CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
PROBLEM SETS
1. Options provide numerous opportunities to modify the risk profile of a portfolio.
The simplest example of an option strategy that increases risk is investing in an ‘all
options’ portfolio of at the money options (as illustrated in the text). The leverage
provided by options makes this strategy very risky, and potentially very profitable.
2. Buying a put option on an existing portfolio provides portfolio insurance, which is
protection against a decline in the value of the portfolio. In the event of a decline in
value, the minimum value of the put-plus-stock strategy is the exercise price of the
3. An investor who writes a call on an existing portfolio takes a covered call position.
If, at expiration, the value of the portfolio exceeds the exercise price of the call, the
writer of the covered call can expect the call to be exercised, so that the writer of
4. An option is out of the money when exercise of the option would be unprofitable. A
call option is out of the money when the market price of the underlying stock is less
than the exercise price of the option. If the stock price is substantially less than the
exercise price, then the likelihood that the option will be exercised is low, and
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CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
A call is in the money when the market price of the stock is greater than the exercise price
of the option. If stock price is substantially greater than exercise price, then the price of
the option approaches the order of magnitude of the price of the stock. Also, since such
5.
Cost Payoff Profit
a.
Call option, X = $145.00
$5.18
$5.00
-$0.18
b. Put option, X = $145.00 0.48 0.00 -0.48
6. In terms of dollar returns, based on a $10,000 investment:
Price of Stock 6 Months from Now
Stock Price
$ 80
$ 100
$ 110
$ 120
All stocks (100 shares)
8,000
10,000
11,000
12,000
Price of Stock 6 Months from Now
Stock Price
$80
$100
$110
$120
All stocks (100 shares)
-20%
0%
10%
20%
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CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
7. a. From put-call parity:
0.25
100
10 100 $7.65
(1 ) 1.10
T
f
X
P C S r
= – + = – + =
+
b. Purchase a straddle, i.e., both a put and a call on the stock. The total cost of the
8. a. From put-call parity:
0.25
50
4 50 $5.18
(1 ) 1.10
T
f
X
C P S r
= + – = + – =
+
b. Sell a straddle, i.e., sell a call and a put, to realize premium income of
c. Buy the call, sell (write) the put, lend $50/(1.10)1/4
The payoff is as follows:
Position Immediate CF CF in 3 months
S T ≤ X S T > X
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CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
82.48
10.1
50
Total
C – P +
00.50
10.1
50
4/1
S T S T
By the put-call parity theorem, the initial outlay equals the stock price:
S0 = $50
In either scenario, you end up with the same payoff as you would if you
bought the stock itself.
9. a. i. A long straddle produces gains if prices move up or down and limited losses
b. i. Long put positions gain when stock prices fall and produce very limited
10. Note that the price of the put equals the revenue from writing the call, net initial
cash outlays = $38.00
Position
T
S
< 35
35
T
S
40
40 <
T
S
Buy stock
T
S
T
S
T
S
T
S
T
S
35-
$35
Profit
$2
-$3
$40
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CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
11. Answers may vary. For $5,000 initial outlay, buy 5,000 puts, write 5,000 calls:
Position
T
S
= $30
T
S
= $40
T
S
=$50
Stock portfolio $150,000 $200,000 $250,000
Compare this to just holding the portfolio:
Position
T
S
= $30
T
S
= $40
T
S
=$50
12. a.
CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
b.
Position S T < X1X1 S T X2
X2X2XX2
X2 < S T
X
1
S
T
X
1
X
2
Payoff
14.
Position S T < X1X1 S T X2
XX2
X2 < S T
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CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
Payoff
0
S
T
X
1
X
2
Payoff
–(X
2
–
X
1
)
15. a. By writing covered call options, Jones receives premium income of $30,000.
If, in January, the price of the stock is less than or equal to $45, then Jones
will have his stock plus the premium income. But the most he can have at that
time is ($450,000 + $30,000) because the stock will be called away from him
if the stock price exceeds $45. (We are ignoring here any interest earned over
this short period of time on the premium income received from writing the
option.) The payoff structure is
Stock price Portfolio value
This strategy offers some extra premium income but leaves Jones subject to
b. By buying put options with a $35 strike price, Jones will be paying $30,000 in
premiums in order to ensure a minimum level for the final value of his
position. That minimum value is ($35 × 10,000) – $30,000 = $320,000.
This strategy allows for upside gain, but exposes Jones to the possibility of a
moderate loss equal to the cost of the puts. The payoff structure is:
Stock price Portfolio value
c. The net cost of the collar is zero. The value of the portfolio will be as follows:
Stock price Portfolio value
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CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
The best strategy in this case would be (c) since it satisfies the two
Our ranking would be: (1) strategy c; (2) strategy b; (3) strategy a.
16. Using Excel, with Profit Diagram on next page.
Stock Prices
Beginning Market
Price 116.5 Price Profit
Ending Market Price 130 Ending Straddle
Buying Options: 50 42.80
Call Options Strike Price Payoff Profit Return % 60 32.80
110 -17.20
Put Options Strike Price Payoff Profit Return % 120 -27.20
170 2.80
Straddle Price Payoff Profit Return % 180 12.80
Selling Options: Ending Bullish
Call Options Strike Price Payoff Profit Return % Stock
Price Spread
90 -3.2
Put Options Strike Price Payoff Profit Return % 100 -3.2
150 6.8
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CHAPTER 20: OPTIONS MARKETS: INTRODUCTION
Money Spread Price Payoff Profit 160 6.8
Bullish Spread 170 6.8
210 6.8
Profit diagram for problem 16:
Straddle Bullish Spread
17. The farmer has the option to sell the crop to the government for a guaranteed
18. The bondholders have, in effect, made a loan that requires repayment of B dollars,
where B is the face value of bonds. If, however, the value of the firm (V) is less than
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