Investments Assignment 3 Solution

7/30/2019 Investments Assignment 3 Solution

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15.433INVESTMENTSAssignment3:Futures

RetoR.GallatiMITSloanSchoolofManagement


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1. Afuturescontractisavailableonacompanythatpaysanannualdividendof$5andwhosestockis currently priced at $200. Each futures contract calls for delivery of 1,000 shares of stock inoneyear,dailymarkingtomarket,an initialmarginof10%andamaintenancemarginof5%.ThecurrentTreasurybillrate is8%. (4points)

(a) Giventheaboveinformation,whatshouldthepriceofonefuturescontractbe? (0.5points)(b) Ifthecompanystockdecreasesby7%,whatwillbe,ifany,thechangeinthefuturesprice?

(0.5points)(c) Asaresultofthecompanystockdecrease,willaninvestorthathasalongpositioninone

futurescontractofthiscompanyrealizeagainora loss? Why? Whatwillbetheamountofthisgainorloss? (1point)

(d) What must the initial balance in the margin account be? Following the stock decrease,what will be, if any, the change in the margin account? Will the investor need to top upthemarginaccount? Ifyes,byhowmuchandwhy? (1point)

(e) Giventhecompanystockdecrease,whatisthepercentagereturnontheinvestorsposition?Isithigher,equalorlowerthanthe7%companystockdecrease? Why? (1point)

Answers:(a) F=200*(1+0.08-(5/200))=$211(b) F=200*(1-0.07)*(1+0.08-(5/200))=$196.23(c) An investorwitha longposition inonefuturescontractagreestobuy1,000stocksofthe

company inoneyearat$211. Thereforethis investorwillbenefitonly ifthe futurespriceincreases. Inthiscase,thefuturespricehasdecreasedandtheinvestorwillthereforerealizealossof:

(196.23211)1,000=$14,770 (1)(d) Thechangeinthemarginaccountwillbeminus$14,770. The initialrequiredmarginwas

1,000*$211*10%=$21,100sonowthebalancewillbe$20,000-$14,770=$6,330. Thisbalance($6,330/$211,000=3%)isbelowtherequired5%($10,550/$211,000=5%)maintenancemargin. Theinvestorwillneedtotopupthemarginaccountbyatleast$10,550-$6,330=$4,220,else, the broker will close out enough of the investors long position to meet the requiredmaintenancemargin.

(e) The percentage return on the investors position will be -$14,770/$21,100=-70% which is10timeshigherthantheactualdecreaseinthestockprice. The10-to-1ratioofpercentagechangesreflectsthe leverageinherentinthefuturescontractposition.

15.433 2 MITSloan


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2. You have recently been appointed CFO of a large multinational corporation based in Frankfurt. The CEO has asked you to raise 8,000,000 Euros one year from now to fund a strategicinvestment. The company has to raise the capital either through a U.K. (in) or a Germany(in Euros) based bank. The annual interest rates on U.K. and German bills are 8% and 6%respectively. Thecurrentexchangerateis1.5Europer1andthefuturespricefordeliveryoneyearfromnow is1.46Eurosper1. (4points)

(a) Wherewouldyoulendandwherewouldyouborrow? (0.5points)(b) Yourealizethatgiventheabovedata,youcanbenefitfromanarbitrageopportunitythat

would allow you to raise the necessary capital at no cost for the company. Describe ina table like the one below the necessary actions (and associated cash flows in Euros) youneedtotakenowand inoneyear inorderearn8,000,000Euros inoneyearatnocost. (2points)

ActionNow CashFlowinEuros

Actionin1Year CashFlowinEuros*

Total Total

(c) Assumingthe interestratesandthecurrentexchangerategivenabovearecorrect. Whatshouldthefuturespriceof1beinEurosaccordingtotheinterestrateparitytheorem? (0.5points)

(d) Discuss why wouldnt all investorsdecideto invest their money inthe U.K., eventhoughthe interestrate intheU.K.(8%) ishigherthan inGermany(6%.) (1point)

Answers:(a) Given the interest rates the best approach would be to borrow the capital in Germany,

wherethe interestrate is lowerand lend itintheU.K.wherethe interestrateishigher.

(b) This is possible by simultaneously lending and borrowing. We can come up with an investment structure that requires an initial outlay of 0 Euros and yet will a benefit ofapproximately8,000,000Euros inthefuture.

15.433 3 MITSloan


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ActionNow CashFlowinEuros

Actionin1Year CashFlowinEuros*

You

lend

XM

in

theU.K. -X*1.5M

The

amount

you

lent is repaid toyou and you exchangeit into

1.08*(XM)*E1

You borrowX*1.5M Euros inGermany

+X*1.5M You repay theamount youborrowed

-1.06*(X*1.5M)

You sell forward1.08*XM in Euros

Unwind 1,08*XM*(1.46E1)

Total 0 Total 8.0Euros1.08*(XM)*E1-1.06*(X*1.5M)+1,08*XM*(1.46-E1)=8.0M-1.06*(X*1.5M)+1,08*XM*1.46=8.0M-1.06*(X*1.5M)+1,08*XM*1.46=8.0MX=606,[email protected]*WhereE1istheexchangeratebetweenEurosand in1year.

Thetransaction

would

be

as

follows:

ActionNow CashFlowinEu

rosActionin1Year 7Cash Flow in

Euros*You lend606.1M intheU.K.

-909.15M The amount youlent is repaid toyou and you exchangeit into

1.08*(606.61M)*E1

You borrow909.15MEurosinGermany

+909.15M You repay theamount youborrowed

-1.06*(909.15M)

You sell forward1.08*606.1M inEuros

Unwind 1,08*476.2M*(1.4E1)

6

Total 0 Total 8.0M

15.433 4 MITSloan
mailto:@%E3%B6%B06.1Mmailto:@%E3%B6%B06.1Mmailto:@%E3%B6%B06.1Mmailto:@%E3%B6%B06.1M


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(c) Thefuturespricewouldbe:F0 =E0[(1+rGERMANY)/(1+rU.K.)]T = 3Euros/1[(1.06)/(1.08)]1 = 2.94DM/1 (2)

(d) They may not because the Euros may be appreciating relative to the . It is true thatinvestmentsinGermanywillgrowlessthaninvestmentsintheU.K.butitisalsothroughthatastimepasses1DMisworthmore. ThisappreciationoftheEuroswithrespecttothecan be seenbythe fact that E0 is1.5Euros/1whileF0 is1.47Euros /1. The futureappreciation of the Euros with respect to the compensates for the difference in interestratesbetweenthetwocountries.

3. You are required to make a payment of 1,000,000 euros in each of the next four years. Yourrevenuesare indollarsandthe current dollar-euro exchange rate is$.90pereuro. You believethat the dollar will depreciate and would like to lock in the four payments of 1,000,000 euroseach at todays exchange rate. In order to do so you decide to enter into a swap agreement.AssumethattheU.S.andeuroyieldcurvesareflatat6%and8%respectively. (2points)

(a) Whatwillbetheswaprateonthisagreementtoexchangecurrencyoverafour-yearperiod?(2points)

Note: Rememberthataswapcanbeviewedasaportfolioofforwardtransactions,but insteadofeachtransactionbeingpricedindependently,oneuniqueforwardpriceisappliedtoalltransactions.Answer:

(a) Solvethefollowingequation:

S/(1.06)1 +S/(1.06)2 +S/(1.06)3 +S/(1.06)4 = [.9(1.06/1.08)1]/(1.06)1 +[.9(1.06/1.08)2]/(1.06)2 +[.9(1.06/1.08)3]/(1.06)3 +[.9(1.06/1.08)4]/(1.06)4 (3)

S/(1.06)1 +S/(1.06)2 + +S/(1.06)3 +S/(1.06)4 = 2.9809 (4)3.4651S = 2.9809 (5)

S = $.8602pereuro (6)

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Ineachofthefollowing4yearsyouwillpayafixedamountof$860,266inexchangefor1,000,000euros.

15.433 6 MITSloan

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Investments Assignment 3 Solution