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17-8. a. An in-the-money option must have positive intrinsic value. The intrinsic values of the options are
Call at $45: $47 - 45 = $2
Call at $50: $47 - 50 = nil
Only the call with the $45 strike price is in-the-money.
b. The time premiums:
c. Price of Intrinsic Profit
the stock value of on the
the call call
$30 $0 ($4)
35 0 ( 4)
the stock value of on the
the call call
$30 $0 ($1)
35 0 ( 1)
The potential profits/losses differ. If you buy the "out of the money" call, the potential loss is less but the
price of the stock must rise more for the option to have positive intrinsic and to assure that you earn a
profit.
e. Price of Intrinsic Profit Profit Total
the stock value of on the on the profit
the call stock call
$30 $0 ($17) $1 ($16)
35 0 (12) 1 (11)
40 0 (7) 1 (6)
As long as the stock sells for greater than $46, the position generates a profit (before commissions).
f. Price of Intrinsic Profit Profit Total
the stock value of on the on the profit
the call stock call
$30 $0 ($17) $4 ($13)
As long as the price of the stock remains above $43, the position yields a profit.
Both (e) and (f) are covered calls, so their answers are similar. The maximum possible profit is $4 in (e)
17-9. This problem illustrated the protective put strategy.
The profit-loss profile at various price of the stock:
Price Profit:
of the Buying the Buying the Total
stock stock at $36 put at $2 profit
$30 ($6) $3 ($3)
17-10.
Price of Profit on Intrinsic Profit Profit Total
the stock 100 shares value of on the on the profit
call call T-bill
$90 ($1,000) $0 ($400) $400 $0
Notice that if the investor selects the T-bill and the call instead of the stock, the investor does not sustain a
loss if the price of the stock falls, and earns the same profit if the price of the stock rises. The call plus the
17-11. This problem compares several strategies designed to profit if the price of the stock rises.
a. the cash inflows/outflows:
buying the stock: $86.00 outflow
buying the call: $10.50 outflow
the covered call: $86.00 - 10.50 = $75.50
selling the put: $ 8.25 inflow
b. profit/loss profile
Price of Bought Bought Covered Sold
the stock the stock the call call the put
$110.00 $24.00 $14.50 $9.50 $8.25
100.00 14.00 4.50 9.50 8.25
c. Break-even prices of the stock:
buying the stock: $86.00
d. Three of the positions require a cash outflow, but the sale of the put produces a cash inflow. The
potential profits are limited if you execute the covered call or the sale of the put, $9.50 and $8.25,
respectively.
The potential loss on the sale of the put is larger than on the covered call, once again by $1.25.
e. Purchasing the call has the smallest potential loss ($10.50), while the losses continue to rise as the
price of the stock declines.
f. Once the price of the stock falls below $75.50, all four possible positions generate losses.
g. The largest potential gain occurs through the purchase of the stock, but the largest percent return
three alternatives with a cash outflow is the purchase of the call.
h. If the price of the stock declines and the put is exercised, your cost basis is the strike price minus the
17-12. a and b. The strategy’s initial cash outflow is the total cost of the stock (i.e., the prices x 100
shares x 10 positions). The inflows are the price of the calls and the dividends received:
Price Annual Call
dividend price
AT&T $30.00 $1.76 $1.00
DuPont 46.00 1.64 2.50
General Electric 18.00 0.68 1.00
c. An increase of $5 generates $5 x 100 shares x 10 positions = $5,000 on the stock plus the $1,502 in
dividends for a total of $6,502. The profits/losses on the call options are
Stock Strike Value of Gain or
price price the call loss
AT&T $35.00 $32.00 $3.00 ($2.00)
DuPont 51.00 52.50 0.00 2.50
General Electric 23.00 20.00 3.00 (2.00)
The net loss on the options is $190 (100 x $1.90). The strategy generated a net gain of $4,602 on an
investment of $37,490.
An increase of $15 generates a gain of $15 x 100 shares = $15,000 on the stock plus the $1,502 in
dividends for a total of $16,502. The profits/losses on the call options are
Stock Strike Value of Gain or
price price the call loss
AT&T $45.00 $32.00 $13.00 ($12.00)
DuPont 61.00 52.50 8.50 (6.00)
General Electric 33.00 20.00 13.00 (12.00)
The loss on the call options is $9,840 (100 x $98.4), but the strategy generated a net gain of $6,662
d. If the price of each stock declines by $5, the loss on the stocks is $5,000 ($500 on each stock). The
e. Using covered calls to create a variation on the Dogs of the Dow is a viable strategy. If stock prices are
stable, the investor receives the dividends and takes advantage of the options’ time premium disappearing.
Teaching Guides for the Investment Assignment (Part 6)
This chapter adds call options to the Investment Assignment. I have assumed that this assignment will
occur late in the semester so it is limited to a short period such as three to six weeks and applies to only
two stocks. The assignment covers the basics of call options and should illustrate the price movements for
in, out, and at the money calls. The questions in the assignment are similar to the questions in problems 3
and 4.
Teaching Guides for the Financial Advisor’s Case: A Speculator's Choices
BACKGROUND: This case highlights several considerations when choosing among common stock,
convertible securities, and options. The investor, Cosima Wagner, has a tendency to speculate. While this
does not mean that she enjoys taking risks, it does imply that this particular investor is willing to bear
more risk than a more conservative investor. Ms. Wagner is attracted to a stock (Fasolt and Fafner
Construction) whose price has fluctuated significantly (from a high of $80 to its current price of $15).
Fasolt and Fafner Construction is in a volatile industry and experiences large swings in sales and
earnings, which tend to produce large fluctuations in the price of the stock. If an investor could correctly
anticipate changes in the firm's earnings, that individual might be able to earn a large return on the stock
and, perhaps, an even larger return through investing in the put and call options.
The alternatives available to Ms. Wagner include the common stock, a debenture that sells at a discount
($780) and yields 10.92 to maturity, six call options to buy the stock, and six put options to sell the stock.
The options are differentiated from the others either by their exercise ("strike") prices or time to
expiration.
1. The first question asks for the current yield offered by each security. The put and call options do not
pay dividends or interest and thus produce no current yield. The stock in this case also does not pay any
dividend. Only the debenture bond has a current flow of income. Its current yield is $72/$780 = 9.23%.
2. The bond may not be converted into stock; it has no value in terms of stock
3. The intrinsic value of each call is the price of the stock minus the strike price:
three-month call at $15 $15 - 15 = $0
The intrinsic value of each put is the strike price minus the price of the stock:
three-month put at $15 $15 - 15 = $0
three-month put at $20 20 - 15 = 5
While the intrinsic values establish the value of each option in terms of the underlying stock, each option
sells for a price that exceeds the intrinsic value (i.e., sell for a time premium).
4. The time premium paid for each option is the option's price minus its intrinsic value:
three-month call at $15 $2 - 0 = $2
three-month call at $20 0.75 - 0 = 0.75
six-month call at $15 3.50 - 0 = 3.50
5. If, after six months, the price of the stock is $15, the price of the bond should be about $720. Unless
there has been a change in interest rates, the price of the bond should be approximately the same. (The
The three month put at $20 would have been exercised or sold three months previously. The six month put
at $20 would now be worth $5, and the position would either be closed or the option would be exercised.
The nine-month options now have three months to go; their prices would be similar to the prices of the
three month options when the problem commenced:
Strike price Prices of the nine month options
with three months remaining to
expiration
call put
(This question illustrates that if the price of the stock is stable, the prices of the options decline as they
approach their expiration date. Investors buy options in order to take advantage of movements in the
stock's price. Failure to get such price movement is the stock will generate losses for the buyers of the
options.)
6. If the price of the stock were to fall to $10, then the price of the bond is not affected.
The prices of the calls would decline dramatically if the price of the stock were to fall to $10. All the calls
7. If the price of the stock rises to $25, the bond's value is not affected. The intrinsic value of the call
option at $15 would be $10, and the intrinsic value of the calls at $20 would be $5.
All put options would now be "out" of the money, and their market prices would have certainly declined.
Which of the various options Ms. Wagner should purchase depends on what she anticipates will happen to
the stock. If the price of the stock remains stable, only purchasing the bond generates any return through
Which options to purchase (or sell) depends on the amount of price movement that is expected and how
quickly the price movement occurs. For example, if the price of the stock were to rise from $15 to $19
Besides the different strategies, the volatility of the stock may be considered. The firm's stock has
demonstrated variability in the past declining form a high of $80 to its current price of $15. Earnings have
also been volatile. If the economy is recovering, perhaps the earnings will rebound. Of course, the firm
could experience higher earnings, and the price of the stock might not rise or increase only moderately.
Finally, the willingness of the investor to bear risk should be considered. While the case does not give
information concerning the background of the investor (e.g., age, family obligations, and occupation), the
