corporate valuation vietnam - final1.pdf
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Jun 17, 2024
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About This Presentation
Corporate valuation materials
Slide Content
Books suggestions
⚫ArnoldG.,TheHandbookofCorporateFinance,PrenticeHall,2004
⚫DamodaranA.,CorporateFinance:TheoryandPractice(2
nd
Edition),Willey
seriesinfinance,2001
⚫DamodaranA.,TheDarkSideofValuation:ValuingYoung,Distressed,and
ComplexBusinesses(2
nd
Edition),2009
⚫DePamphilisD.,Mergers,AcquisitionsandotherRestructuringActivities,
AcademicPress,2001
⚫FernandezP.,“Valuationofbrandsandintellectualcapital”,workingpaper,2001
⚫FernandezP.,CarabiasJ.M.,“96CommonErrorsinCompanyValuations”,
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=895151,2006
⚫KollerT.,GoedhartM.,WesselsD.,Valuation:MeasuringandManagingthe
ValueofCompanies,5
th
Edition(WileyFinance),2010
⚫PalepuK.G.,HealyP.M.,PeekE.,BusinessAnalysisandValuation,South
WesternEditions,2008
⚫ThauvronA.,Évaluationd’entreprises,Economica,2005
⚫Vernimmen(2005),Financed’entreprise,Dalloz
⚫ArnoldG.,TheHandbookofCorporateFinance,PrenticeHall,2004
⚫DamodaranA.,CorporateFinance:TheoryandPractice(2
nd
Edition),Willey
seriesinfinance,2001
⚫DamodaranA.,TheDarkSideofValuation:ValuingYoung,Distressed,and
ComplexBusinesses(2
nd
Edition),2009
⚫DePamphilisD.,Mergers,AcquisitionsandotherRestructuringActivities,
AcademicPress,2001
⚫FernandezP.,“Valuationofbrandsandintellectualcapital”,workingpaper,2001
⚫FernandezP.,CarabiasJ.M.,“96CommonErrorsinCompanyValuations”,
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=895151,2006
⚫KollerT.,GoedhartM.,WesselsD.,Valuation:MeasuringandManagingthe
ValueofCompanies,5
th
Edition(WileyFinance),2010
⚫PalepuK.G.,HealyP.M.,PeekE.,BusinessAnalysisandValuation,South
WesternEditions,2008
⚫ThauvronA.,Évaluationd’entreprises,Economica,2005
⚫Vernimmen(2005),Financed’entreprise,Dalloz
Cosmetic
Cosmeticdifferencecanbeuseofdifferentwordtorefertothe
sameitems.Afewexamplesareasfollows,internationalterm
followedbyU.S.counterpart
3
Cosmeticdifferencecanbeuseofdifferentwordtorefertothe
sameitems.Afewexamplesareasfollows,internationalterm
followedbyU.S.counterpart
3
Contents
Introduction
1.The Cost of Capital
2.Income Models
3.Method of Comparables
4. Residual Income Model
5.The Value of Control
Introduction
1.The Cost of Capital
2.Income Models
3.Method of Comparables
4. Residual Income Model
5.The Value of Control
Introduction
⚫1.Astraightforwardviewofeconomictransformations:thenew
shareholdersview(transformatingbeliefsandtransformating
behaviors)
⚫2.Understandtheproblemofvaluation
5
⚫1.Astraightforwardviewofeconomictransformations:thenew
shareholdersview(transformatingbeliefsandtransformating
behaviors)
⚫2.Understandtheproblemofvaluation
5
1. Shareholders revolution around the 80’s
➢Theultimatetestofmanagementisbecomingvaluecreation:topqualityCEOs
deliverconsistentlysuperiorshareholderreturns:Maximisinggoodgrowth
andeliminatingbadgrowthisessentialtoachievingthegoverningobjective
➢Why:ERISA(earning-retirement-income-security-art)(1974)andthe73
petroleumchocforadvancedeconomies
➢ImportanceofCoreBusiness:diversifiedriskmanageddirectlyby
shareholders
➢CorporateGovernanceistheruleinUSinthe80’sandEuropeinthe90’s
➢Financerulestheworld!
Focusing on
Shareholder
Value
Transforming
Beliefs
Transforming
Behaviour
Transforming
Management
Performance
Derivatives
Forex
Financial Transactions
Real Economy
Total
699,0
384,4
39,4
32,3
1 155,0
Total World
Transations
10
12
$ (2002)
➢Theultimatetestofmanagementisbecomingvaluecreation:topqualityCEOs
deliverconsistentlysuperiorshareholderreturns:Maximisinggoodgrowth
andeliminatingbadgrowthisessentialtoachievingthegoverningobjective
➢Why:ERISA(earning-retirement-income-security-art)(1974)andthe73
petroleumchocforadvancedeconomies
➢ImportanceofCoreBusiness:diversifiedriskmanageddirectlyby
shareholders
➢CorporateGovernanceistheruleinUSinthe80’sandEuropeinthe90’s
➢Financerulestheworld!
Focusing on
Shareholder
Value
Transforming
Beliefs
Transforming
Behaviour
Transforming
Management
Performance
Derivatives
Forex
Financial Transactions
Real Economy
Total
699,0
384,4
39,4
32,3
1 155,0
Total World
Transations
10
12
$ (2002)
➢Changeorganisationstructuretoensureclarityofaccountabilityforvalue
e.g,accountabilityformarketsegments
➢Changeorganisationstructuretoensurenewlearningaboutnewsourcesof
competitiveadvantage
➢Delegateaccountabilityforvalueascloseaspossibletothecustomerand
competition
➢Avoidexcessivecentralisation
Single
Business
Market-Based
Segmentation
Multiple
Product
Specialist
Value Centres
Value Centres
for Products
and Customer
Relationships
Move from managing the value of the Group as one business,
to managing the value of the Group through multiple “value centres”
Organisation
Structure
Organization structure
e.g,accountabilityformarketsegments
➢Changeorganisationstructuretoensurenewlearningaboutnewsourcesof
competitiveadvantage
➢Delegateaccountabilityforvalueascloseaspossibletothecustomerand
competition
➢Avoidexcessivecentralisation
Single
Business
Market-Based
Segmentation
Multiple
Product
Specialist
Value Centres
Value Centres
for Products
and Customer
Relationships
Move from managing the value of the Group as one business,
to managing the value of the Group through multiple “value centres”
Organisation
Structure
Organization structure
Why it is important for You ?
8-100
0
100
200
300
400
500
600
700
800
1978 1982 1986 1990 1994 1998 2002 2006
Flux privˇs
Flux publics
Donnˇes IIF
Origine des flux (USD milliards)
AsianCrisis
Privatevs Public funds(USD Bilions)
8-100
0
100
200
300
400
500
600
700
800
1978 1982 1986 1990 1994 1998 2002 2006
Flux privˇs
Flux publics
Donnˇes IIF
Origine des flux (USD milliards)
AsianCrisis
Privatevs Public funds(USD Bilions)
Why it is important for Corporate Valuation ?
Core Business : Dupont Analysis & Return on EquityLeverage Turnover Asset Total Margin Profit
Equity
Assets Total
Assets Total
Sales
Sales
IncomeNet
Equity
IncomeNet
=ROE
=
=
MinoringBook Value and BoostingValue Creation
Core Business : Dupont Analysis & Return on EquityLeverage Turnover Asset Total Margin Profit
Equity
Assets Total
Assets Total
Sales
Sales
IncomeNet
Equity
IncomeNet
=ROE
=
=
MinoringBook Value and BoostingValue Creation
Focus on the Fixed-Asset Turnover Ratio
This ratio measures how effectively a company manages its fixed assets to
generate revenue.
Net sales
Averagefixed assets
Fixed asset
turnover
ratio
=
Dell generates nearly two times more sales dollars for
each dollar invested in fixed assets than Apple does.
= 15.4 $57,420
($2,409 + $1,993)/2
= 26
$24,006
($1,832 + $1,281)/22007 2006 2007 2006
Property, plant, and
equipment (net) 2,409$ 1,993$ 1,832$ 1,281$
Net sales 57,420 24,006
Dell Apple
This ratio measures how effectively a company manages its fixed assets to
generate revenue.
Net sales
Averagefixed assets
Fixed asset
turnover
ratio
=
Dell generates nearly two times more sales dollars for
each dollar invested in fixed assets than Apple does.
= 15.4 $57,420
($2,409 + $1,993)/2
= 26
$24,006
($1,832 + $1,281)/22007 2006 2007 2006
Property, plant, and
equipment (net) 2,409$ 1,993$ 1,832$ 1,281$
Net sales 57,420 24,006
Dell Apple
2. Valuation Concepts
Thereisnosinglevalue.Valuecanchangedramaticallydependingonthe
answerstothesequestions:
➢a.FairValueandValues
➢b.SomeValuation“Myths”
➢c.WhatisbeingvaluedandWhyisitbeingvalued?
➢d.Whatistheappropriatepremiseofvalue?
➢e.Howwillyouvalueit?
➢f.Whatdiscountsorpremiumsareappropriate?
➢g.Byersandsellersvalueperspectives?
➢h.Valuation–TheBigPicture
Thereisnosinglevalue.Valuecanchangedramaticallydependingonthe
answerstothesequestions:
➢a.FairValueandValues
➢b.SomeValuation“Myths”
➢c.WhatisbeingvaluedandWhyisitbeingvalued?
➢d.Whatistheappropriatepremiseofvalue?
➢e.Howwillyouvalueit?
➢f.Whatdiscountsorpremiumsareappropriate?
➢g.Byersandsellersvalueperspectives?
➢h.Valuation–TheBigPicture
Fair Value
a. Fair Value and Values
=
Investment Value
Source: IFRS 3 Appendix A
Purchase Price
Willing buyer & willing seller
Hypothetical buyer concept
Stand-alone valuation
“Fair Value is the amount for which an
asset could be exchanged, or a liability
settled between knowledgeable, willing
parties in an arm’s length transaction.“
•Synergisticorstrategicvalue
•Willingbuyerisnotahypothetical
marketplacebuyerbutratherisa
particularbuyerwithspecific
expectationsaboutfutureevents,
costofcapital,taxation,andother
issues
•Theselleriscompelledtosell
•Thebuyermaybeawillingbuyer,but
thesellermustsellunwillingly
Liquidation Value (net realisable value)
including Forced Sale
For example
a. Fair Value and Values
=
Investment Value
Source: IFRS 3 Appendix A
Purchase Price
Willing buyer & willing seller
Hypothetical buyer concept
Stand-alone valuation
“Fair Value is the amount for which an
asset could be exchanged, or a liability
settled between knowledgeable, willing
parties in an arm’s length transaction.“
•Synergisticorstrategicvalue
•Willingbuyerisnotahypothetical
marketplacebuyerbutratherisa
particularbuyerwithspecific
expectationsaboutfutureevents,
costofcapital,taxation,andother
issues
•Theselleriscompelledtosell
•Thebuyermaybeawillingbuyer,but
thesellermustsellunwillingly
Liquidation Value (net realisable value)
including Forced Sale
For example
b. Some Valuation “Myths”
1.Sincevaluationmodelsarequantitative,valuationisobjective
•modelsarequantitative,inputsaresubjective
2.Awell-researched,well-donemodelistimeless
•valueswillchangeasnewinformationisrevealed
3.Agoodvaluationprovidesapreciseestimateofvalue
•avaluationbynecessityinvolvesmanyassumptions
4.Themorequantitativeamodel,thebetterthevaluation
•thequalityofavaluationwillbedirectlyproportionaltothetimespent
incollectingthedataandinunderstandingthefirmbeingvalued
5.Themarketisgenerallywrong
•thepresumptionshouldbethatthemarketiscorrectandthatitisup
totheanalysttoprovetheirvaluationoffersabetterestimate
Source:A.Damodaran,“InvestmentValuation:ToolsandTechniquesforDeterminingThe
ValueofAnyAsset”
1.Sincevaluationmodelsarequantitative,valuationisobjective
•modelsarequantitative,inputsaresubjective
2.Awell-researched,well-donemodelistimeless
•valueswillchangeasnewinformationisrevealed
3.Agoodvaluationprovidesapreciseestimateofvalue
•avaluationbynecessityinvolvesmanyassumptions
4.Themorequantitativeamodel,thebetterthevaluation
•thequalityofavaluationwillbedirectlyproportionaltothetimespent
incollectingthedataandinunderstandingthefirmbeingvalued
5.Themarketisgenerallywrong
•thepresumptionshouldbethatthemarketiscorrectandthatitisup
totheanalysttoprovetheirvaluationoffersabetterestimate
Source:A.Damodaran,“InvestmentValuation:ToolsandTechniquesforDeterminingThe
ValueofAnyAsset”
➢Transactions
➢Buying/Selling/Merging
➢Privatization
➢Strategic internal decisions
➢ESOPs
➢Tax
➢Estate, gift & inheritance taxes
➢Estate recapitalizations
➢Charitable contributions
➢Buy/Sell agreements
➢Litigation
➢Dissolution of corporation or
partnership
➢Review/critique of another
expert’s report
➢Damages
➢Lost profits
➢Marital dissolution
➢Certain assets
➢Interest-bearing debt
➢Preferred stock
➢Common stock
➢Controlling
interest
➢Non-controlling
interest
➢Enterprise Value
Why is it being
valued?
What is being
valued?
c. What is being valued and Why is it being
valued ?
➢Cash flow generating
ability
➢Risks associated with
achieving the projected
cash flows
➢Value of the net assets
owned by the business
➢Right to vote and
influence business
decisions
➢Marketability of
ownership position
Special
consideration ?
➢Buying/Selling/Merging
➢Privatization
➢Strategic internal decisions
➢ESOPs
➢Tax
➢Estate, gift & inheritance taxes
➢Estate recapitalizations
➢Charitable contributions
➢Buy/Sell agreements
➢Litigation
➢Dissolution of corporation or
partnership
➢Review/critique of another
expert’s report
➢Damages
➢Lost profits
➢Marital dissolution
➢Certain assets
➢Interest-bearing debt
➢Preferred stock
➢Common stock
➢Controlling
interest
➢Non-controlling
interest
➢Enterprise Value
Why is it being
valued?
What is being
valued?
c. What is being valued and Why is it being
valued ?
➢Cash flow generating
ability
➢Risks associated with
achieving the projected
cash flows
➢Value of the net assets
owned by the business
➢Right to vote and
influence business
decisions
➢Marketability of
ownership position
Special
consideration ?
⚫Valueasagoingconcern
⚫Assetsincontinueduseasa
viablebusinessenterprise
⚫Valueasanassemblageofassets
(reorganization)
⚫Includeassetsnotincurrentuse
intheproductionofincomeand
notasagoing-concernbusiness
enterprise
⚫Valueasanorderlydisposition
⚫Assetssoldindividuallywith
normalexposuretothemarket
⚫Valueasaforcedliquidation
⚫Assetssoldindividuallywith
limitedornoexposuretothe
market
d. What is the appropriate premise of value ?
1.Theverticalscaleestablishestheconditions
underwhichtheassetisbeingdisposed,such
asliquidation,orderlydisposal,reorganization
orgoingconcern.
2.Thehorizontalscalemeasurestimeinmonthly
increments.
CONTEXT + TIME = VALUE
Source : CONSOR Intellectual Asset Management
⚫Assetsincontinueduseasa
viablebusinessenterprise
⚫Valueasanassemblageofassets
(reorganization)
⚫Includeassetsnotincurrentuse
intheproductionofincomeand
notasagoing-concernbusiness
enterprise
⚫Valueasanorderlydisposition
⚫Assetssoldindividuallywith
normalexposuretothemarket
⚫Valueasaforcedliquidation
⚫Assetssoldindividuallywith
limitedornoexposuretothe
market
d. What is the appropriate premise of value ?
1.Theverticalscaleestablishestheconditions
underwhichtheassetisbeingdisposed,such
asliquidation,orderlydisposal,reorganization
orgoingconcern.
2.Thehorizontalscalemeasurestimeinmonthly
increments.
CONTEXT + TIME = VALUE
Source : CONSOR Intellectual Asset Management
e. How will you value it ?
2 (principal) Principles of Valuation
⚫BookValue
⚫Depreciatedvalueofassetsminus
outstandingliabilities
⚫Adjustednetassetvaluemethod
adjustsallindividualassetsand
liabilitiestomarketvalue.
⚫LiquidationValue
⚫Amountthatwouldberaisedifall
assetsweresoldindependently
⚫MarketValue(P)
⚫Valueaccordingtomarketprice
ofoutstandingstock
⚫Relativevaluationestimatesthe
valueofanassetbylookingat
thepricingof'comparable'assets
relativetoacommonvariablelike
earnings,cashflows,bookvalue
orsales.
⚫IntrinsicValue(V)=Income
approach
⚫NPVoffuturecashflows
(discountedatinvestors’required
rateofreturn)
Looks Backward Looks Forwards
MarketValue > IntrinsicValue > Book Value > Liquidation Value
2 (principal) Principles of Valuation
⚫BookValue
⚫Depreciatedvalueofassetsminus
outstandingliabilities
⚫Adjustednetassetvaluemethod
adjustsallindividualassetsand
liabilitiestomarketvalue.
⚫LiquidationValue
⚫Amountthatwouldberaisedifall
assetsweresoldindependently
⚫MarketValue(P)
⚫Valueaccordingtomarketprice
ofoutstandingstock
⚫Relativevaluationestimatesthe
valueofanassetbylookingat
thepricingof'comparable'assets
relativetoacommonvariablelike
earnings,cashflows,bookvalue
orsales.
⚫IntrinsicValue(V)=Income
approach
⚫NPVoffuturecashflows
(discountedatinvestors’required
rateofreturn)
Looks Backward Looks Forwards
MarketValue > IntrinsicValue > Book Value > Liquidation Value
17
Book value Vs. Market value
⚫Marketvalueisorientedtovalueinuseoreconomicvalue:theabilityto
generatefuturecashflows.
⚫Shareholdersandmanagersareconcernedaboutthemarketvalueof
theirstock,sotheirfocusisonamarketvaluedrivenbalancesheet.
⚫Equityandasset“MarketValues”areusuallyhigherthantheir“Book
Values”.Marketvaluesofassetsandliabilitiesaredrivenbyeconomic
valuefactors.Seldomaretheythesame.
Importance of the life cycle and the owner strategy
Example : Google
• Market value (Jan 25 2011) $197 billion (price per share x number of shares)
• Book value (Sep 30 2010) $43 billion
Book value Vs. Market value
⚫Marketvalueisorientedtovalueinuseoreconomicvalue:theabilityto
generatefuturecashflows.
⚫Shareholdersandmanagersareconcernedaboutthemarketvalueof
theirstock,sotheirfocusisonamarketvaluedrivenbalancesheet.
⚫Equityandasset“MarketValues”areusuallyhigherthantheir“Book
Values”.Marketvaluesofassetsandliabilitiesaredrivenbyeconomic
valuefactors.Seldomaretheythesame.
Importance of the life cycle and the owner strategy
Example : Google
• Market value (Jan 25 2011) $197 billion (price per share x number of shares)
• Book value (Sep 30 2010) $43 billion
⚫Earnings
AssumeWACC=
(10%x1500)+(10%x500)=10%
(1500+500)
Discountedearnings=
Net Profit/Discount rate
150/10 % = 1 500
Income statement (1)
First case : BV = MV
⚫BV
Assets 2000
Oustandingliabilities-500
BV 1500
HERE, ROE= COSTOF CAPITAL
(NO DESTRUCTION OR VALUE CREATED)
CurrentAssets
FixedAssets
800
1 200
Liabilities
Equities
500
1 500
Sales
Expenses
Net
earnings
1 650
(1500)
150
AssumeWACC=
(10%x1500)+(10%x500)=10%
(1500+500)
Discountedearnings=
Net Profit/Discount rate
150/10 % = 1 500
Income statement (1)
First case : BV = MV
⚫BV
Assets 2000
Oustandingliabilities-500
BV 1500
HERE, ROE= COSTOF CAPITAL
(NO DESTRUCTION OR VALUE CREATED)
CurrentAssets
FixedAssets
800
1 200
Liabilities
Equities
500
1 500
Sales
Expenses
Net
earnings
1 650
(1500)
150
⚫Earnings
AssumeWACC=10%
(10%x1543)+(10%x500)=10%
(1543+500)
Discountedearnings=
Net Profit/Discount rate
193/10 % = 1 930
Income statement (2)
Second case: BV < MV
⚫BV
Assets 2043
Oustandingliabilities-500
BV 1543
MV = BV + VALUE CREATED (ABNORMAL EARNINGS)
CurrentAssets
FixedAssets
843
1 200
Liabilities
Equities
500
1 543
Becareful:“Profits”recordincome
andexpensesatthetimeofsales,
notwhenthecashexchanges
actuallyoccur
“Profits”donotconsiderchangesin
workingcapital
Sales
Expenses
Net earnings
1 650
(1457)
193
AssumeWACC=10%
(10%x1543)+(10%x500)=10%
(1543+500)
Discountedearnings=
Net Profit/Discount rate
193/10 % = 1 930
Income statement (2)
Second case: BV < MV
⚫BV
Assets 2043
Oustandingliabilities-500
BV 1543
MV = BV + VALUE CREATED (ABNORMAL EARNINGS)
CurrentAssets
FixedAssets
843
1 200
Liabilities
Equities
500
1 543
Becareful:“Profits”recordincome
andexpensesatthetimeofsales,
notwhenthecashexchanges
actuallyoccur
“Profits”donotconsiderchangesin
workingcapital
Sales
Expenses
Net earnings
1 650
(1457)
193
BV Problem : failing to overlook Intangible
Assets and, moreover, intellectual capital
✓Intangible Assets : valuable holdings that have no physical form
➢Gapbetweenbookvaluespershareandstockprices:physicalassetsaccount
forabout15%oftotalassetsandhightechfirmsfeatureevenwidergap
➢Traditionalmethodsfailtocapturerapidgrowth
➢Difficultyidentifyingandmeasuringvalueof:
✓Brands(Coca-Cola)
✓Distributionnetworks(Walmart)
✓R&Dexpenditures(IBM)
Watch accountingrules
Assets and, moreover, intellectual capital
✓Intangible Assets : valuable holdings that have no physical form
➢Gapbetweenbookvaluespershareandstockprices:physicalassetsaccount
forabout15%oftotalassetsandhightechfirmsfeatureevenwidergap
➢Traditionalmethodsfailtocapturerapidgrowth
➢Difficultyidentifyingandmeasuringvalueof:
✓Brands(Coca-Cola)
✓Distributionnetworks(Walmart)
✓R&Dexpenditures(IBM)
Watch accountingrules
Comparing US
GAAP and IFRSs :
Intangible Assets
21
GAAP and IFRSs :
Intangible Assets
21
‘Intellectualcapitalisthegroupofknowledgeassetsthatareattributedtoan
organisationandmostsignificantlycontributetoanimprovedcompetitivepositionof
thisorganisationbyaddingvaluetodefinedkeystakeholders’(MarrandSchiuma,
2001)
Classification of intellectualcapital
Humancapital Relational(customer) capital
Know-how
Education
Vocationalqualification
Work-relatedknowledge
Work-relatedcompetenciesEntrepreneurial
elan, innovativeness, proactive and reactive
abilities, changeability
Brands
Customers
Customer loyalty
Companynames
Distribution channels
Business collaborations
Licensingagreements
Favourablecontracts
Franchising agreements
Organisational(structural) capital
Intellectualproperty
Patents
Copyrights
Trade secrets
Trademarks
Infrastructure assets
Management philosophy
Corporateculture
Management processes
Information systems
Networking systems
Financial relations
organisationandmostsignificantlycontributetoanimprovedcompetitivepositionof
thisorganisationbyaddingvaluetodefinedkeystakeholders’(MarrandSchiuma,
2001)
Classification of intellectualcapital
Humancapital Relational(customer) capital
Know-how
Education
Vocationalqualification
Work-relatedknowledge
Work-relatedcompetenciesEntrepreneurial
elan, innovativeness, proactive and reactive
abilities, changeability
Brands
Customers
Customer loyalty
Companynames
Distribution channels
Business collaborations
Licensingagreements
Favourablecontracts
Franchising agreements
Organisational(structural) capital
Intellectualproperty
Patents
Copyrights
Trade secrets
Trademarks
Infrastructure assets
Management philosophy
Corporateculture
Management processes
Information systems
Networking systems
Financial relations
Valuation issues across the life cycle
Value
Temps
CreationRapid
expansion
High
Growth
Mature
Growth
Decline
MV
BV
Value
Temps
CreationRapid
expansion
High
Growth
Mature
Growth
Decline
MV
BV
f. What discounts or premiums are
appropriate?
Valuemaybeinfluencedbyextenuatingfactors
⚫Premiums
⚫Control
⚫Strategicacquisition
⚫Discounts
⚫Lackofcontrol
⚫Lackofmarketability
⚫Keyperson
⚫Known(orpotential)environmentalliability
⚫Pendinglitigation
⚫Concentrationofcustomerbaseorsupplierbase
appropriate?
Valuemaybeinfluencedbyextenuatingfactors
⚫Premiums
⚫Control
⚫Strategicacquisition
⚫Discounts
⚫Lackofcontrol
⚫Lackofmarketability
⚫Keyperson
⚫Known(orpotential)environmentalliability
⚫Pendinglitigation
⚫Concentrationofcustomerbaseorsupplierbase
g. Byers and sellers value perspectives ?
25
Theseller’smanagementteammaintainedthatthebrand’svalue(includingthe
intellectualcapital)underitsmanagementwas337million.Thebuyer’smanagementteam
wouldusethecompany’sassetsandthebrandinadifferentwayfromtheseller’s
managementteam.
Itisalsoobviousthatthevalueofthesharesandthebrandwouldbedifferentforanother
prospectivebuyer.Finally,thesharesweresoldfor1.05billioneuros.
Value for whom and
for what purpose ?
25
Theseller’smanagementteammaintainedthatthebrand’svalue(includingthe
intellectualcapital)underitsmanagementwas337million.Thebuyer’smanagementteam
wouldusethecompany’sassetsandthebrandinadifferentwayfromtheseller’s
managementteam.
Itisalsoobviousthatthevalueofthesharesandthebrandwouldbedifferentforanother
prospectivebuyer.Finally,thesharesweresoldfor1.05billioneuros.
Value for whom and
for what purpose ?
LA BECOB
750 millions francs
Economic Value
450 millions
Relational Capital
300 millions
Crony (French) Capitalism
No Due Diligence !
Bernard Henri Levy François Pinault
Source : Nicolas Beau et Olivier Toscer, 2006
Mysterious purposes ?
750 millions francs
Economic Value
450 millions
Relational Capital
300 millions
Crony (French) Capitalism
No Due Diligence !
Bernard Henri Levy François Pinault
Source : Nicolas Beau et Olivier Toscer, 2006
Mysterious purposes ?
h. Valuation –The Big Picture
Accounting and Financial Analysis
⚫Alwaysbesuspicious:Accountinganalysis:Studyingtransactionsand
eventsjudginghowaccountingpoliciesaffectfinancialstatements,andadjusting
FStobetterreflecttheunderlyingeconomicsandmakethemmoreamenableto
analysis.
⚫Warren’sposition:Financialanalysisistheuseoffinancialstatementsto
analyzeacompany’sfinancialpositionandperformanceandtoassessfuture
financialperformance,andincludesanexaminationofprofitability,risk,andcash
flows(sourcesandusesoffunds).Itwillanswerquestionsregardingafirm’spast,
presentandfuturesituation,including
⚫Howprofitableisthecompany?
⚫Didearningsmeetanalystforecasts?
⚫Howstrongisthecompany’sfinancialposition?
⚫Whatare[thecompany’s]sourcesofprofitability?
⚫Doesthecompanyhavetheresourcestosucceedandgrow?
⚫Doesthecompanyhaveresourcestoinvestinnewprojects?
⚫Whatisthecompany’sfutureearningpower?
⚫Alwaysbesuspicious:Accountinganalysis:Studyingtransactionsand
eventsjudginghowaccountingpoliciesaffectfinancialstatements,andadjusting
FStobetterreflecttheunderlyingeconomicsandmakethemmoreamenableto
analysis.
⚫Warren’sposition:Financialanalysisistheuseoffinancialstatementsto
analyzeacompany’sfinancialpositionandperformanceandtoassessfuture
financialperformance,andincludesanexaminationofprofitability,risk,andcash
flows(sourcesandusesoffunds).Itwillanswerquestionsregardingafirm’spast,
presentandfuturesituation,including
⚫Howprofitableisthecompany?
⚫Didearningsmeetanalystforecasts?
⚫Howstrongisthecompany’sfinancialposition?
⚫Whatare[thecompany’s]sourcesofprofitability?
⚫Doesthecompanyhavetheresourcestosucceedandgrow?
⚫Doesthecompanyhaveresourcestoinvestinnewprojects?
⚫Whatisthecompany’sfutureearningpower?
Conduct of the Valuation Engagement
—Ownership Information
⚫The valuation analyst should obtain and analyze sufficient ownership
information in order to:
⚫Understand any other matters that may affect value, such as:
⚫For business interests
▪Shareholder agreements
▪Partnership agreements
▪Operating agreements
▪Voting trust agreements
▪Buy-sell agreements
▪Loan covenants
▪Restrictions and other contractual obligations
⚫For intangible assets
▪Licensing agreements
▪Sublicense agreements
▪Nondisclosure agreements
▪Development rights
▪Commercialization or exploitation rights
▪Other obligations
29
—Ownership Information
⚫The valuation analyst should obtain and analyze sufficient ownership
information in order to:
⚫Understand any other matters that may affect value, such as:
⚫For business interests
▪Shareholder agreements
▪Partnership agreements
▪Operating agreements
▪Voting trust agreements
▪Buy-sell agreements
▪Loan covenants
▪Restrictions and other contractual obligations
⚫For intangible assets
▪Licensing agreements
▪Sublicense agreements
▪Nondisclosure agreements
▪Development rights
▪Commercialization or exploitation rights
▪Other obligations
29
Chapter 1.
The Cost of Capital
The Cost of Capital
The Cost of Capital
⚫1.1. Once Again : What is Value Creation ?
⚫1.2. The Cost of Equity : the Capital Asset Pricing Model
⚫1.3. Estimating CAPM items
⚫1.4. Evolution from the CAPM
31
⚫1.1. Once Again : What is Value Creation ?
⚫1.2. The Cost of Equity : the Capital Asset Pricing Model
⚫1.3. Estimating CAPM items
⚫1.4. Evolution from the CAPM
31
32
⚫A Risk must be rewarded
⚫For usual claimants the hurdle rate
on invested capital must exceed
the return on capital employed
1.1.Once Again: WhatisValue
Creation?
⚫A Risk must be rewarded
⚫For usual claimants the hurdle rate
on invested capital must exceed
the return on capital employed
1.1.Once Again: WhatisValue
Creation?
Capital Employed and Invested Capital ?
33
Current Assets :
-Cash
-Marketable Securities
-Accounts & Notes Receivable
-Inventory
Fixed Assets :
-Equipment
-Building
-Land
Assets
Liabilities &
Stockholder’s Equity
Current Liabilities :
-Accounts Payable
-Notes Payable
-Accrued Tax
Long-term Liabilities :
-Long-term bank loans
-Bonds
Stockholder’s Equity :
Balance Sheet
Current
Working Capital
Fixed Assets
Net cash
[Long-term bank loans
-cash]
Equity
Operational
(Capital employed)
Financing
(Invested Capital)
Value Addedwhen
Return on Capital Employed> (Hurdle) Return on investedCapital
33
Current Assets :
-Cash
-Marketable Securities
-Accounts & Notes Receivable
-Inventory
Fixed Assets :
-Equipment
-Building
-Land
Assets
Liabilities &
Stockholder’s Equity
Current Liabilities :
-Accounts Payable
-Notes Payable
-Accrued Tax
Long-term Liabilities :
-Long-term bank loans
-Bonds
Stockholder’s Equity :
Balance Sheet
Current
Working Capital
Fixed Assets
Net cash
[Long-term bank loans
-cash]
Equity
Operational
(Capital employed)
Financing
(Invested Capital)
Value Addedwhen
Return on Capital Employed> (Hurdle) Return on investedCapital
Capital Employed Capital Invested
Fixed Assets
Current
Working Capital
Equity
Net cash
Equity Cost
k
e
Debt Cost
k
d
HurdleRate on InvestedCapital
= the Costof Capital
Value is created when a company is able to get a
return on its assets higher than its WACC
Fixed Assets
Current
Working Capital
Equity
Net cash
Equity Cost
k
e
Debt Cost
k
d
HurdleRate on InvestedCapital
= the Costof Capital
Value is created when a company is able to get a
return on its assets higher than its WACC
The weighted average cost of capital (WACC)
⚫The weighted average cost of capital is the market-based weighted average of
the after-tax cost of debt and cost of equity :
WACC = D/V*k
d(1 − T
m)+ E/V*k
e
⚫where
⚫D/V = Target level of debt to enterprise value using market-based values
⚫E/V = Target level of equity to enterprise value using market-based values
⚫k
d= Costof debt
⚫k
e= Costof equity
⚫T
m= Company’s marginal income tax rate
35
⚫The weighted average cost of capital is the market-based weighted average of
the after-tax cost of debt and cost of equity :
WACC = D/V*k
d(1 − T
m)+ E/V*k
e
⚫where
⚫D/V = Target level of debt to enterprise value using market-based values
⚫E/V = Target level of equity to enterprise value using market-based values
⚫k
d= Costof debt
⚫k
e= Costof equity
⚫T
m= Company’s marginal income tax rate
35
Value Creation
Value Created = (Return On Investment -Cost of Capital) XCapital employed
Dependent Upon :
⚫Cost of Capital Spread (see chapter 1)
⚫Duration of Spread
⚫Amount of Capital Employed
Also called :
✓Residual income
✓Abnormal earnings (assuming that over the long term the firm is expected to earn
its cost of capital (from all sources), any earnings in excess of the cost of capital
can be termed abnormal earnings.
One example of several competing commercial implementations is Economic Value
Added(EVA®) trademarked by Stern Stewart & Company.
EVA® = NOPAT –(C% х TC)
NOPAT is the firm’s net operating profit after taxes,
C% is the cost of capital and
TC is total capital.
Value Created = (Return On Investment -Cost of Capital) XCapital employed
Dependent Upon :
⚫Cost of Capital Spread (see chapter 1)
⚫Duration of Spread
⚫Amount of Capital Employed
Also called :
✓Residual income
✓Abnormal earnings (assuming that over the long term the firm is expected to earn
its cost of capital (from all sources), any earnings in excess of the cost of capital
can be termed abnormal earnings.
One example of several competing commercial implementations is Economic Value
Added(EVA®) trademarked by Stern Stewart & Company.
EVA® = NOPAT –(C% х TC)
NOPAT is the firm’s net operating profit after taxes,
C% is the cost of capital and
TC is total capital.
An example of residual income
⚫AxisManufacturingCompany(AMC)hastotalassetsof€2,000,000financed50%withdebt
and50%withequitycapital.WACC=12%.NetincomeforAMCcanbedeterminedas
follows:
EBIT €200,000
Less:InterestExpense 70,000
Pre-TaxIncome €130,000
IncomeTaxExpense 39,000
NetIncome €91,000
⚫Whatisit’sresidualincome?Oneapproachistocomputethecostofcapital(intermsof
currency),whichwetermacapitalcharge,andsubtractthisfromnetincome,asfollows:
CapitalCharge=CapitalхCostofCapitalin%
CostofCapital=€2,000,000х12%=€240,000
NetIncome €91,000
CapitalCharge 240,000
ResidualIncome €(149,000)
AMC did not earn enough to cover the cost of capital.
As a result, it has negative residual income.
⚫AxisManufacturingCompany(AMC)hastotalassetsof€2,000,000financed50%withdebt
and50%withequitycapital.WACC=12%.NetincomeforAMCcanbedeterminedas
follows:
EBIT €200,000
Less:InterestExpense 70,000
Pre-TaxIncome €130,000
IncomeTaxExpense 39,000
NetIncome €91,000
⚫Whatisit’sresidualincome?Oneapproachistocomputethecostofcapital(intermsof
currency),whichwetermacapitalcharge,andsubtractthisfromnetincome,asfollows:
CapitalCharge=CapitalхCostofCapitalin%
CostofCapital=€2,000,000х12%=€240,000
NetIncome €91,000
CapitalCharge 240,000
ResidualIncome €(149,000)
AMC did not earn enough to cover the cost of capital.
As a result, it has negative residual income.
ROCE (capital employed) and WACC
38
Overthelast15years,thelargestEuropeanlistedgroups,registeredspreadsbetween
0.1%(1994)and3.9%(2006).Inanutshell,thisisnotimpossiblebutveryhard,evenfor
themostpowerfulgroups,toachieve!
38
Overthelast15years,thelargestEuropeanlistedgroups,registeredspreadsbetween
0.1%(1994)and3.9%(2006).Inanutshell,thisisnotimpossiblebutveryhard,evenfor
themostpowerfulgroups,toachieve!
The Length of Value CreationPeriod
39
SomecompanieshavepeakROCEsthatareveryhighbutofferlittle
sustainability.OthercompanieshavepeakROCEsnearthecostofcapitalbut
cangenerateexcessreturnsoveranextremelylongperiod
39
SomecompanieshavepeakROCEsthatareveryhighbutofferlittle
sustainability.OthercompanieshavepeakROCEsnearthecostofcapitalbut
cangenerateexcessreturnsoveranextremelylongperiod
⚫Initsearlylife,thecompanywasa
pioneerinthecomputerchips(random
accessmemory-RAM).Intelcreatedvalue
fornearly10years,buttheJapanese
governmentmadeRAMahighpriority,
andcompaniessuchasNECandFujitsu
begantofloodthemarketwithsimilar
chipsatlowerprices.
⚫Thepricecompetitionwassointensethat
itnearlydroveInteloutofbusiness.
⚫WithafinancialinfusionfromIBM,the
companyreinventeditself,creatingthenew
“brains”ofthepersonalcomputer.Through
aninformalpartnershipwithMicrosoft,Intel
ledthepersonal-computermicroprocessor
market.
⚫Bythelate1990s,facingincreased
competitionandageneraldownturnin
technology,Intelcouldnolongerpostthe
enormousROCEsofthemid-1990s.
Intel has twice sustained high ROCEs over
the last 30 years
ROCE
measured
as three-
year rolling
average
pioneerinthecomputerchips(random
accessmemory-RAM).Intelcreatedvalue
fornearly10years,buttheJapanese
governmentmadeRAMahighpriority,
andcompaniessuchasNECandFujitsu
begantofloodthemarketwithsimilar
chipsatlowerprices.
⚫Thepricecompetitionwassointensethat
itnearlydroveInteloutofbusiness.
⚫WithafinancialinfusionfromIBM,the
companyreinventeditself,creatingthenew
“brains”ofthepersonalcomputer.Through
aninformalpartnershipwithMicrosoft,Intel
ledthepersonal-computermicroprocessor
market.
⚫Bythelate1990s,facingincreased
competitionandageneraldownturnin
technology,Intelcouldnolongerpostthe
enormousROCEsofthemid-1990s.
Intel has twice sustained high ROCEs over
the last 30 years
ROCE
measured
as three-
year rolling
average
Historically,Johnson&Johnsonhasearnedstrongreturnsoncapitalthroughitspatented
pharmaceuticalsandbrandedconsumerproductslines,suchasTylenolandJohnson’sBaby
Shampoo.Throughstrongbrandsandcapabledistribution,J&Jhasbeenabletomaintaina
pricepremium,eveninthefaceofnewentrantsandalternativeproducts.
41
ROCE
measured
as three-
year rolling
average
Over the past 30 years, Johnson & Johnson has maintained an ROIC
greater than the cost of capital during the entire period
pharmaceuticalsandbrandedconsumerproductslines,suchasTylenolandJohnson’sBaby
Shampoo.Throughstrongbrandsandcapabledistribution,J&Jhasbeenabletomaintaina
pricepremium,eveninthefaceofnewentrantsandalternativeproducts.
41
ROCE
measured
as three-
year rolling
average
Over the past 30 years, Johnson & Johnson has maintained an ROIC
greater than the cost of capital during the entire period
Determinants of the Length of Value CreationPeriod
Size of the firm
Success usually makes
a firm larger. As firms
become larger, it
becomes much more
difficult for them to
maintain high growth
rates
On an other hand, it is
difficult for competitors to
overcome the economies
of scale
Current growth rate
While past growth is not
always a reliable
indicator of future
growth, there is a
correlation between
current growth and future
growth. Thus, a firm
growing at 30% currently
probably has higher
growth and a longer
expected growth period
than one growing 10% a
year now
Barriers to entry and
differential advantages
The question of how long
growth will last and how
high it will be can
therefore be framed as a
question about what the
barriers to entry are, how
long they will stay up and
how strong they will
remain.
Size of the firm
Success usually makes
a firm larger. As firms
become larger, it
becomes much more
difficult for them to
maintain high growth
rates
On an other hand, it is
difficult for competitors to
overcome the economies
of scale
Current growth rate
While past growth is not
always a reliable
indicator of future
growth, there is a
correlation between
current growth and future
growth. Thus, a firm
growing at 30% currently
probably has higher
growth and a longer
expected growth period
than one growing 10% a
year now
Barriers to entry and
differential advantages
The question of how long
growth will last and how
high it will be can
therefore be framed as a
question about what the
barriers to entry are, how
long they will stay up and
how strong they will
remain.
Determinants of the Length of Value CreationPeriod
Boeing Home Depot Infosoft
Firm
Size/Market
Size
Firm has the dominant
market share of a slow-
growing market
Firm has dominant market
share of domestic market,
but is entering new
businesses and new
markets (overseas)
Firm is a small firm in a
market that is
experiencing significant
growth
Current
Excess
Returns
Firm is earning less than its
cost of capital, and has
done so for last 5 years
Firm is earning
substantially more than its
cost of capital
Firm is earning
significant excess
returns
Competitive
Advantages
Huge capital requirements
and technological barriers
to new entrants.
Management record over
the last few years has been
poor
Significant economies of
scale are used to establish
cost advantages over
rivals. Has a management
team that is focused on
growth and efficiency
Has both a good product
and good software
engineers. Competitive
advantage is likely to be
limited, since employees
can be hired away, and
competitors are
extremely aggressive
Length of
High Growth
period
10 years 10 years 5 years
10 years, entirely because
of competitive advantages
and barriers to entry
10 years; it will be difficult
for competitors to
overcome the economies
of scale
5 years. In spite of the
firm’s small size, the
competitive nature of
this market and the lack
of barriers to competition
make us conservative
Boeing Home Depot Infosoft
Firm
Size/Market
Size
Firm has the dominant
market share of a slow-
growing market
Firm has dominant market
share of domestic market,
but is entering new
businesses and new
markets (overseas)
Firm is a small firm in a
market that is
experiencing significant
growth
Current
Excess
Returns
Firm is earning less than its
cost of capital, and has
done so for last 5 years
Firm is earning
substantially more than its
cost of capital
Firm is earning
significant excess
returns
Competitive
Advantages
Huge capital requirements
and technological barriers
to new entrants.
Management record over
the last few years has been
poor
Significant economies of
scale are used to establish
cost advantages over
rivals. Has a management
team that is focused on
growth and efficiency
Has both a good product
and good software
engineers. Competitive
advantage is likely to be
limited, since employees
can be hired away, and
competitors are
extremely aggressive
Length of
High Growth
period
10 years 10 years 5 years
10 years, entirely because
of competitive advantages
and barriers to entry
10 years; it will be difficult
for competitors to
overcome the economies
of scale
5 years. In spite of the
firm’s small size, the
competitive nature of
this market and the lack
of barriers to competition
make us conservative
44
The Tree of Value Creation
Increase the cash
flows from existing
assets to the firm
Increase the expected
growth rate in these
cash flows
Extend the length
of the high
growth period
Reduce the cost of
capital
increasing after-tax earnings from assets
in place
reducing reinvestment needs in net
capital expendituresor working capital
Changingthe financialmix
Improving the return on capital on those
reinvestments
Increasing the rate of reinvestment in the
firm
Reducing the operating risk in
investments/assets
Changingthe financialcomposition
Build on existing competitive advantage
Find new competitive advantage
Brand name
Legal Protection
Cost advantage
The Tree of Value Creation
Increase the cash
flows from existing
assets to the firm
Increase the expected
growth rate in these
cash flows
Extend the length
of the high
growth period
Reduce the cost of
capital
increasing after-tax earnings from assets
in place
reducing reinvestment needs in net
capital expendituresor working capital
Changingthe financialmix
Improving the return on capital on those
reinvestments
Increasing the rate of reinvestment in the
firm
Reducing the operating risk in
investments/assets
Changingthe financialcomposition
Build on existing competitive advantage
Find new competitive advantage
Brand name
Legal Protection
Cost advantage
Ways of Increasing Cash Flows from Assets in Place
45
Value EnhancementthroughGrowth
Revenues
*Operating Margin
= EBIT
-Taxe Rate * EBIT
= EBIT*(1 -t)
+ Depreciation
-Capital Expenditures
-Chgin WorkingCapital
= FCF
DivestAssetsthathave
negativeEBIT
ReduceTaxRate :
movingincometo lower
taxlocales
Live off pastover-
investment
Bette inventory
Management and tighter
Creditpolicies
ReinvestmentRate
*Return on Capital
= ExpectedGrowthRate
More efficient operations
and costcutting:
HigherMargins
Reinvestmore in
projects
Increaseoperating
margins
Do Acquisitions
IncreaseCapital
Turnover Ratio
45
Value EnhancementthroughGrowth
Revenues
*Operating Margin
= EBIT
-Taxe Rate * EBIT
= EBIT*(1 -t)
+ Depreciation
-Capital Expenditures
-Chgin WorkingCapital
= FCF
DivestAssetsthathave
negativeEBIT
ReduceTaxRate :
movingincometo lower
taxlocales
Live off pastover-
investment
Bette inventory
Management and tighter
Creditpolicies
ReinvestmentRate
*Return on Capital
= ExpectedGrowthRate
More efficient operations
and costcutting:
HigherMargins
Reinvestmore in
projects
Increaseoperating
margins
Do Acquisitions
IncreaseCapital
Turnover Ratio
Reducing Cost of Capital
46
Changing
product
characteristics
Makeproductor service
lessdiscretionaryto
customers
Changingfinancingmix
Reduceoperating
leverage
Outsourcing
Flexible wagecontracts
and coststructure
Match debtto assets,
reducingdefault risk
More effective
advertising
Swaps DerivativesHybrids
Costof Equity(E/(D+E)) + Pre-taxCostof Debt(D/(D+E)) = Costof capital
Corporate
Governance
Mecanisms
46
Changing
product
characteristics
Makeproductor service
lessdiscretionaryto
customers
Changingfinancingmix
Reduceoperating
leverage
Outsourcing
Flexible wagecontracts
and coststructure
Match debtto assets,
reducingdefault risk
More effective
advertising
Swaps DerivativesHybrids
Costof Equity(E/(D+E)) + Pre-taxCostof Debt(D/(D+E)) = Costof capital
Corporate
Governance
Mecanisms
Shareholder
value
creation
ROCE
Economic
Profit
Margin
Capital
Turnover
Sales
Targets
cogs/
sales
Development
Cost/Sales
Inventory
Turnover
Capacity
Utilization
Cash
Turnover
Order Size
Customer Mix
Sales/Account
Deficit Rates
Cost per Delivery
Maintenance cost
New product
development time
Indirect/Direct
Labor
Customer
Complaints
Downtime
Accounts Payable
Time
Accounts
Receivable Time
CEO Corporate/Divisional Functional Departments & Teams
Organizationalperspective :
LinkingValue Drivers to Performance Targets
value
creation
ROCE
Economic
Profit
Margin
Capital
Turnover
Sales
Targets
cogs/
sales
Development
Cost/Sales
Inventory
Turnover
Capacity
Utilization
Cash
Turnover
Order Size
Customer Mix
Sales/Account
Deficit Rates
Cost per Delivery
Maintenance cost
New product
development time
Indirect/Direct
Labor
Customer
Complaints
Downtime
Accounts Payable
Time
Accounts
Receivable Time
CEO Corporate/Divisional Functional Departments & Teams
Organizationalperspective :
LinkingValue Drivers to Performance Targets
48
The Balanced Scorecard
balances the financial
perspective with the
organisational, customer and
innovation perspectives
which are crucial for the
future of an organisation
Organizationalperspective : the Balanced Scorecard
The Balanced Scorecard
balances the financial
perspective with the
organisational, customer and
innovation perspectives
which are crucial for the
future of an organisation
Organizationalperspective : the Balanced Scorecard
F
I
N
A
N
C
I
A
L
F1 Return on Capital Employed
F2 Cash Flow
F3 Profitability
F4 Lowest Cost
F5 Profitable Growth
F6 Manage risk
Strategic Objectives
Financially
Strong
* ROCE
* Cash Flow
* Net Margin
* Full cost per gallon delivered to customer
* Volume growth rate Vs. industry
* Risk index
Strategic Measures
C O
U M
S E
T R
-
C1 Continually delight the targeted consumer
C2 Improve dealer/distributor profitability
* Share of segment in key markets
* Mystery shopper rating
* Dealer/distributor margin on gasoline
* Dealer/distributor survey
Delight the
Consumer
Win-Win
Relationship
I1 Marketing
1. Innovative products and services
2. Dealer/distributor quality
I2 Manufacturing
1. Lower manufacturing costs
2. Improve hardware and performance
I3 Supply, Trading, Logistics
1. Reducing delivered cost
2. Trading organization
3. Inventory management
I4 Improve health, safety, and environmental performance
I5 Quality
I
N
T
E
R
N
A
L
* Non-gasoline revenue and margin per square foot
* Dealer/distributor acceptance rate of new programs
* Dealer/distributor quality ratings
* ROCE on refinery
* Total expenses (per gallon) Vs. competition
* Profitability index
* Yield index
Delivered cost per gallon .Vs. competitors
* Trading margin
* Inventory level compared to plan & to output rate
* Number of incidents
* Days away from work
* Quality index
L
E &
A G
R R
N O
I W
N T
G H
L1 Organization Involvement
L2 Core competencies and skills
L3 Access to strategic information
* Employee survey
* Strategic competing (?) availability
* Strategic information availability
Safe and
Reliable
Competitive
Supplier
Good Neighbor
On Spec
On time
Motivated and
Prepared
Balanced Scorecard for Mobil N. American Marketing & Refining
Example
I
N
A
N
C
I
A
L
F1 Return on Capital Employed
F2 Cash Flow
F3 Profitability
F4 Lowest Cost
F5 Profitable Growth
F6 Manage risk
Strategic Objectives
Financially
Strong
* ROCE
* Cash Flow
* Net Margin
* Full cost per gallon delivered to customer
* Volume growth rate Vs. industry
* Risk index
Strategic Measures
C O
U M
S E
T R
-
C1 Continually delight the targeted consumer
C2 Improve dealer/distributor profitability
* Share of segment in key markets
* Mystery shopper rating
* Dealer/distributor margin on gasoline
* Dealer/distributor survey
Delight the
Consumer
Win-Win
Relationship
I1 Marketing
1. Innovative products and services
2. Dealer/distributor quality
I2 Manufacturing
1. Lower manufacturing costs
2. Improve hardware and performance
I3 Supply, Trading, Logistics
1. Reducing delivered cost
2. Trading organization
3. Inventory management
I4 Improve health, safety, and environmental performance
I5 Quality
I
N
T
E
R
N
A
L
* Non-gasoline revenue and margin per square foot
* Dealer/distributor acceptance rate of new programs
* Dealer/distributor quality ratings
* ROCE on refinery
* Total expenses (per gallon) Vs. competition
* Profitability index
* Yield index
Delivered cost per gallon .Vs. competitors
* Trading margin
* Inventory level compared to plan & to output rate
* Number of incidents
* Days away from work
* Quality index
L
E &
A G
R R
N O
I W
N T
G H
L1 Organization Involvement
L2 Core competencies and skills
L3 Access to strategic information
* Employee survey
* Strategic competing (?) availability
* Strategic information availability
Safe and
Reliable
Competitive
Supplier
Good Neighbor
On Spec
On time
Motivated and
Prepared
Balanced Scorecard for Mobil N. American Marketing & Refining
Example
1.2. The Cost of Equity :
the Capital Asset Pricing Model
⚫Thecapitalassetpricingmodelistheoldestandstillthemostwidelyused
modelforriskintheinvestmentworld.
⚫Itisderivedinfoursteps:
1.Usesvarianceasameasureofrisk
2.Specifiesthataportionofvariancecanbediversifiedaway,andthatisonlythe
non-diversifiableportionthatisrewarded.
3.Measuresthenon-diversifiableriskwithbeta,whichisstandardizedaround
one.
4.Translatesbetaintoexpectedreturn-
⚫ExpectedReturn=Riskfreerate+Beta*RiskPremium
the Capital Asset Pricing Model
⚫Thecapitalassetpricingmodelistheoldestandstillthemostwidelyused
modelforriskintheinvestmentworld.
⚫Itisderivedinfoursteps:
1.Usesvarianceasameasureofrisk
2.Specifiesthataportionofvariancecanbediversifiedaway,andthatisonlythe
non-diversifiableportionthatisrewarded.
3.Measuresthenon-diversifiableriskwithbeta,whichisstandardizedaround
one.
4.Translatesbetaintoexpectedreturn-
⚫ExpectedReturn=Riskfreerate+Beta*RiskPremium
The Capital Asset Pricing Model
⚫A. Risk and Reward under CAPM Assumptions
⚫B. Portfolio Theory and Risk
⚫C. CAPM : from the Capital Market Line to the Security Market
line
51
⚫A. Risk and Reward under CAPM Assumptions
⚫B. Portfolio Theory and Risk
⚫C. CAPM : from the Capital Market Line to the Security Market
line
51
A. Risk and Reward under CAPM
Assumptions
⚫2 sets of Assumptions :
[1] Perfect market :
⚫Frictionless, and perfect information
⚫No imperfections like tax, regulations, restrictions to short selling
⚫All assets are publicly traded and perfectly divisible
⚫Perfect competition –everyone is a price-taker
[2] Investors :
⚫Same one-period horizon
⚫Rational, and maximize expected utility over a mean-variance space
⚫Homogenous beliefs
Accordingto Efficient
MarketHypothesis
Allavailableinformationisintegratedinprice:
Marketpricesreflectvaluesandinformation
accuratelyandquickly(E.Fama,1966)
➢Pricechangeispracticallycontinuous
➢Pricechangesfollowrandompatterns.Future
sharepricesareunpredictable(BrownianMotion)
Assumptions
⚫2 sets of Assumptions :
[1] Perfect market :
⚫Frictionless, and perfect information
⚫No imperfections like tax, regulations, restrictions to short selling
⚫All assets are publicly traded and perfectly divisible
⚫Perfect competition –everyone is a price-taker
[2] Investors :
⚫Same one-period horizon
⚫Rational, and maximize expected utility over a mean-variance space
⚫Homogenous beliefs
Accordingto Efficient
MarketHypothesis
Allavailableinformationisintegratedinprice:
Marketpricesreflectvaluesandinformation
accuratelyandquickly(E.Fama,1966)
➢Pricechangeispracticallycontinuous
➢Pricechangesfollowrandompatterns.Future
sharepricesareunpredictable(BrownianMotion)
Randomwalk
N = 1
N = 3
N = 1000
up
down
T
ln(S)
Long term
tendency Lognormal
return (S
T)
A simplified representation of hazard permits to describe an asset by its
Expected Returnand its Standard Deviation
N = 1
N = 3
N = 1000
up
down
T
ln(S)
Long term
tendency Lognormal
return (S
T)
A simplified representation of hazard permits to describe an asset by its
Expected Returnand its Standard Deviation
Risk/Reward tradeoff definition
⚫Return : ⚫Expected Return :
R
t=
D
t
+ (P
t
–P
t-1
)
P
t-1
E
r
t+1=
E
D
t+1
+ (
E
P
t+1
–P
t
)
P
t
D
t
: Dividend in t
P
t-1
: Price in t –1
P
t
: Price in t
P
t
-P
t-1
: Capital gain between
t-1 and t
E : Expected value
E
D
t+1
: Dividend expected value in t+1
E
P
t+1
: Expected price in t+1
E
p
t+1
-P
t
: Expected capital gain between t-1 and t
Expected Reward Definition
=
=
n
1s
si,sreturnp
⚫Return : ⚫Expected Return :
R
t=
D
t
+ (P
t
–P
t-1
)
P
t-1
E
r
t+1=
E
D
t+1
+ (
E
P
t+1
–P
t
)
P
t
D
t
: Dividend in t
P
t-1
: Price in t –1
P
t
: Price in t
P
t
-P
t-1
: Capital gain between
t-1 and t
E : Expected value
E
D
t+1
: Dividend expected value in t+1
E
P
t+1
: Expected price in t+1
E
p
t+1
-P
t
: Expected capital gain between t-1 and t
Expected Reward Definition
=
=
n
1s
si,sreturnp
Small Risk
Huge Risk
Risk Definition
Financial translation :
disparity between actual
and expected returns
The first symbol is the symbol for “danger”, while
the second is the symbol for “opportunity”,
making risk a mix of danger and opportunity.
Huge Risk
Risk Definition
Financial translation :
disparity between actual
and expected returns
The first symbol is the symbol for “danger”, while
the second is the symbol for “opportunity”,
making risk a mix of danger and opportunity.
Risk = Standard Deviation
: confidence interval at 68%
: confidence interval at 95%
: confidence interval at 99,7 %
==
−=−=
n
i
i
n
i
i RR
n
RR
n
RV
1
_
1
2
_
²²
1
)(
1
)(
SD (R)
: confidence interval at 68%
: confidence interval at 95%
: confidence interval at 99,7 %
==
−=−=
n
i
i
n
i
i RR
n
RR
n
RV
1
_
1
2
_
²²
1
)(
1
)(
SD (R)
Source : Mandelbroot, 2009
Assets Returns Real volatility
Brownian
Motion
Assets Returns Real volatility
Brownian
Motion
B. Portfolio Theory and Risk
58
ConventionalWisdomcirca1950
"Onceyouattaincompetency,diversificationisundesirable.Oneortwo,orat
mostthreeorfour,securitiesshouldbebought.Competentinvestorswillnever
besatisfiedbeatingtheaveragesbyafewsmallpercentagepoints.“
GeraldM.Loeb“TheBattleforInvestmentSurvival”,1935
➢Analyzesecuritiesonebyone
➢Focusonpickingwinners
➢Concentrateholdingstomaximizereturns
➢Broaddiversificationisconsideredundesirable
1952,DiversificationandPortfolioRisk
➢HarryMarkowitz(NobelPrizeinEconomics,1990)
➢Diversificationreducesrisk.
➢Assetsevaluatednotbyindividualcharacteristicsbutbytheireffect
onaportfolio
➢Anoptimalportfoliocanbeconstructedtomaximizereturnfora
givenstandarddeviation
Paradigmrevolution
58
ConventionalWisdomcirca1950
"Onceyouattaincompetency,diversificationisundesirable.Oneortwo,orat
mostthreeorfour,securitiesshouldbebought.Competentinvestorswillnever
besatisfiedbeatingtheaveragesbyafewsmallpercentagepoints.“
GeraldM.Loeb“TheBattleforInvestmentSurvival”,1935
➢Analyzesecuritiesonebyone
➢Focusonpickingwinners
➢Concentrateholdingstomaximizereturns
➢Broaddiversificationisconsideredundesirable
1952,DiversificationandPortfolioRisk
➢HarryMarkowitz(NobelPrizeinEconomics,1990)
➢Diversificationreducesrisk.
➢Assetsevaluatednotbyindividualcharacteristicsbutbytheireffect
onaportfolio
➢Anoptimalportfoliocanbeconstructedtomaximizereturnfora
givenstandarddeviation
Paradigmrevolution
a. Distinction between rewarded and
unrewarded risk
⚫Total risk = Systematic risk + Unsystematic risk
⚫Firm Specific Risk orUnsystematic risk is risk that influences a single
company and can be diversified away in a diversified portfolio.
⚫Systematic risk orMarket Risk is risk that influences a large number of
assets and cannot be diversified away.
⚫The marginal investor is assumed to hold a “diversified” portfolio.
Thus, only market risk will be rewarded and priced.
RewardedRisk UnrewardedRisk
unrewarded risk
⚫Total risk = Systematic risk + Unsystematic risk
⚫Firm Specific Risk orUnsystematic risk is risk that influences a single
company and can be diversified away in a diversified portfolio.
⚫Systematic risk orMarket Risk is risk that influences a large number of
assets and cannot be diversified away.
⚫The marginal investor is assumed to hold a “diversified” portfolio.
Thus, only market risk will be rewarded and priced.
RewardedRisk UnrewardedRisk
⚫Two-SecurityPortfolioReturn:
E
RP: X E
RA+ (1 –X) E
RB
X : Equity A weight
(1 –X) : Equity B weight
⚫Two-Security Portfolio Risk
²
RP= X² ²
RA+ (1 –X)²²
RB+ [2X (1 –X)
RA
RB
RA,RB]
RP= ²
RP
b. Diversification principle
BA
AB
AB
COV
=
[+ 1.0 >> -1.0]
E
RP: X E
RA+ (1 –X) E
RB
X : Equity A weight
(1 –X) : Equity B weight
⚫Two-Security Portfolio Risk
²
RP= X² ²
RA+ (1 –X)²²
RB+ [2X (1 –X)
RA
RB
RA,RB]
RP= ²
RP
b. Diversification principle
BA
AB
AB
COV
=
[+ 1.0 >> -1.0]
⚫Therelationship‘risk-expectedreturn’dependsonthecorrelation
coefficient:[-1.0<<+1.0]
⚫Thesmallerthecorrelation,thegreaterthepotentialbenefitsfrom
diversification
⚫If=+1.0,noriskreductionispossible
⚫If=-1.0,perfecthedgingopportunityexist(zerovarianceportfolio)
Correlation Effects
⚫Example1 :
RA,RB= 1 : total risk= sumof risks
⚫²
RP = [X
RA+ (1 –X)
RB]
2
⚫
RP = X
RA+ (1 –X)
RB
⚫Example2 :
RA,RB= 0
⚫²
RP = [X² ²
RA+ (1 –X) ²
RB]
⚫
RP < X
RA+ (1 –X)
RB
⚫Example3 :
RA,RB= -1
⚫²
RP = [X
RA-(1 –X)
RB]
2
⚫
RP = X
RA-(1 –X)
RB
coefficient:[-1.0<<+1.0]
⚫Thesmallerthecorrelation,thegreaterthepotentialbenefitsfrom
diversification
⚫If=+1.0,noriskreductionispossible
⚫If=-1.0,perfecthedgingopportunityexist(zerovarianceportfolio)
Correlation Effects
⚫Example1 :
RA,RB= 1 : total risk= sumof risks
⚫²
RP = [X
RA+ (1 –X)
RB]
2
⚫
RP = X
RA+ (1 –X)
RB
⚫Example2 :
RA,RB= 0
⚫²
RP = [X² ²
RA+ (1 –X) ²
RB]
⚫
RP < X
RA+ (1 –X)
RB
⚫Example3 :
RA,RB= -1
⚫²
RP = [X
RA-(1 –X)
RB]
2
⚫
RP = X
RA-(1 –X)
RB
Expected Return and Standard Deviation
with Various Correlation Coefficients
with Various Correlation Coefficients
The Importance of Diversification : Risk Types
63
UnrewardedRisk RewardedRisk
63
UnrewardedRisk RewardedRisk
c. The Job of a Rational Investor
⚫TwoOperations:
⚫c’.MaximisingRisk/Rewardinaweightedportfolio:choosethe
bestcombinationofassetsinyourportfolio
⚫c’’.FiretheUnsystematicrisk:increasethenumberofassets
inyourportfolio
⚫TwoOperations:
⚫c’.MaximisingRisk/Rewardinaweightedportfolio:choosethe
bestcombinationofassetsinyourportfolio
⚫c’’.FiretheUnsystematicrisk:increasethenumberofassets
inyourportfolio
c’. Maximising Risk/Reward in a weighted
portfolio :
choose the best combination of assets in your portfolio
⚫Example : Portfolio with Boeing and Home Depot (1998)
⚫²
RP/X = 2x²
RA+ (2X -2)²
RB+ 2
RA,RB
RA
RB–4
RA,RB
RA
RB = 0
⚫X
*
= 70,96%Pondération de Boeing Pondération de Home Depot Rentabilité prévue Ecart-type
100% 0% 8,38% 31,10%
90 10 12,52 25,27
80 20 16,67 21,13
70 30 20,81 19,78
60 40 24,96 21,75
50 50 29,11 26,29
40 60 33,25 32,34
30 70 37,40 39,21
20 80 41,55 46,54
10 90 45,69 54,14
0 100 49,84 61,90
Boeing Weight Home DepotWeight ExpectedReturn SD
portfolio :
choose the best combination of assets in your portfolio
⚫Example : Portfolio with Boeing and Home Depot (1998)
⚫²
RP/X = 2x²
RA+ (2X -2)²
RB+ 2
RA,RB
RA
RB–4
RA,RB
RA
RB = 0
⚫X
*
= 70,96%Pondération de Boeing Pondération de Home Depot Rentabilité prévue Ecart-type
100% 0% 8,38% 31,10%
90 10 12,52 25,27
80 20 16,67 21,13
70 30 20,81 19,78
60 40 24,96 21,75
50 50 29,11 26,29
40 60 33,25 32,34
30 70 37,40 39,21
20 80 41,55 46,54
10 90 45,69 54,14
0 100 49,84 61,90
Boeing Weight Home DepotWeight ExpectedReturn SD
Risk-Return Trade-Off
66ExpectedStandard
Inputs ReturnDeviation
Risky Asset 1 14.0% 20.0%
Risky Asset 2 8.0% 15.0%
Correlation 30.0%
Efficient Set--Two Asset Portfolio
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
0% 5% 10% 15% 20% 25% 30%
Standard Deviation
Expected Return
⚫Fortheplot,theupperleft-handboundaryistheMarkowitzefficientfrontier
⚫Alltheotherpossiblecombinationsareinefficient.Thatis,investorswould
notholdtheseportfoliosbecausetheycouldgeteithermorereturnfora
givenlevelofrisk,orlessriskforagivenlevelofreturn
66ExpectedStandard
Inputs ReturnDeviation
Risky Asset 1 14.0% 20.0%
Risky Asset 2 8.0% 15.0%
Correlation 30.0%
Efficient Set--Two Asset Portfolio
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
0% 5% 10% 15% 20% 25% 30%
Standard Deviation
Expected Return
⚫Fortheplot,theupperleft-handboundaryistheMarkowitzefficientfrontier
⚫Alltheotherpossiblecombinationsareinefficient.Thatis,investorswould
notholdtheseportfoliosbecausetheycouldgeteithermorereturnfora
givenlevelofrisk,orlessriskforagivenlevelofreturn
E(R)
R
The Markowitz Efficient frontier
Efficient Frontier
Portefeuille de
variance minimale
⚫TheMarkowitzEfficientfrontieristhesetofportfolioswiththemaximum
returnforagivenriskANDtheminimumriskgivenareturn
R
The Markowitz Efficient frontier
Efficient Frontier
Portefeuille de
variance minimale
⚫TheMarkowitzEfficientfrontieristhesetofportfolioswiththemaximum
returnforagivenriskANDtheminimumriskgivenareturn
c’’.Increasethe numberof assetsin yourportfolio
⚫Firm-specificriskcanbereduced,ifnoteliminated,byincreasingthe
numberofinvestmentsinyourportfolio(i.e.,bybeingdiversified).
⚫Oneconomicgrounds,diversifyingandholdingalargerportfolioeliminates
firm-specificriskfortworeasons-
⚫(a)Eachinvestmentisamuchsmallerpercentageoftheportfolio,
mutingtheeffect(positiveornegative)ontheoverallportfolio.
⚫(b)Firm-specificactionscanbeeitherpositiveornegative.Inalarge
portfolio,itisargued,theseeffectswillaverageouttozero.(Forevery
firm,wheresomethingbadhappens,therewillbesomeotherfirm,
wheresomethinggoodhappens.)
68
⚫Firm-specificriskcanbereduced,ifnoteliminated,byincreasingthe
numberofinvestmentsinyourportfolio(i.e.,bybeingdiversified).
⚫Oneconomicgrounds,diversifyingandholdingalargerportfolioeliminates
firm-specificriskfortworeasons-
⚫(a)Eachinvestmentisamuchsmallerpercentageoftheportfolio,
mutingtheeffect(positiveornegative)ontheoverallportfolio.
⚫(b)Firm-specificactionscanbeeitherpositiveornegative.Inalarge
portfolio,itisargued,theseeffectswillaverageouttozero.(Forevery
firm,wheresomethingbadhappens,therewillbesomeotherfirm,
wheresomethinggoodhappens.)
68
69
Increasethe numberof assetsin yourportfolio
Increasethe numberof assetsin yourportfolio
70
Atanextreme,onestandalonestockrepresentsitsownindex,butithasa
veryhighriskandoffersnoadditionalexpectedreturnovertheassetclass
towhichitbelongs.
Increasethe numberof assetsin yourportfolio
Atanextreme,onestandalonestockrepresentsitsownindex,butithasa
veryhighriskandoffersnoadditionalexpectedreturnovertheassetclass
towhichitbelongs.
Increasethe numberof assetsin yourportfolio
71
Increasethe numberof assetsin yourportfolio
Transaction
costs
Nowwecanentry intothe CAPM and seethe linear
relation betweenan assethurdlerate and itsrisk
Increasethe numberof assetsin yourportfolio
Transaction
costs
Nowwecanentry intothe CAPM and seethe linear
relation betweenan assethurdlerate and itsrisk
C. CAPM : from the Capital Market Line to the
Security Market line
⚫IntheCAPM,allinvestorshaveaGlobalPortfoliowithaproportionXof
theMarket(riskyportfoliowithtotaldiversification)and(1-X)ofarisk
freeasset(T-bills)
E
RP=XE
RM+(1–X)r
f
Asr
f=0, ²
RP=X²²
RMou
RP=X
RM
Theseparationpropertytellsusthattheportfoliochoiceproblemmaybe
separatedintotwoindependenttasks:
➢Determinationoftheoptimalriskyportfolioispurelytechnical(sameforall
clients)
➢AllocationofthecompleteportfoliotoT-billsversustheriskyportfolio(P)
dependsonpersonalpreference
The Capital MarketLine representsthe relation between
the Riskof the Global Portolioand itsExpectedReturn
Security Market line
⚫IntheCAPM,allinvestorshaveaGlobalPortfoliowithaproportionXof
theMarket(riskyportfoliowithtotaldiversification)and(1-X)ofarisk
freeasset(T-bills)
E
RP=XE
RM+(1–X)r
f
Asr
f=0, ²
RP=X²²
RMou
RP=X
RM
Theseparationpropertytellsusthattheportfoliochoiceproblemmaybe
separatedintotwoindependenttasks:
➢Determinationoftheoptimalriskyportfolioispurelytechnical(sameforall
clients)
➢AllocationofthecompleteportfoliotoT-billsversustheriskyportfolio(P)
dependsonpersonalpreference
The Capital MarketLine representsthe relation between
the Riskof the Global Portolioand itsExpectedReturn
Capital Market Line (CML) : linear relation between
hurdle rate and risk for a GLOBAL PORTFOLIO
⚫Suppose X =
RP/
RM
⚫We get : E
RP= r
f + (E
RM-r
f) x
RP
RM
a linear relation between expected Return and Total Risk of the
Global Portfolio.
The slope [E
RM-r
f] /
RMgives the Market Premium for
RM
Capital Market Line
Market Portfolio
r
f
E
RP
RP
Markowitz
Frontier
hurdle rate and risk for a GLOBAL PORTFOLIO
⚫Suppose X =
RP/
RM
⚫We get : E
RP= r
f + (E
RM-r
f) x
RP
RM
a linear relation between expected Return and Total Risk of the
Global Portfolio.
The slope [E
RM-r
f] /
RMgives the Market Premium for
RM
Capital Market Line
Market Portfolio
r
f
E
RP
RP
Markowitz
Frontier
Risk Free
Rate
Market
Portfolio M
Expected
Return
Standard Deviation
M
Markowitz
Frontier
Hurdle Rate
on the Market
Market Premium Risk Adverse
Investor
CML
Investors’ indifference curves are based on their degree
of risk aversion and investment objectives
Risk Lover
Investor
Weare lookingfor the
Security MarketLine
(relation between
the firmsystematicRisk
and itsExpectedReturn)
Rate
Market
Portfolio M
Expected
Return
Standard Deviation
M
Markowitz
Frontier
Hurdle Rate
on the Market
Market Premium Risk Adverse
Investor
CML
Investors’ indifference curves are based on their degree
of risk aversion and investment objectives
Risk Lover
Investor
Weare lookingfor the
Security MarketLine
(relation between
the firmsystematicRisk
and itsExpectedReturn)
From the Capital Market Line to the Security
Market Line
⚫Considerthefollowingportfolio:holda%inassetiand(1-a%)inthe
marketportfolio.Theexpectedreturnandstandarddeviationofsucha
portfoliocanbewrittenas:
⚫Arbitrage:Considerthechangeinthemeanandstandarddeviationwith
respecttothepercentagechangeintheportfolioinvestedinasseti.)1(2a)1()(
][)1(][ ][
2222
mimip
mip
aaaR
REaRaERE
−+−+=
−+= ( )
mimi
p
p
mi
p
pp
p
p
aaa
Ra
R
RERE
a
RE
a
R
a
RE
Rd
RdE
)21()1(
)(
1)(
][][
][
)(][
)(
][
22
−+−−=
−=
=
Market Line
⚫Considerthefollowingportfolio:holda%inassetiand(1-a%)inthe
marketportfolio.Theexpectedreturnandstandarddeviationofsucha
portfoliocanbewrittenas:
⚫Arbitrage:Considerthechangeinthemeanandstandarddeviationwith
respecttothepercentagechangeintheportfolioinvestedinasseti.)1(2a)1()(
][)1(][ ][
2222
mimip
mip
aaaR
REaRaERE
−+−+=
−+= ( )
mimi
p
p
mi
p
pp
p
p
aaa
Ra
R
RERE
a
RE
a
R
a
RE
Rd
RdE
)21()1(
)(
1)(
][][
][
)(][
)(
][
22
−+−−=
−=
=
Sincethemarketportfolioalreadycontainsasseti,therefore,the
percentaintheaboveequationsrepresentexcessdemandsfora
riskyasset.
Weknowthatinequilibrium,Demand=Supplyforallasset.
Therefore,a=0hastobetrueinequilibrium.
•theslopeoftheriskreturntrade-offevaluatedatpointMinmarket
equilibriumis
•butweknowthattheslopeoftheopportunitysetatpointMmustalso
equaltheslopeofthecapitalmarketline.Theslopeofthecapital
marketlineis:
•Therefore,settingtheslopeoftheopportunitysetequaltotheslopeof
thecapitalmarketline:
m
2
mim
mi
p
p
-
)RE( - )RE(
=
a)/R(
a)/RE(
m
fmR - )RE(
(evaluated at a = 0)
percentaintheaboveequationsrepresentexcessdemandsfora
riskyasset.
Weknowthatinequilibrium,Demand=Supplyforallasset.
Therefore,a=0hastobetrueinequilibrium.
•theslopeoftheriskreturntrade-offevaluatedatpointMinmarket
equilibriumis
•butweknowthattheslopeoftheopportunitysetatpointMmustalso
equaltheslopeofthecapitalmarketline.Theslopeofthecapital
marketlineis:
•Therefore,settingtheslopeoftheopportunitysetequaltotheslopeof
thecapitalmarketline:
m
2
mim
mi
p
p
-
)RE( - )RE(
=
a)/R(
a)/RE(
m
fmR - )RE(
(evaluated at a = 0)
( )
( )rf-][
2
rf-][
2
rf-][
2
][
rf-][
2
][][
m
RE
m
mi
i
RE
rf
mm
RE
mimi
RE
m
m
RE
m
mmi
m
RE
i
RE
=
−=
=
−
−
i
Market premium
ifmfi ] R - )R[E( + R = )RE(
CAPM Equation
Where :
E(return) = Risk-free rate of return + Risk premium specific to asset i
E(R
i)= R
f+ (Market price of risk)x(quantity of risk of asset i)
E(R
i) = Expected Return on asset i
R
f = Equilibrium Risk-free rate of return
i = Quantity of risk of asset i = COV(R
i, R
M)/Var(R
M)
[E(R
M)-R
f] = Market Price of risk
( )rf-][
2
rf-][
2
rf-][
2
][
rf-][
2
][][
m
RE
m
mi
i
RE
rf
mm
RE
mimi
RE
m
m
RE
m
mmi
m
RE
i
RE
=
−=
=
−
−
i
Market premium
ifmfi ] R - )R[E( + R = )RE(
CAPM Equation
Where :
E(return) = Risk-free rate of return + Risk premium specific to asset i
E(R
i)= R
f+ (Market price of risk)x(quantity of risk of asset i)
E(R
i) = Expected Return on asset i
R
f = Equilibrium Risk-free rate of return
i = Quantity of risk of asset i = COV(R
i, R
M)/Var(R
M)
[E(R
M)-R
f] = Market Price of risk
Interpreting
⚫if =
⚫asset is risk free
⚫if =
⚫asset return = market return
⚫if
⚫asset is riskier than market index
▪
⚫asset is less risky than market index
=
% change in asset return
% change in market returnAmazon 2.23
Anheuser Busch -.107
Microsoft 1.62
Ford 1.31
General Electric 1.10
Wal Mart .80
Sample betas
⚫if =
⚫asset is risk free
⚫if =
⚫asset return = market return
⚫if
⚫asset is riskier than market index
▪
⚫asset is less risky than market index
=
% change in asset return
% change in market returnAmazon 2.23
Anheuser Busch -.107
Microsoft 1.62
Ford 1.31
General Electric 1.10
Wal Mart .80
Sample betas
Pictorial Result of CAPM
E(R
i)
E(R
M)
R
f
Security Market
Line
=
[COV(R
i, R
M)/Var(R
M)]
= 1.0
slope = [E(R
M) -R
f]= Eqm. Price of risk
E(R
i)
E(R
M)
R
f
Security Market
Line
=
[COV(R
i, R
M)/Var(R
M)]
= 1.0
slope = [E(R
M) -R
f]= Eqm. Price of risk
Security Market Line Equilibrium
A
1
i
A
M
E(R
i)
B
B
Security Market Line
UpontheMarketLineanassetis
undervalued.Indeeditsreturnistoo
highconsideringitsrisk.Wellinformed
investorswillbuytheasset;priceup
andreturndown.
DowntheMarketLineanassetis
overvalued.Indeeditsrikistoohigh
consideringitsreturn;investorswill
sellit;pricedownandreturnup.
A
1
i
A
M
E(R
i)
B
B
Security Market Line
UpontheMarketLineanassetis
undervalued.Indeeditsreturnistoo
highconsideringitsrisk.Wellinformed
investorswillbuytheasset;priceup
andreturndown.
DowntheMarketLineanassetis
overvalued.Indeeditsrikistoohigh
consideringitsreturn;investorswill
sellit;pricedownandreturnup.
81
Portfolios in upwardstrend
Portfolios in upwardstrend
Portefeuille in downwardstrend
Telecoms : 18 months of volatilityCours base 100 de Telecom Monde (INT)
40
60
80
100
120
140
160
180
200
220
mars 99juin 99sept 99déc 99mars 00juin 00sept 00déc 00mars 01juin 01sept 01déc 01mars 02juin 02
Telecom Global S&P 500 (US)
Source JCFQuant
40
60
80
100
120
140
160
180
200
220
mars 99juin 99sept 99déc 99mars 00juin 00sept 00déc 00mars 01juin 01sept 01déc 01mars 02juin 02
Telecom Global S&P 500 (US)
Source JCFQuant
Estimating the Cost of Equity :
Deutsche Bank 2008 versus 2009
⚫Inearly2008,weestimatedabetaof1.162forDeutscheBank,whichusedin
conjunctionwiththeEurorisk-freerateof4%(inJanuary2008)andarisk
premiumof4.50%(thematuremarketriskpremiuminearly2008),yieldedacost
ofequityof9.23%.
CostofEquity
Jan2008=RiskfreeRate
Jan2008+Beta*MatureMarketRiskPremium
=4.00%+1.162(4.5%)=9.23%
(Weusedthesamebetaforearly2008andearly2009)
⚫Inearly2009,theEuroriskfreeratehaddroppedto3.6%andtheequityrisk
premiumhadrisento6%formaturemarkets:
Costofequity
jan2009=RiskfreeRate
Jan2009+Beta(EquityRiskPremium)
=3.6%+1.162(6%)=10.572%
84
Deutsche Bank 2008 versus 2009
⚫Inearly2008,weestimatedabetaof1.162forDeutscheBank,whichusedin
conjunctionwiththeEurorisk-freerateof4%(inJanuary2008)andarisk
premiumof4.50%(thematuremarketriskpremiuminearly2008),yieldedacost
ofequityof9.23%.
CostofEquity
Jan2008=RiskfreeRate
Jan2008+Beta*MatureMarketRiskPremium
=4.00%+1.162(4.5%)=9.23%
(Weusedthesamebetaforearly2008andearly2009)
⚫Inearly2009,theEuroriskfreeratehaddroppedto3.6%andtheequityrisk
premiumhadrisento6%formaturemarkets:
Costofequity
jan2009=RiskfreeRate
Jan2009+Beta(EquityRiskPremium)
=3.6%+1.162(6%)=10.572%
84
⚫A. The Riskfree Rate
⚫B. The risk premium [E(R
m) –R
f]
⚫C. Estimating Beta
85
1.3. Estimating CAPM items
⚫B. The risk premium [E(R
m) –R
f]
⚫C. Estimating Beta
85
1.3. Estimating CAPM items
A. The Riskfree Rate
⚫Using along term government rate as the riskfree rate on all of the cash flows in a
long term analysis will yield a close approximation of the true value.
⚫Note,however,thatnotallgovernmentscanbeviewedasdefaultfree!
⚫Therecanbenouncertaintyaboutreinvestmentrates,whichimpliesthatitisa
zerocouponsecuritywiththesamematurityasthecashflowbeinganalyzed.
⚫Butifthereissubstantialuncertaintyaboutexpectedcashflows,thepresent
valueeffectofusingtimevaryingriskfreeratesissmallenoughthatitmaynot
beworthit.
⚫The riskfree rate should be in the same currency that your cashflows.
⚫if your cashflows are in U.S. dollars, your riskfree rate has to be in U.S. dollars
as well.
⚫If your cash flows are in Euros, your riskfree rate should be a Euro riskfree rate.
86
⚫Using along term government rate as the riskfree rate on all of the cash flows in a
long term analysis will yield a close approximation of the true value.
⚫Note,however,thatnotallgovernmentscanbeviewedasdefaultfree!
⚫Therecanbenouncertaintyaboutreinvestmentrates,whichimpliesthatitisa
zerocouponsecuritywiththesamematurityasthecashflowbeinganalyzed.
⚫Butifthereissubstantialuncertaintyaboutexpectedcashflows,thepresent
valueeffectofusingtimevaryingriskfreeratesissmallenoughthatitmaynot
beworthit.
⚫The riskfree rate should be in the same currency that your cashflows.
⚫if your cashflows are in U.S. dollars, your riskfree rate has to be in U.S. dollars
as well.
⚫If your cash flows are in Euros, your riskfree rate should be a Euro riskfree rate.
86
Using time varying riskfree : Premium on Treasury bonds
Premium rises when supply of Treasury securities falls
Premium rises when consumer confidence falls
A “flight-to-liquidity” premium –some investors have strong preference for securities that are
actively traded every minute
Premium rises when supply of Treasury securities falls
Premium rises when consumer confidence falls
A “flight-to-liquidity” premium –some investors have strong preference for securities that are
actively traded every minute
B. The risk premium [E(R
m) –R
f]
⚫Estimatesoftheequitymarketriskpremium,ie,thedifferencebetweenthe
marketreturnandtheriskfreeinterestrate,arecurrentlyarrivedatusingtwo
possibleapproaches:
⚫Eitheronthebasisofhistoricaldatarelatingtoratesofreturnsreceivedby
investorssinceoververy,verylongperiods.Onefficientmarkets,historical
ratesofreturnshouldbeequaltofutureratesofreturn.Inthiscasewerefer
tothehistoricalriskpremium.
⚫Oronthebasisofforecastdata(futurefreecashflows)andthecurrent
shareprice,fromwhichwededuct,afterafewcalculations,thediscountrate
used,andthustheriskpremiumsincethediscountrateisequalforthewhole
ofthemarketattheriskfreeinterestrateplustheriskpremium.Inthiscase,
werefertotheanticipatedorforwardriskpremium,becauseitisbasedon
investors'currentexpectations,bothanticipatedandnotanticipated,because
itistheriskthatisanticipatednotthepremium,whichiscurrent.
88
m) –R
f]
⚫Estimatesoftheequitymarketriskpremium,ie,thedifferencebetweenthe
marketreturnandtheriskfreeinterestrate,arecurrentlyarrivedatusingtwo
possibleapproaches:
⚫Eitheronthebasisofhistoricaldatarelatingtoratesofreturnsreceivedby
investorssinceoververy,verylongperiods.Onefficientmarkets,historical
ratesofreturnshouldbeequaltofutureratesofreturn.Inthiscasewerefer
tothehistoricalriskpremium.
⚫Oronthebasisofforecastdata(futurefreecashflows)andthecurrent
shareprice,fromwhichwededuct,afterafewcalculations,thediscountrate
used,andthustheriskpremiumsincethediscountrateisequalforthewhole
ofthemarketattheriskfreeinterestrateplustheriskpremium.Inthiscase,
werefertotheanticipatedorforwardriskpremium,becauseitisbasedon
investors'currentexpectations,bothanticipatedandnotanticipated,because
itistheriskthatisanticipatednotthepremium,whichiscurrent.
88
The Historical Premium Approach
⚫This is the default approach used by most (Damodaran)
⚫This approach does the following :
⚫defines a time period for the estimation (1926-Present, 1962-Present....)
⚫calculate average returns on a stock index during the period
⚫calculateaveragereturnsonarisklesssecurityovertheperiod
⚫calculatethedifferencebetweenthetwoandusesitasapremiumlooking
forward
⚫The limitations of this approach are :
⚫it assumes that the risk aversion of investors has not changed in a systematic
way across time.
⚫it assumes that the riskiness of the “risky” portfolio (stock index) has not
changed in a systematic way across time.
89
⚫This is the default approach used by most (Damodaran)
⚫This approach does the following :
⚫defines a time period for the estimation (1926-Present, 1962-Present....)
⚫calculate average returns on a stock index during the period
⚫calculateaveragereturnsonarisklesssecurityovertheperiod
⚫calculatethedifferencebetweenthetwoandusesitasapremiumlooking
forward
⚫The limitations of this approach are :
⚫it assumes that the risk aversion of investors has not changed in a systematic
way across time.
⚫it assumes that the riskiness of the “risky” portfolio (stock index) has not
changed in a systematic way across time.
89
Historical Average Premiums for the US
90
Arithmeticaverage GeometricAverage
Stocks-Stocks- Stocks-Stocks-
HistoricalPeriodT.BillsT.Bonds T.Bills T.Bonds
1928-2005 7.83% 5.95% 6.47% 4.80%
1964-2005 5.52% 4.29% 4.08% 3.21%
1994-2005 8.80% 7.07% 5.15% 3.76%
Whatistherightpremium?
⚫Gobackasfarasyoucan.Otherwise,thestandarderrorintheestimatewillbe
large.
Standard error in estimate = Annualized Standard Deviation in Stock Prices
(Number of years of Historical Data)
1/2
⚫Beconsistentinyouruseofariskfreerate.
⚫Usearithmeticpremiumsforone-yearestimatesofcostsofequityandgeometric
premiumsforestimatesoflongtermcostsofequity.
HistoricalU.S.equity
riskpremiumchanges
considerablydepending
ontheintervalusedto
calculateit!
Arithmetic Average =
R
1+ R
2+ …….R
T
T
Geometric Average =
[(1+R
1) (1+ R
2) ….. (1+ R
T)]
1/T
–1
Historical data for markets outside the United States is available for much
shorter time periods. The problem is even greater in emerging markets
90
Arithmeticaverage GeometricAverage
Stocks-Stocks- Stocks-Stocks-
HistoricalPeriodT.BillsT.Bonds T.Bills T.Bonds
1928-2005 7.83% 5.95% 6.47% 4.80%
1964-2005 5.52% 4.29% 4.08% 3.21%
1994-2005 8.80% 7.07% 5.15% 3.76%
Whatistherightpremium?
⚫Gobackasfarasyoucan.Otherwise,thestandarderrorintheestimatewillbe
large.
Standard error in estimate = Annualized Standard Deviation in Stock Prices
(Number of years of Historical Data)
1/2
⚫Beconsistentinyouruseofariskfreerate.
⚫Usearithmeticpremiumsforone-yearestimatesofcostsofequityandgeometric
premiumsforestimatesoflongtermcostsofequity.
HistoricalU.S.equity
riskpremiumchanges
considerablydepending
ontheintervalusedto
calculateit!
Arithmetic Average =
R
1+ R
2+ …….R
T
T
Geometric Average =
[(1+R
1) (1+ R
2) ….. (1+ R
T)]
1/T
–1
Historical data for markets outside the United States is available for much
shorter time periods. The problem is even greater in emerging markets
One solution : Look at a country’s bond rating
and default spreads as a start
⚫RatingsagenciessuchasS&PandMoody’sassignratingstocountriesthatreflect
theirassessmentofthedefaultriskofthesecountries.
⚫Whiledefaultriskpremiumsandequityriskpremiumsarehighlycorrelated,one
wouldexpectequityspreadstobehigherthandebtspreads.Ifwecancompute
howmuchmoreriskytheequitymarketis,relativetothebondmarket,wecould
usethisinformation.
Country Risk Premium = Country Risk spread x Relative Market Volatility
91
Standard Deviation in Equity Market
Standard Deviation in Long term Bond
Relative Market Volatility =
and default spreads as a start
⚫RatingsagenciessuchasS&PandMoody’sassignratingstocountriesthatreflect
theirassessmentofthedefaultriskofthesecountries.
⚫Whiledefaultriskpremiumsandequityriskpremiumsarehighlycorrelated,one
wouldexpectequityspreadstobehigherthandebtspreads.Ifwecancompute
howmuchmoreriskytheequitymarketis,relativetothebondmarket,wecould
usethisinformation.
Country Risk Premium = Country Risk spread x Relative Market Volatility
91
Standard Deviation in Equity Market
Standard Deviation in Long term Bond
Relative Market Volatility =
Country RiskSpreadfor EmergingCountries
2005 -2008 (EMBI
+
JP Morgan)
Source: CBonds
2005-2007= Huge liquidity + interest rate +
Growth of emerging countries = country risk spreads
2007-08 =
subprims + credit crunch
2005 -2008 (EMBI
+
JP Morgan)
Source: CBonds
2005-2007= Huge liquidity + interest rate +
Growth of emerging countries = country risk spreads
2007-08 =
subprims + credit crunch
Example
⚫Suppose,BrazilhaddollardenominatedC-Bonds,tradingataninterestrateof
10.01%.TheUStreasurybondratethatdaywas4%,yieldingadefaultspreadof
6.01%forBrazil.
⚫Ifwecancomputehowmuchmoreriskytheequitymarketis,relativetothebond
market,wecouldusethisinformation.Forexample,
⚫StandardDeviationinBovespa(Equity)=36%
⚫StandardDeviationinBrazilC-Bond=28.2%
⚫DefaultspreadonC-Bond=6.01%
⚫CountryRiskPremiumforBrazil=6.01%(36%/28.2%)=7.67%
⚫IfyouassumethattheriskpremiumintheUSis4.82%(1998-2003average),the
riskpremiumforBrazilwouldbe12.49%.
93
⚫Suppose,BrazilhaddollardenominatedC-Bonds,tradingataninterestrateof
10.01%.TheUStreasurybondratethatdaywas4%,yieldingadefaultspreadof
6.01%forBrazil.
⚫Ifwecancomputehowmuchmoreriskytheequitymarketis,relativetothebond
market,wecouldusethisinformation.Forexample,
⚫StandardDeviationinBovespa(Equity)=36%
⚫StandardDeviationinBrazilC-Bond=28.2%
⚫DefaultspreadonC-Bond=6.01%
⚫CountryRiskPremiumforBrazil=6.01%(36%/28.2%)=7.67%
⚫IfyouassumethattheriskpremiumintheUSis4.82%(1998-2003average),the
riskpremiumforBrazilwouldbe12.49%.
93
Discussion :
Weaknesses of the historical premium ?
⚫Fromaconceptualpointofview,onlytheanticipatedriskpremiumisacceptablefor
calculatingadiscountrate.Thepriceofanassettoday=expecteddiscountedcash
flowsthatitshouldgenerategiventherateofreturnrequiredbytheinvestortoday.
⚫Inthehistoricalpremiummethod,calculationshavetobebasedondataovera
verylongperiodinordertoreducethestandarddeviationofobservationsandto
arriveatarelevantaverage.Evenover75years,thetheoreticalstandarddeviation
ofobservationsfollowinganormalruleis2.5%,whichmeansthatapremiumof5%,
forexample,hasasmuchchanceofbeing2.5%as5%or7.5%.
94
So UBS estimates that the risk premium for the USA, calculated by Ibbotson since
1926, often cited and used (7.1% on arithmetical average and 5.2% on geometric
average), would change by one point if it were calculated from 1925 or 1927.
Weaknesses of the historical premium ?
⚫Fromaconceptualpointofview,onlytheanticipatedriskpremiumisacceptablefor
calculatingadiscountrate.Thepriceofanassettoday=expecteddiscountedcash
flowsthatitshouldgenerategiventherateofreturnrequiredbytheinvestortoday.
⚫Inthehistoricalpremiummethod,calculationshavetobebasedondataovera
verylongperiodinordertoreducethestandarddeviationofobservationsandto
arriveatarelevantaverage.Evenover75years,thetheoreticalstandarddeviation
ofobservationsfollowinganormalruleis2.5%,whichmeansthatapremiumof5%,
forexample,hasasmuchchanceofbeing2.5%as5%or7.5%.
94
So UBS estimates that the risk premium for the USA, calculated by Ibbotson since
1926, often cited and used (7.1% on arithmetical average and 5.2% on geometric
average), would change by one point if it were calculated from 1925 or 1927.
Historical inconsistent use of premiums ?
95
Fromapracticalpointofview,weseethat
thoseusingthehistoricalapproachtotherisk
premium,oftenbecausetheybelievethe
currentriskpremiumtobevolatile,whichis
true,forgetthattherisk-freeinterestrateis
evenmorevolatile,asillustratedbyfiguresfor
theFrenchsituationsince1980
95
Fromapracticalpointofview,weseethat
thoseusingthehistoricalapproachtotherisk
premium,oftenbecausetheybelievethe
currentriskpremiumtobevolatile,whichis
true,forgetthattherisk-freeinterestrateis
evenmorevolatile,asillustratedbyfiguresfor
theFrenchsituationsince1980
⚫Itisinconsistenttocalculatetheriskpremium(E(rm)–rf)usingagivenrisk-free
interestrateandintheformular=rf+ß×(E(rm)–rf),replacingrfwitha
differentfigurefromthatusedtocalculatetheriskpremium(becausemostofthe
timewedon’tknowwhatrisk-freeinterestratewasusedtocalculatetherisk
premium).
⚫Wheninterestratesrise,theriskpremiumtendstofall.Andalso,therequired
rateofreturndoesn’triseashighastheperformanceoftherisk-freeinterestrate
mightleadonetoassume,astheriskpremiumabsorbspartoftheratehike.
Andviceversaintheeventofafallininterestrates.
96
Be consistent in your use of a riskfreerate
Toconclude:contingencyoftheriskpremium
Forexample,afigurearrivedatinJuly2006(onthebasisofestimationsforthe
firsthalfof2006)isunlikelytobeofmuchrelevanceinApril2007.SinceJanuary
2006,theCAC40,theDowJonesandtheS&P500haverisenbybetween16
and19%,althoughearningsforecastshavenotbeenrevisedbythisamount.
Overthesameperiod,therisk-freeinterestrateinEuropehasrisenby80points
andintheUSAby45points,resultinginafallintheriskpremiumsincethisperiod
ofaround70basepoints.
interestrateandintheformular=rf+ß×(E(rm)–rf),replacingrfwitha
differentfigurefromthatusedtocalculatetheriskpremium(becausemostofthe
timewedon’tknowwhatrisk-freeinterestratewasusedtocalculatetherisk
premium).
⚫Wheninterestratesrise,theriskpremiumtendstofall.Andalso,therequired
rateofreturndoesn’triseashighastheperformanceoftherisk-freeinterestrate
mightleadonetoassume,astheriskpremiumabsorbspartoftheratehike.
Andviceversaintheeventofafallininterestrates.
96
Be consistent in your use of a riskfreerate
Toconclude:contingencyoftheriskpremium
Forexample,afigurearrivedatinJuly2006(onthebasisofestimationsforthe
firsthalfof2006)isunlikelytobeofmuchrelevanceinApril2007.SinceJanuary
2006,theCAC40,theDowJonesandtheS&P500haverisenbybetween16
and19%,althoughearningsforecastshavenotbeenrevisedbythisamount.
Overthesameperiod,therisk-freeinterestrateinEuropehasrisenby80points
andintheUSAby45points,resultinginafallintheriskpremiumsincethisperiod
ofaround70basepoints.
97
C. Estimating Beta
a. Bottom-up Beta
b. Top-down Beta
C. Estimating Beta
a. Bottom-up Beta
b. Top-down Beta
⚫Thestandardprocedureforestimatingbetasistoregressstockreturns(R
j)
againstmarketreturns(R
m)-
R
j= a + b R
m
⚫whereaistheinterceptandbistheslopeoftheregression.
⚫Theslopeoftheregression(b)correspondstothebetaofthestock,and
measurestheriskinessofthestock.
i
R
i
R
M
ESTIMATION DU BÊTA
a. Bottom-up Beta
j)
againstmarketreturns(R
m)-
R
j= a + b R
m
⚫whereaistheinterceptandbistheslopeoftheregression.
⚫Theslopeoftheregression(b)correspondstothebetaofthestock,and
measurestheriskinessofthestock.
i
R
i
R
M
ESTIMATION DU BÊTA
a. Bottom-up Beta
Estimating Performance
Jensen’s Alpha
⚫Theinterceptoftheregressionprovidesasimplemeasureofperformance
duringtheperiodoftheregression,relativetothecapitalassetpricingmodel.
R
j=R
f+b(R
m-R
f)
=R
f(1-b)+bR
m ...........CapitalAssetPricingModel
R
j=a +bR
m ...........RegressionEquation
⚫If
a>R
f(1-b)....Stockdidbetterthanexpectedduringregressionperiod
a=R
f(1-b)....Stockdidaswellasexpectedduringregressionperiod
a<R
f(1-b)....Stockdidworsethanexpectedduringregressionperiod
99
ThedifferencebetweentheinterceptandR
f(1-b)isJensen'salpha.Ifitis
positive,yourstockdidperformbetterthanexpectedduringtheperiodof
theregression.
Jensen’s Alpha
⚫Theinterceptoftheregressionprovidesasimplemeasureofperformance
duringtheperiodoftheregression,relativetothecapitalassetpricingmodel.
R
j=R
f+b(R
m-R
f)
=R
f(1-b)+bR
m ...........CapitalAssetPricingModel
R
j=a +bR
m ...........RegressionEquation
⚫If
a>R
f(1-b)....Stockdidbetterthanexpectedduringregressionperiod
a=R
f(1-b)....Stockdidaswellasexpectedduringregressionperiod
a<R
f(1-b)....Stockdidworsethanexpectedduringregressionperiod
99
ThedifferencebetweentheinterceptandR
f(1-b)isJensen'salpha.Ifitis
positive,yourstockdidperformbetterthanexpectedduringtheperiodof
theregression.
Jensen’s Alpha
A 1
A
M
E(R
i)
A
B
A was undervalued
B was overvalued
B
Security Market Line
A 1
A
M
E(R
i)
A
B
A was undervalued
B was overvalued
B
Security Market Line
Setting up for the Estimation
⚫Decideonanestimationperiod
⚫Servicesuseperiodsrangingfrom2to5yearsfortheregression
⚫Longerestimationperiodprovidesmoredata,butfirmschange.
⚫Shorterperiodscanbeaffectedmoreeasilybysignificantfirm-specific
eventthatoccurredduringtheperiod
⚫Decideonareturninterval-daily,weekly,monthly
⚫Shorterintervalsyieldmoreobservations,butsufferfrommorenoise.
⚫Noiseiscreatedbystocksnottradingandbiasesallbetastowardsone.
⚫Estimatereturns(includingdividends)onstock
⚫Return=(Price
End-Price
Beginning+Dividends
Period)/Price
Beginning
⚫Chooseamarketindex,andestimatereturns(inclusiveofdividends)
ontheindexforeachintervalfortheperiod
101
⚫Decideonanestimationperiod
⚫Servicesuseperiodsrangingfrom2to5yearsfortheregression
⚫Longerestimationperiodprovidesmoredata,butfirmschange.
⚫Shorterperiodscanbeaffectedmoreeasilybysignificantfirm-specific
eventthatoccurredduringtheperiod
⚫Decideonareturninterval-daily,weekly,monthly
⚫Shorterintervalsyieldmoreobservations,butsufferfrommorenoise.
⚫Noiseiscreatedbystocksnottradingandbiasesallbetastowardsone.
⚫Estimatereturns(includingdividends)onstock
⚫Return=(Price
End-Price
Beginning+Dividends
Period)/Price
Beginning
⚫Chooseamarketindex,andestimatereturns(inclusiveofdividends)
ontheindexforeachintervalfortheperiod
101
Example : Disney
⚫Period used : 5 years
⚫Return Interval = Monthly
⚫Market Index: S&P 500 Index.
⚫For instance, to calculate returns on Disney in December 1999,
⚫Price for Disney at end of November 1999 = $ 27.88
⚫Price for Disney at end of December 1999 = $ 29.25
⚫Dividends during month = $0.21
⚫Return = ($29.25 -$27.88 + $ 0.21)/$27.88= 5.69%
⚫To estimate returns on the index in the same month
⚫Index level (including dividends) at end of November 1999 = 1388.91
⚫Index level (including dividends) at end of December 1999 = 1469.25
⚫Return =(1469.25 -1388.91)/1388.91 = 5.78%
⚫Using monthly returns from 1999 to 2003, we ran a regression of returns on
Disney stock against the S*P 500. The output is below:
Returns
Disney= 0.0467% + 1.01 Returns
S & P 500 (R squared= 29%)
(0.20)
102
⚫Period used : 5 years
⚫Return Interval = Monthly
⚫Market Index: S&P 500 Index.
⚫For instance, to calculate returns on Disney in December 1999,
⚫Price for Disney at end of November 1999 = $ 27.88
⚫Price for Disney at end of December 1999 = $ 29.25
⚫Dividends during month = $0.21
⚫Return = ($29.25 -$27.88 + $ 0.21)/$27.88= 5.69%
⚫To estimate returns on the index in the same month
⚫Index level (including dividends) at end of November 1999 = 1388.91
⚫Index level (including dividends) at end of December 1999 = 1469.25
⚫Return =(1469.25 -1388.91)/1388.91 = 5.78%
⚫Using monthly returns from 1999 to 2003, we ran a regression of returns on
Disney stock against the S*P 500. The output is below:
Returns
Disney= 0.0467% + 1.01 Returns
S & P 500 (R squared= 29%)
(0.20)
102
Estimating Disney Performance
⚫Intercept = 0.0467%
⚫This is an intercept based on monthly returns. Thus, it has to be compared to a
monthly riskfree rate.
⚫Between 1999 and 2003,
⚫Monthly Riskfree Rate = 0.313% (based upon average T.Bill rate: 99-03)
⚫Riskfree Rate (1-Beta) = 0.313% (1-1.01) = -..0032%
⚫The Comparison is then between
InterceptversusRiskfree Rate (1 -Beta)
0.0467% versus0.313%(1-1.01)= -0.0032%
⚫Jensen’s Alpha = 0.0467% -(-0.0032%) = 0.05%
⚫Disney did 0.05% better than expected, per month, between 1999 and 2003.
⚫Annualized, Disney’s annual excess return = (1.0005)
12
-1= 0.60%
103
Disney has a positive Jensen’s alpha of 0.60% a year between 1999 and 2003. This
can be viewed as a sign that management in the firm did a good job, managing the
firm during the period.
a)True
b)False
⚫Intercept = 0.0467%
⚫This is an intercept based on monthly returns. Thus, it has to be compared to a
monthly riskfree rate.
⚫Between 1999 and 2003,
⚫Monthly Riskfree Rate = 0.313% (based upon average T.Bill rate: 99-03)
⚫Riskfree Rate (1-Beta) = 0.313% (1-1.01) = -..0032%
⚫The Comparison is then between
InterceptversusRiskfree Rate (1 -Beta)
0.0467% versus0.313%(1-1.01)= -0.0032%
⚫Jensen’s Alpha = 0.0467% -(-0.0032%) = 0.05%
⚫Disney did 0.05% better than expected, per month, between 1999 and 2003.
⚫Annualized, Disney’s annual excess return = (1.0005)
12
-1= 0.60%
103
Disney has a positive Jensen’s alpha of 0.60% a year between 1999 and 2003. This
can be viewed as a sign that management in the firm did a good job, managing the
firm during the period.
a)True
b)False
Agencies adjustments
⚫Bloomberg :
Adjusted Bêta = Raw Bêta x 0,67 + 1 x 0,33
⚫Dividend are no considered
⚫Period regression is limited to 2 years
US isa mature economy
2/3 of US listedfirmshave a beta between0,8 et 1,2
⚫Bloomberg :
Adjusted Bêta = Raw Bêta x 0,67 + 1 x 0,33
⚫Dividend are no considered
⚫Period regression is limited to 2 years
US isa mature economy
2/3 of US listedfirmshave a beta between0,8 et 1,2
Beta : Exploring Fundamentals
⚫IndustryEffects:Thebetavalueforafirmdependsuponthesensitivityofthe
demandforitsproductsandservicesandofitscoststomacroeconomicfactors
thataffecttheoverallmarket.
⚫Cyclicalcompanieshavehigherbetasthannon-cyclicalfirms
⚫Firmswhichsellmorediscretionaryproductswillhavehigherbetasthanfirms
thatselllessdiscretionaryproducts
⚫Operatingleverage:Otherthingsremainingequal,higheroperatingleverage
resultsingreaterearningsvariabilitywhichinturnresultsinhigherbetas.
⚫FixedCostsMeasure=FixedCosts/VariableCosts
⚫EBITVariabilityMeasure=%ChangeinEBIT/%ChangeinRevenues
⚫Thismeasureshowquicklytheearningsbeforeinterestandtaxeschangesas
revenuechanges.Thehigherthisnumber,thegreatertheoperatingleverage.
⚫FinancialLeverage:Asfirmsborrow,theycreatefixedcosts(interest
payments)thatmaketheirearningstoequityinvestorsmorevolatile.This
increasedearningsvolatilitywhichincreasestheequitybeta
105
⚫IndustryEffects:Thebetavalueforafirmdependsuponthesensitivityofthe
demandforitsproductsandservicesandofitscoststomacroeconomicfactors
thataffecttheoverallmarket.
⚫Cyclicalcompanieshavehigherbetasthannon-cyclicalfirms
⚫Firmswhichsellmorediscretionaryproductswillhavehigherbetasthanfirms
thatselllessdiscretionaryproducts
⚫Operatingleverage:Otherthingsremainingequal,higheroperatingleverage
resultsingreaterearningsvariabilitywhichinturnresultsinhigherbetas.
⚫FixedCostsMeasure=FixedCosts/VariableCosts
⚫EBITVariabilityMeasure=%ChangeinEBIT/%ChangeinRevenues
⚫Thismeasureshowquicklytheearningsbeforeinterestandtaxeschangesas
revenuechanges.Thehigherthisnumber,thegreatertheoperatingleverage.
⚫FinancialLeverage:Asfirmsborrow,theycreatefixedcosts(interest
payments)thatmaketheirearningstoequityinvestorsmorevolatile.This
increasedearningsvolatilitywhichincreasestheequitybeta
105
Equity Betas and Leverage
⚫The beta of equity alone can be written as a function of the unlevered beta
and the debt-equity ratio :
L
=
u
(1+ ((1-t)D/E))
Where :
L
= Levered or Equity Beta
u
= Unlevered Beta
t = Corporate tax rate
D = Market Value of Debt
E = Market Value of Equity
106
TheregressionbetaforDisneyis1.01duringtheperiodoftheregression(1999to
2003)andtheaveragedebtequityratioduringthisperiodwas27.5%.
TheunleveredbetaforDisneycanthenbeestimated(usingataxrateof37.3%)
=CurrentBeta/(1+(1-taxrate)(AverageDebt/Equity))
=1.01/(1+(1-0.373))(0.275)=0.8615
⚫The beta of equity alone can be written as a function of the unlevered beta
and the debt-equity ratio :
L
=
u
(1+ ((1-t)D/E))
Where :
L
= Levered or Equity Beta
u
= Unlevered Beta
t = Corporate tax rate
D = Market Value of Debt
E = Market Value of Equity
106
TheregressionbetaforDisneyis1.01duringtheperiodoftheregression(1999to
2003)andtheaveragedebtequityratioduringthisperiodwas27.5%.
TheunleveredbetaforDisneycanthenbeestimated(usingataxrateof37.3%)
=CurrentBeta/(1+(1-taxrate)(AverageDebt/Equity))
=1.01/(1+(1-0.373))(0.275)=0.8615
Boeing :Beta and Leverage
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
0.860.921 1.11.231.421.72.163.15.89
Debt/EquityRatio
(%)
Bêta
0,00 0,86
11,11 0,92
25,00 1,00
42,86 1,10
66,67 1,23
100,00 1,42
150,00 1,70
233,33 2,16
400,00 3,10
900,00 5,89
With : r
f= 4,5%
[E(R
M) –R
f] = 6,38%
Boeing’sCostof Equity
0%
5%
10%
15%
20%
25%
30%
35%
40%
45%
0.860.921 1.11.231.421.72.163.15.89
Debt/EquityRatio
(%)
Bêta
0,00 0,86
11,11 0,92
25,00 1,00
42,86 1,10
66,67 1,23
100,00 1,42
150,00 1,70
233,33 2,16
400,00 3,10
900,00 5,89
With : r
f= 4,5%
[E(R
M) –R
f] = 6,38%
Boeing’sCostof Equity
b. Top-down Beta
⚫The top-down beta for a firm comes from a regression
⚫The bottom up beta is a better estimate than the top down beta for
the following reasons :
⚫The standard error of the beta estimate will be much lower
⚫The betas can reflect the current (and even expected future) mix
of businesses that the firm is in rather than the historical mix
⚫The top-down beta for a firm comes from a regression
⚫The bottom up beta is a better estimate than the top down beta for
the following reasons :
⚫The standard error of the beta estimate will be much lower
⚫The betas can reflect the current (and even expected future) mix
of businesses that the firm is in rather than the historical mix
Find the betas of
other firms in these
businesses
Find the
unlevered
betas of
other firms
in these
businesses
Lever up using
the firm’s
debt/equity ratio
Average
Sectorial
Beta
Take a weighted (by sales or
operating income) average
of these unlevered betas
Find out the businesses that a firm operates in
Several Business
Bottom-up Beta
other firms in these
businesses
Find the
unlevered
betas of
other firms
in these
businesses
Lever up using
the firm’s
debt/equity ratio
Average
Sectorial
Beta
Take a weighted (by sales or
operating income) average
of these unlevered betas
Find out the businesses that a firm operates in
Several Business
Bottom-up Beta
A single Business : Home DepotNom de l’entreprise Bêta Capitalisation
boursière
(millions Euro)
Endettement à
moins d’un an
(Euro)
Endettement à
long terme
(Euro)
D/CP
(%)
Building Materials
Catalina Lighting
Cont’I Materials Corp
Eagle Hardware
Emco Limited
Fastenal Co
Homebase Inc.
Hugues Supply
Lowe’s Cos.
Waxman Industries
Westburne Inc.
Wolohan Lumber
1,05
1
0,55
0,95
0,65
1,25
1,1
1
1,2
1,25
0,65
0,55
0,93
136
16
32
612
187
1 157
227
610
12 554
18
607
76
16 233
1
7
2
6
39
16
1
111
6
9
2
200
113
19
7
146
119
-
116
335
1 046
121
34
20
2 075
14,01
Source : Value Line
Home Depot unlevered Beta = 0,93 / [1 + (1 –0,35) (0,1401)] = 0,86
Home Depot Market value of Equity = 51 739 millions USD ???
Home Depot Market value of Debt = 1 137 millions USD ???
Home Depot Bottom up Beta = 0,86 [1 + (1 –0,35) (1 137/ 51 739)] = 0,87
Comparable firms Beta
MarketValue
of Equity
MarketValue
of Short term
Debt
MarketValue
of Long term
Debt
Debtto
Capital
boursière
(millions Euro)
Endettement à
moins d’un an
(Euro)
Endettement à
long terme
(Euro)
D/CP
(%)
Building Materials
Catalina Lighting
Cont’I Materials Corp
Eagle Hardware
Emco Limited
Fastenal Co
Homebase Inc.
Hugues Supply
Lowe’s Cos.
Waxman Industries
Westburne Inc.
Wolohan Lumber
1,05
1
0,55
0,95
0,65
1,25
1,1
1
1,2
1,25
0,65
0,55
0,93
136
16
32
612
187
1 157
227
610
12 554
18
607
76
16 233
1
7
2
6
39
16
1
111
6
9
2
200
113
19
7
146
119
-
116
335
1 046
121
34
20
2 075
14,01
Source : Value Line
Home Depot unlevered Beta = 0,93 / [1 + (1 –0,35) (0,1401)] = 0,86
Home Depot Market value of Equity = 51 739 millions USD ???
Home Depot Market value of Debt = 1 137 millions USD ???
Home Depot Bottom up Beta = 0,86 [1 + (1 –0,35) (1 137/ 51 739)] = 0,87
Comparable firms Beta
MarketValue
of Equity
MarketValue
of Short term
Debt
MarketValue
of Long term
Debt
Debtto
Capital
Two areas of Business : Boeing
ToestimateBoeing’sbetatoday,wedivideditsbusinessintotwoareas:
Commercial Aircraft;
Corebusiness of
manufacturing
commercial jet aircraftand
providingrelatedsupport
services
Information, Space, and
DefenseSystems (ISDS);
Research, development,
production, and support
of militaryaircraft,
helicopters, and missile
systems
ToestimateBoeing’sbetatoday,wedivideditsbusinessintotwoareas:
Commercial Aircraft;
Corebusiness of
manufacturing
commercial jet aircraftand
providingrelatedsupport
services
Information, Space, and
DefenseSystems (ISDS);
Research, development,
production, and support
of militaryaircraft,
helicopters, and missile
systems
Two areas of Business : Boeing
Boeing unlevered beta =
value-weighted average of the betas of each of the different business areas = 0.88
Equity Beta for Boeing = 0,88 [1 + (1 –0,35) (8,2/32,60)] = 1,014
Segment Revenues Estimated
Value
Unlevered
Beta
Segment
Weight
Weighted
Beta
Commercial Aircraft*
ISDS**
Firm
$26,929
18,125
$30,160.48
12,687.50
42,848
0.91
0.80
70.39%
29.61%
100.00%
0.6405
0.2369
0.88
EstimatingUnleveredBetas for Boeing’sBusiness Areas
*We looked at Boeing’s own beta prior to its expansion in the defense business and computed the unlevered
beta using this estimate
**For ISDS, we used 17 firms that derive the bulk of their revenues from defense contracting, and we computed
the average beta and debt/equity ratio for these firms
Value of DebtMarketValue of Equity
Boeing unlevered beta =
value-weighted average of the betas of each of the different business areas = 0.88
Equity Beta for Boeing = 0,88 [1 + (1 –0,35) (8,2/32,60)] = 1,014
Segment Revenues Estimated
Value
Unlevered
Beta
Segment
Weight
Weighted
Beta
Commercial Aircraft*
ISDS**
Firm
$26,929
18,125
$30,160.48
12,687.50
42,848
0.91
0.80
70.39%
29.61%
100.00%
0.6405
0.2369
0.88
EstimatingUnleveredBetas for Boeing’sBusiness Areas
*We looked at Boeing’s own beta prior to its expansion in the defense business and computed the unlevered
beta using this estimate
**For ISDS, we used 17 firms that derive the bulk of their revenues from defense contracting, and we computed
the average beta and debt/equity ratio for these firms
Value of DebtMarketValue of Equity
Beta of firm after an acquisition:
Boeing and Mc Donnell Douglas
⚫In1997,BoeingannouncedthatitwasacquiringMcDonnelDouglas,another
companyinvolvedintheaerospaceanddefensesystem.Atthetimeofthe
acqusition,thetwofirmshadthefollowingmarketvalueandbetas:
Boeing’s unlevered beta = 0,95/[1 + 0,65 (3 980/32 438)] = 0,88
Mc Donnell Douglas unlevered beta = 0,90/[1 + 0,65 (2 143/12 555)] = 0,81
Unlevered beta for combined firm =
0,88 (36 418/51 116) + 0,81 (14 698/51 116) = 0,86
Company Beta Debt Equity FirmValue
Boeing
Mc DonnellDouglas
0.95
0.90
$3,980
2,143
$32,438
12,555
$36,418
14,698
Weightsbasedon the marketvalue of the twofirms
Boeing and Mc Donnell Douglas
⚫In1997,BoeingannouncedthatitwasacquiringMcDonnelDouglas,another
companyinvolvedintheaerospaceanddefensesystem.Atthetimeofthe
acqusition,thetwofirmshadthefollowingmarketvalueandbetas:
Boeing’s unlevered beta = 0,95/[1 + 0,65 (3 980/32 438)] = 0,88
Mc Donnell Douglas unlevered beta = 0,90/[1 + 0,65 (2 143/12 555)] = 0,81
Unlevered beta for combined firm =
0,88 (36 418/51 116) + 0,81 (14 698/51 116) = 0,86
Company Beta Debt Equity FirmValue
Boeing
Mc DonnellDouglas
0.95
0.90
$3,980
2,143
$32,438
12,555
$36,418
14,698
Weightsbasedon the marketvalue of the twofirms
⚫Boeing’sacquisitionofMcDonnellDouglaswasaccomplishedbyissuingnew
stockinBoeingtocoverthevalueofMcDonnellDouglas’sequityof$12,555
million.Sincenonewdebtwasissuedtofinancethedeal,thedebtoutstanding
inthefirmaftertheacquisitionisjustthesumofthedebtoutstandingatthetwo
companiesbeforetheacquisition:
Debt
Boeing
=McDonnelDouglasOldDebt+Boeing’sOldDebt=
$3,980 + $2,143 = $6,123 million
Equity
Boeing
= Boeing’s old Equity + New Equity used for Acquisition
$32,438 + $12,555 = $44,993 million
D/E = $6,123/$44,993 = 13,61 %
New beta = 0,86 [1 + 0,65 (0,1361)] = 0,94
Beta of firm after an acquisition:
Boeing and Mc Donnell Douglas
stockinBoeingtocoverthevalueofMcDonnellDouglas’sequityof$12,555
million.Sincenonewdebtwasissuedtofinancethedeal,thedebtoutstanding
inthefirmaftertheacquisitionisjustthesumofthedebtoutstandingatthetwo
companiesbeforetheacquisition:
Debt
Boeing
=McDonnelDouglasOldDebt+Boeing’sOldDebt=
$3,980 + $2,143 = $6,123 million
Equity
Boeing
= Boeing’s old Equity + New Equity used for Acquisition
$32,438 + $12,555 = $44,993 million
D/E = $6,123/$44,993 = 13,61 %
New beta = 0,86 [1 + 0,65 (0,1361)] = 0,94
Beta of firm after an acquisition:
Boeing and Mc Donnell Douglas
1.4. Evolution from the CAPM
⚫CAPM:
⚫Maxreturn&minriskbydiversification
⚫Diversified-marketportfolioreturntoexplainstockreturn
⚫Otherfactorsthatexplainreturns?
115
A.The Size Effet : Small Caps versus Large Caps
B.The Value Effect
C.The Fama-French 3 Factor Model
ProfessorsGeneFamaandKenFrench(1992,1993)arguethattwoadditional
factorsshouldbeaddedandappeartobeusefulinexplainingtherelationship
betweenriskandreturn.
➢Size,asmeasuredbymarketcapitalization:Smallcompanystockshave
higherexpectedreturnsthanlargecompanystocks.
➢Thebookvaluetomarketvalueratio,i.e.,B/M:Lower-priced"value"stocks
havehigherexpectedreturnsthanhigher-priced"growth"stocks.
Whetherthesetwoadditionalfactorsaretrulysourcesofsystematicriskisstill
beingdebated.
⚫CAPM:
⚫Maxreturn&minriskbydiversification
⚫Diversified-marketportfolioreturntoexplainstockreturn
⚫Otherfactorsthatexplainreturns?
115
A.The Size Effet : Small Caps versus Large Caps
B.The Value Effect
C.The Fama-French 3 Factor Model
ProfessorsGeneFamaandKenFrench(1992,1993)arguethattwoadditional
factorsshouldbeaddedandappeartobeusefulinexplainingtherelationship
betweenriskandreturn.
➢Size,asmeasuredbymarketcapitalization:Smallcompanystockshave
higherexpectedreturnsthanlargecompanystocks.
➢Thebookvaluetomarketvalueratio,i.e.,B/M:Lower-priced"value"stocks
havehigherexpectedreturnsthanhigher-priced"growth"stocks.
Whetherthesetwoadditionalfactorsaretrulysourcesofsystematicriskisstill
beingdebated.
A. The Size Effet :
Small Caps versus Large Caps
⚫Rolf Banz (1981), University of Chicago
⚫Analyzed NYSE stocks, 1926-1975.
⚫Finds that, in the long term, small companies have higher expected returns
than large companies and behave differently.
⚫Dimensional Fund Advisorsis founded in 1981 and launches the first
passive small cap strategy (the US Micro Cap Portfolio).
116
Small Caps versus Large Caps
⚫Rolf Banz (1981), University of Chicago
⚫Analyzed NYSE stocks, 1926-1975.
⚫Finds that, in the long term, small companies have higher expected returns
than large companies and behave differently.
⚫Dimensional Fund Advisorsis founded in 1981 and launches the first
passive small cap strategy (the US Micro Cap Portfolio).
116
Small Caps versus Large Caps
USAEurope
Source : Conseil d’Analyse Économique, september 2008
InternationalSizeEffectStevenL.Heston,K.GeertRouwenhorst,andRobertoE.
Wesselsfindevidenceofhigheraveragereturnstosmallcompaniesintwelveinternational
markets.“TheStructureofInternationalStockReturnsandtheIntegrationofCapitalMarkets,”
JournalofEmpiricalFinance2,no.3(September1995):173-97.
USAEurope
Source : Conseil d’Analyse Économique, september 2008
InternationalSizeEffectStevenL.Heston,K.GeertRouwenhorst,andRobertoE.
Wesselsfindevidenceofhigheraveragereturnstosmallcompaniesintwelveinternational
markets.“TheStructureofInternationalStockReturnsandtheIntegrationofCapitalMarkets,”
JournalofEmpiricalFinance2,no.3(September1995):173-97.
B. The Value Effect
Returns to Value and Growth Stocks
by Country 1975-1995
0%
5%
10%
15%
20%
25%
Average
Annual
Rate
of
Return
Growth
Value
Source : Robert A. Haugen
Prentice Hall, 1999
Returns to Value and Growth Stocks
by Country 1975-1995
0%
5%
10%
15%
20%
25%
Average
Annual
Rate
of
Return
Growth
Value
Source : Robert A. Haugen
Prentice Hall, 1999
119
C. The Fama-French 3 Factor Model
⚫FamaandFrench(1992)investigate100NYSEportfoliosfortheperiod
1963-1990
⚫Theportfoliosaregroupedinto10sizeclassesand10betaclasses
⚫Theyfindthatreturndifferential(riskpremium)onisnegative(and
nonsignificant)
⚫whereasreturndifferentialonsizeislargeandsignificant.
C. The Fama-French 3 Factor Model
⚫FamaandFrench(1992)investigate100NYSEportfoliosfortheperiod
1963-1990
⚫Theportfoliosaregroupedinto10sizeclassesand10betaclasses
⚫Theyfindthatreturndifferential(riskpremium)onisnegative(and
nonsignificant)
⚫whereasreturndifferentialonsizeislargeandsignificant.
Beta vs. Return by size classes
NYSE 1941-1990
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Beta
5%
10%
15%
20%
25%
30%
Return Big Caps
Small Caps
Source : Robert A. Haugen
Prentice Hall, 1999
CAPM seems correct !
NYSE 1941-1990
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Beta
5%
10%
15%
20%
25%
30%
Return Big Caps
Small Caps
Source : Robert A. Haugen
Prentice Hall, 1999
CAPM seems correct !
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Bêta
5%
10%
15%
20%
25%
30%
Rendements
annualisés
Small Caps
Beta vs. Return : each size classes is divided in betas classes
NYSE 1941-1990
Big Caps
Source : Robert A. Haugen
Prentice Hall, 1999
For eachsize classe, thereisan inverse relation betweenriskand return !
The riskand return relation isin facta relation size-return
Bêta
5%
10%
15%
20%
25%
30%
Rendements
annualisés
Small Caps
Beta vs. Return : each size classes is divided in betas classes
NYSE 1941-1990
Big Caps
Source : Robert A. Haugen
Prentice Hall, 1999
For eachsize classe, thereisan inverse relation betweenriskand return !
The riskand return relation isin facta relation size-return
What are the Fama-French findings combining
Value and size effects ?
⚫1. “The Cross-Section of Expected Stock Returns”, Eugene F. Fama and
Kenneth R. French, The Journal of Finance, Vol. 47, No. 2 (Jun., 1992),
pp. 427-465
⚫2.“Commonriskfactorsinthereturnsonstocksandbonds”,EugeneF.
FamaandKennethR.French,JFE33,1993
122
High returns of small and value stocks are compensation of risks not
captured by CAPM
Value and size effects ?
⚫1. “The Cross-Section of Expected Stock Returns”, Eugene F. Fama and
Kenneth R. French, The Journal of Finance, Vol. 47, No. 2 (Jun., 1992),
pp. 427-465
⚫2.“Commonriskfactorsinthereturnsonstocksandbonds”,EugeneF.
FamaandKennethR.French,JFE33,1993
122
High returns of small and value stocks are compensation of risks not
captured by CAPM
The Fama-French 3 Factor
123
R
FPL : an initial estimate of the FPL cost
of common equity during period t
R
f,t: the return on the risk-free asset
β’s are the “betas” for each factor
β
i,mis the CAPM “beta”
RPM:differencebetweenreturnsonadiversified
marketportfolioandarisk-freereturn
SMB(smallminusbig):differencebetweenreturns
ondiversifiedportfoliosofsmallandlarge
capitalizationstocks
HML(highminuslow):differencebetweenreturns
ondiversifiedportfoliosofhigh(distressedfirms)
andlowB/M(not–distressedfirms)stocks( ) () ( )HMLSMLRPMRR
hmlFPLsmlFPLmFPLfFPL ,,, +++=
Application : Home Depot’sFama-French Costof Equity
123
R
FPL : an initial estimate of the FPL cost
of common equity during period t
R
f,t: the return on the risk-free asset
β’s are the “betas” for each factor
β
i,mis the CAPM “beta”
RPM:differencebetweenreturnsonadiversified
marketportfolioandarisk-freereturn
SMB(smallminusbig):differencebetweenreturns
ondiversifiedportfoliosofsmallandlarge
capitalizationstocks
HML(highminuslow):differencebetweenreturns
ondiversifiedportfoliosofhigh(distressedfirms)
andlowB/M(not–distressedfirms)stocks( ) () ( )HMLSMLRPMRR
hmlFPLsmlFPLmFPLfFPL ,,, +++=
Application : Home Depot’sFama-French Costof Equity
⚫Stockmarketefficiency
⚫Highreturnsarecompensationforhighrisks.Theknowledgeofthe
performanceiswidespread.
⚫Outperformanceisunlikelytocontinue
⚫Stockmarketisnotefficient
⚫Anopportunityforsophisticatedinvestorstoconsistentlyoutperformthe
market.Noexplanationforrisk-returncompensation.
⚫Shortwindowofopportunity
The difficulty in identifying the
sources of SMB and HML risks
⚫Highreturnsarecompensationforhighrisks.Theknowledgeofthe
performanceiswidespread.
⚫Outperformanceisunlikelytocontinue
⚫Stockmarketisnotefficient
⚫Anopportunityforsophisticatedinvestorstoconsistentlyoutperformthe
market.Noexplanationforrisk-returncompensation.
⚫Shortwindowofopportunity
The difficulty in identifying the
sources of SMB and HML risks
Pros and Cons
Pros:
⚫Recentlydevelopedadditiontothetoolkitforestimatingthecostofcommonequity
capital
⚫Explainsagreaterproportionofthenon-diversifiablevolatilityofstocksreturns
relativetoCAPM
Cons:
⚫Notbasedontheory,justa“bruteforce”waytoexplainmoreofthevolatilityin
returns
⚫Factorsarehighlyvolatileasarecostofcapitalestimates
⚫AddinganyvariabletoaregressionincreasesR-square
125
Indice Style Dec. 2000 Dec. 2003 Dec. 2007
Larges Caps
Small Caps
Growth
Value
Large Cap Growth
Small Cap Value
Indice général
14,1
7,2
13,7
12,4
14,6
6,0
13,2
4,7
20,6
-4,3
5,4
-6,5
24,1
-1,9
12,8
2,9
12,5
12,2
12,2
2,6
12,5
Returns on 3 years
(annual %)
Source :
www.demarche.com
Pros:
⚫Recentlydevelopedadditiontothetoolkitforestimatingthecostofcommonequity
capital
⚫Explainsagreaterproportionofthenon-diversifiablevolatilityofstocksreturns
relativetoCAPM
Cons:
⚫Notbasedontheory,justa“bruteforce”waytoexplainmoreofthevolatilityin
returns
⚫Factorsarehighlyvolatileasarecostofcapitalestimates
⚫AddinganyvariabletoaregressionincreasesR-square
125
Indice Style Dec. 2000 Dec. 2003 Dec. 2007
Larges Caps
Small Caps
Growth
Value
Large Cap Growth
Small Cap Value
Indice général
14,1
7,2
13,7
12,4
14,6
6,0
13,2
4,7
20,6
-4,3
5,4
-6,5
24,1
-1,9
12,8
2,9
12,5
12,2
12,2
2,6
12,5
Returns on 3 years
(annual %)
Source :
www.demarche.com
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