Handbook of Portfolio Construction: Contemporary Applications of Markowitz Techniques

808 Pages·2016·10.87 MB·English

by  Guerard J.B.

Handbook of Portfolio Construction
John B. Guerard, Jr.
Editor
Handbook of Portfolio
Construction
Contemporary Applications of Markowitz
Techniques
123
JohnB.Guerard,Jr.
McKinleyCapital
Management,LLC
3301C.Street
Anchorage,AK99503
USA
[email protected]
ISBN978-0-387-77438-1 e-ISBN978-0-387-77439-8
DOI10.1007/978-0-387-77439-8
SpringerNewYorkDordrechtHeidelbergLondon
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Foreword
I am deeply honored by the articles that appear in this collection. In particular,
I thank John Guerard for organizingthis recognition of my work. I have thought
aboutwhetherIshouldindividuallythankparticularauthors.Ihesitatetodosobe-
cause a complete list would be too long, and an incomplete list would leave out
namesthatshouldnotbeomitted.Idonotsuppose,however,thatanyone’sfeelings
will be hurt if I specifically thank Paul Samuelson for his contribution.I am sure
thattheothercontributorstothisvolume–includingoldfriendsandcolleaguesas
wellasothernotablecontributorstofinancepracticeandliterature–havethesame
admirationforPaulforwhathehastosayandhowhesaysit.ToPaulinparticular,
andtoeachoftheothercontributorsingeneral,thankyou.
TheremainderofthisnoteisdevotedtopointsaboutmyworkthatIwouldvery
much like the reader to “please note.” For example, many writers seem to know
onlythisaboutmywork:in1952,Iwroteanarticlethatdefinedandrecommended
mean-variance analysis. They seem to be unaware that there is a large difference
betweentheviewsIheldin1952andthoseIheldandexpressedin1959.Ofcourse,
thedefinitionofmean-varianceefficiencyandtheformulasforportfoliomeanand
portfolio variance are the same in the two works, but the justification for mean-
varianceanalysis,therelationshipbetweensingle-periodandmany-periodanalysis,
and the method of computing efficient sets for large numbers of securities are all
newinbothmy1956articleandmy1959book.
Many ascribe assumptions underlying mean-variance analysis to me; they are,
in fact, credited to Tobin (1958) and eschewed by Markowitz (1959). Many con-
trasttherationaldecisionmakingofthemean-varianceoptimizerwiththeeconomic
actordescribedinbehavioralfinance,andassumethatIamuninterestedinorinop-
positiontothelatter.Infact,whilemyportfolioselectionpaper,referencedhereas
Markowitz(1952a),isgenerallynotedasestablishingmeas“thefatherofportfolio
theory,”myMarkowitz(1952b)articleisrecognizedbyleadingbehavioralfinance
specialiststosharea“grandfatherlyrelationship”withbehavioralfinance.
Below,IflushoutthedistinctionsbetweenworkthatIdidatdifferenttimes,on
onesubjectoranother,betweentheviewsIhaveexpressedandthosethatareoften
attributed to me. Each section below has a title such as “Markowitz (1952a) and
Markowitz(1952b).”Thesectiontitleshouldbethoughtofasfollowingthephrase
“Pleasenotethedifferencebetween...”
v
vi Foreword
Markowitz(1952a)and Markowitz(1952b)
The“Utilityanalysisofchoicesinvolvingrisk”byFriedmanandSavage(1948)was
an assignmentin which I took Friedman’scourse around1949. I foundsome dif-
ficulties with the assigned paper. My 1952bpaper, “The utility of wealth,” details
these difficulties. At first, the latter paper attracted some but not much attention.
Then,KahnemanandTversky(1979)publishedtheirpaperonprospecttheory.This
isreferredtoasMarkowitz(1952b)inafootnote,becausetheideaofmeasuringutil-
ityasadeviationfromcurrentwealthhasbeenusedbymeaswellasbyKahneman
andTversky.
Thethree-volumehandbookbyShefrin(2001)reprintsacopyof“Theutilityof
wealth” as the first article in its historical review volume. In this volume, Shefrin
describesthenatureandroleof“Theutilityofwealth”asfollows:
Markowitz(1952)trulyqualifiesasabehavioralwork,withitsfocusonhowpeopleactually
behave. Markowitz addresses a classic question posed by Friedman and Savage (1948):
whydopeoplesimultaneouslypurchaseinsuranceandlotterytickets?FriedmanandSavage
proposed a solution to this question, a solution that Markowitz criticized on behavioral
grounds.InarguingagainsttheFriedman–Savagesolution,Markowitzdescribedtheresults
of how people behave, citing an experiment conducted by Mosteller and Nogee (1951)
abouthowpeoplebet.Relianceonexperimental datafelloutoffashion forawhile,and
stillengenderssomecontroversyamongfinancialeconomists.
Looked at in hindsight, Markowitz showed amazing insight. The theory he proposes as
analternativetoFriedman andSavagecontains basicelementsthatwere laterdeveloped
muchmorefully.Hisdiscussionaboutthedifferencebetweenpresentwealthandcustomary
wealthgaverisetothecodingofgainsandlossesrelativetoareferencepoint.Herecognized
thatlossesloomlargerthangains.Heproposedautilityfunctionwiththreeinflectionpoints
tocapturetheideathatattitudeorriskvariedwiththesituationbeingfaced.Inthisrespect
heemphasizedtheimportanceofwhetheragambleisframedintermsofgainsorlosses,as
wellaswhetherthestakesaresmallorlarge.Hisdiscussiontouchesonaspirationpoints,the
preferenceforpositiveskewness,andapropertyThalerandJohnson(1990)subsequently
calledthe“housemoneyeffect.”
TheideasintroducedinMarkowitz(1952)werelaterdevelopedinprospecttheory,aframe-
workproposedbypsychologistsKahnemanandTversky(1979).Prospecttheorycombines
theinsightsofMarkowitzwiththoseofAllais(1952).ItdrawsonMarkowitzforthecon-
ceptsof framing, gains, losses, reference points, andautilityfunction withconcave and
convexsegments.ItdrawsonAllaisforitstreatmentofprobabilities.
IamcurrentlyworkingwithMeirStatman,anotedbehavioralfinanceaficionado
onproceduresthatspeaktoinvestorsintermsofthe“mentalaccounts”ofbehavioral
finance,yetproduceportfoliosthatarenearlymean-varianceefficient.
Markowitz(1952a)Versus Markowitz(1959)
Markowitz (1952a) differs from Markowitz (1959) in various ways as outlined in
thefollowingparagraphs.
Foreword vii
Markowitz (1952a) proposed mean-variance both as a maxim for recom-
mended behavior and as a hypothesis concerning actual investor behavior. In
Markowitz (1959), no mention is made of mean variance as a hypothesis about
actualbehavior.
NeitherMarkowitz(1952a)norMarkowitz (1959)assumed thatmean-variance
wastobeappliedtoa“single-periodworld.”Bothconsideredmean-varianceanaly-
sisasasingle-periodanalysiswithinamany-periodworld.Markowitz(1952a)gave
twoproposalsfortherelationshipbetweenthesingle-periodanalysisandthemany-
periodworld.Thefirstproposalconsidersthemeans,variances,andcovariancesof
portfolioanalysisasapplicabletothe presentvalueoffuturedividends.Thealter-
nateproposalassumesthatprobabilitydistributionsofreturnsareinasteadystate,
andconsidersthemeans,variances,andcovariancesoftheanalysistobetheparam-
etersofthissteadystate.Ontheotherhand,Markowitz(1959),Chaps.11and13,
considersthesingle-periodanalysistobeapplicabletothequadraticapproximation
(seebelow)tothederivedutilityfunctionofdynamicprogramming.1
Tobin (1958) notes that mean-variance analysis is implied if the user has a
quadratic utility function or if probability distributions are Gaussian. Neither
Markowitz (1952a) nor Markowitz (1959) assumes Gaussian probability distri-
butions.Markowitz(1952a)givesnojustificationformean-varianceanalysisother
than that variance (or, equivalently,standard deviation) is a commonlyused mea-
sure of dispersion. Markowitz (1959),Chaps. 6 and 13, assumes that the investor
shouldacttomaximizeexpectedutility,andproposesmean-varianceanalysisasan
approximationtothemaximizationofexpectedutility.Thisviewisspelledoutmore
completelyinYoungandTrent(1964)formean-varianceapproximationstothege-
ometricmeanorexpectedlogarithm,andinLevyandMarkowitz(1979)forvarious
utility functions. More recent studies include Dexter et al. (1980), Pulley (1981,
1983),KallbergandZiemba(1981,1983,1984),Krolletal.(1984),Simaan(1993),
andHlawitschka(1994).
Theconclusionsoftheabovestudiesaregenerallysupportiveofmean-variance
approximations, including Hlawitschka’s conclusion that it is applicable to port-
folios of puts and calls. However, Grauer (1986) illustrates that, if leverage is
permitted, mean-variance approximations may produce poor results unless the
choiceofportfolioisconstrainedtoavoidtheportfolio’sbankruptcy.
Markowitz(1956)Versus Markowitz(1959)
Markowitz (1956) and Markowitz (1959), Chap. 8 and Appendix A, present
the critical line algorithm for tracing out the entire mean-variance efficient set.
Markowitz(1959),AppendixA,showsthatthealgorithmworksevenifthecovari-
ancematrixissingular.
1Pleasecheckifthesentence“Ontheotherhand....”conveystheintendedmeaning.
viii Foreword
IamunderstandablydelightedwiththeresultsofNiedermayerandNiedermayer
(2008), which appear in the present volume, an indication of how amazingly fast
theirvariantofthecriticallinealgorithmiswhencomparedtoalternatemethodsfor
tracingouttheentireefficientfrontier.
Sharpe (1964)Versus Markowitz(2005)
MajorresultsfromSharpe(1964)andLintner(1965)arethat,giventheassumptions
of CAPM, the marketportfoliois a mean-varianceefficientportfolio,and there is
alinearrelationshipbetweentheexcessreturn(expectedreturnminustherisk-free
rate)ofasecurityanditsbeta(regressionagainstmarketreturn).Markowitz(2005)
pointsoutthatwhen investorscannotborrowall theywantat the risk-freerate or,
alternatively,cannotshortandusetheproceedstobuylong(which,infact,isnota
realisticmodelofshortsales),thentypicallythemarketisnotanefficientportfolio,
andtypicallythereisnolinearrelationshipbetweenexcessreturnandbeta.
Sharpe (1964)andMossin(1966)Versus Markowitz(2008)
The assumptions of CAPM imply a linear relationship between excess return and
the beta of a security, defined as its regression against the return on the market
portfolio. This was interpreted as the investor being paid to bear risk. In fact, as
explainedin Markowitz (2008),causation goesin the other direction.The CAPM
assumptions(as formalizedby Mossin)imply thatsecuritieswith higherexpected
returns per share have their prices bid up so they become a larger fraction of the
marketportfolio.Specifically,theirpricesarebiduptothepointwheretheexcess
returnperdollarinvestedis proportionalto the regressionof eachsecurityagainst
themarketportfolio,andwherethemarketportfolio(ofcourse)includesthesecurity
itself.
MarkowitzandvanDijk(2003)andKritzman, Myrgren
and Page(2007)
As explained in Chap. 13 of Markowitz (1959), mean-variance analysis assumes
perfectlyliquidassets.Thisisnotrealistic,especiallyinthefaceofunrealizedcap-
italgains.Markowitz(1959)conjecturesvariousproceduresthatcanbeusedinthe
case of various kinds of illiquidities. But these are unevaluated conjectures only.
Markowitz and van Dijk present a heuristic for dealing with problems with illiq-
uid assets and changingprobability distributions. They show that their “quadratic
surrogate”heuristicworksremarkablywellfora problemthatissmallenoughfor
Foreword ix
itsoptimumsolutiontobecomputed.Kritzman,MyrgrenandPage(2007)testthe
heuristiconsomelarger,practicalproblemsandfindthatitworksremarkablywell
onthesealso.
HarryMarkowitz
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