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TheGoldenConstant

ClaudeB.ErbLosAngeles,CA90272

CampbellR.Harvey

DukeUniversity,Durham,NC27708NationalBureauofEconomicResearch,Cambridge,MA02138

ABSTRACTInTheGoldenDilemma,ErbandHarvey(2012)exploredthepossiblerelationbetweenthereal,inflationadjusted,priceofgoldandfuturerealgoldreturns.Thisupdatesuggeststhattherealreturnofgoldoverthenext10yearscouldbeabout3%peryeariftherealpriceofgoldmeanrevertsor11%peryeariftherealpriceofgoldovershootsanddeclinestopreviouslowrealpricelevels.Thisviewreflectsagoldenconstanthypothesisthatinflationisthefundamentaldriverofthepriceofgold.Ofcourseitispossibletoentertainotherhypotheses.Agoldenconstantperspectivesuggestsafairvaluepriceforgoldof$825anounceandapossibleovershootpriceof$350anounce.Keywords:Gold,goldenconstant,realgold,overshoot,inflationhedge.Seeourtwoearlierpapersongold:TheGoldenDilemmaAnImpressionisticViewoftheRealPriceofGoldAroundtheWorld_________________*FirstpostedtoSSRN:August3,2015.

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ErbandHarvey(2012,2013)observedthatacommonargumentmadeforinvestingingoldinthatitisaninflationhedge,agoldenconstant.Oneway to thinkabout thegoldenconstantperspective isasacollectionof statements thatassert that:1)overa longperiodof time thepurchasingpowerofgoldremains largely thesame;2) in the long run, inflation isa fundamentaldriverof thepriceofgold;3)deviationsinthepriceofgoldrelativetoinflationwillbecorrected;and4)inthelongrun,therealreturnfromowninggoldiszero.Thereareatleasttwowaystovisuallyupdatethisview.Thefirstistolookatthehistoricalrelationshipbetweenthepriceofgoldandacommonmeasureofinflation.Thesecondistolookatthemovementovertimeintherealpriceofgold,thepriceofgoldadjustedforinflation.Dotheseviewssuggestafavorableoraproblematicoutlookforaninvestmentingold?Thisupdatesuggeststhatthenext10yearscouldbechallengingforgold.Exhibit1 illustratestherelationbetweenthepriceofgold inU.S.dollarsandtheU.S.ConsumerPriceIndexsinceJanuary1975,whenfuturestradingingoldcommenced.Relatedtotheideathatgoldisaninflationhedgeistheideathatthepurchasingpowerofgoldisconstant,atleastovera longperiodoftime.TherustcoloredlineinExhibit1isawayofthinkingaboutwhatthegoldenconstantvalueofgoldmightlooklike,ifitexists.First,wecalculatetheaveragerealpriceofgold(averageofthenominalpricedividedbytheCPIlevel).Overourdatatheaveragerealpriceofgoldis3.46.ThelineinExhibit1issimplytheaveragerealpricemultipliedbythecurrentlevel,eachmonth,oftheCPIindex.Forexample,inJune2015,theCPIlevelis237.8.MultiplyingtheaveragerealpricetimesthecurrentCPI(3.46x237.8)deliversapriceofapproximately$825.Thisrepresentswhatthenominalpriceofgoldshouldbetoday ifweassumetherealpriceofgoldisconstant.Importantly, thepriceofgoldhas fluctuated substantiallyover timeaswellas relative to thegoldenconstantvalueestimate.Sincethereisnogenerallyagreedupondefinitionofaninflationhedge,somemightseeinExhibit1evidencethatgoldisagoldenconstantinflationhedge,atleastinalongrunsense,andothersmaylookatthesamedataandbelievethatperhapsaninflationhedgeshouldtrackrealizedinflationmoreclosely.Thegoldenconstantisnotafactitisonehypothesisaboutthevalueofanassetthatembedstheideathatgold isan inflationhedge. It ispossibletoenthusiasticallybelieve inotherhypotheses,suchasagoldenversionofmarketefficiency(inwhichtheobservablepriceofgoldisanunbiasedestimateoftheotherwiseunobservablevalueofgold),theideathatthepriceofgoldisultimatelydrivenbytheactionsoftheChinesegovernmentandChineseconsumers,ortheideathatthepriceofgoldisdrivenbythecostofproductionofgoldminingcompanies.Ofcourse,whiletheremaybeanefficientmarketexplanationforgold,ortheChinesemaybedrivingthepriceofgold,itisworthconsideringwhetherthesepossibledriversof thepriceofgoldareconsistentwith the ideaofgoldbeingan inflationhedge.1DoChinesepurchasesofgoldproxyforwhatpeople,intheU.S.andeverywhereelse,reallythinkinflationhappenstobe, isanassertion thatpriceequalsvaluea step forward inhedging inflation,ordoes the costofproductionof theaverageormarginalgoldminer reallycapture thestoryof inflation?All thegoldenconstanthypothesisperspectivesuggestsisthat,ifitistrue,thepriceofgold($1096inJuly2015)ismuchhigherthanitsgoldenconstantvalue($825).Anobviousquestiontoaskis,ifthegoldenconstantprovides

1Anotherwayofthinkingaboutthisis:tosomedegreeitispossibletopointtosomemeasureofinflationbutitisprobablyhardtopointtosomemeasureofmarketefficiencyorofChinesegoldactivity.Alternatively,becauseitissohardtodefineeitherofthesearguments,itishardtodisproveeitheroftheseassertions.

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aguidetothevalueofgold,whattypicallyhappenswhenthepriceofgoldisaboveorbelowitsgoldenconstantvalue.Followingthepathoftherealpriceofgoldmaybehelpful.

Exhibit2showshowtherealpriceofgoldhasfluctuatedsinceJanuary1975.Asmentionedearlier,theratioofthepriceofgoldrelativetotheU.S.ConsumerPriceIndexhasaveragedabout3.46overthistimeperiod.2OfcoursethevalueofthisratiomightbedifferentusingadifferentinflationindexoraresettingofthebasedateoftheU.S.CPI.Thegeneralideaofagoldenconstantonlysuggeststhatonceaninvestorthoughtfullyselectsan inflation index,viewing inflationasafundamentaldriverofthepriceofgold,thereisnoreasontoexpectthattherealpriceofgold,relativetothatindex,willpersistentlytrendupordown over a long period of time. Using the U.S. Consumer Price Index3 as an arbitrary, though

2Thelongrunfuturerealpriceofgold,measuredthisway,maystaythesameorchange.Iftheaveragerealpriceofgoldrisesovertimethenitdoesmorethanprovideaninflationhedge(itisanassetthatgeneratesthereturnofinflationandanadditionalpremium).Iftheaveragepriceofgoldfallsovertimethanitmaynotliveuptoinvestorexpectationsofwhataninflationhedgeshouldbe(sinceitwouldprovidethereturnofinflationminussomepenalty).Itisonlyiftherealpriceofgoldstaysthesame,overalongperiodoftime,thatitispossibletoconsideritaninflationhedgewithoutaverylengthylistofqualificationsaboutwhatoneexpectsfromaninflationhedge.InTheGoldenDilemma,ErbandHarvey(2012)examinethegoldenconstantfrom1792.3 Erb andHarvey (2013) go beyondUnited Statescentric view (gold priced inUS dollars and real gold pricescalculatedusingtheUSCPI)andexplore22othercountries.However,theseextracountiesdidnotaltertherealgoldpriceanalysis.Therearetworeasons.Unlikestocksorbonds,whichtosomedegreearedifferentfromonecountrytoanother,goldisgoldeverywhere.Itspriceisthesameeverywhere(afteradjustingforexchangerates).Ifthepriceof gold was not the same everywhere, there would be an attractive arbitrage opportunity from buying goldinexpensivelyinonecountryandsellingitforalotmoreinsomeothercountry.Thisideathatthenominalpriceofgoldisthesameeverywherealsoleadstotheideathattherealpriceofgoldisthesameeverywhere,eventhoughcountriesdifferinthewaysthattheyhonestlyordishonestlycalculateinflation.

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conventional,fundamentaldriverofthepriceofgold,thehighrealpriceofgoldhasbeenabout8.73,thelowrealpriceofgoldhasbeenabout1.47andthecurrentrealpriceofgoldisabout4.63.4

Inthefuturehighandlowrealpricesofgoldmaybemoreorlessextremethaninthepast.Thehistoricallowrealpriceofgoldof1.47reflectsthehistoricalvolatilityoftherealpriceofgoldanditisameasureofhowlowtherealpriceofgoldactuallysankinthepast.Itisnotanindicationthattherealpriceofgoldcannotfalltoalowerlevelinthefuture.Thehighandlowrealpricesofgoldhighlightthatevenifthereisonaverageagoldenconstanttherealpriceofgoldhasstrayed,andprobablywillstray,farfromthispossiblecentraltendency.Itisalsopossiblethatthefuturewillbeunlikethepast.Thereareatleasttwowaystothinkaboutthecurrenthistoricallyhighrealpriceofgold.Oneisthattherealpriceofgoldmaymeanreverttowardsthehorizontalrustcoloredline,thegoldenconstantvalueforgoldlinkedwiththeaveragerealpriceofgold.Oritisalsopossiblethatallofhistoryismoreorlessbunk,asHenryFordonceputit,reflectinganideathatboldinvestorsandinnovatorswereneverslavestohistory.Meanreversionmaybeconsistentwiththeideaofalongrungoldenconstantinwhichtherealpriceofgoldmeanrevertstoitsaverage.However,inaveryobviousway,Exhibit2alsosuggeststhatwhentherealpriceofgoldfallsthegoldenconstantlevelisnotaflooraprotectivelineinthesandthattherealpriceofgoldwillnotcross.Sincethefuturehasnothappenedyet,itispossibletoforcefullyopinethattherealpriceofgoldwillnotfallbelowitsaverage,thegoldenconstant,levelinthefuture.Ofcourse,itisworthconsideringhowrewardingan investment ingoldmightbe iftherealpriceofgoldfallsto itspreviouslowlevel,orlower.Focusingontheideathatinflationisthefundamentaldriverofthepriceofgold,somewhatsimilar inspirittothinkingaboutearningsorcashflow5asthefundamentaldriversof4Currentpriceofgold/CurrentCPI=$1096/237.79~4.635Ifinflationisthefundamentaldriverofgold,inflationmaynotbemoredifficulttoforecastthanearningsorcashflowsforstocks.

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stocks, the realpriceof gold canbe thoughtof as a valuation ratio.Historicallyhas therebeen anyrelationshipbetween the realpriceofgoldand subsequentgold real returns?Or,alternatively,doesvaluationmatter?Exhibit3depictsthehistoricalrelationshipbetweentherealpriceofgoldandsubsequent10yearrealgoldreturns.Historically,belowaveragerealgoldpriceshavebeenfollowedbyaboveaverage10yearrealgoldreturnsandaboveaveragerealgoldpriceshavebeenfollowedbybelowaverage10yearrealgoldreturns.Sincetherealpriceofgoldiscurrentlyaboveitshistoricalaverage,Exhibit3suggeststhatoverthenext10yearsrealgoldreturnscouldbebelowaverage.Thinkingoftherealpriceofgoldasavaluationmetricthismayseemtosuggestthatvaluationmatters.Sincethedevilisinthedetails,itdoesanditdoesnot.Inagoldenconstantsense,valuationmatterssincedeviationsfromanormalrealpriceofgoldareinconsistentwiththeconceptthatgoldisaninflationhedge,thelongrunrealpriceofgoldisconstantovertimeandthelongrunrealreturnofgoldiszero.Thereare,ofcoursealternativeviews,suchastheideathatthepriceofgoldequalsthevalueofgold,orabeliefthattheChinesecontrolthegoldmarket,inwhichtherealpriceofgoldhasnoobviousrole.OnecanviewExhibit3asatypicalpredictivechartthatechoestheworkofCampbellandShiller(1998)andmanyothers.TherealpriceofgoldinJanuary1975ismatchedwiththerealgoldreturnfromJanuary1975toJanuary1985,therealgoldpricefromFebruary1975ismatchedwiththerealgoldreturnfromFebruary 1975 to February 1985, etc. Itmay be common to look 10 years into the future in theseillustrations,however it isworthnoting that it iseasier toview the choiceofa10yearhorizonasaconvenientconventionratherthanascientificrevelation.6

6Itispossibletocomparetherealpriceofgoldwithrealgoldreturnsoverthenextday,week,month,yearoranytimeperiod.Itiscommontobelievethatifvaluationplayssomeroleinsubsequentreturnsthatitsimpactwillprobablybemoresignificantata longerhorizon,suchas10years,thanatashorthorizon,suchasoneday.Forexample,CampbellandShiller(1998)examinedtherelationshipbetweenameasureofstockmarketvaluationandsubsequentrealstockmarketreturns.Achallengewithlongrunreturnpredictabilitystudiesisthatifaresearcher,say,hasadesiretofindevidencethatthereisausefulvaluemetricitmaynotbesurprisingtoseeevidencethatismoreapparentthanrealsupportingtheresearchersbeliefs.

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Givenagoldenconstantperspective,Exhibit4triestoanswerthequestionhowlowmightthepriceofgoldgoifthepreviouslowrealpriceofgoldisrevisited?GiventhevalueoftheU.S.ConsumerPriceIndexforJune2015andthepreviouslowrealpriceofgold,apossiblelowpriceforgoldisabout$350anounce.Thisdoesnotmeanthatthepriceofgoldwillimmediatelyfallto$350anounce.Ratheritisasuggestionthat,giventhevolatilehistoryofrealgoldpricesthatexists,therealpriceofgoldoncefellto1.47anditcouldfalltothatlevelagain.Aconsiderationoftheopportunitiesandthepitfallsofaninvestmentbenefitfromaconsiderationofprobableandpossibleoutcomes.Ifthequestion iswhat isthe likelypriceforgoldgivenabeliefinthegoldenconstantthenanansweris$825anounce.Ifthequestionishowlowcouldthepriceofgoldgogiventhehistoryofrealgoldpricesandabeliefinthegoldenconstantthenananswerisabout$350anounce.Aternativelyitispossibletoinvokethehistoryisbunkviewandignorethepossibility,ordeclaretheimpossibility,thattherealpriceofgoldcouldfalltoalowrealpricelevel.Inagoldenconstantcontext,$350anounceisthedownsiderisktothepriceofgoldgiventheexistenceofagoldenconstantframework,apriorlowrealpriceofgoldandthecurrentleveloftheU.S.ConsumerPriceIndex.

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If,inagoldenconstantsense,afairvalueofgoldiscurrently$825anounceandapossiblelowvalueofgoldiscurrently$350anounce,howdoesthattranslateintoexpectednominalandrealreturn?Resortingtotheconventionofpeering10yearsintothefuture,Exhibit5providesaframework.Lookatthecaseinwhichinflationisexpectedtobe2%peryearforthenext10years(thisassumptioncanbecomparedwiththeJuly31,201510yearTreasurybreakevenrateof1.75%).Thegoldenconstantvalueofgoldwouldincreasefrom$825anounceto$1,006anounce,andtheovershootpricewouldrisefrom$350anounceto$427anounce.Ifovera10yearinvestmenthorizonthepriceofgoldfellfrom$1,096anounceto$1,006anounceitwouldexperienceanominalreturnof0.9%peryearandarealreturnof2.8%peryear.Ifthepriceofgoldfellfrom$1,096anouncetoa10yearhenceovershootlevelthenominalandrealreturnswouldbe9.0%peryearand10.8%peryear,respectively.Exhibit5alsoshowswhat10yearnominalandrealreturnsmightlooklikeifinflationforthenext10yearswas0%peryearor1%peryear.Notsurprisingly, if the levelof inflationdiffers fromonescenario toanother thennominalreturnsdiffer fromonescenario toanotherby thedifference in inflationrates.Whatmaybeabitmore interesting isthatrealreturnsdonotseemtovaryacross inflationscenarios.Regardlessofthefutureinflationratetherealrateofreturnis2.8%peryearifgolddeclinesover10yearstoitsgoldenconstantfairvalue.Regardlessofthefutureinflationratetherealrateofreturnis10.8%peryearifgolddeclinesover10yearstoitsovershootlevel.Thisobservationthatthelevelofinflationdoesnotaffecttherealrateofreturn issimilartotheobservation inErbandHarvey(2013)thatfrom1980to2000therealreturnofgoldwasthesameinBrazilandtheU.S.eventhoughinflationrateswerequitedifferent.

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Supposeaninvestorviewsgoldasapossibleinflationhedgeandtheinvestorisabletoperfectlyforecastinflationoverthenext10years. InahistoricalU.S.contexthowvaluablemightthisskillhavebeen inforecastingfuture10yearnominalgoldreturns?Exhibit6providessomeperspective.Exhibit6showsrolling10yeartotalreturnsforthenominalpriceofgold,therealpriceofgoldandtherateofinflation.Therateofinflationhasdeclinedovertimebuttheredoesnotseemtobemuchofalinkagebetweenthe10yearrateof inflationandeitherthenominalorrealreturnofgold.Exhibit6highlightsthateven ifinflation isa longtermfundamentaldriverofthefairvalueofgold, it is importantto identifythosecircumstancesunderwhichclairvoyantforecastsoffutureinflationwillbehelpful.

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Exhibit7presentsanotherwayofthinkingaboutthevalueofperfectforecastsofinflationandtherealizednominalreturnsfromgold.TheyaxisofExhibit7showstherolling10yearnominalreturnsforgoldandthe xaxisplots the rolling10year returns forboth inflationand the real rateof returnofgold.ThemessageinExhibit7issimple.Exactlyknowingtheinflationrateoverthenext10yearsisofnohelpinforecastingthefuturenominalreturnongold.Ontheotherhandbeingabletoknowthefuturerealreturnongolddeliversahighlyaccurate forecastof thenominal returnongold.This insight shouldalsobeobviousfromExhibit6.Inflation,measuredover10yearperiods,hasverylowvolatility.Incontrast,thepriceofgoldhas largevolatility.Asa result,beingable to forecast inflationdoesnot reallyhelpyouforecastthevolatilenominalpriceofgold.Importantly,eventhoughthere is littlerelationbetweenthenominalpriceofgoldand inflationwhenmeasuredover10yearperiods,theevidenceinErbandHarvey(2012)suggeststhatgoldholdsitsvalueovertheverylongrun.TheypresenthistoricalevidencethatthewageofaRomancenturion(ingold)wasapproximatelythesameasanUSArmycaptainspay.Theyalsodetailthatthepriceofbread(ingold)thousandsofyearsagoisaboutthesameaswewouldpaytodayatanupscalebakery.Sowhilegoldmightprotectagainst inflation inthevery longrun,10years isnotthe longrun. Intheshorterrun,gold isavolatileinvestmentwhichiscapableandlikelytoovershootorundershootanynotionoffairvalue.

ConclusionAgoldenconstantframeworksuggeststhat$825anounceisapossibleestimateofgoldsfairvalueandthatthepriceofgoldcouldfallaslowas$350anounce.Thoughtofintermsofpossiblerealreturnsoverthenext10years,anexpectedrealreturnforgoldisabout3%peryearusingthisnotionoffairvalueandinthecaseofanovershootscenario,therealreturnofgoldcouldbeabout11%peryear.

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Dependingupononesbeliefs,thegoldenconstantframeworkmayormaynotbeausefulwaytothinkaboutthefairandpossiblevaluesofthepriceofgold.Thegoldenconstantframeworksuggeststhatinflationisafundamentaldriverofthepriceofgoldinthelongerterm.Itiscommonforstockandbondinvestorstopointoutthatstocksandbondshavecashflowsthatdrivetheirfundamentalvalues.Fixedratebondshavefixedcashflowsandfixedmaturities.Stockshaveexpectedcashflowsandnospecifiedmaturity.Goldhasneitherfixednorexpectedcashflowsanditdoesnothaveamaturity.Asaresult,itismuchmoredifficulttodefinegoldsfundamentalvalue.Giventhechallengeofspecifyingapricingmodel,itisnotsurprisingthatgoldexhibitssubstantialpricevolatilityevenmeasuredoverlongertermhorizons.ReferencesCampbell,JohnY.andRobertJ.Shiller.1998.ValuationRatiosandtheLongRunStockMarketOutlook,JournalofPortfolioManagement,vol.24,no.2:1126Erb,ClaudeB.andCampbellR.Harvey.2012.AnImpressionisticViewoftheRealPriceofGoldAroundtheWorld,SSRNworkingpaperErb,ClaudeB.andCampbellR.Harvey.2013.TheGoldenDilemma,FinancialAnalystsJournal,July/August,vol.69,no.4:1042.