CFA level 2 study notebook5 2015

StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- Forward Markets and ContractsThe general form for the calculation of the forwardcontractpricecanbe statedas S0 =spotp

BOOK 5 - DERIVATIVES AND

PORTFOLIO MANAGEMENT

StudySession16- Derivative Investments:Forwards andFutures, 9

StudySession17- Derivative Investments:Options,Swaps, andInterest Rate

StudySession 18-Portfolio Management: Capital Market Theory and the

SCHWESERNOTES™ 2015 CFALEVELIIBOOK5:DERIVATIVESAND

PORTFOLIO MANAGEMENT

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Page2

READINGS AND

READINGSThefollowing materialisa reviewoftheDerivativesandPortfolioManagementprinciples

designedtoaddress the learningoutcome statements setforthby CFAInstitute

Reading Assignments

DerivativesandPortfolioManagement, CFA ProgramCurriculum,Volume6,Level II

(CFA Institute, 2014)

47.Forward Markets and Contracts

48 Futures Marketsand Contracts

49.Option Markets andContracts

50 Swap Markets and Contracts

51.Interest Rate Derivative Instruments

52 Credit Default Swaps

page58page100

page128page136

STUDY SESSION 18

Reading Assignments

DerivativesandPortfolioManagement,CFA ProgramCurriculum,Volume6,

Level II(CFA Institute, 2014)

53 Portfolio Concepts

54.Residual Risk and Return: The InformationRatio

55.The Fundamental LawofActiveManagement

56.The PortfolioManagementProcess and the InvestmentPolicy

Statement

page153

page 218

page 232page243

LEARNING OUTCOME STATEMENTS (LOS)The CFAInstituteLearning Outcome Statements are listed below These arerepeatedineachtopicreview; however,the order may have been changedinorderto getabetterfitwith the

flow ofthereview

The topical coverage corresponds with thefollowing CFAInstituteassigned reading:

47.Forward Markets andContracts

The candidate should be ableto:

a. explain how the value ofaforwardcontractisdeterminedat initiation,duringthe lifeof thecontract,andatexpiration, (page14)

b calculate and interpret the price and value ofanequity forwardcontract,

assuming dividendsarepaid either discretelyorcontinuously, (page16)

c. calculate and interpret the price and value of1)aforwardcontractona

fixed-income security, 2)aforwardrate agreement(FRA),and3)aforwardcontract

on acurrency,(page20)

d evaluate credit riskinaforwardcontract,and explain how market valueisa

measureof exposureto a partyinaforwardcontract,(page29)

The topical coverage corresponds with thefollowingCFA Instituteassigned reading:

48 FuturesMarketsandContracts

The candidate should be ableto:

a. explain why the futures pricemustconvergetothespotpriceatexpiration

(page37)

b determine the valueofafuturescontract,(page38)

c. explain why forward and futures pricesdiffer,(page39)

d describemonetaryandnonmonetarybenefits andcostsassociated with holdingthe underlyingasset,and explain how they affect the futures price, (page43)

e describe backwardation andcontango,(page44)

f explain the relation between futures prices and expectedspotprices, (page44)

g describe the difficultiesinpricing Eurodollar futures and creatingapurearbitrage opportunity, (page47)

h calculate and interpret the prices ofTreasurybondfutures,stock indexfutures,

andcurrencyfutures,(page48)

The topicalcoveragecorresponds with thefollowingCFAInstituteassigned reading:

49.Option Markets and ContractsThe candidate should be ableto:

a. calculate and interpret the prices ofasynthetic call option, syntheticputoption,syntheticbond,and synthetic underlyingstock,and explain whyaninvestor

wouldwant to createsuchinstruments,(page59)

b calculate and interpret prices ofinterestrateoptions and optionsonassetsusing

one-and two-period binomialmodels,(page62)

Book5- DerivativesandPortfolioManagementReadings andLearning Outcome Statements

c. explain and evaluate the assumptions underlying the Black-Scholes-Merton

model,(page76)

d explain howanoption price,asrepresented by the Black-Scholes-Merton

model, isaffectedbyachangeinthe valueof each of the inputs, (page78)

e. explain the delta ofanoption, and demonstrate howit isusedindynamic

j compare AmericanandEuropeanoptions onforwards andfutures,and identify

theappropriatepricing model forEuropean options, (page90)

Thetopicalcoveragecorresponds with thefollowing CFAInstituteassigned reading:

50 SwapMarketsand Contracts

The candidate should be ableto:

a. distinguish between the pricing and valuation of swaps, (page100)

b explain the equivalence of1) interestrateswapsto aseriesof off-market forward

rate agreements (FRAs)and2) aplain vanillaswapto acombinationofan

interestratecall andan interestrate put.(page101)

c. calculate and interpret the fixedrateonaplain vanillainterestrateswap and the

market value of theswapduringitslife,(page102)

d calculate and interpret the fixedrate,if applicable, and theforeignnotional

principal foragiven domestic notional principalonacurrencyswap, and

estimatethe market valuesof each of the differenttypesofcurrencyswaps

during theirlives,(page109)

e. calculate and interpret the fixedrate,if applicable,onanequityswapand the

market valuesof the differenttypesof equity swaps during theirlives,(page113)

f explain and interpret the characteristics andusesof swaptions, including the

difference betweenpayerandreceiverswaptions, (page115)

g calculate thepayoffs and cash flows ofan interestrateswaption, (page115)

h calculate and interpret the value ofan interestrateswaptionatexpiration

(page116)

i evaluateswapcredit risk for eachpartyandduring the life of theswap,

distinguishbetweencurrentcredit risk and potential creditrisk,and explain how

swapcredit riskisreduced by both netting and markingto market, (page117)

j define swap spread and explainitsrelationtocreditrisk,(page118)

ThetopicalcoveragecorrespondswiththefollowingCFAInstituteassigned reading:

51.Interest Rate Derivative Instruments

The topical coverage corresponds with thefollowing CFAInstituteassigned reading:

52 Credit Default SwapsThe candidate should be ableto:

a. describe credit default swaps(CDS),single-name and indexCDS,and the

parametersthat defineagiven CDSproduct, (page137)

b describe crediteventsand settlement protocols withrespect toCDS (page138)

c. explain the principlesunderlying,andfactors thatinfluence,the marketspricing

of CDS (page139)

d describe theuseof CDStomanagecredit exposures andtoexpressviews

regarding changesinshape and/or level of the creditcurve, (page142)

e. describe theuseof CDStotakeadvantageof valuation disparities among

separatemarkets,suchasbonds, loans,equities, and equity-linkedinstruments

(page143)

The topical coverage corresponds with thefollowing CFAInstituteassigned reading:

53 Portfolio ConceptsThe candidate should be ableto:

a. explainmean-varianceanalysis anditsassumptions, and calculate theexpected

returnand the standard deviationofreturnforaportfolio oftwoorthreeassets.

(page153)

b describe theminimum-varianceand efficientfrontiers,and explain thesteps to

solve for theminimum-variancefrontier,(page158)

c. explain the benefits of diversification and how the correlationina assetportfolio and the number ofassetsinamulti-asset portfolio alfect thediversificationbenefits,(page162)

two-d calculate thevarianceofanequallyweightedportfolio ofn stocks,explain thecapital allocation and capital market lines(CALandCML)and the relationbetweenthem,and calculate the valueofoneof the variables given values of theremainingvariables,(page165)

e explain the capitalassetpricing model(CAPM),includingitsunderlyingassumptions and the resultingconclusions,(page175)

f explain thesecuritymarket line(SML),the betacoefficient,the market riskpremium, and theSharperatio,and calculate the value ofoneof these variablesgiven the values of the remainingvariables,(page176)

g explain the marketmodel,andstateandinterpretthe market model’s predictionswithrespect to asset returns, variances,andcovariances,(page183)

h calculateanadjustedbeta,and explain theuseof adjusted and historical betasas

predictors of futurebetas,(page185)

i explainreasonsfor and problems relatedtoinstabilityintheminimum-variance

frontier,(page187)

j describe and comparemacroeconomicfactormodels,fundamentalfactor

models,and statistical factormodels,(page188)

k calculate the expectedreturnonaportfolio oftwostocks,given the estimated

macroeconomicfactor model for eachstock,(page193)

1 describe the arbitrage pricing theory(APT),includingitsunderlyingassumptions anditsrelationtothe multifactormodels,calculate the expectedreturn onanassetgivenan assetsfactorsensitivitiesand thefactor risk

Book5- DerivativesandPortfolioManagementReadings andLearning Outcome Statements

premiums, and determine whetheranarbitrage opportunityexists,including

howtoexploit the opportunity, (page194)

m. explainsourcesofactive risk,interprettrackingerror,trackingrisk,and the

informationratio,and explain factor portfolio and tracking portfolio, (page196)

n. compareunderlying assumptions and conclusions of the CAPM andAPT

model,and explain whyan investorcanpossiblyearn asubstantial premium for

exposuretodimensionsof risk unrelatedtomarketmovements,(page200)

The topical coverage corresponds with thefollowing CFAInstituteassigned reading:

54.Residual Risk and Return: The InformationRatio

The candidate should be ableto:

a. define theterms“alpha” and “information ratio”inboth theirex postandex

ante senses,(page218)

b comparethe informationratioand the alpha’s T-statistic (page218)

c. explain theobjectiveofactivemanagementintermsof valueadded,(page221)

d calculate the optimal level of residual risktoassumefor given levels of manager

ability andinvestorriskaversion,(page223)

e justify why the choice foraparticularactivestrategydoesnotdependon

investorriskaversion,(page225)

The topical coverage corresponds with thefollowingCFA Instituteassigned reading:

55 The FundamentalLawofActiveManagement

The candidate should be ableto:

a. define theterms“information coefficient” and “breadth” and describe howthey

combinetodetermine the informationratio, (page232)

b describe how the optimal level of residual risk ofaninvestmentstrategy

changes with information coefficient andbreadth,andhowthe value added

ofan investmentstrategychanges with information coefficient and breadth

(page235)

c contrastmarket timing and security selectionintermsof breadth and required

investmentskill,(page235)

d describe how the informationratiochanges when the originalinvestment

strategyisaugmented with other strategiesorinformationsources, (page236)

e. describe the assumptionsonwhich the fundamental law ofactivemanagementis

based,(page237)

The topical coverage corresponds with thefollowing CFAInstituteassigned reading:

56.The Portfolio ManagementProcessand theInvestmentPolicyStatement

The candidate should be ableto:

a. explain the importance of the portfolio perspective, (page244)

b describe thestepsof the portfoliomanagementprocessand thecomponentsof

thosesteps,(page244)

c. explain the role of theinvestmentpolicystatementinthe portfoliomanagement

process, and describe the elements ofan investmentpolicystatement,(page245)

d explain how capital market expectations and theinvestmentpolicystatement

f contrastthetypesofinvestment time horizons,determine thetimehorizonfor

aparticularinvestor,and evaluate theeffects of thistimehorizononportfoliochoice,(page250)

g justify ethical conductas arequirementfor managinginvestmentportfolios

(page250)

©2014 Kaplan,Inc.

Page 8

The following is a review of the Derivative Investments: Forwards and Futures principles designed to

address the learning outcome statements set forth by CFA Institute This topic is also covered in:

Study Session 16EXAM FOCUS

This topicreview coversthe calculation of price and value for forwardcontracts,

specifically equity forwardcontracts,T-bondforwardcontracts,currency forwards,

and forward(interest)rate agreements.Youneedtohaveagood understanding of the

no-arbitrage principle that underlies these calculations becauseit isusedinthe topic

reviewsof futures andswapspricingaswell Thereareseveral important price and value

formulasinthisreview Aclearunderstandingof thesourcesand timing of forward

contractsettlementpaymentswill enableyoutobe successfulonthis portion of the

examwithout dependingonpurememorizationof these complex formulas In thepast,

candidates have been testedontheir understanding of the relationship of thepayments

atsettlementtointerestratechanges,assetpricechanges, and index level changes The

pricingconventionsfor the underlyingassetshave been tested separately The basic

contractmechanicsarecertainly “fair game,”sodon’t overlook theeasystuff by spending

toomuchtimetryingtomemorizethe formulas

WARM-UP: FORWARD CONTRACTS

Theparty tothe forwardcontractthat agreestobuy the financialorphysicalassethas

along forwardpositionandiscalled the long Theparty tothe forwardcontractthat

agreestosell/deliver theassethasashort forward position andiscalled the short

Wewill illustrate the basic forwardcontractmechanics throughanexample basedon

the purchase and sale ofaTreasury bill.Notethat while forwardcontracts onT-billsare

usually quotedintermsofadiscountpercentagefrom facevalue,we usedollar prices

heretomake the exampleeasytofollow

Considera contractunder whichPartyAagreestobuya$1,000face value 90-day

Treasury bill from PartyB 30days fromnowat aprice of $990 PartyA isthe long and

PartyBisthe short Both parties have removeduncertaintyabout the price they will

payorreceivefor the T-billatthefuture date If 30 days fromnowT-billsaretradingat

$992,the shortmustdeliver the T-billtothe longinexchange fora$990payment.If

T-billsaretradingat$988onthefuturedate,the longmustpurchase the T-bill from the

shortfor$990,thecontractprice

will haveapositive value ofequalamount.Following thisexample, if the T-bill priceis

$992atthe(future)settlementdate,andthe shortdoesnotdelivertheT-billfor $990aspromised,the short hasdefaulted

vO

§

a<D

Professor’sNote: Avideo explaining the basicsofforwardcontracts canbefound

in the online SchweserLibrary

>s

3

WARM-UP:FORWARDCONTRACT PRICE DETERMINATION

TheNo-Arbitrage Principle

Thepriceofaforwardcontractisnotthepricetopurchase thecontractbecause thepartiesto aforwardcontracttypicallypaynothingto enterintothecontract atitsinception.Here,pricereferstothecontractpriceoftheunderlyingassetunder theterms

oftheforwardcontract.This price may beaU.S.dollaroreuro pricebutit isoften

expressedas aninterestrate orcurrencyexchangerate.For T-bills,the price willbe

expressedas anannualizedpercentagediscountfrom facevalue;forcoupon bonds, itwillusually be expressedas ayieldtomaturity;for theimplicitloan inaforwardrate

agreement (FRA), itwillbeexpressedasannualized LondonInterbankOfferedRate(LIBOR);andforacurrency forward, it isexpressedas anexchangeratebetweenthe

twocurrenciesinvolved.However it isexpressed, thisrate,yield,discount,ordollar

amountisthe forward priceinthecontract.

The price thatwewishtodetermineistheforwardprice that makes the valuesof

both thelong andthe short positionszero at contract initiation.Wewillusetheno¬

arbitrage principle-, there shouldnotbeariskless profittobegained byacombinationof

aforwardcontractposition with positionsinotherassets.This principleassumesthat

(1)transactionscosts are zero, (2) thereare norestrictionsonshort salesor ontheuse

of short saleproceeds, and(3)bothborrowing and lendingcanbedoneinunlimited

amounts attherisk-freerateofinterest.Thisconceptissoimportant,we’llexpress it in

aformula:

forwardprice =pricethat wouldnotpermitprofitable riskless arbitrageinfrictionless

markets

ASimpleVersionof the Cost-of-Carry Model

Inordertoexplain the no-arbitrage conditionasitappliesto the determinationof

forward prices,wewill firstconsideraforwardcontract on an assetthatcostsnothing

to storeand makesno payments toitsowneroverthe lifeofthe forwardcontract.Azero-coupon(purediscount) bondmeetsthesecriteria.Unlike goldorwheat, ithas

no storage costs;unlikestocks, thereare nodividendpayments toconsider;and unlike

coupon bonds,itmakesnoperiodicinterestpayments.

©2014 Kaplan,Inc.

Page 10

StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- Forward Markets and Contracts

The general form for the calculation of the forwardcontractpricecanbe statedas

S0 =spotpriceatinception of thecontract (t = 0)

Rf =annual risk-freerate

T =forwardcontract termin years

Example: Calculating the no-arbitrage forwardprice

Considera3-monthforwardcontract on azero-coupon bond withaface value of

$1,000thatiscurrentlyquotedat $500,andsuppose that theannualrisk-freerate is

6%.Determine the priceoftheforwardcontractundertheno-arbitrageprinciple

Cash and CarryArbitrageWhen the Forward ContractisOverpriced

Suppose the forwardcontractisactually tradingat$510rather than the no-arbitrage

price of$507.34 Ashort positioninthe forwardcontractrequires the delivery of this

bond three monthsfromnow.Thearbitragethatwe examinein thiscase amounts

toborrowing $500attherisk-freerateof 6%,buyingthebondfor $500,and

simultaneously taking the short positioninthe forwardcontract onthezero-coupon

bondsothatwe areobligated todeliverthebondatthe expiration of thecontractfor

the forwardcontract(theforwardcontractprice)torepaythe $500 loan The totalamount torepaytheloan, sincethetermof the loanisthreemonths, is:

loanrepayment=$500x(l ,06)°'25 =$507.34

Thepaymentof $510wereceivewhenwedeliver the bondatthe forward priceis

greaterthanourloanpayoff of$507.34,andwewill have earnedanarbitrageprofit of

$510-$507.34=$2.66.Noticethat thisisequaltothe difference between the actualforward price and the no-arbitrage forward price Thetransactionsareillustratedin

Figure1

Figure1 :Cash andCarryArbitrage When ForwardisOverpriced

Today ThreeMonths FromTodaySpotprice ofbond

Forward price

$500

$510Cashflow

Shortforward $0 Settle short position

by deliveringbond $510.00-$500

Buybond

Total cash flow =

arbitrage profit

- $507.54

+$2.66

Professor’sNote: Here’sacouplehintstohelpyouremember whichtransactions

toundertakeforcash and carry arbitrage:(1)always buyunderpricedassetsandsell overpricedassets(“buylow,sell high”), and(2)takeopposite positions inthe

spotandforwardmarkets.So,ifthefuturescontractisoverpriced,you want totakeashort positioninthosefutures(whichobligatesyoutosellatafixedprice)

Becauseyou goshortintheforwardmarket, youtake theoppositepositioninthe

spotmarket and buy theasset.Youneedmoneyto buy theasset, soyouhavetoborrow Therefore,thefirststepincash andcarryarbitrageat its mostbasicis:

forwardoverpriced:

short(sell)forward=Fborrowmoney=>long (buy)spot asset

ReverseCash and CarryArbitrageWhen the Forward ContractisUnderpriced

Suppose the forwardcontractisactually tradingat$502 instead of theno-arbitrageprice of $507.34.We reversethe arbitrage trades from the previouscaseandgenerate

anarbitrage profitasfollows.Wesell the bond short today for $500 and simultaneouslytake the long positioninthe forwardcontract,which obligatesustopurchase the bond

©2014 Kaplan,Inc.

Page 12

StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- ForwardMarketsandContracts

in90 daysatthe forward price of $502.We investthe $500 proceeds from the short sale

atthe 6% annualratefor three months

In thiscase, atthe settlementdate,wereceivetheinvestmentproceeds of$507.34,

acceptdelivery of the bondinreturnfora paymentof$502,and closeoutourshort

position by delivering the bondwejustpurchasedatthe forward price

Thepaymentof $502wemakeasthe long positioninthecontractisless thaninvestment

proceeds of$507.34,andwehave earnedanarbitrage profit of $507.34-$502=$5.34

ThetransactionsareillustratedinFigure2

Figure2:ReverseCashandCarryArbitrage When ForwardisUnderpriced

Spotpriceof bond

Forward price

$500

$502

Long forward $0 Settle longposition

by buying bond -$502.00

Shortsell bond +$500 Deliver bondtoclose

shortposition $0.00 Invest short-sale

long (buy)forward =>borrowasset=>short(sell) spotasset=>lendmoney

Wecan nowdetermine that the no-arbitrage forward price that yieldsazerovaluefor

both the long and short positionsinthe forwardcontract atinceptionisthe no-arbitrage

price of $507.34

Professor’sNote:Daycountand compoundingconventionsvary amongdifferent financialinstruments.Therearethreevariationsusedinthe CFA curriculum:

• 360 days peryearand simpleinterest(multiply by days/360)

All LIBOR basedcontractssuchasFRAs,swaps, caps, floors,etc.

• 365daysperyear andcompoundinterest(raisedbyexponentofdays/365)

Equities,bonds, currencies*and stockoptions

• 365 days peryear andcontinuouscompounding(eraisedbyexponentof

days/365)

Equity indexes

*One exceptioniscoveredinterestparityintheeconomicsportionofthecurriculum (StudySession 4), whichuses360daysperyear andsimpleinterest

LOS47.a:Explain how thevalue ofaforwardcontractisdeterminedat

initiation,duringthe lifeof thecontract,andatexpiration

CFA®ProgramCurriculum, Volume6,page18

Ifwedenote the valueof the long positioninaforwardcontract attimet as V(,thevalueof the long positionat contract initiation, t=0,is:

FP

VQ(oflong positionatinitiation) = S0

(l + Rf)T

Notethat the no-arbitrage relationwederivedinthe priorsectionensuresthat the value

of the long position(andof the short position)at contractinitiation iszero.

= — Vt (oflong position during life ofcontract)

StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- ForwardMarketsandContracts

Noticethat the forward price,FP, isthe forward price agreedto attheinitiationof the

contract, notthecurrentmarket forward price In otherwords,asthespotand forward

market prices changeoverthe lifeof thecontract,oneside(i.e.,shortorlongposition)

winsand the other side loses.Forexample, if the marketspotand forward prices

increaseafter thecontractis initiated,the long position makesmoney,the valueof the

long positionispositive, and the value of the short positionisnegative If thespotand

forward pricesdecrease,the short position makesmoney

Professor’sNote:Unfortunately,youmustbe ableto usetheforwardvaluation

formulasontheexam.Ifyou’re goodatmemorizingformulas,thatprospect

shouldn’tscare youtoomuch.However,ifyoudon’t like memorizingformulas,

here’s another waytoremember howtovalueaforwardcontract:the long

position willpaytheforwardprice (FP)atmaturity (time T)andreceivethe

spotprice(ST). The valueofthecontract to the longpositionatmaturityis

what he willreceiveless what he willpay:ST-FP.Priortomaturity(attimeT), the valuetothe longisthepresentvalueof ST(whichisthespotpriceat time tof St)less thepresentvalueoftheforwardprice:St — FP

(l+ Rf)T-‘ ‘

So, ontheexam,think “longpositionis spotprice minuspresentvalueof forwardprice.”

Example: Determining value ofaforwardcontractpriortoexpiration

Inour3-monthzero-couponbondcontractexample,wedetermined that theno¬

arbitrage forwardpricewas$507.34 Suppose that aftertwomonths thespotprice on

the zero-coupon bondis $515,and the risk-freerateisstill 6% Calculate the value of

the long and short positionsinthe forwardcontract.

Answer:

$507.34

V2 (oflong position aftertwomonths) =$515—

V2 (ofshort position aftertwomonths) =—$10.12

=$515-$504.88=$10.12

1.061/12

Anotherwayto seethisisto notethat because thespotprice has increasedto$515,

thecurrentno-arbitrage forward priceis:

FP=$515x1.061/12 =$517.51

The long position has mademoney (andthe short position has lost money) because

the forward price has increased by $10.17 from$507.34to$517.51sincethecontract

i Atcontractexpiration,wedonotneedtodiscount the forward price because thetime

leftonthecontract is zero.Sincethelongcanbuytheassetfor FP and sellitfor themarket priceST,thevalueof thelongpositionistheamountthelongposition willreceiveif thecontractissettledin cash:

VT (oflongpositionatmaturity) =S-p —FP

V-p(ofshortpositionatmaturity) =FP—Sp= —Vp(oflong positionatmaturity)

Figure3 summarizesthe keyconcepts youneedtorememberfor thisLOS

Figure3:Forward Valueof LongPositionat Initiation,During theContract Life,and

atExpiration

Forward Contract Valuation Time

Zero, because the contract is

pricedto preventarbitrage

HowMightForwardContractValuation BeTested?

Lookfortheseways inwhich the valuationofaforwardcontractmightappearas partof

an examquestion:

• To mark-to-market for financialstatementreportingpurposes

• Tomark-to-market becauseitisrequiredas partof theoriginalagreement.For

example, thetwoparties might have agreedtomark-to-marketa180-day forward

contractafter 90 daystoreducecredit risk

• To measure credit exposure

• Tocalculate how muchitwouldcost to terminatethecontract.

LOS47.b: Calculate and interpret the price and value ofanequity forward

contract,assuming dividendsarepaid either discretelyorcontinuously

CFA®Program Curriculum, Volume6,page 26

Equity ForwardContractsWithDiscreteDividendsRecall that theno-arbitrageforwardpricein our earlierexamplewascalculatedforan

assetwithnoperiodicpayments.A stock,astockportfolio,or anequityindexmay

have expected dividendpayments overthe lifeofthecontract.Inordertopricesuch

a contract, we musteither adjust thespotprice for thepresentvalueof the expected

©2014 Kaplan,Inc.

Page 16

Study Session 16 Cross-Reference to CFA Institute Assigned Reading#47—Forward Markets and Contracts

dividends(PVD) overthelifeofthecontract oradjusttheforwardprice forthefuture

valueof the dividends(FVD) overthe lifeof thecontract.Theno-arbitrageprice ofan

equity forwardcontractin eithercaseis:

Professor’sNote:In practice, wewould calculate thepresentvaluefromthe

ex-dividenddate, notthepaymentdate Ontheexam, use paymentdates unlessthe ex-dividend datesare given

For equitycontracts, use a365-daybasisforcalculating T ifthe maturity of thecontract

isgivenindays.Forexample, ifit isa60-daycontract,T=60/365.If thematurity is

giveninmonths (e.g.,two months)calculateT using maturitydividedbynumberof

months(e.g., T= 2 / 12).

Example: Calculatingthe price ofaforwardcontract on astock

Calculate theno-arbitrageforward price fora100-dayforwardon astock thatis

currently pricedat$30.00 and isexpectedtopayadividendof $0.40 in15 days,

$0.40 in85 days,and $0.50 in175 days.Theannualrisk-freerateis5%,and the

yieldcurve isflat

Thetimelineof cash flowsisshown in thefollowing figure

Pricinga100-Day Forward ContractonDividend-PayingStock

I Tocalculate the valueof thelong positioninaforwardcontract on adividend-paying

stock,wemake theadjustmentfor thepresentvalueof the remainingexpecteddiscrete

dividendsat time t (PVD ) to get:

by subtractingoutthepresentvalueofthedividends becausethelong position in

theforwardcontractdoesnot receivethe dividends paidonthe underlying stock

So, nowthink “adjustedspotpricelesspresentvalueof forwardprice.”

Example: Calculatingthe valueofanequity forwardcontract on astockAfter 60days,the valueof the stock in the previousexampleis$36.00 Calculate thevalue of the equityforwardcontract onthestocktothe longposition,assumingthe

risk-freerate isstill 5% and theyieldcurveisflat

StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- ForwardMarketsandContracts

Equity Forward Contracts WithContinuousDividends

To calculate the price ofanequity index forwardcontract,rather than take thepresent

value of each dividendon(possibly) hundreds ofstocks, wecanmake the calculation

asif the dividendsarepaid continuously(ratherthanatdiscretetimes) atthe dividend

yieldrateonthe index Usingcontinuous timediscounting,wecancalculate theno¬

arbitrage forward priceas:

equityindex) = S0XeÿRf 6

= |so 6cxT|xeRfxT

FP(on an Xe~

where:

Rj? = continuously compounded risk-freerate

8C = continuously compounded dividend yield

Professor’sNote:Therelationship between the discreterisk-freerateRj-and thecontinuously compoundedrate Rj* isRjr = ln[l+ )•Forexample, 5%

compounded annuallyisequaltoln(1.05)= 0.04879 = 4.879%compoundedcontinuously The2-year5%futurevaluefactorcanthen be calculatedaseither

1.052=1.1025ore°-04879*2=1.1025

Example: Calculating the price ofaforwardcontract on anequity index

The value of theS&P500 indexis 1,140.The continuously compounded risk-free

rateis4.6% and thecontinuousdividend yieldis 2.1%.Calculatethe no-arbitrage

price ofa140-day forwardcontractonthe index

LOS47.c:Calculate and interpret the price and value of1) aforwardcontract

onafixed-incomesecurity, 2)aforwardrateagreement(FRA),and3)aforwardcontractonacurrency

CFA®ProgramCurriculum, Volume6,page30

Inordertocalculate the no-arbitrage forwardprice onacoupon-payingbond,we can usethesameformulaas weusedforadividend-paying stockorportfolio, simplysubstituting thepresentvalue of theexpectedcouponpayments (PVC) overthelife ofthe

contractforPVD, orthefuture value of thecouponpayments(FVC)forFVD,to getthefollowing formulas:

FP(onafixedincomesecurity) = (S0 — PVC)x(l + Rf )T

or

= S0x(l+ Rf)T —FVCThe valueof the forwardcontractpriortoexpirationisasfollows:

if thecontractmaturityisgivenindays

Example: Calculating the price ofaforwardon afixedincome security

Calculate the price ofa250-day forwardcontract on a7% U.S.Treasury bond witha spotprice of$1,050(including accruedinterest)that hasjustpaidacouponand willmake anothercouponpaymentin182days The annual risk-freerateis6%

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StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- Forward Markets and Contracts

LO6182/365

The forward price of thecontract istherefore:

FP(onafixedincomesecurity) = ($1,050 — $34.00)Xl.062ÿ0ÿÿ=$1,057.37

Example: Calculating the value ofaforwardon afixedincome security

After100days, the value ofthebondinthe previous exampleis$1,090.Calculatethe

valueof the forwardcontract onthe bondto thelongposition, assuming the risk-free

WARM-UP:LIBOR-BASEDLOANSANDFORWARDRATE AGREEMENTS

Eurodollar depositis thetermfordepositsinlargebanksoutsidetheUnited States

denominatedinU.S.dollars The lendingrate ondollar-denominated loans between

banksiscalled the London Interbank OfferedRate(LIBOR).Itisquotedas an

annualizedratebasedon a360-dayyear.Incontrast toT-billdiscount yields,LIBOR is

anadd-onrate,likeayieldquote on ashort-termcertificateofdeposit.LIBORisused

as areferenceratefor floatingrateU.S.dollar-denominated loans worldwide

i Example:LIBOR-based loans

Computetheamountthatmustberepaidon a$1 million loan for 30days if 30-day

LIBOR isquotedat6%

Answer:

Theadd-oninterest iscalculatedas$1million x0.06x (30/360) =$5,000.Theborrowerwouldrepay$1,000,000 + $5,000=$1,005,000 attheendof 30days

LIBORispublished daily bythe British Banker’s Association andiscompiledfrom

quotesfromanumberoflargebanks; somearelarge multinational banks basedin

othercountriesthat have London offices Thereisalsoanequivalenteurolendingrate

calledEuribor, orEuropeInterbankOfferedRate.Euribor,established inFrankfurt, is

published bytheEuropeanCentralBank

Thelong positioninaforwardrate agreement (FRA) isthepartythatwouldborrow

themoney(longthe loanwith thecontractpricebeingthe interestrate ontheloan).Ifthe floatingrate at contractexpiration(LIBORforU.S.dollar deposits and Euribor for

eurodeposits) isabove theratespecifiedinthe forwardagreement,the long positioninthecontract canbeviewedastherighttoborrowat below marketratesand thelongwillreceivea payment.Ifthefloatingrate atthe expirationdateisbelowtheratespecifiedin

the forwardagreement,the short willreceiveacashpaymentfromthelong.(Theright

tolendatabove marketrateswould haveapositivevalue.)

Professor’sNote: Wesay “can be viewed as” becausean FRAissettledin cash,

sothereis norequirementtolendorborrow theamountstatedinthecontract.

Forthisreason, the creditworthinessofthelongpositionis not afactorin

the determinationoftheinterest rate on the FRA.However, tounderstandthepricingand calculationofvalueforanFRA, viewingthecontractasa

commitment tolendorborrowat a certain interest rate at afuturedateis

helpful

Thenotationfor FRAs is unique Thereare twonumbers associatedwithanFRA:

thenumberof monthsuntilthecontractexpiresandthenumberof monthsuntilthe

underlying loanissettled The difference between thesetwoisthematurityof theunderlying loan.Forexample,a2x3FRA isa contractthatexpiresintwomonths(60

days), and the underlyingloan issettledin threemonths(90days) The underlyingrate

is1-month(30-day)LIBORon a30-dayloan in 60days SeeFigure4

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Study Session 16 Cross-Reference to CFA Institute Assigned Reading#47—Forward Markets and Contracts

Figure4:Illustrationofa 2 x3 FRA

1 LIBORrates inthe Eurodollar marketareadd-onratesandarealways quotedon a

30/360 day basisinannualterms.Forexample, if theLIBORquote on a30-dayloan

is6%,the actualunannualized monthlyrate is6%x (30/360)=0.5%

2. Thelongposition inan FRA,ineffect, islongtherateandwinswhen therate

increases.

3 Althoughtheinterest ontheunderlyingloanwon’tbepaiduntil theendof the loan

(e.g.,inthree monthsinFigure4),thepayoffonthe FRAoccurs attheexpirationof

theFRA(e.g.,in twomonths) Therefore,thepayoffontheFRAisthepresentvalue

of theinterestsavingsonthe loan (e.g., discountedonemonthinFigure4).

The forward “price”inanFRA isactuallyaforwardinterest rate.The calculationofa

forwardinterest rate ispresentedinLevel Iasthe computation of forwardratesfrom

spot rates.Wewill illustrate this calculation withanexample

Example: Calculatingthe price ofanFRA

Calculatethe price ofa 1 x4FRA(i.e., a90-dayloan,30daysfrom now).The

current30-dayLIBORis4%and the120-dayLIBORis5%

Answer:

The actual(unannualized) rate onthe30-dayloanis:

The actual(unannualized) rate onthe120-dayloanis:

VO

120

R120=0.05x-=0.01667c

Thisisthe no-arbitrage forwardrate—the forwardratethat will make the valuesof

thelongand the short positions in the FRA bothzero attheinitiationof thecontract.

Thetimelineisshowninthefollowing figure

annual rate = 0.05 actual rate= 0.01667

annual rate = 0.04 actual rate=0.00333

FRA price=0.0532 actual rate=0.0133

Valuingan FRAat Maturity

To understandthe calculationof thevalueof theFRAaftertheinitiationofthecontract,

recall that in the previousexamplethelongin theFRA has the“right”toborrowmoney30daysfrom inception foraperiodof 90daysattheforwardrate.Ifinterest

rates increase(specifically the 90-day forwardcontract rate),the long will profitasthe

contracthas fixedaborrowingratebelow thenow-currentmarketrate.These “savings”

willcome atthe endof the loanterm, so tovaluethe FRAweneedtotake thepresentvalueof these savings Anexampleincorporating thisfact will illustratethe cash

settlement valueofanFRAatexpiration

StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- Forward Markets and Contracts

Example: CalculatingvalueofanFRAatmaturity(i.e.,cashpayment at settlement)

Continuingthe priorexamplefora 1 x4FRA, assume anotionalprincipalof

$1million and that,at contractexpiration,the 90-dayratehas increasedto6%,

whichisabovethecontract rateof5.32%.Calculate the valueof theFRAatmaturity,

whichisequaltothecashpayment atsettlement

Thepresentvalueof thisamount attheFRA settlementdate(90dayspriortotheend

of the loanterm)discountedatthecurrent rateof 6%is:

$1,700

=$1,674.88

901+ 0.06x

360This will be the cash settlementpaymentfrom the shorttothe longatthe expiration

of thecontract.Note thatwehave discounted the savings in interestatthe endof the

loantermbythe marketrateof 6% thatprevailsatthecontractsettlementdatefora

90-dayterm, asshownin thefollowing figure

Valuinga 1 x4FRAatMaturity

= $1,700

discount back 90daysat 6%

FRA value=

$1,674.88

ValuinganFRA PriortoMaturity

To valueanFRApriortothe settlementdate,weneedtoknow the number ofdays that

havepassedsincetheinitiationofthecontract.Forexample, let’ssupposewe want to

valuethesame1x4FRAtendaysafter initiation.Originallyit was a1x4FRA,which

meansthe FRA now expires in20days.Thecalculationof the“savings”onthe loanwill

be thesame asinourpreviousexample,exceptthatweneedto usethe“new”FRA price

that would be quotedon a contractcoveringthesameperiodastheoriginal “loan.”

In thiscasethe“new” FRA priceisthenow-currentmarket forwardratefora90-day

loanmadeatthe settlementdate(20daysinthefuture).Also,weneedtodiscount the

interestsavings implicitin theFRAbackan extra20days,or110days, instead of90

daysas wedidfor the valueatthe settlement date

Example: Calculating value ofanFRA priortosettlement

Valuea5.32%1x4FRA withaprincipalamountof $1 million 10daysafter

initiationif110-dayLIBORis5.9% and 20-dayLIBORis5.7%

Answer:

Step1: Findthe“new”FRA priceon a90-dayloan20daysfromtoday.This is the

current90-day forwardrate atthe settlementdate,20days fromnow.

Study Session 16 Cross-Reference to CFA Institute Assigned Reading#47—Forward Markets and Contracts

Valuinga 1 x4 FRAPrior toSettlement

= $1,514.20

discount back 110 days at 5-9%

FRA value

=$1,487.39

Professor’sNote: Ihave triedtoexplain these calculationsinsuchaway that

you can valuean FRAatany datefrominitiation tosettlementusingbasictools thatyoualready know Once you understand where the valueofanFRA

comesfrom(the interestsavingson aloanto be madeatthe settlement datej

andwhen this valueistobereceived(attheendoftheloan),youcancalculate

thepresentvalueofthesesavingseven under somewhatstressfultestconditions

Justremember thatiftherateinthefutureisless than theFRA rate, the longis

“obligatedtoborrow”atabove-marketratesand will havetomakea payment

tothe short.Iftherate is greaterthan theFRArate,the long willreceivea

paymentfromthe short

PricingCurrencyForward Contracts

Thepriceand valueofacurrencyforwardcontractisrefreshingly straightforward after

thatlastbitof mentalexercise.The calculationof thecurrencyforwardrate is justan

applicationof covered interestparity from the topicreviewofforeign exchangeparity

relations inStudySession4

Recall that theinterest rateparityresultisbasedon anassumption that you should make

thesame amountwhenyoulendattherisklessratein yourhomecountry asyouwould

ifyouboughtone unitoftheforeigncurrencyatthecurrent spot rate,SQ,investedit at

theforeign risk-freerate,and enteredinto aforwardcontract toexchangetheproceeds

Coveredinterestrateparity givesusthe no-arbitrage forward price ofaunitof foreign

currency intermsof the homecurrencyforacurrencyforwardcontractof length Tinyears:

Rye= foreigncurrency interestrate

Forforeigncurrencycontractsusea365-day basistocalculateT if thematurity isgiven

indays

Professor’sNote:Thisisdifferentfrom thewayweexpressedinterestrateparity backinStudySession 4,where Fand Swerequotedintermsofforeign

currencyperunitofdomesticcurrency The keyistorememberour numerator/

denominator rule:ifthespotandforwardquotes are inCurrencyAperunitof

CurrencyB,the CurrencyAinterest rateshould beon topand the Currency B

interestrateshould beonthe bottom Forexample,ifSand Fare ineurosperSwissfranc,putthe Europeaninterestrate onthetopand theSwiss interestrate

onthe bottom

Example: Calculating thepriceofacurrencyforwardcontract

The risk-freerates are6%inthe United States and8% in Mexico.Thecurrent spot

exchangerateis$0.0845 per Mexican peso(MXN).Calculate the forwardexchangeratefora180-day forwardcontract.

Answer:

1.06180/365

Fy(currencyforwardcontract) =$0.0845x =$0.0837

10818°/365

ValuingCurrency Forward Contracts

Atany timepriortomaturity,the valueofacurrencyforwardcontract tothe long willdependonthespot rate attimet,St,andcanbe calculatedas:

StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- Forward Markets and Contracts

Example: Calculatingthe valueofacurrency forwardcontract

Calculatethevalueofthe forwardcontractin the previousexampleif,after15 days,

thespot rateis$0.0980 per MXN

V inbothcasesisthe valueindomesticcurrency unitsfora contractcoveringoneunit

of theforeigncurrency Forthesettlementpaymentin the homecurrencyon a contract,

simply multiply thisamountbythe notionalamountof theforeigncurrencycoveredin

thecontract.

LOS47.d: Evaluate credit riskinaforwardcontract,andexplain how market

valueisa measureof exposuretoa partyinaforwardcontract.

CFA®Program Curriculum, Volume6,page41

At anydateafterinitiationofaforwardcontract,itislikelytohavepositivevalueto

either the longorthe short Recall that this valueistheamountthat would be paidto

settle thecontractin cashatthat point intime.Thepartywith thepositionthat has

positivevaluehascreditrisk in thisamountbecausethe otherpartywouldowethem

thatamountif thecontract wereterminated.Thecontractvalueand, therefore,the

creditrisk, mayincrease,decrease,or evenchange signoverthe remainingtermof the

contract However, atanypointintime,the market valuesofforwardcontracts, as we

havecalculatedthem,are ameasure of thecreditriskcurrentlybornebytheparty to

whichacashpaymentwould be madetosettle thecontract atthatpoint One wayto

reduce the credit riskinaforwardcontractisto mark-to-marketpartwaythrough

Vt(oflongpositionduring life ofcontract)= St — (l+ Rf)T-t

Vy(oflongpostionatmaturity)=Sy-FP

Vy(ofshort positionatmaturity)=FP-SyLOS47.b

The calculation of the forward price foranequity forwardcontractisdifferent becausethe periodic dividendpaymentsaffect theno-arbitrageprice calculation The forwardpriceisreduced by the future value of the expected dividendpayments;alternatively, the

spotpriceisreduced by thepresentvalueof the dividends

urity) = (S0-PVD)x(l + Rf )T = [s0x(l + Rf )T ]-FVD

FP(onanequitysec

The valueofanequity forwardcontract tothe longisthespotequity priceminusthe

presentvalueof the forward priceminusthepresentvalueofanydividends expected

overthetermof thecontract:

FP

Vt (long position) = [St-PVDt ]

-(T-t)

.(i+Rf)

Wetypicallyusethecontinuous time versionstocalculate the price and value ofa

forwardcontract on anequity index usingacontinuously compounded dividend yield

FP(onan equityindex)=S0XeÿRf 6

presentvalueof the couponstimesthequantity oneplus the risk-freerate.

FP(onafixedincomesecurity) = (S0 — PVC)X(1|Rf)T = S0 x(l + Rf )T —FVC

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StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- ForwardMarketsandContracts

The value ofaforwardon acoupon-paying bondtyearsafter inceptionisthespot

bond priceminusthepresentvalue of the forward priceminusthepresentvalue ofany

couponpaymentsexpectedoverthetermof thecontract:

FP

Vt (long position) = [St-PVCt]

-(l + Rf)(T 0

The “price” ofan FRA isthe implied forwardratefor the periodbeginningwhen the

FRAexpirestothematurityof the underlying “loan.”

The valueofan FRAatmaturityistheinterestsavingstobe realizedatmaturity of

the underlying “loan” discounted backtothe dateof the expiration of the FRAatthe

currentLIBOR.The valueofanFRA priortomaturity istheinterestsavings estimated

by the implied forwardratediscounted backtothe valuation dateatthecurrentLIBOR

Foracurrency forward,the priceisthe exchangerateimplied by coveredinterestrate

parity The valueatsettlementisthe gainorlosstothe long from makingacurrency

exchangeintheamountsrequired by thecontract atthecontractexchangerate,rather

thanatthe prevailing marketrate:

Priortosettlement,the valueofacurrencyforwardisthepresentvalueofanygain

orlosstothe long from makingacurrencyexchangeintheamountsrequired by the

contract atthecontractexchangerate,comparedtoanexchangeattheprevailing

forward exchangerate atthe settlement date

i CONCEPT CHECKERS

Astockiscurrently pricedat$30andisexpectedtopayadividendof$0.30

20days and65days from now.Thecontractprice fora60-day forwardcontract

when theinterest rate is5%isclosestto:

A $29.46

B $29.70

C $29.94

1

After37 days,the stock in Question1 ispricedat$21,andtherisk-freerate is

still5%.The valueof the forwardcontract onthe stocktothe short positionis:

4 A6% Treasury bondistradingat$1,044(including accruedinterest)per$1,000

offace value It will makeacouponpayment98 daysfromnow.The yieldcurve

isflatat5%overthenext150 days The forward priceper$1,000of face value

fora120-day forwardcontract, isclosestto:

A 545.72

B 555.61

C 568.08

5

Ananalystwhomistakenlyignores thedividendswhenvaluingashort position

inaforwardcontract on astock that paysdividends willmostlikely:

A overvalue the position by thepresentvalueof the dividends

B undervalue the position bythepresentvalueof the dividends

C overvalue the position bythefuture value of thedividends

6

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StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- Forward Markets and Contracts

AportfoliomanagerownsMacrogrow,Inc.,whichiscurrently tradingat$35

per share Sheplanstosell the stock in 120days, butisconcerned abouta

possiblepricedecline She decidestotakeashortposition ina120-day forward

contract onthe stock The stock willpaya$0.50 pershare dividendin35 days

and $0.50 again in125 days.Therisk-freerate is4%.The valueofthe trader’s

position in theforwardcontractin45days,assuming in45daysthestockprice

is$27-50 and therisk-freeratehasnotchanged,isclosestto:

A $7.17

B $7.50

C $7.92

7

Aportfoliomanagerexpects toreceivefundsfroma newclientin 30days

Theseassets are tobe invested inabasketof equities He decidestotakea

longposition in20,30-day forwardcontracts onthe S&P500stockindexto

hedge againstanincrease in equity prices Theindexiscurrentlyat 1,057.The

continuously compounded dividend yieldis1.50%,and the discrete risk-free

rateis4% Fifteen days later the index valueis1,103.The valueof the forward

position after15 days,assumingnochangein the risk-freerate orthedividend

yield,isclosestto:

A $831.60

B $860.80

C $898.60

8

TheCFOof YellowRiverCompany receiveda reportfrom theeconomics

department whichstatesthat short-termrates areexpectedtoincrease50basis

points in thenext90 days.Asafloatingrateborrower(typicallyagainst90-day

LIBOR),the CFO recognizesthat hemusthedge againstan increaseinfuture

borrowingcosts overthenext90 days because ofapotentialincrease inshort¬

terminterestrates.He considers many options,but decidesonenteringintoa

long forwardrate agreement (FRA).The30-dayLIBORis4.5%,90-dayLIBOR

is4.7%,and 180-dayLIBORis4.9%.To besthedgethis risk, YellowRiver

shouldenterintoa:

A 3x3FRAat a rateof4.48%

B 3x6FRAat a rateof4.48%

C 3x6FRAat a rateof5-02%

9

i ConsideraU.K.-basedcompanythatexportsgoodstotheEU.TheU.K.

companyexpects to receivepaymenton ashipmentofgoodsin60 days Because

thepaymentwill be ineuros,theU.K.companywants tohedgeagainsta

declinein thevalueof theeuroagainstthepoundoverthenext60days The

U.K.risk-freerateis3%,and theEUrisk-freerateis4%.Nochangeisexpected

in theserates overthenext60days.Thecurrent spot rate is0.9230£ per € To

hedgethe currencyrisk,the U.K companyshouldtakeashort position ina euro contract at aforwardpriceof:

StudySession 16 Cross-Reference to CFA InstituteAssigned Reading#47- Forward Markets and Contracts

C Thedividendin65 daysoccurs after the contract has matured, so it’s not relevant to

computing the forward price.

1.0598/365

Theforwardpriceofthe contract is therefore:

fixed incomesecurity) =($1,044—$29.61)x(l.05)'2°ÿ365 =$1,030.79

ANSWERS - CHALLENGE PROBLEMS

The value of 20 contracts is44.93x 20=$898.60.

9 C A 3 x 6 FRA expires in 90daysand is based on90-dayLIBOR, so it is the appropriate

hedgefor 90-day LIBOR 90 days from today The rate is calculated as:

90 R90=0.047x-=0.0118

360

180 R1 80=0.049 x-=0.0245

360

1.0245 360

price of 3x6 FRA= -lx -=0.0502=5.02%

10 B The U.K company will be receiving euros in 60 days, so it should short the 60-day

forwardon the euro as ahedge.Theno-arbitrage forwardprice is:

The following is a review of the Derivative Investments: Forwards and Futures principles designed to

address the learning outcome statements set forth by CFA Institute This topic is also covered in:

Study Session 1 6EXAM FOCUS

This topicreviewfocusesonthe no-arbitrage pricing relationships for futurescontracts.

The pricing offuturesisquitesimilar,and insome cases identical, tothe pricing of

forwards.Youshould understand the basicfutures pricingrelationand howitisadjusted

forassetsthat havestorage costs orpositive cash flows

WARM-UP: FUTURESCONTRACTS

Futurescontracts areverymuchlike theforwardcontracts welearned aboutin the

previous topicreview.Theyaresimilarinthat:

• Deliverablecontractsobligatethelongtobuy andthe shorttosella certainquantity

ofan assetforacertain priceon aspecified future date

• Cash settlementcontracts aresettledby paying thecontractvalueincashonthe

expirationdate

• Bothforwards andfuturesarepricedtohavezerovalueatthetimetheinvestor

enters intothecontract.

Thereareimportantdifferences,including:

• Futuresaremarkedtomarketatthe endofeverytrading day Forwardcontracts are

notmarkedtomarket

• Forwardsareprivatecontractsand donottradeonorganized exchanges Futures

contractstradeonorganized exchanges

• Forwardsarecustomizedcontractssatisfying the needs of the parties involved

Futurescontracts arehighlystandardized

• Forwardsare contractswiththe originatingcounterparty; aspecialized entity calleda

clearinghouseis thecounterparty toallfuturescontracts.

• Forwardcontracts areusuallynotregulated Thegovernmenthaving legal

jurisdiction regulates futures markets

LOS48.a:Explainwhy the futures pricemustconvergetothespotpriceat

expiration

CFA®ProgramCurriculum,Volume6,page 85

i Atexpiration, thespotpricemustequal the futures price because the futures price has

become the pricetodayfordelivery today,which is thesame asthespot.Arbitragewillforce the pricestobe thesame at contractexpiration

Example: Why the futures pricemustequal thespotpriceatexpiration

Supposethecurrent spotprice of silveris$4.65 Demonstrateby arbitragethat the

futuresprice ofafuturessilvercontractthat expires inoneminutemustequalthespotprice

Answer:

Suppose thefuturespricewas$4.70 Wecould buy thesilveratthespotprice of

$4.65,sell thefuturescontract,and deliverthe silverunderthecontract at$4.70.Ourprofit wouldbe $4.70-$4.65=$0.05 Because thecontract maturesinone minute,

thereisvirtuallynorisktothis arbitrage trade

Suppose instead the futures pricewas$4.61 Nowwewouldbuy the silvercontract,

takedelivery of the silver by paying$4.61,and then sell thesilveratthespotprice

of $4.65 Our profitis$4.65 - $4.61=$0.04.Once again, thisis arisklessarbitragetrade

Therefore,inorderto preventarbitrage,thefuturespriceatthe maturity of the

contract must be equaltothespotprice of $4.65

WARM-UP: FUTURES MARGINSANDMARKINGTOMARKETEachexchangehasaclearinghouse.Theclearinghouseguaranteesthat tradersin thefutures market will honor theirobligations.Theclearinghousedoes thisby splittingeach

tradeonce it ismade and actingasthe oppositesideof each position Tosafeguardthe

clearinghouse, the exchangerequiresboth sidesof the tradeto postmargin and settletheiraccounts on adaily basis.Thus,the margininthefutures marketsisaperformanceguarantee.

Markingtomarketistheprocessof adjusting themargin balance inafuturesaccount

eachdayfor thechangein thevalueof thecontractfrom the previoustrading day,basedonthe settlementprice Thefutures exchangescanrequireamarktomarketmore

frequently(thandaily) under extraordinarycircumstances

LOS48.b:Determinethe valueofafuturescontract.

CFA®ProgramCurriculum, Volume6,page 85

Likeforwardcontracts,futurescontractshavenovalueat contractinitiation.Unlikeforwardcontracts,futurescontractsdonotaccumulate value changesovertheterm

ofthecontract.Sincefuturesaccounts aremarkedtomarketdaily, the valueafterthe

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StudySession 16 Cross-Reference to CFA InstituteAssigned Reading #48- Futures Markets and Contracts

margindeposit has been adjusted for the day’s gains and lossesincontractvalueisalways

zero.Thefuturespriceatany point intimeisthe price that makes the value ofa new

contractequalto zero.Thevalueofafuturescontract straysfromzeroonly duringthe

trading periods between thetimes atwhich theaccount ismarkedtomarket:

value of futurescontract=currentfuturesprice - previousmark-to-marketprice

Ifthefuturespriceincreases,the valueofthelongposition increases Thevalueisset

backto zeroby the marktomarketatthe endof the mark-to-market period

LOS48.c:Explainwhy forward and futures prices differ

CFA®ProgramCurriculum,Volume 6,page 86

Theno-arbitrageprice ofafuturescontractshouldbe thesame asthat ofaforward

contractthatwaspresentedintheprevious topic review:

FP= S0x(l + Rf)T

where:

FP =futures price

S0 =spotpriceatinceptionof thecontract(t = 0)

Rf =annualrisk-freerate

T =futurescontract termin years

However,thereare anumberof “real-world” complications that willcausefuturesand

forward pricestobedifferent Ifinvestorspreferthe mark-to-marketfeatureof futures,

futurespriceswillbehigher than forwardprices.Ifinvestorswould rather holda

forwardcontract toavoid the markingtomarketofafuturescontract,the forward price

would be higher than the futures price.Fromatechnical standpoint, the differences

between the theoretical(no-arbitrage)prices offuturesandforwardscenter onthe

correlation between interest ratesandthe mark-to-market cash flowsoffutures:

• Higher reinvestmentratesforgains and lowerborrowingcosts tofund losses leadto

apreferencefor the mark-to-marketfeatureof futures, andhigherprices forfutures

than forwards,wheninterestratesandassetvaluesarepositively correlated

• Apreferencetoavoid the mark-to-market cash flows will leadto ahigherpricefor

theforward relativetothefuture ifinterestratesandassetvaluesarenegatively

correlated

Apreference for the mark-to-market feature willarisefromapositive correlation

betweeninterest ratesand the price of thecontract asset.When thevalueof the

underlyingasset increasesand the marktomarketgeneratescash,reinvestment

incomeprices Fixedincomevalues fall wheninterestrates rise, so ratesand values

arenegativelycorrelated.Borrowingcosts arehigherwhenfundsareneeded and

reinvestmentrates arelowerwhen fundsaregenerated bythe marktomarketof the

futurescontracts.Figure1summarizes theseresults

B Ifthe correlation between the

underlyingasset value and interest

rates is

\f\

Investors will

Prefer to golongin a futures contract, and thefutures

price will be greater than the price of an otherwise

comparableforward contract

Positive

Have nopreference

Zero

Prefer to golongin a forward contract,andthe

forwardprice will be greater than the price of an

otherwisecomparablefutures contract Negative

FUTURESARBITRAGE

Professor’sNote: The tradesnecessarytoconductfuturesarbitragearethesame as

thoseforforwardarbitrageasoutlinedintheprevious topicreview.

Acash-and-carry arbitrageconsistsof buying theasset,storing/holdingtheasset,and

sellingtheasset atthefuturespricewhenthecontractexpires Thestepsina

cash-and-carryarbitrageare asfollows:

Attheinitiationofthecontract:

• Borrow money for thetermof thecontract atmarketinterest rates.

• Buy theunderlyingasset atthespotprice

• Sell (goshort)afuturescontract atthecurrentfuturesprice

Atcontractexpiration:

• Deliver theassetandreceivethefuturescontractprice

• Repaythe loan plusinterest.

Ifthefuturescontractisoverpriced, this 5-steptransactionwillgenerate ariskless profit

Thefuturescontractisoverpriced if the actual market priceisgreaterthan theno¬

arbitrageprice