreases
D.AII of the above
tion on a stock
16. A European call and a European put on a stock have the same strike price and time to
maturity. At 10:00am on a certain day, the price of the call is $3 and the price of the put is
$4. At 10:0 lam news reaches the market that has no effect on the stock price or interest
volatilities. As a result the price of the call changes to $4.50. Which of
rates, but incre
the following s corre t?
A. The put price Increases to $6.00
ate
The
put
price
decreases
to
$2.00
B.
C. The put price increases to $5.50
D. It is possible that there is no effect on the put price
17. Which of the following can be used to create
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
3
90
position in a European put option
Il, Calculation (66%)
1. (4%) On a particular day there are 3,000 trades in a particular futures contract. Of the
3,000 traders on the long side of the market, 1,700were closing out position and 1,300
were entering into new positions. Of the 3,000 traders on the short side of the market, 1,000
were closing out position and 2,000 were entering into new positions. What is the impact of
the day's trading on open interest?
2/000 he IO
(troo
clost
urchas 20,000 barrels of crude oil
2. It is June 8. A company knows that it will need
some time in October or November. Each contract is for the delivery of 1,000 barrels. The
current December oil futures price is $68.00 per barrel. Its hedging strategy is as follows:
I. Take a long position in 20 December oil futures contracts on June 8 at a futures
price of $68.
2. Close out the contract when ready to purchase the oil.
One possible outcome is:
Company is ready to purchase oil on November 10
Spot price on November 10 = $75
December futures price on November 10 = $72
Basis on November 10 $3
(4%) (a)Please calculate the net cost of oil after hedging.
(4%) (b) Suppose that the company decides to use a hedge rati@03. How does the
decision affect the way in which the hedge is implemented and the result in (a)?
(
3. A fund manager has a portfolio worth $10 million with a beta of 1.08. The manager is
concerned about the performance of the market over the next 2 months and plans to use 3month futures contracts on the S&P 500 to hedge the risk. The current level of the index is
850, one contract is on 250 times the index, the risk-free rate is 3% per annum, and the
urrent 3-mon futures price is 860.
dividend yield on the index is 3% per annum. T
ta
(3%) (a) What position should the fund manager e to hedge a I exposure to the market
over the next 2 months?
(7%) (b) Calculate the effect of your strategy on the fund manager's return if the index in 2
months is 800. Assume that the I-month futures price is 0.25% higher than the index
level at this time.
Index in Two Months
Futures Price $
Gain on Futures $
Portfolio Return %
Portfolio Gain $
Total Gain $
800
1%
000
-5. bozqq
1%
1%
4
4. The followin table
ives the rices of bonds:
Bondprincipal
Time to
maturity
(years)
0.50
1.00
1.50
2.00
100
100
100
100
Annual coupon *
Bondprice
0.0
0.0
5.0
7.0
99
97
6)
101
105
*Half the stated coupon is assumed to be paid every six months.
(6%) (a) Apply the bootstrap method to generate the zero curve. Calculate zero rates for
maturities of 6 months, 12 months, 18 months, and 24 months.
Zero rate (%)
Maturity (years)
o
0-5
1-5
2
2.5
(4%) (b) What are the forward rates for the following periods: 6 months to 12 months, 12
months to 18 months, and 18 months to 24 months?
(4%) (c) What are the 12-month and 24-month par yields for bonds that provide
semiannual coupon payments?
(2%) (d) Estimate the price of a 2-year bond providing a semiannual coupon of 7% per
annum.
Maturi
0.5
1.0
ears
Zero Rate %
? 2-0101%
Forward Rate %
Par Yield %
? 4.0610
1.5
2.0
*Please express all your answers in (a) to (c) as continuous compounded rate.
(e) (4%) Use the rates in (b) to value an FRA where you wi pay % on a principal of $1
million between the end of year 1.5 and the end of year 2.
5
5. (5%) A trader owns gold as part of a long-term investment portfolio. The trader can buy
gold for $1505 per ounce and sell gold for S 1500 per ounce. The trader can borrow funds at
2.5% per year and invest funds at 2% per year. (Both interest rates are expressed with
annual compounding.) For what range of one-year forward prices of gold does the trader
have no arbitrage opportunities? Assume there is no bid—offerspread for forward prices.
6. The 2-year interest rates in Australia and the U.S. are 7% and 5%. The spot exchange
rate between the Australian dollar (AUD) and the US dollar (USD) is 0.6200 USD per
AUD, and 2-year forward exchange rate is 0.6300.
(3%) (a) Given spot exchange rate, what is the "right" -ye orward exchange rate?
the detailed arbitrage strategy.
(5%) (b) Is there arbitrage opportunity? If yes, please s
Please
7. (6%) The price of a European put that expires in 6 months and has a strike price of $30
is $2. The underlying stock price is $31, and a dividend of $1 is expected in 2 months and
again in 5 mo s. The term structure is flat, with all risk-free interest rates being 10%. If
the Euro ean cal rice is $3, ex lain in detail the arbitra e o ortunities.
t=0
Strate
i
ii
Cashflow
6.50qu
8. (5%) Suppose that PI ,
and
are the prices of European put options with strike
>
prices , , and , respectively, where
options have the same maturity. Show that
> Kl and
S 0.5(P1 + po
—1<2
=
I(-9f
(Hint: Consider a portfolio that is long one option with strike price
, and short two options with strike price 1<2.)
with strike price
6
—Kl.All
, long one option