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FINANCE 4720BARUCH COLLEGE

Professor RentzlerProblems from Kolb, Futures, Options, and Swaps, Blackwell publishing, 4thed. 2003.

HOMEWORK SOLUTIONS FOR TOPIC 1

a. History & Developmentb. Futures vs. forwardsc. Institutional aspects

Ch 1:#1, 2, 12Ch 1: #4; Ch 3: #1, 17Ch 2: #9 - 12, 16, 18; Ch 3 #19

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Chapter 11. If an arbitrage opportunity did exist in a market, how would traders react? Would thearbitrage opportunity persist? If not, what factors would cause the arbitrage opportunityto disappear?Traders are motivated by profit opportunities, and an arbitrage opportunity represents thechance for riskless profit without investment. Therefore, traders would react to anarbitrage opportunity by trading to exploit the opportunity. They would buy the relativelyunderpriced asset and sell the relatively overpriced asset. The arbitrage opportunitywould disappear, because the presence of the arbitrage opportunity would create excessdemand for the underpriced asset and excess supply of the overpriced asset. Thearbitrageurs would continue their trading until the arbitrage opportunity disappeared.2. Explain why it is reasonable to think that prices in a financial market will generally befree of arbitrage opportunities.Generally arbitrage opportunities will not be available in financial markets because well-informed and intelligent traders are constantly on the lookout for such chances. As soonas an arbitrage opportunity appears, traders trade to take advantage of the opportunity,causing the mispricing to be corrected.12. Iffinancial derivatives are as risky as their reputation indicates, explain in generalterms how they might be used to reduce a preexisting risk position for a firm.While an outright position in a financial derivative considered in isolation generallyembodies considerable risk, these instruments can be used to offset other preexisting risksthat a firm might face. For example, a savings and loan association might face potentiallosses due to rising interest rates, and this risk might arise from the normal conduct of itsbusiness. Such an association could use interest rate futures, options on interest ratefutures, or swap agreements to offset that preexisting risk. Properly managed, financialderivatives can reduce a preexisting business risk through hedging.

Chapter 14. What is the essential feature of a forward contract that makes a futures contract a typeof forward contract?A forward contract always involves the contracting at one moment in time with theperformance under the contract taking place at a later date. Thus, futures represent a kindof forward contract under this definition.

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Chapter 31. Explain the function of the settlement committee. Why is the settlement priceimportant in futures markets in a way that the day's final price in the stock market is notso important?In futures markets, the settlement committee determines the settlement price for eachcontract each day. The settlement price estimates the true value of the contract at the endof the day's trading. In active markets, the settlement price will typically equal the lasttrade price. In inactive markets, the settlement price is the committee's estimate of theprice at which the contract would have traded at the close, if it had traded.The settlement price is important, because it is used to calculate margin requirements andthe cash flows associated with daily settlement. In the stock market, there is no practicecomparable to daily settlement, so the closing price in the stock market lacks the specialsignificance of the futures settlement price.17. Explain why futures and forward prices might differ. Assume that platinum prices arepositively correlated with interest rates. What should be the relationship betweenplatinum forward and futures prices? Explain.Futures are subject to daily settlement cash flows, while forwards are not. If the price ofthe underlying good is not con-elated with interest rates, futures and forward prices willbe equal. Ifthe price of the underlying good is positively con-elated with interest rates, along trader in futures will receive daily settlement cash inflows when interest rates arehigh and the trader can invest that cash flow at the higher rate from the time of receipt tothe expiration of the futures. Because forwards have no daily settlement. cash flows, theyare unable to reap this benefit. Therefore, if a commodity's price is positively con-elatedwith interest rates, there will be an advantage to a futures over a forward. Thus, forplatinum in the question, the futures price of platinum should exceed the forward price.The opposite price relationship can occur if there is negative con-elation. Generally, thisprice relationship is not sufficiently strong to be observed in the market.Chapter 29. Explain the difference between initial and maintenance margin.Initial margin is the amount a trader must deposit before trading is permitted.Maintenance margin is the minimum amount that must be held in the trader's accountwhile a futures position is open. If the account value falls below the amount specified asthe maintenance margin, the trader must deposit additional fundsto bring the account value back to the level of the initial margin.10. Explain the difference between maintenance and variation margin.Maintenance margin is the amount a trader must keep in the account to .avoid a margincall. Variation margin is the payment a trader must make in a margin call. The margincall occurs when the account value drops below the level set for the maintenance margin.Upon receiving a margin call, the trader must make a cash payment of the variationmargin. The maintenance margin is a stock variable, while the variation margin is a flowvariable.

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11. On February 1, a trader is long the JUN wheat contract. On February 10, she sells aSEP wheat futures, and sells a JUN wheat contract on February 20. On February 15, whatis her position in wheat futures? On February 25, what is her position? How would youcharacterize her transaction on February 20?On February 15, the trader holds an intracommodity spread, being long the JUN and shortthe SEP wheat. On February 25, the trader is short. one SEP wheat contract. Thetransaction on February 20 was a transaction offsetting the original long position in SEPwheat.12. Explain the difference between volume and open interest.Open interest is the number of contracts currently obligated for delivery. The volume isthe number of contracts traded during some period. For every purchase there is a sale,and the purchase and sale of one contract generates one contract of trading volume.16. Explain price discovery.In futures markets, price discovery refers to the revealing of information about futureprices that the market facilitates. It is one of the two major social functions of the futuresmarket. (The other is risk transference.) As an example, the futures price for wheat fordelivery in nine months reveals information to the public about the expected future spotprice of wheat at the time of delivery. While controversial, there is some reason tobelieve that the futures price (almost?) equals the spot price that is expected to hold at thefutures expiration. This price discovery function helps economic agents plan theirinvestment and consumption by providing information about future commodity prices.18. What isfront running?Front running is a market practice in which a broker holds a customer's order forexecution and executes a similar order of his or her own before executing the customer'sorder. This practice can be particularly pernicious if the customer's order is large,because the order may itself move prices. By front running, the broker seeks to capitalizeon the privileged information that the order is coming to market. This practice isunethical and against the rules of the futures exchange.

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Chapter 3 : #19. Consider the following information about the CMX gold futures contract:Contract size: 100 troy ounceInitial margin: $1,013 per contractMaintenance margin: $750 per contractMinimum tick size: 10 cents/troy ounce ($1O/contract)There are four traders, A, B, C, and D, in the market when next year's June contractcommences trading.A. Complete the following table showing the open interest for the contract.

DiI.~ Buyer Selkr e o . m u l l Prite Dpo.lntRm;J u '; 6 ,t . 8 5 $.l94.50J U I ' 6 C 8 1 0 $291 ,00M~ 6 Set t1errert F ti re ~.OOJu p 0 A 10 $2>5.50J u ," 7 E i D 5 ~.9JJ u ~ ' 7 S e t t 1 e rr n r t P r i re ~.oo

l l1 !' 8 B II 7 $295.70J u tl'8 S e tt 1e r re r t F l l( e $l9J.5Q

\ Vh e ll t !' ad in g OOfl l tnen i : es , C'M:,h trade! ' has ~ z e ru ne t POsir : t!. lll, The ope n m rm 'e s t , " ,,1]kh is the su m oc t t het rad'e f's n et hmgplJ3i . t ions , isa!so re m Lookil1,!!; areaeh t rade s eq ue nt ia IJ )" v ,e 1':,1IltfOci: t !h e t f, iH il er s' n etpOfhiollS and open . I n t e r eS t a s [u lk lW S :

!lftttMitlooT r a d e Tr~A T r l l d l ! f B Trlulilr" rMlklrD ap 1 . 1 l t ! 1 ' I I i ! t1 +5 -5 02 +5 -]5 +1 0 0 1 :53 -5 -1 5 +1 0 +10 2 .04 -5 -1 0 + ] 1 ) +5 155 -11 -3 +1 0 +5 15

.R CJikuhlte the g ai ns i l' ll d l(l~seli r u r T~a d l' ,r A, A~s l .1m that at the t im e of olldl cJlange ill _p(),sj[ju.n:,J r ( luer Amust bring tile margiillback to the lniti~.l l:nargln am!J lUnt. Compute ,the l Im iJ U ll t il l 1 ' i : o c i o J ' Ns malg1l1nccoun t !Ii: tbe e nd o f e ach tr aG i:n ! ;d By.W iU 'lr ac ie r A ge t a m ~rgJn tam If ~o , when a nd ho w l l .1ucb ~dd i - t h :ma l I l' Il L rg ln must be posteni '

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Nt! : Gai. ~4!r!lff ltaril.lIo:Il aR HO.lt lillY S!l l l i!Olit iDn Pri!:~ { Ios$) Y ar iatln l Margll \ I 111 '1 i i l . i ooiL lr 6 5 H S294,~ S O S!\,Ofd $5,0&5, I l l, 0s e ine r r s r t +5 S2 .9~ IO ( $250) $4,815 $ lJ $4,815i i l y t 10 . . . , . _ : 5 S ! . r o . 5 ) ($~50) $4;~5 $5)0 $5.0&5J L l ~ "J5 1 : 1 t l e r r e r t -5 $ J ! J J 5 e J ) ( S1~ ) $4 ,915 $I) S 4 , r I 1 5J u '{ a 7 -1 2 $293.70 $5 0 $4,9)3 $7,191 $12 ,150J u r asenerre rt -1 2 $2g9.50 ($)5,9rn) $ 5 , . 1 9 6 $t5,9rn $12 . ,156

O n July 6 , 'I 'r ll de ~ A gOO ! : [ t ln g 5 c on tra cts a t.a prlci !lof$194.$O, At th il l t im e , s he iJ ; r eq uir ed to po st $ 1,( 11 3m a rg h lJ p ~ conlr ; tct [crt n t ot al [If$ S ;O j} 5. T h e J ul y I)se t t l emen t pci{)e o fS19 :4 . 00 results in a $ 50 ' pe r con m.ctloss ( 1 O O : x . - !W ,, 5 0 ), ' 1 :r >1 d 'l : :{N s ,5 cont racts 1000 a total o f $2,50. which Is ta ke n. fr om tih e m ar gin acOO\wt .Ttader irs margin aeeount ~ullh aa 8 96 3 per COI lt r ac t w hich is in ex e cs s o f me minimum rnamrenal lcc milJ '-gi n (If 1 1 I S { ) perc( :mtJ ract ' fh e r ll lf o rc , n tl I l l i 1 r g i n c n H occu r s .O n Jl1lJ 7 , T I - n .d e rit1.'C'iUfSeS h er lo ng p os it ion a :n d gallS sho r t 5 con tr ac ts . A S l 50 1 (J 5 !I ,Q c c !U ! r~01 1 t h e r eYf f i '~1lon g p oslt ie n w hic h i s a W U S O O U i li ll 'r un s t t h e ! I' It Ir g in u l X i ' J t m ~ b r l n g i n g it dm m to $ 4,5 6 ;, S in ce ' '" H ad er ti . ISnow sho rt 5 con tr :tcts , she fIrlct~$ SU I ) to m t margm lI(COlmt to bring It ( - M e R to . t he in it Ia l m ar gin J t. "q ll :I cm e nt

of ! t5 , ' 1J65,A t se ttle me nt '( .m J ' l l i l l y 7, Th l . d i ( , ' l ' ! fs p 05 it io i1 l l os t $ 15 1 1 w hic h is L 1ik en fr om 1 1C rlT hw gin a ce ou atbrh1glng it lo$4,9t!t No IlHlirgln can OCCJllfS,O n Juty S , T l '.a d~ r A ~ .H o ;a,n~dt l t t iol laf 1 oont rn 'cu , hrillgi 'lIg . r u l , r wta l to short ilcontrncw" A t th e t im e o f th ..transae t lDIl, lmr ori ,gilla l position ool'S s!lQirt ecntraets 1 1 m ; g'ained ~50 which is credited. te her margillaccoun t , bri Il igIng' it to $ 4 :, 96 5 . T il e : nl 'i .j U t. re d . ll li ti ai m ar gin fm ' 12 oontradll l $ 1 I 12 ,1 5 n , so Trade r A adds$f, i9 1 r o h e r m a rg in m:c01:.lnt,July 8 is no t a ~;.od dny . for Trader A. The futures lIl'rk'fl of gold [I I ' lCI"C'IUle. s by$5~80 pel' ounce , T tade J: N s12-wnlntct ~h11.rtposi t ion loses S 6,9 6(}, br in gin g h er Im.rgin llCCrllllH