Chapter 17 - Stock Index Futures and Options
SOLUTIONS MANUAL
CHAPTER 17
STOCK INDEX FUTURES AND OPTIONS
Answers to Text Discussion Questions
1. Why are stock index futures and options sometimes referred to as derivative products? Why
do some investors believe derivative products make the markets more volatile?
17-1. Stock index futures and options are sometimes referred to as derivative products
because they derive their existence from actual market indexes, but have no intrinsic
characteristics of their own. The reason some believe they lead to greater market
volatility is that enormous amounts of securities can be controlled by relatively small
amounts of margin or option premiums.
2. Why does a hedging position require less initial margin than a speculative position?
17-2. Since a hedged position is not as risky as a speculative position, less initial margin is
required.
3. What is meant by the concept of cash settlement?
17-3. Under a cash settlement arrangement, all contracts are closed out on a cash basis.
There is never the implied potential for future delivery.
4. What does the term basis mean in the futures market? If there is a premium and it expands
with the passage of time, what is the general implication?
17-4. The term basis represents the difference between the futures price and the underlying
item (such as a stock index). If there is a premium and it expands with the passage of
time, this is generally thought to be a positive sign for the underlying index.
5. Why does a down market put tremendous pressure on a speculator if he or she is the
purchaser of a contract in anticipation of a market increase? Relate this answer directly to
margin.
17-5. The investor will be continually called upon to put up more margin as his margin
position is being depleted. He must decide whether to put up more margin and hold his
position in hopes of a comeback or close out his position and take his losses.
6. Why is it unrealistic for a portfolio manager to sell a large portion of his portfolio if he
thinks the market is about to decline?
17-1
Chapter 17 - Stock Index Futures and Options
17-6. There are large transaction costs associated with selling off part or all of a portfolio
and then repurchasing it at a later point in time. Also, it may be difficult to liquidate a
position in certain securities that are thinly traded. The same problem would apply to
reacquiring the securities.
7. How does the beta of a portfolio influence the number of contracts that must be used in the
hedging process?
17-7. The higher the portfolio beta, the larger is the potential movement (volatility) in the
portfolio. With a large potential movement in the portfolio, more futures contracts are
required to hedge the position. Thus, a large portfolio beta means more contracts will
be required to establish a hedge.
8. What are some complicating factors in attempting to hedge a portfolio?
17-8. There may not be an appropriate index to hedge against the portfolio. Also, there may
be a change in the basis over time. This means the futures contract may not move fully
in accord with the underlying index. Also, the portfolio may change more or less than
its beta would indicate.
9. Why might the overuse of portfolio insurance be dangerous to the market?
17-9. An overload of stock index futures sales will hit the market at the same time. This has
the effect of not only driving down stock index futures but the stocks in the index as
well (such as those in the Standard & Poor's 500 Stock Index). Thus, as overall panic
can set in if too many portfolio insurance strategies are implemented simultaneously.
The chain reaction is that a whole new round of portfolio insurance induced sales are
triggered.
10. What is an arbitrage position?
17-10. An arbitrage is instituted when a simultaneous trade (a buy and a sell) takes place in
two different markets at two different prices and a profit is locked in.
11. What is an essential difference between stock index options and options on individual
securities in terms of settlement procedures?
17-11. With stock index options, there is only a cash settlement of the position. With options
on individual securities, the owner of the option can force the option writer to deliver
the securities.
17-2
Chapter 17 - Stock Index Futures and Options
12. Under what circumstance might a portfolio manager be more likely to use index option
contracts instead of futures contracts to hedge a portfolio? What is the counter argument for
futures contracts over index options?
17-12. Options may offer a hedging advantage over futures to investors who are limited by
law from purchasing futures contracts. On the other hand, futures generally allow for a
more efficient hedge than options.
13. Explain the difference between a stock index option and an option on stock index futures.
17-13. A stock index option is an option to purchase the underlying index. An option on a
stock index futures contract is an option to purchase a futures contract on the
underlying index.
14. Suggest two reasons an option on a stock index futures contract that has a distant
expiration date might have a high premium.
17-14. The high premium might be due to the far off expiration date. It might also be related
to a high value for the futures contract in relation to the underlying index (high
positive basis).
PROBLEMS
Stock index futures
1. Based on the information in Table 17–1, what is the total value of an S&P 500 Index
futures contract for December 2006? Use the settle price and the appropriate multiplier. Also,
if the required margin is $20,000, what percent of the contract value does margin represent?
17-1.
December 2006settle price
Multiplier
Total Value
1, 271.60
250
317,900
Margin
$20, 000

 6.29%
Contract value $317,900
17-3
Chapter 17 - Stock Index Futures and Options
Gain on S&P futures
2. In problem 1, if the S&P Index futures contract goes up to $1,283.60, what will be the total
dollar profit on the contract? What is the percent return on the initial margin? If this price
change occurred over four months, what is the annualized return? (Multiply by 12/4.)
17-2.
Latest value
Original value
Gain
Multiplier
Total Profit
1, 283.60
1, 271.60
12.00
250
$3, 000.00
$3, 000
Percent return on initial margin
 15%
$20, 000
12
 45%
4
Loss on S&P futures and margin
3. Return to problem 1 and assume that margin must be maintained at a minimum level of
$16,000. If the S&P Index futures contract goes from its initial value down to $1,251.80, will
there be a call for more margin?
Annualized return 15% 
17-3.
Latest value
1, 251.80
Original value
1, 271.60
Loss
(19.80)
Multiplier
250
Total Loss
($4,950)
Current margin  Orginal margin  loss
$15, 050
 $20, 000  $4,950
Since the current margin position of $15,050 is below the minimum maintenance level
of $16,000, there will be a call for more margin of $950.
Computing settle price
4. Based on the information in Table 17–1, assume you buy a Dow Jones (DJ) Industrial
Average September contract at the settle price. You hold the contract for six months and
enjoy a gain in value of $15,000. What is the settle price after six months?
17-4
Chapter 17 - Stock Index Futures and Options
7-4.
September settle price
11,127
Gain in value after six months $10, 000
$15, 000
 $1,500
 1,500
10
Settle price after 6 months
12,627
Computing settle price
5. Based on the information in Table 17–1, assume you buy a Nasdaq 100 December contract
at the settle price. You hold the contract for one month and suffer a loss of $3,000. What is
settle price after one month?
17-5. December settle price
Loss in value after six months $3,000
Translated by 100 unit multiplier
 $3,000
100
Settle price after one month
1,571
 $30
 30
1,541
Computing basis
6. Examine Table 17–1. Using settle prices, what is the value of the basis for each of the
September 2006 and December 2006 DJ Industrial Contracts? Assume the actual DJ is
11,100.
17.6.
September 2006
Stock index futures price
11,127
Actual underlying index
11,100
Basis =
27
December 2006
11,212
11,100
Basis =
112
Hedging and betas
7. Northern States Life Insurance Company has a $14 million stock portfolio. The company is
very aggressive and the portfolio has a weighted beta of 1.30.
a. Assume they use S&P 500 Index futures contracts to hedge the portfolio for the next 90
days and the contracts can be sold at 1,290. The contracts have a multiplier of 250. With the
appropriate beta adjustment factor, how many contracts should be sold? Round the final
answer to the nearest whole number.
b. If Dow Jones (DJ) Industrial Average contracts selling at 11,150 were used instead, how
many contracts should be sold? These contracts have a multiplier of 10. Once again, consider
the appropriate beta adjustment factor and round your final answer to the nearest whole
number.
17-5
Chapter 17 - Stock Index Futures and Options
$ Value of Portfolio
 Weighted beta of portfolio
$ Value of Contract
$14, 000, 000


1.30
1, 290  250
17-7. a) Number of contracts 
$14, 000, 000

1.30
322,500
 43.411.30  56.43or 56 contracts

b) Number of contracts

$ Value of Portfolio
 Weighted beta of portfoilio
$ Value of Contract
$14, 000, 000
11,150 10
 $14, 000, 000


1.30

1.30
111,500
 125.56  1.30  163.23or
163contracts
Hedging and betas
8. The New Horizon Pension Fund decides to hedge its $40 million stock portfolio on June 1.
The portfolio has a beta of 1.10. It will use Nasdaq futures contracts selling at 1,571 to hedge.
These contracts have a multiplier of 100.
a. With the appropriate beta adjustment factor and rounding the final answer to the nearest
whole number, how many contracts should be sold?
b. Assuming that by September 1 the market has gone down by 20 percent and the stock
portfolio moves in accordance with its beta, what will be the total dollar decline in the
portfolio?
c. Assume the Nasdaq Index futures contracts decline by 20 percent from 1,571. What will be
the total dollar gain on the futures contracts? In the process, compare the sale price of 1,571
with the current value, multiply by 100, and then multiply this value by the number of
contracts. How does the total dollar gain on the futures contracts compare with the portfolio
loss in part b?
d. Now assume that because of changing basis, the stock index futures contract does not move
parallel to the market. Although the market goes down by 20 percent, the stock index futures
decline by only 15 percent. What will be the gain on the futures contracts? How does this
compare with the loss in portfolio value in part b ?
17-6
Chapter 17 - Stock Index Futures and Options
17.8. a) Number of Contracts 
$40, 000, 000
1,571 100
 $40, 000, 000


$ Value of Portfolio
 Weighted beta O f portfoilio
$ Value of Contract
1.10
 1.10
157,100
 254.61  1.10  280.07 or
b) Market Decline
Beta
280 contracts
20%
1.10
Portfolio decline
Value of Portfolio
22%
$40, 000, 000
Portfolio decline (%)
Actual portfolio decline
c) Futures contract (sales price)
Current value (80%)
22%
$8,800, 000
1,571.00
1, 256.80
Gain
314.20
100
Multiplier
Profit per contract
Number of contracts
Total dollar gain on contracts
$ 31, 420
280
$8, 797, 600
The total dollar gain in futures contracts covers the dollar loss in the portfolio. (The
only difference is due to rounding.)
d) Futures contract (sales price)
Current value (85%)
1,571.00
1,335.35
Gain
235.65
100
Multiplier
Profit per contract
Number of contract
Total dollar gain on contracts
$ 23,565
280
$6,598, 200
17-7
Chapter 17 - Stock Index Futures and Options
Because of the changing basis, only about 75 percent of the portfolio loss was
hedged. A less than perfectly executed hedge is not unusual.
S&P 500 call options
9. The following problem relates to data in Table 17–6. Assume you purchase an August 1250
(strike price) S&P 500 call option. Compute your total dollar profit or loss if the index has the
following values at expiration:
a. 1305
b. 1285
c. 1230
17-9. a) Purchase price (August1250 call option)
Expiration value (1305  1250)
30
 55
Profit
Total profit 25 100  $ 2,500
 25
b) Purchase price (August1250 call option)
Expiration value (1285 1250)
30
 35
5
Loss
Total profit 5 100  $500
c) Purchase price (August1250 call option)
Expiration value (no value)
30
0
 30
Loss
Total loss  30 100  $3, 000
S&P 500 call options
10. Using data from Table 17–6, assume you purchase a September 1250 (strike price) S&P
500 put option. Compute your total dollar profit or loss if the index has the following values
at expiration:
a. 1260
b. 1210
c. 1170
17-10. a) Purchase price (September1250 Put option)
Expiration value (no value)
28.00
0
 28.00
Loss
Total loss  28.00 100   2,800
17-8
Chapter 17 - Stock Index Futures and Options
b) Purchase price (September1250 Put option)
28.00
Expiration value (1210 1250)
 40.00
Gain
 12.00
Total gain100  12.00  $1, 200
c) Purchase price (September1250 Put option)
28.00
Expiration value (1170 1250)
 80.00
Gain
 52.00
Total gain 100  52.00  $5, 200
Hedging with the S&P 500 options
11. The Topps Company has a $1 million funded pension plan for its employees. The
portfolio beta is equal to 1.12. Assume the company sells (writes) 60 July 1255 (strike price)
call option contracts on the S&P 500 Index as shown in Table 17–6. Each contract trades in
units of 100. At the time the options were written, the index had a value of 1,250.26.
a. What are the proceeds from the sale of the call options?
b. Assume the market goes down by 14 percent. Considering the portfolio beta, what will be
the total dollar decline in the portfolio?
c. Assume the S&P 500 Index shown at the bottom of Table 17–6 also goes down by 14
percent at expiration. What will be the value of the index at that time?
d. Based on your answer to part c, what will be your profit on the option writes?
e. Considering your answers to parts b and d, what is your net gain or loss?
17-11. a) Option premium
Multiplier
Total premium per contract
Number of contracts
Total proceeds
17
100
1, 700
60
$102, 000
17-9
Chapter 17 - Stock Index Futures and Options
b) Market decline
Beta
14%
1.12
Portfolio decline
$ Valueof portfolio
Portfolio decline
15.68%
$1,000,000
15.68%
Actual portfolio loss
($156,800)
c) S& P Index
14% decline
New value of index
1, 250.26
175.04
1, 075.22
d) Your profit will be equal to your proceeds in part a: $102,000. You get to keep the
entire premium because the options that were sold will not have to be bought back.
e) Loss (part b)
Gain (part d)
Net loss with hedge
(156,800)
102, 000
($54,800)
Using puts to hedge
12. Assume that in problem 11 the firm had purchased 80 July 1260 put option contracts on
the S&P 500 Index listed in Table 17–5 instead of selling the call options. If the S&P 500
Index goes down by 14 percent (see 11 c) at expiration,
a. What will be your profit on the puts? Comparing that to your loss on the stock portfolio in
problem 11 b, what is your net overall gain or loss?
b. Compare the protection afforded by the call-writing hedge in problem 11 with the
protection afforded by the put purchase in this problem.
c. Suggest any modifications to the call writing or put purchase strategy that would allow you
to increase your protection even more. A general statement is all that is required.
17-10
Chapter 17 - Stock Index Futures and Options
17-12. a)
Sell (strike) price of Index
Value of Index at expiration (answer11 c)
1260.00
1075.22
Ending value of puts
184.78
Purchase price of puts (Figure17 - 6)
20.10
Profit
164.68
Multiplier
Total profit per contract
100
16, 468.00
Number of contracts
Total profit on puts
Loss on portfolio (answer11b)
80
$131, 744
156,800
Net loss with hedge
($ 25, 056)
b) The put purchase is a more effective hedge. It cuts the loss to $25,056, whereas
with writing the call option the loss is $54,800.
c) You could purchase more contracts of either. Also, you could write call options at
a lower strike price or buy put options at a higher strike price.
Using calls and puts to hedge
13. Garner Money Management, Inc., is in charge of a $50 million portfolio. Its beta is equal
to the market. To hedge its position, it sells (writes) 200 July 1225 call option contracts on the
S&P 500 Stock Index as shown in Table 17–5. It also buys 300 August 1225 put option
contracts on the same index shown in Table 17–5. Instead of going down, the market goes up
by 10 percent (as does the portfolio), and the S&P 500 Stock Index ends at 1,375.
Consider the change in the portfolio value and the gains or losses on the call and put
options. Each option contract trades in units of 100. What is the overall net gain or loss of
Garner Money Management as a result of the changes in the market?
17-13. Value of portfolio
$50, 000, 000
Portfoilio increase
10%
Gain in portfoilio value
Loss on Call Options
$ 5, 000, 000
Option premium received (July1225)
38.50
Final value of Dec. options (1375 1225)
150.00
Loss
Multiplier
111.50
100
Total loss per contract
Number of contracts
(11,500)
200
Total loss on call options
$2,300, 000
17-11
Chapter 17 - Stock Index Futures and Options
Loss on Put Options
Purchase price of puts (August1225)
Value at expiration (1375 market value
exceeds1225option price)
15.80
0
Loss
Multiplier
15.80
100
Total loss per contract
Number of contracts
1,580
300
Total loss on put purchase
Summary
Gain in portfolio value
Loss on call options
($474, 000)
$5, 000, 000
(2,300, 000)
Loss on put options
(474, 000)
Net gain
$2, 226, 000
Chapter 17 Solution to Investment Advisor Problem
a.
b.
Based on the date in table 17-2, the best choice would be the Mini NASDAQ 100.
The NASDAQ100 is composed of the 100 largest stock on the NASDAQ stock
market. The majority of these stocks are in technology, which meets one of Katie’s
preferences. More importantly, the margin requirement appears to be within her
range. With a contract value of $31,420 and a margin requirement normally in the
six to seven percent range, the dollar margin figure would be between $1,885 and
$2,199. This is within her $2,150 range.
She could also ge maximum “bang for her bucks” if she invested in stock index
options or options on stock index futures, particularly if she invested in out-of-themoney options for either choice.
17-12