Selling Short, With Formulas and Examples

1/10/2016 SellingShort,withFormulasandExamples

http://thismatter.com/money/stocks/sellingshort.htm 1/6

SellingShort

Mostinvestorsmakemoneybybuyingasecurityatalowprice,thensellingitlaterforahigherprice.Owningasecurityishavingalong positioninthatsecurity.Selling shortisawaytoprofitwhenthesecuritiesdeclineinprice,byborrowingthesecurities,sellingit,thenhopingtobeabletobuyitbacklateratalowerpricetoreplacethesecuritiesborrowed.However,ifthesecuritiespayadividendorinterestbeforetheshortiscovered,thentheshortsellermustpaythoseamountstothelenderofthesecurities.

Inordertoborrowthesecuritiestosellshort,thebrokermaylendoutsecuritiesfromthebrokerage'sowninventory,orfromthatofanotherbrokerage,orhemaylendoutsecuritiesheldinthemarginaccountsofotherinvestors.Ifthebrokerisunabletoborrowthesecurities,assometimeshappenswithilliquidsecurities,forinstance,thenthesecuritycannotbesoldshort.

Abrokercanlendoutsecuritiesfromthemarginaccountsofotherinvestors,becausethestandard margin agreementallowsit.Whenaninvestoropensamarginaccountatabrokerage,anysecuritiesboughtfortheaccountareheldinthestreet name,thenameofthebrokerageforthebeneficialinterestoftheinvestorandascollateralforanyborrowing.Thestandardmarginagreementallowsthebrokertolendoutthesecuritiesheldinitsmarginaccountstoshortsellers.Andsincemarginisrequiredtosellshort,theinvestormusthaveamarginaccount.

Before1998,manyinvestorssoldshortstocksthattheyactuallyownedselling shortagainst the boxasameanstoprotectcapitalgains,ortoconvertashorttermgainintoalongtermgain,whichhasalowertaxrate.However,thismethodhasbeenrenderedineffectivebytheTaxpayer Relief Act of 1997.AnyshortsaleagainsttheboxafterJune8,1997,isconsideredaconstructive salebytheIRS,andissubjecttoacapitalgainstaxintheyearofthesale.

Alargeinvestormayalsosellshortagainsttheboxtopreventthedisclosureofownershipinthesecurity.

CalculatingtheRateofReturnforaShortSale

Althoughashortsellerreceivesmoneyfromashortsale,theshortsellermustpostanadditionalmarginrequirementthatistypicallyequaltoofthevalueoftheshortedstock.Soif$10,000ofstockisshorted,thentheshortsellermusthaveatleast$5,000inhisaccounttocoverhisliabilityfortheshortsale.Hence,rightaftertheshortsale,theshortsellerwouldhaveatleastatotalof$15,000incashorequityinhisaccount.

Therateofreturnforashortsaleiscalculatedbythefollowingformula:

RateofReturnforaShortSaleFormula

Example1ProfitsandLossesfromSellingShort.

Aninvestorborrows 100sharesofXYZstock thatiscurrentlytradingat $35pershare andpaysa 4%dividend ,andsellsit.Assumethatthestockpaida dividendof$1.40persharebeforetheshortsellercoveredhisshort.Thisputs $3,500 intheshortsellersmarginaccount,ofwhich $140 willeventuallybedeductedtopayforthedividend.Ifthepricesubsequentlydeclinesto $30 ,theinvestorcanbuyitbackfor $3,000 toreturntheborrowedshares,thuscoveringtheshort position,andnetting $500 $140 = $360 fromthetrade.If,however,thepriceofGMstockrisesto $40 ,thentheshortsellerwillhavetobuybackthestockfor $4,000 ,resultinginanetlossof $500 + $140 = $640 .Brokeragecommissionsmustalsobesubtractedfromanyprofitoraddedtoanyloss.Notethatforthesamepricemovementofthestock,the lossfromanunfavorablemove ismuchgreaterthanthe profitgainedfromafavorablemove .

Examples



ShortRateofReturn =StockSalePriceDividendsPaidStockPurchasePrice

InitialMarginRequirement

SotherateofreturninExample1fortheprofitableinvestmentis( $3,500 $140 $3,000 )/$1,750= $360 /$1,750=20.57%,whilethereturnofreturnfortheinvestmentloss= $640 /$1,750=36.57%.

Margin

Shortsalescanonlybemadefromamarginaccount.Typically,amarginaccountallowstheaccountholdertoborrowupto50%oftheequityintheaccountforthepurchaseofnewsecurities.Thereisalsoamaintenance requirementthatistypically30%oftheequity.Ifthevalueoftheequitydropsbelow30%ofthetotalamount,thenthebrokerissuesamargincall.Theinvestoreitherhastosendmorecashorotherequity,orthebrokerwillsellenoughofthesecurities,toincreasethetotalequitybackto50%.Thus,iftheinvestorinitiallydeposits$5,000intoanewmarginaccount,hecanbuyupto$10,000worthofstocks.Ifthevalueofthosestockssubsequentlydeclinestobelow$7,000,thentheinvestorwillbesubjecttoamargincall,because$2,000iswhatremainsoftheinvestor'sequity,whichislessthan30%ofthetotalamountintheaccount.Hewillhavetodepositanother$1,500tobringtheequitytobackto50%.

ThemarginandthemarginmaintenancerequirementarespecifiedbyRegulation T,enactedbytheFederal Reserve Board.CurrentlyRegulationTrequiresaninitialdepositof$2,000ormoreforamarginaccount,and,initially,50%ormoreincashoreligiblesecuritiesassecurityforanyborrowingtobuysecurities.Asappliedtoashortsale,theinvestormusthaveatleast50%oftheshortsaleproceedsinequity.Brokersmayestablishmorestringentrequirements.

Inashortsale,moneyisdepositedintotheshortseller'saccount,butthismoneyisborrowed,becausetheyaretheproceedsofborrowedsharesthatweresold,andtherefore,thismoneyearnsnointerestfortheaccountholder.Thus,insteadofsecurities,theshortsellerhasborrowedmoneyinhisaccount,whichissubjecttothesamemarginrestrictionsasbuyingstock.Theamountofshortsalesproceedsdoesn'tchangeafterthesale,butthepriceoftheborrowedsecuritydoes,andmarginrequirementsaretiedtothepriceoftheshortedsecurity,notthemoneyintheaccount,because,eventually,theshortedsecuritieswillhavetobeboughttoreplacetheborrowedshares.Therefore,the current margin of the account is dependent on the currentmarket price of the shorted security because the short seller has a legalobligation to buy back and return the securities that were borrowed.

Theequityofashortaccountisequaltotheamountondepositminusthecurrentvalueoftheshortedsecurity:

Equity=AccountValueMarketValueofShortedSecurity

Theshortselleralsohasanobligationtopayanydividendstotheshareholderoftheborrowedstocks,andsinceneitherthelendernortheshortsellerownstheshortedstock,neitherreceivethedividendspaidbythecorporation,butthelenderisstillentitledtodividendpayments,sotheshortsellermustpaywhatisknownassubstitute payments in lieu of dividendstothestocklender.Thebrokerpaysthisautomaticallyfromtheshortseller'saccount,whichdecreasestheamountondeposit,andtherefore,theshortseller'sequityandmargin.

ExampleCalculatingtheEquityofaShortAccount

Ifyoudeposit$5,000andsell 1,000sharesofXYZstock shortfor $10pershare ,thenthereis$15,000ondeposit inyouraccount,butyour equity isstill $15,000 $10,000 = $5,000 ,whichis,ofcourse,whatyouinitiallydeposited.

IfXYZpricerisesto $12pershare ,thenyourequity= $15,000 $12,000 = $3,000 .

IfXYZpricedropsto $8pershare ,thenyourequity= $15,000 $8,000 = $7,000 .

Examples



Tocalculatemargin,justdivideequitybythemarketvalueoftheshortedsecurity:

CalculatingtheCurrentMarginofaShortAccount

Margin =EquityCMV

CMV=CurrentMarketValueofShortedSecurityMathNote:Multiplyfractionby100togetapercentage.

DeterminingtheValueofShortedSecuritiesThatWillElicitaMarginCall

Theformulaforcalculatingthevalueofsecuritiesthatwillelicitamargincallforshortedstockcanbederivedfromtheformulaforcalculatingmargin:

1. Margin=(AccountValueValueofShortedSecurities)/ValueofShortedSecurities2. Letm=marginratioa=accountvalueandv=valueofshortedsecurities.3. m=(av)/v4. m*v=avMultiplybothsidesbyv.5. v+m*v=aAddvtobothsides.6. v(1+m)=aFactoroutvfromtheleftside.7. v=a/(1+m)Dividebothsidesby1+m.8. ValueofShortedSecurities=AccountValue/(1+Margin)

Thus,theshortaccountvaluethatwilltriggeramargincallcanbecalculatedwiththefollowingformula:

CalculatingtheMarginCallAccountValueofaShortedSecurity

ExampleCalculatingtheCurrentMarginandCurrentEquityofaShortSale.

Youopenamarginaccountanddeposit $5,000 .Yousellshort 1,000shares XYZstockfor $10pershare .Theproceedsofthesale, $10,000 ,isdepositedinyouraccount.Thereisnow$15,000 inyouraccount.However,youstillonlyhave $5,000ofequity inyouraccount,becausethe $10,000ofshortsaleproceeds isfromborrowedsecurities.

Scenario1Thestockpricedeclinesto $6pershare ,sothe1,000sharesthatyousoldshortiscurrentlyworth $6,000 .Thus:

yourequity= $15,000 $6,000 = $9,000yourmargin= $9,000 / $6,000 =1.5=150%

Thus,thisshortsalewouldbeprofitableifyouboughtbackthesharesnowtocoveryourshort,foranetprofitof $4,000 minusbrokeragecommissionsandanydividendsthathadtobepaidwhilethestockwasborrowed.

Scenario2Thestockpricerisesto $12.00pershare ,thusitwillcostyou $12,000 tobuybackthesharesnow.

yourequity= $15,000 $12,000 = $3,000yourmargin= $3,000 / $12,000 =.25=25%

Becauseyourcurrentmarginisnowlessthan30%,youwillbesubjectedtoamargincall.Ifyoudecidetobuybackthesharesnowtocoveryourshort,your netlosswillbe$2,000 plusbrokeragecommissionsandanydividendsthathadtobepaidwhilethestockwasborrowed.

Examples



MarginCallAccountValue =AccountValue

1+MMR

MMR=MarginMaintenanceRequirement(whichisusually.3=30%).PriceperShare=MarginCallAccountValue/NumberofShares

RestrictionsonSellingShorttheShortSaleRule

Sellingsecuritiestendstodecreasetheirpricebyincreasingsupplyandreducingdemand,soshortsellerscanactuallydrivedownthepriceoftheborrowedstockthroughtheirshortsales.Inthepast,shortsellersformedpoolsforthispurpose.

Topreventthis,theSecuritiesandExchangeCommissionenactedtheshortsale rule,alternatelyknownastheplus tickoruptick rule,whichrequiresthatastockcanonlybesoldshortifthelasttransactionofthestockwasauptick,oranincreaseinprice,oriftherewasnopricechangeinthelasttransaction,butthepreviouschangeinpricewasanuptick,whichisknownasthezeroplus tick ruleorthezerouptick rule.

Thisruledoesnotgenerallyapplytoderivativesecuritiessecuritieswhosepricesdependonanothersecurityorbasketofsecurities,suchasexchangetradedfunds.Althoughthecurrentpricesofderivativesaredependentontheinstantaneousmarketsupplyanddemand,justlikeanyothersecurity,thepriceofderivativesisdeterminedbythepricesofthederivedsecurities.Ifthepriceofthederivativefelltoofarbelowthepriceoftheunderlyingasset,theninvestorswouldseeitasabargainandbuyit,increasingthedemand,and,thus,itsprice.Incertaincases,arbitrageurscantakeadvantageofanysignificantdifferentialinprices,which,ineffect,closesthepricegapbetweenthesecurities.

Acompanyinsideralsomaynotsellshortthecompany'sstock,whichmakessense,sinceallowingthiswouldallowcompanyinsiderstostealmoneyfrominvestorsofthecompany,bysellingthestockshort,thenissuingbadnewstodrivedownthepriceofthestock.

NakedShortSelling

Naked short sellingissellingastockshortwithoutfirstborrowingit.Thisoftenresultsfrom

afailure to deliver(akafail)thecertificatestothebuyerofthestockatsettlement,whichis

ExampleCalculatingtheMarginCallPriceofaShortedSecurity

Usingtheaboveexample,whatmarketpriceoftheshortedsecuritywilltriggeramargincall?

The totalamountondepositintheaccountis$15,000 andthemarginmaintenancerequirementis30% .Therefore,themargincallvalue= 15,000 /(1+ .3 )= 15,000 / 1.3 =$11,538.46 .Thisisequaltoaprice per shareof $11,538 / 1,000 = $11.54 (rounded)pershare.Soamargincallwillbetriggeredwhenthepriceoftheshortedsecurityrisesto $11.54 .

Toverify,wesubstitute $11,538.46 intothemarginformulaabove,andfindthat( 15,000 11,538.46 )/ 11,538.46 =0.30= 30% ,themarginmaintenancerequirement.Notethatifanydividendswerepaidout,thiswouldhavetobesubtractedfromtheamountondeposit.

Examples

NewsUpdateShortSaleUptickRuleEliminated

On June 13, 2007, the Commission voted to remove the short sale uptick rule test ofRule 10a1: http://www.sec.gov/news/digest/2007/dig062807.txt

News!



afailure to deliver(akafail)thecertificatestothebuyerofthestockatsettlement,whichistheresultofinstitutionalfailuretoeffectthetransfer.However,marketmakersarepermittedtodosomenakedshortsellingtoincreasetheliquidityofthemarketwhenitisdifficulttoborrowthestockquicklyenoughtosatisfymarketdemand.However,nakedshortsellingisillegalasameanstodrivedownstockpricesinordertobuyatabetterprice.

RisksofSellingShort

Thereareriskstosellingshort.Themostobviousriskisthatthestockpricecanriseandcontinuetorise.Thepriceofastockcanrisemuchhigherthanitcanfall,and,therefore,thepotentialforlossesismuchgreaterthanthepotentialforprofits.

Anotherriskisthattheshortsellermaybeforcedtobuybackthestock,becausethesharessoldshortwereborrowed,andthelendermayrequestthosesharesbackatanytime.Usuallythebrokercanobtainothersharesfromotherinvestors,butifthesharesarescarce,suchasoccurswithsecuritieswithlittlefloat,thenthebrokermayhavenochoicebuttobuybackthesharesatthecurrentmarketprice.Sometimes,investorswhoarelonginastockwithalargeshortinterestwillbuymoreofthestock,orasktheirbrokertodelivertheactualstockcertificatestothem,inthehopeofforcingtheshortsellerstocovertheirpositionbybuyingthestockbackthisiscalledashort squeeze.

ShortInterestSupposedIndicatorofMarketSentiments

Becauseinvestorssellshortsotheycanprofitbyexpectedpricedeclinesintheshortedsecurities,ortheywanttohedgetheirpositionsbecausetheyatleastthinkapricedeclineisagoodpossibility,manyinvestorslookatthetotalshortinterestasagoodindicatorofmarketsentiments.

Short interestisthetotalnumberofsharesthathavebeensoldshort,butnotrepurchasedyet,tocovertheshortpositionsonanexchange.TheNewYorkStockExchange(NYSE),AmericanStockExchange(AMEX),andtheNASDAQreleasetheshortinterestvolumefortheirexchangesbythemiddleofthemonth,andisreportedinTheWallStreetJournalaboutaweekafterthat.

Theshortsale ratio(also,short ratio),isthetotalnumberofsharesshorted,butnotcovered,dividedbytheaveragedailyvolumeofallsharestradedontheexchange.

ShortRatio =NumberofSharesShorted,butNotCovered

AverageDailyVolumeofAllSharesTradedonExchange

Notethatwhilethenumeratoroftheshortratioincreaseswithshortinterest,thedenominator,theaveragedailyvolumeforthatmonth,isnotrelatedtotheshortinterest,and,therefore,theshortratiomayactuallydeclinewhentheshortinterestincreases,whichwouldoccurwhentheaveragedailyvolumeincreasesmorethantheshortinterestandviceversa.Note,also,that,forthesamereason,theshortratiodoesnotquantifytheshortinterest.

Someinvestors,however,consideralargeshortinteresttobeabullishsign,becausetheshortsellerswillhavetopurchasetheshortedsecurityatsomepoint,whichwilltendtoincreaseitsprice.Thisissometimescalledtheshort interest theory,orthecushion theory.Technicalanalystsconsiderashortpositionthatistwicetheaveragedailytradingvolumetobea

verybullishsign,andagoodpossibilityforashort squeeze,whichresultswhenshortsellers

RealWorldExampleDivergenceofShortInterestandtheShortSaleRatio

On August 22, 2006, The Wall Street Journal reported that, for the month endingAugust 15, 2006, the short interest on the NYSE increased from the mid-July total of9,298,283,040 shares to 9,638,209,066 sharesan increase of about 3.7% butthe short ratio actually decreased from 6.1% to 5.9% for the same month.

News!



verybullishsign,andagoodpossibilityforashort squeeze,whichresultswhenshortsellersbuytocovertheirposition,raisingthestockprice,which,inturn,causesmoreshortsellerstocovertheirpositions,therebyraisingthestockpriceevenmore.

Therearemorespecializedshortinterestratiosthatsomeinvestorsconsider.Theoddlotshortsale ratio(akaoddlot selling indicator)isthetotalofoddlotshortsalesdividedbythetotaloddlotsales.

OddLotShortSaleRatio =TotalOddLotShortSales

TotalOddLotSales

Thissupposedprognosticatorisbasedontheoddlot theory,whichisbasedonthesuppositionthatpeoplewhobuyandselloddlots(lessthan100sharesoraroundlot)arenoviceinvestors,andareactingindirectoppositiontotruemarketconditions.Thus,whenoddlotsellingishigh,thenthemarkethasbottomedout,andit'stimetobuy,andviceversa.Thereisnorealevidencethattheoddlottheoryistrue,butevenifitis,itmaybebecauseinvestorsbelievethatitistrue,andactaccordingly.

Themember shortsale ratio,usingsimilar,speciousreasoning,issupposedtobethetruemarketindicator,andtheremaybeagrainoftruthtothis.Afterall,ifanyonewouldknowthemarket,itwouldbethemembersoftheNYSEwhospecialists,floortraders,andoffthefloortradersspecializeintheparticularsecuritiesthattheysellshort.ThemembershortsaleratioisthetotalsharessoldshortintheaccountsoftheNYSEmembersin1weekdividedbythetotalshortsalesoutstandinginthesameweek.

MemberShortSaleRatio =TotalSharesShortedbyNYSEMembersin1Week

TotalShortSalesOutstandinginSameWeek

ThemembershortsaleratioispublishedweeklyinThe Wall Street JournalandBarron's.

Thespecialist's shortsale ratioiscomputedinthesamewayasthemembershortsaleratio,butonlyincludestheaccountsofthespecialistsontheNYSE.

SpecialistShortSaleRatio =TotalSharesShortedbyNYSESpecialistsin1Week

TotalShortSalesOutstandinginSameWeek

Someshortsalesaremadetoprovideanorderlymarketinthesecuritiesassignedtothespecialistoneoftheirdutiesbutmanyinvestors,especiallytechnicalinvestors,usethisasaprognosticatorofthemarkets.

Informationisprovided'asis'andsolelyforeducation,notfortradingpurposesorprofessionaladvice.Copyright19822016byWilliamC.Spaulding

Selling Short, With Formulas and Examples

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