Chapter Fifteen
Other Derivative Assets
Answers to Problems and Questions
1. At-the-money puts and calls should sell for the same price.
2. Warrants sell for their greatest premium over intrinsic value when they are atthe-money. This is as predicted by Black-Scholes.
3. If you buy when-issued stock, you enjoy a delay between the time you
establish the investment position and the time when you have to pay for your
investment. It does appear, however, that when-issued prices are higher than
the time value of money adjustment indicates they should be, meaning that
when-issued shares are too expensive relative to regular-way shares.
4. a) In the cases where this has happened, “warrant holder goodwill” has been
cited as the reason. In a sense, extension of the life of the warrants appears to
be not in the best interest of the shareholders of the firm. If the warrants are
simply allowed to expire, this “undilutes” earnings per share and removes a
contingent liability from the books. Presumably the firm feels that the benefit
from the goodwill overrides the accounting benefits. An alternate view is that
the warrants will eventually become a source of capital, but only if they remain
outstanding long enough to go in-the-money. Extending them increases the
likelihood that the firm will eventually receive this capital inflow.
b) If the warrant’s life is extended, this instantly increases its value, which is
not advantageous to the warrant hedger. This would either reduce or delay
the hedger’s profit.
5. Probably the single most important advantage is the fact that no futures
account activity is involved. This means that the speculator need not be
concerned with good faith deposits, or with special brokerage firm
requirements. The speculator can probably buy foreign currency options in an
existing cash or margin account, but would need a futures broker to trade in
futures options.
6. If a put option version of a warrant were available, it would be attractive to
many in the marketplace. Such a security would provide a floor value on an
investment in shares of stock in that company. This could provide a long-term
“protective put” function. From the company’s perspective, sale of the
security would generate capital, but would most likely require the setting aside
of reserves against the possibility of future exercise of the “option.”
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Chapter Fifteen. Other Derivative Assets
(Note: There is a security variation known as “puttable stock.” See, for
instance, Chen and Kensinger, “Puttable Stock: A New Innovation in Equity
Financing, Financial Management, 1988 v17(1), 27 – 37.
7. Rather than promising to deliver the crop, the farmer could acquire the right to
promise to deliver by buying a futures put. While this would require a cash
outlay, it would leave open the possibility of profits if the commodity price
were to rise.
8. Just as with futures contracts, futures options can enable you to guarantee a
specific crop price. (See the answer to question 7.)
9. The owner of the option has the ball in their court. The writer of an option
must “perform” if the option holder exercises the option. The right to go long
at my discretion, for instance, is different from an obligation to go long at
someone else’s discretion.
10. The statement is correct. The right to buy DM for dollars is the same as the
right to sell dollars and get DM.
11. Basis can change, and frequently does. The size of the basis can be different
for different delivery months, and the spreader is usually betting on a general
increase or decrease in the value of a commodity. If the basis changes
differently for the two parts of the spread, it can negate any gain that would
have otherwise accrued to the spreader.
12. A deep-in-the-money call, for instance, tends to behave very much like the
underlying asset; its delta is near 1.0. You earn no interest if you hold a call
option. You can, however, earn interest on the good faith deposit with a
futures contract. By exercising the call, the investment essentially goes from
being non-interest bearing to interest bearing. Depending on the value of the
call and the size of the good faith deposit, it is sometimes advantageous to
replace the call with the associated futures position. The same logic is true for
futures put that are deep-in-the-money.
13. An at-the-money futures option would probably not ever be exercised early.
As with other options, early exercise amounts to abandoning the remaining
time value.
14. a) The breakeven point is the option premium plus the striking price, or 12.60
+ 1160 = 1,172.60.
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Chapter Fifteen. Other Derivative Assets
b) At an index level of 1175.00, the 1160 call is in-the-money. Its intrinsic
value is 1175 – 1160 = 15.00. With each index point worth $250, the
person has a gain: (15.00 – 12.60) x $250 = $600.00 gain
15.
6.40
1160
1170
1164.50
3.60
16. The diagram happens to be exactly the same.
6.40
1160
1170
1164.50
3.60
17. You can do this using trial and error with the Black.xls file. Input the initial
data, then change the volatility input until the program predicts a call price of
$17.00. This happens with a volatility of 9.70%.
18. From the Black.xls file with a volatility of 9.70%, the theoretical call value is
$4.25.
19. From the Black file, the delta is 0.4161.
20. a) 3 x 17.00 x $250 = $12,750
b) The futures have a delta of 1.0; from the Black file, the calls have a delta of
0.5607. The position delta is (5 x 1.0) – (3 x .5607) = 3.32.
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Chapter Fifteen. Other Derivative Assets
21. At expiration the stock is up $3 per share for a gain of $300. The warrant is
in-the-money by $1.00. Each warrant, however, permits the purchase of
1.12 shares, so the warrant has intrinsic value of $1.12. Sold short at $7,
there is a $5.88 per warrant gain, or $588 on 100 warrants. The total gain is
$888.
22. a) The purchase price of the puts is 30¾ . With the futures selling for 832
at expiration, the 8400 puts have intrinsic value of 8. On three of these
put contracts there is a loss of 3 x 5000 x (8 – 30¾ cents per bushel) =
$3,412.50 loss.
b)
8.0925
8.0925
8.40
0.3075
23. Individual response.
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