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Unformatted text preview: Hu—I- ——
—|..-_n-I.-rrl 'lf—i-I-f-hI-l-ml-d- —l—i———-—- -— ——- ill—III-
.- U1.) A buyer of a crude oil futures contract makes money if the acknown more price of erode oil is
higher than a price agreed to today. (it) Give an example of an entity that might be interested in buying ch a contract. to) Give an example of an entity that might be interested in selling St ch a contract. e oil are very popular. Several years ago, a. .ordeaus wine futures contract
That contract is not traded anymore. the trading volume aever
hint: of reasons why it is more diftiult to establish a ﬁxtures Eotures contracts on crud
was introduced at'an exchange.
reached a critical mass. Can you t
contract for wine than for another commodity such as crude oil? XYZ stock has a bid price of $97.50 and an ask price of $98.20. You roold like to buy 100 shares.
and contact two brokers about their cost structure. Broker A has a prportional transaction cost of
0.2% and a $5 account setup fee. while broker B has a transaction cot of $30. ' ' - - Who should you buy the shares from“? Would your answer to Q'uestiOrl 1.3 change if you" wanted to buy 150 shares? XYZ stock has an ask price of $50.25. Suppose you boy 50 shares. If there is a brokerage
commission of $15, and your ronhdtri p transaction costs are $57.50.. r hat is the bid price of XYZ stock? Suppose that the XYZ stock has a bid price of" $50.25 ahd an ask pric of $51.37- You buy 10 shares _
of XYZ. and immediately after that. 'the‘bid price moves to $5 l .25 an the ask price mores to ' . -
$52.22. What are your roundtrip transaction costs? What is the profit (or loss} of the market maker who sold you the sec trity in Question .1 .6? Suppose you short—sell 200 shares of MNO stock. The bid price for h NO stock is $2.32., the ask
price is $12.66. " Suppose your counterparty tells you that she is concerned about your credit risk. Therefore. she tells
you that she will keep the proceeds from the short sale and asks you o provide an additional 2.0% of
the proceeds as a haircut. How much money do you have to transfer 1 your counterparty‘? Z M-cDonald * Derivatives Market's; Second Edition 9.. Suppose you wish to short-sell 100 shares of MNO stock, which has a bid pric of $44.22 and an ask
price of $46.42. You cover the short position 270 days later when the bid pric is $46.87 and the ask price is $49.05. Suppose that there is a 0.4% Commission to engage in the she t—saie and a 0.3%
commission to close the short-sale. Suppose the lender keeps the entire proceds from the short sale as collateral... (a) What profit did you make?
(13) Suppose the 9—month interest rate is 6%, and that the rebate for MNO stok offered by the lender
is 2%. How much interest accrues during the 9 months in which you have the short position? Does this reduce or increase your proﬁt? 10. Do an'ohline search of the term “hard to borrow.” In the contest of. short—sale, what does this mean? u—u—m.
.r-"" Chapter 1 I. i . U1 Introduction to Derivatives (a) The airline industry is a very good example. Theprofit of an airlite company is severely
affected when the price of oil is rising. Passengers oftentimes bu tickets in advance. and sudden
price increases for keroseoe cannot be passed on to the passenger if a contract pays off iii tie-res
of higher crude oil prices. airline companies can hedge their eapsure to the oil price risk. ' (b) An example would be countries whose principal revenues stem tom oil export. Their revenues are severely hit if the price of oil declines. Any contract that pay. off in times of declining oil '-
prices would be attractive to them. it ' - Note that speculators are also very active in the crude oil market. The drastic increase ira- crude
oil prices that we witnessed in July 2.004 was rumored to-he parti lly driven by speculators
hoping for ruptures in supply of crude oil. ' One ot‘the problems with wine is that it is much less standardized. Y a can set exact quality standards for crude oil. and market participants know and respeCt the 'e standards. The wine futures
contract traded at the exchange promised to deliver at the end of the ontract five cases of wine that
the seller could choose from a wide list of estates that were classified based on the French '
classification system of 1855. However. there could be large differen es in the development of
prices for different estates. This made trading complicated. because a was not absolutely clear what _
would eventually be delivered. " The concept of standardization is very important. In later chapters. th book will deal more detail
with the problem”; of standardization and delivery. Broker A: ($98.20 >< 100) + ($98.20 x 100) X 0002 + $5 = 3; £44.64 Broker B:
($98.20 >< 100) -+ $30 = sassooo You should buy the shares from broker A. because‘yoor total outhof— ocket expenses are smaller. B roker A: ($98.20 X 150) + ($98.20 x 150:) X 0.002. + $5 = $1 1' 364.46
($98.20 X 100) + $30 : $14.760 Yes. your answer would change. Now you should boy from broker B Proportional transaction costs
are cheaper for sitiall quantities. That is why you__ofteh see advertiser} eats such as “We charge 0.5%. '
with a minimum charge of $15.” ' . ’5" . . .. 1. ..
‘ Remember that the terminology bid and ask is formulated from the I arket makers perspective. Therefore. the price at which you can buy is called the ask price. Yot pay: ($50.25 x 50) + s15 : $2527.50 You can sell at the market maker’s bid price. You will have to pay a I elm-mission. and your broker
will deduct the commission from the sales price of the shares. You raise: .(bidx50)-—s15 60 McDonald 1? Derivatives Markets. Second Edition Your round-trip transaction costs amount to: 57.50 2 $2,527.50 —— (bid X 50 an $15)
22> bid = $49.70 W e need to take into account the increase in the quotes after our trade was excnted. This has an influence on the roundtrip transaction costs. Why should the bid and ask increse after we buy the
stock? If the stock is very illiquid (Le... it is rarely traded). our purchase might “ignal that we have
good news about the development of company XYZ. and the market maker ra .ses the price to take into account this conjecture. TAC = $51.37 x 10 + $10 -— ($51.25 x10 m $10)
= $21-20 Oar transaction costs are smaller than without an increase in the quotes. Remember that the market maker can buy at the bid and sell at the ask—that '. how he makes
a profit for the provision of liquidity. Therefore. Proﬁt of Market Maker : $51.37 X '10 — $51.25 X 10
= $1.20 Despite the increase in quotes agaiast him. the market maker is able to make :- proﬁt. A short sale of MNO entails borrowing shares of MNO and then selling them t the bid. Therefore,
initially. we will receive 200 x ($12.32) = $2,404 The counterparty will keep that amount. but requires an additional 20% as a hircut. Therefore. we
will have to transfer 020 x $2.464 2: $492.80 to her. (a) A short sale of MNO stock entails borrowing shares of MNO and then sel ing them. receiving
cash. and we learned that we sell assets at the bid price. Therefore. initiall . . we will receive the
proceeds from the sale of the asset at the bid (ignoring the commissions a d interest). After 270
days. we cover the short position by buying the MNO stock. and we saw t at we will always buy at the ask. Therefore. we earn the following profit: 100 x ($44.22) — 100 x ($44.22) x 0.004 _ (100 x ($49.05) ><: 0.003 + 100 ($49.05)) .—-=
$4,422 x 0.996 —-— sages x 1.003 = $4.4043 '1 — $5,052.15 = ——$6 7.84 Therefore. we actually made a ioss of $647.84. The stock price rose durin ;_ the life of the short
sale. and with rising stock prices. a short position loses money. (b) The proceeds from short sales, less the commission charge are $4.4043l. Since the 9ﬂmonth
interest rate is 6%. but the lender only offers 2% on our collateral. we 103 an additional $4.40431 X 0.04 2 $176.17. Our short sale turned out not to be proﬁtable _— —_——..J-I—mm1wI-Iml—II—FI—F-Irr—I—Fl—I—rrr—h———-—— - ' IF-II-r-—|—H-'I-I-l-|-|-lmI-—I—I'I—'I—"-I—"-""-""'"""-'"-""'-i"'- ' '- I'Ff'n-II-I-I-I-rr'I-FI—F-I——I—'-H--P-—\-- --n---'-- -- —"I"I Aaswchectioa . ' "a: 10. Sometimes. a particular stock is scarce and difficult to borrow. Very f w investors are willing to lead r '
the stock. 3le the demand for borrowing that particular stock exceeds by far the supply. Ofteritimes. '
shares right after an [P0 or shares of companies that are speculated'to be involved in a merger-are! _ -
hard to borrow. 1P0 stocks can be hard to borrow. because there exist} empirical evidence that after.
the high return on the initial day of the listing. there is a gradual decli e in the stock price. Since a '
short seller benefits from declining prices. she is very ioteres—ted in so h stocks. Furthermore. iii. an
initial public offering. usually only 2.1. 511121” number of shares is. sold. the supply of shares is
scarce. NASD@ (the National Association of Securities Dealers) has impleme ited a hard to borrow list via
Rule 3370. which is designed to prevth abusive short selling arid ens ties that short sellers make
sure they can return the shares they borrowed. ' Chapter 2 _ An Introduction to Forwards and'Optia-ns l. Page 2l of the book defines a futures contract- A futures contract:
1. Specifies the quantity and exact type of the asset or cor'rimodity [1 e seller must deliver.
2. Specifies delivery logistics. such as time. date. and place.
3. Specifies the price the buyer will pay at the time of delivery. _
4. Obli gates the seller to sell and the buyer to buy. subject to the abve specifications. In the context of the delivery pizza. I. You specify the quantity (2 number of pizzas) and the exact type of the commodity (one
. medium pepperoni. sausage. and extra cheese). '
2.. Please deliver to my home address today. You might also ask: When will you approximately
deliverm—will it be within the nest twenty minutes?” -
3. You know how much the pizza will costmyou usually have 21 del very menu at home.
4. The pizza store often calls you back to verify you indeed ordered and if ever you decide you do
not want to have the pizza. makes sure that you are blacklisted! - (a) The payoff to a short forward at expiration is equal to: E‘s.) Payoff to short forward 2 Forward price —- Spot price at expiratioi
Therefore. we can construct the following table: Price of Asset in 6 Months Agreed Forward Price Payoff . the Short orward 950 . LOSG ' lOO
LOOO LUSO . 50
1.050 ' . 1.050 _ ' - O - l.l00 1.050 #50 l.l50 * 1.050 ' mlOO (b) The payoff to a sold call option at expiration is: Payoff to 501d can Opt-gen : _ maxw. spot price. at expiration --—- stiiite price} ...
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- Spring '12