growth, inflation and terminal value
TRANSCRIPT
Chair of Finance, 1 Prof. Dr. Bernhard Schwetzler
Prof. Dr. Bernhard Schwetzler
CCT Center for Corporate Transactions
Chair of Financial Management and Banking
Growth, Inflation and Terminal Value
Dahlem lectures on FACTS
12.11.2009
Chair of Finance, 2 Prof. Dr. Bernhard Schwetzler
1. Motivation
2. Conventional wisdom: The Gordon-Shapiro model
3. A challenge to conventional wisdom: The Bradley/Jarrell model
4. Analyzing growth and inflation
5. Bonus track: Beta stability
Agenda
Chair of Finance, 3 Prof. Dr. Bernhard Schwetzler
Motivation
Inflation obviously plays a role in corporate valuation, but there is no consensus how to properly take inflation into account
Recent claims: Valuation formulas and accounting numbers have to be adjusted
German Institute of CPA (IDW) proposes a stepwise procedure to combine retention – based growth and inflation – based growth
Bradley and Jarrell (2003, 2008) conclude that the well known Gordon-Shapiro model for terminal value calculation does not properly account for the effects of inflation
Our question: How should terminal values be calculated under inflation?
Chair of Finance, 4 Prof. Dr. Bernhard Schwetzler
1. Motivation
2. Conventional wisdom: The Gordon-Shapiro model
3. A challenge to conventional wisdom: The Bradley/Jarrell model
4. Analyzing growth and inflation
5. Bonus track: Beta stability
Agenda
Chair of Finance, 5 Prof. Dr. Bernhard Schwetzler
Earnings before Interest and Taxes (EBIT)*- Taxes
= Net Operating Profit less adjusted Taxes (NOPLAT)
+ Depreciation- Investment (fixed assets)± Change of Net Operating Working Capital
(- investments/+ divestments in operating current assets ± change of short-term liabilities)
± Change of pension reserves
= Free Cash Flow (Entity Approach)
* after interest on pension reserves
Starting point: NOPLAT, retention and free cash flow
• NOPLAT is the fictional profit less adjusted taxes of an all equity-financed firm
• In terminal value calculations retention determines the change in the firm´s assets
Retention as difference between earnings (NOPLAT) and free cash flow
Chair of Finance, 6 Prof. Dr. Bernhard Schwetzler
resp. Int · RoI = g · NOPLATt
Growth requires net investments > 0!
In1 · RoI = ∆ NOPLAT2
NOPLATt = FCFt
t1 2 3 4 5
In1
∆NOPLAT2
NOPLATt,FCFt
NOPLATt
FCFt
Starting point = steady state:• Depreciation = Capex or net
investments (Int) = 0
• Net investments into net working capital ∆ NWC = 0
• ∆ Long-term reserves = 0
Steady state ⇒ No growth!⇒ Perpetuity Model
Required retentionin period 1= net
investment
Return on net investment
Additional NOPLAT from period 2…∞
Gordon-Shapiro (GS) model combines growth and return (1)
qt · RoI = gt
As Int/NOPLATt = retention rate q:
Chair of Finance, 7 Prof. Dr. Bernhard Schwetzler
NOPLATt,FCFt
NOPLATt
FCFt
t1 2 3 4 5
In1,EC
∆ NOLPAT2
In2,EC
In3,ECIn4,EC
In5,EC
NOPLAT5
FCF5
∆ NOLPAT3
∆ NOLPAT4
∆ NOLPAT5
Retain in every future period:
Gordon-Shapiro (GS) model combines growth and return (2)
q · RoI = g ∀ t
[ ]gWACC
q1NOPLATV 1T
T −−
= +
τ
gWACCRoIg1NOPLAT
V1T
T −
−
=τ
+
Chair of Finance, 8 Prof. Dr. Bernhard Schwetzler
gWACCRoIg1NOPLAT
V1T
LT −
−
=τ
+
• The return on net investments RoI (Return on invested capital)
• The retention rate q
Along with the Free Cash Flow and the WACC , the perpetual growth rate and the Terminal Value is driven by two factors:
or [ ]RoIqWACC
q1NOPLATV 1TLT ⋅−
−= +
τ
q · RoI = g
Gordon-Shapiro (GS) model combines growth and return (3)
τ
Chair of Finance, 9 Prof. Dr. Bernhard Schwetzler
For a given growth rate g, RoI determines the fraction of NOPLAT that has to be retained and reinvested to "generate" g.
⇒ is the retention rate (portion of NOPLAT to be retained and invested)RoIg
Company A
g = 6 %; RoI = 20 %
⇒ %302.0
06.0RoIg
==
g = 6 %; RoI = 15 %
⇒ %4015.006.0
RoIg
==
1 2 3 4
NOPLATt 100 106 112.36 119.1
- Int = 0.3 ·NOPLAT -30 -31.8 -33.71 -35.73
FCFt 70 74.2 78.65 88.37
1 2 3 4
NOPLATt 100 106 112.36 119.1
- Int = 0.4 ·NOPLATt -40 -42.4 -44.94 -47.64
60 63.6 67.42 71.46
⇒ Both companies have identical growth rates g for NOPLAT and FCF.⇒ Company A has higher Free Cash Flows than Company B!
Company B
The major impact factor is the return on net investments (RoI)
Chair of Finance, 10 Prof. Dr. Bernhard Schwetzler
Profitability of net investments:
Perpetual Formula; Terminal Value is independent of g
⇒ WACCt = RoI Neutral growth; no excess returns
⇒ WACCt > RoI Growth destroys value: Company does not earn its cost of capital!The higher the growth rate g, the lower the terminal value
⇒ WACCt < RoI Growth increases value: Company generates excess returns! The higher the growth rate g, the higher the terminal value
τWACCNOPLATV 1TL
T+=
⇒ for RoI ⇒ ∞ NOPLAT and FCF grow without any growth in assets!
Gordon-Shapiro model allows sanity checks for growth assumptions
Chair of Finance, 11 Prof. Dr. Bernhard Schwetzler
Is the (NOPLAT-related) retention rate necessary to achieve the growth rate g
Calculate the retention rate for the projected estimates of FCF and NOPLAT for phase II
1T
1T1T
NOPLATFCFNOPLATq+
++ −=
Link the projected growth rate and the retention rate to calculate the implied Return (RoI) on the net investments
qgRoI =
Cross-check for the profitability assumption behind the growth rate
Compare the implied RoI and the Cost of Capital (WACC) of the firm
1.
2.
3.
RoIg
q =
τWACCRoI ><
The Gordon-Shapiro model may be used to cross-check the assumptionsabout growth and profitability
Chair of Finance, 12 Prof. Dr. Bernhard Schwetzler
Basic idea: Retention · Return = Growth
Analysis
Different combinations of retention and return create the same growth rate
I 50 % · 8 % = 4 %
II 25 % · 16 % = 4 %
Not all combinations create value
I RoIØ – WACC = 6 % > 0 %
II RoIØ – WACC = -2 % < 0 %
RoIØNet investments
Retention rate q25 % 50 %
8 %
10 %
16 %g = 4 %
I
WACC
Creating value
IIg = 4 %
Destroyingvalue
Using GS model for terminal value calculation allows for recombining growth by retention and return
Chair of Finance, 13 Prof. Dr. Bernhard Schwetzler
For investments with limited lifetime there can be significant differences between RoI and IRR over the years
In € 0 1 2 3 4Cash Flows -900 450 350 450 350Dep. book value -225 -225 -225 -225Profit book value 225 125 225 125Residual book value 900 675 450 225 0RoI Book Value 25% 19% 50% 56%
In € 0 1 2 3 4Cash Flows -900 450 350 450 350Market Value IRR 900 708 561 272 0 Dep market value -192 -147 -289 -272 EVA 258 203 161 78 RoI Market Value 29% 29% 29% 29%
WACC = 10 %, NPV = 341,36 €, IRR = 28,67 % WACC = 10 %, NPV = 341,36 €, IRR = 28,67 %
0%
20%
40%
60%
1 2 3 4
RoI book value RoI market value
Caveat I: We should compare IRR and WACC, not RoI and WACC
Chair of Finance, 14 Prof. Dr. Bernhard Schwetzler
Misleading conclusion when comparing average rates of return against WACC
RoIØ = 25 % > WACC = 12 % ⇒ Invest beyond 200!
RoI2 = 0 % < WACC = 12 % ⇒ Scale down investment to 100!
Example
Average
Marginal
Cash-Flowt = 1
Investment
WACC = 12 %RoI2 = 0 %
200
250
150
100
RoIØ = 25 %
RoI1 = 50 %
Caveat II: Important is the marginal rate of return, not the average rate of return
Chair of Finance, 15 Prof. Dr. Bernhard Schwetzler
Analyzing investment strategies by comparing RoIØ against WACC allows for two different conclusions
Further industry expertise is needed No further expertise needed
Cash-Flow
Investment
RoIØ > WACC
WACC
RoIØ
J
I
II
RoIØ – WACC > 0
RoII – WACC < 0RoIII – WACC > 0
Depends on the shape of invest-ment curve
Investment
RoIØ < WACC
WACC RoIØ
J
RoIØ – WACC < 0
RoI’ – WACC < 0as RoI’ < RoIØ
Cash-Flow
Average:
Marginal:
Average:
Marginal:
Chair of Finance, 16 Prof. Dr. Bernhard Schwetzler
RoI not only links earnings and assets, but also says something about the relation between assetgrowth and earnings growth
Case 1: Asset growth = earnings growth
Case 2: Asset growth > earnings growth
Case 3: Asset growth < earnings growth
RoI
t
RoI
t
RoI
t
Implies a decreasingRoI over time
Implies a constantRoI over time
Implies an increasingRoI over time
Infinite time frame (TV calculation) & constant WACC Case 1 is reasonable
RoI
12 %
Operating assets
100 mill.€
Operating earnings
NOPLAT12 mill.€
Asset growth, earnings growth and rates of return RoI
Chair of Finance, 17 Prof. Dr. Bernhard Schwetzler
RoI
12 %
RoI
12 %
Operating assets
100 mill.€
Operating earnings
NOPLAT12 mill.€
Operating assets
100 mill.€
4,8 mill. €
Operating earnings
NOPLAT12,576 mill.€
Retention rateq = 40 %
Payout ratio(1 – q) = 60 %
Retention rate q and RoI determine asset growthAssuming a constant RoI yields the identical earnings growth
Simplification: Check on validity of assumption „constant average return (RoI) @ growing asset base“
Asset growth =Op. assetst-1 * RoI * q
Op. assetst-1
RoI * q
12 % * 40 % 4,8 %
=
= =
Earnings growth =RoI*Op.ass.t-1*[RoI*q+1]
RoI * Op. assetst-1
RoI * q
12,576 / 12 -1 = 4,8 %
-1 -1
=
=
FCF 7,2 mill.€
There is a link between earnings and asset growth via the retention rate
Chair of Finance, 18 Prof. Dr. Bernhard Schwetzler
• Standard GS model suggests that, given a significant retention rate, a firm can grow significantlyeven at moderate RoIs
q = 50 %, RoI = 12 % g = 6 % to infinity
• Standard argument against: „If your firm grows faster than the world economy, then at somepoint your firm will be the world economy.“
Let‘s check this: (mill. US dollars)Siemens NOPLAT 2008: 2.5131
World GDP 2008: 60.115.2202
How long is the wait?
It‘s 189 years!
It‘s not about quoting M. Keynes, but the contributionof Free Cash Flows beyond t = 100 (t = 50) tobusiness EV @ WACC = 12 % is just 3 % (16 %)
Assumptionsq = 50 %, g = 8 %g = 2 %
Siemens FCF
World GDP
1 Siemens annual report 2008, Income from continuing operations after income tax; exchange rate: 1,35185 $/€2 World Development Indicators database, World Bank, 15 September 2009
189Years
The killer argument: Firms becoming larger than world GDP
Chair of Finance, 19 Prof. Dr. Bernhard Schwetzler
1. Motivation
2. Conventional wisdom: The Gordon-Shapiro model
3. A challenge to conventional wisdom: The Bradley/Jarrell model
4. Analyzing growth and inflation
5. Bonus track: Beta stability
Agenda
Chair of Finance, 20 Prof. Dr. Bernhard Schwetzler
Bradley/Jarrell 2003/2008: „...misapplication of the constant-growth model under conditions ofinflation found throughout the finance and valuation literature.“ (2003, p.5)
Terminal Value ModelGordon / Shapiro
Adjusted Terminal Value ModelBradley / Jarrell
[ ]RoIqk
q1 NOPLATVT ⋅−
−⋅=
[ ]][ π⋅+⋅−
−⋅=
q)-(1 RoIqkq1 NOPLAT
VT
Growth earnings / cash flows:
g = q * RoI
Growth earnings / cash flows:
g = q * RoI + (1-q) *
Growth causedby retention and
investment
Growth causedby retention and
investment
Growth caused byinflation via
increase in asset‘sbook values
Requires inflation an adjustment of the TV-valuation formula?
π
π
Chair of Finance, 21 Prof. Dr. Bernhard Schwetzler
The link between asset and earningsgrowth in the GS model
The link between asset and earnings growth in the BJ model
Old assets
100 mill.€
New assets
20 mill.€
Old assets
10 mill.€
New assets
2 mill.€RoI
RoI
BV assets Earnings
Growth in earnings / cash flows is purelycaused by new, additionally acquiredassets
Old assets
100 mill.€
New assets
20 mill.€
Old assets
10 mill.€
New assets
2 mill.€RoI
RoI
BV assets Earnings
AppreciationBV old assets
10 mill.€
Earnings on apprec. BV
1 mill.€
RoI
„...value of initial invested capital will growwith inflation and, with a constant real returnon invested capital, the firm‘s free cash flows... will grow at the same rate (2003, p.4)
Growth in earnings / cash flows is also caused by inflated asset base via appreciation
The additional growth factor is caused by inflation of the book values of the firm’s assets
Chair of Finance, 22 Prof. Dr. Bernhard Schwetzler
1. Motivation
2. Conventional wisdom: The Gordon-Shapiro model
3. A challenge to conventional wisdom: The Bradley/Jarrell model
4. Analyzing growth and inflation
5. Bonus track: Beta stability
Agenda
Chair of Finance, 23 Prof. Dr. Bernhard Schwetzler
• Basic version of the Gordon-Shapiro Model
– With q = retained funds:
– Using the link between RoI and retained funds, , we obtain:
• Bradley/Jarrell (2008) propose to adjust the GS-Model under inflation by
Is this adjustment justified?
( )π−+= q1RoIq'G
RoIqG ⋅=
( )GK
q1IncV 10 −
−=
GKRoIG1Inc
V1
0 −
−
=
Inflation, growth and the Gordon-Shapiro model
Chair of Finance, 24 Prof. Dr. Bernhard Schwetzler
• The firm has access to one representative project in each period
• The nominal cash flows of the representative project are:
• The real cash flows of the representative project are:
• Link between nominal and real cash flows:
• Assumption: There is a unique internal rate of return:
( )T1 C,,C,b
( )T1 c,,c,b
( )ttt 1cC π+=
A model of the firm* – Cash flow definitions
( ) ( )π+π−= 1Rr
* See: Friedl / Schwetzler (2008): „Terminal Value, Accounting Numbers and Inflation“ available under: http://ssrn.com/abstract=1268930
Chair of Finance, 25 Prof. Dr. Bernhard Schwetzler
• We capture growth by change of the size of the representative project
• Nominal growth:
• Note that the internal rate of return does not change with growth
Objective: Calculate terminal values
π+π+= ggG
A model of the firm – Growth definitions
• Real growth g as a percentage change of the size of the representative project (applies to all cash flows)
Chair of Finance, 26 Prof. Dr. Bernhard Schwetzler
( )( ) ( ) ( )( ) ( )( ) 1TT
1211 g11cg11c1cg11bCF +−− +π++++π++π+++π+−=
( ) ( ) ( ) ( ) ( ) ( ) ( )( ) ( )11
1
2T2T
22
21
222
g11CF
g11c1cg11cg11bCF
+π+=
+π+++π+++π+++π+−= +−
( )GK
CFK1CFV 1
1t
tt0 −
=+= ∑∞
=
−
A model of the firm – Cash flows of the firm and terminal value calculation
3b−−
-3 -2 -1 0 1 2 33
1−C 3
2C− 33C−
21C− 2
2−C
11C− 1
3C−
01C
23C−
12C−
02C 0
3C
11C 1
2C 13C
2b−
2b−−
1b−−
0b−
1b−
21C 2
2C
Reference object in t=0
Chair of Finance, 27 Prof. Dr. Bernhard Schwetzler
CFs (real)Project -3 -94,23 37,69 37,69 37,69Project -2 -96,12 38,45 38,45 38,45Project -1 -98,04 39,22 39,22 39,22Project 0 -100,00 40,00 40,00 40,00Project 1 -102,00 40,80 40,80 40,80Project 2 -104,04 41,62 41,62Project 3 -106,12 42,45Project 4 -108,24
Sum CF real 15,36 15,66 15,98 16,30 16,62Growth 2,00% 2,00% 2,00% 2,00%
CFs (nominal)Project -3 -86,24 35,53 36,60 37,69Project -2 -90,60 37,33 38,45 39,60Project -1 -95,18 39,22 40,39 41,60Project 0 -100,00 41,20 42,44 43,71Project 1 -105,06 43,28 44,58 45,92Project 2 -110,38 45,47 46,84Project 3 -115,96 47,78Project 4 -121,83
Sum CF nominal 15,36 16,13 16,95 17,81 18,71Growth 5,06% 5,06% 5,06% 5,06%
Assumptions:Cost of Capital(nominal): 9%Inflation: 3%Growth: 2%
Numerical example: Cash flows
Chair of Finance, 28 Prof. Dr. Bernhard Schwetzler
• For the representative project, we define accounting earnings as:
• Total accounting earnings of the firm:
• Accounting earnings grow at nominal rate G:
• Book values grow at G as well:
• Return on Investment stays constant:0
1
1t
tt BV
IncBVIncRoI ==
−
( ) bd1cbdCInc tt
tttot −π+=−=
π+=−1t
tt BV
IncRoI
Bradley/Jarrell (2003)
A model of the firm – Accounting earnings and accounting returns
( ) 1t1t G1IncInc −+=
( )t0t G1BVBV +=
Project in t=0 Project in t=-1 Project in t= -T+1
( ) ( )[ ] ( ) 12
22111 G1bd1cbd1cInc −+⋅⋅−π++⋅−π+= ( )[ ] ( ) 1T
TT
T G1bd1c +−+⋅⋅−π++...
Chair of Finance, 29 Prof. Dr. Bernhard Schwetzler
Book valuesProject -3 86,24 57,49 28,75 0,00Project -2 90,60 60,40 30,20 0,00Project -1 95,18 63,46 31,73 0,00Project 0 100,00 66,67 33,33 0,00Project 1 105,06 70,04 35,02 0,00Project 2 110,38 73,58 36,79Project 3 115,96 77,31Project 4 121,83
Sum Book values 193,66 203,45 213,75 224,57 235,93Growth 5,06% 5,06% 5,06% 5,06%
ProfitProject -3 0,00 6,78 7,85 8,95Project -2 0,00 7,13 8,25 9,40Project -1 0,00 7,49 8,66 9,88Project 0 0,00 7,87 9,10 10,38Project 1 0,00 8,26 9,56 10,90Project 2 0,00 8,68 10,05Project 3 0,00 9,12Project 4 0,00
Sum Profit 24,68 25,93 27,24 28,62 30,07Growth 5,06% 5,06% 5,06% 5,06%
Numerical example: Book values and earnings
Chair of Finance, 30 Prof. Dr. Bernhard Schwetzler
( )( ) ( )( )( )
+π+−+π+=− ∑
=
+−T
1j
1jj11 g11dg11bCFInc
( )( ) ( ) ( ) ( )( ) ( ) 1TT
T
12211
g11c
...g11c1c1g1bCF+−
−
+π++
+π++π++π++⋅−=–
Earnings/Income in t=1: Cash flow in t=1:
Retention:
Effect of investmentin t=1
Effect of depreciationof investments prior t=1
Requirement for zero net investment-case: ( )( ) 1g11 =+π+ (because ) ∑=
=T
1jj 1d
For the zero net investment case, real growth and inflationneed to neutralize each other. This yields also G = 0 .
The model facilitates the analysis of special cases
( ) ( )[ ] ( )( )[ ] ( ) 1T
TT
T
12
22111
G1bd1c
...G1bd1cbd1cInc+−
−
+⋅⋅−π++
++⋅⋅−π++⋅−π+=
Chair of Finance, 31 Prof. Dr. Bernhard Schwetzler
1. Zero real growth and positive inflation: g* = 0, π > 0
In this case, nominal growth of income and cash flow equals the inflation rate: G* = π. Therefore, terminal value is:
2. Positive real growth and zero inflation: g* > 0, π = 0 In this case, terminal value is:
( ) ( )( ) 01d1bCFIncRETn
1j
1jj111 >
π+−π+=−= ∑
=
+−
Two special cases
( )*
1*
10 gK
q1IncGK
CFV−−
=−
=
( )π−−
=−
=K
q1IncGK
CFV 1*
10
Chair of Finance, 32 Prof. Dr. Bernhard Schwetzler
• First, BV1 – BV0 = G BV0. Thus retention in period 1 is RET1 = G BV0.
• Second, absolute retention can be expressed by combining retention rate and accounting income in period 1: RET1 = q Inc1.
• Setting the two equations equal to each other, we get:
Hence, the presence of inflation does not affect the GS relation
RoIqBVIncq*GIncqGBV
0
11
*0 ==⇔=
General case: Arbitrary growth and inflation
Chair of Finance, 33 Prof. Dr. Bernhard Schwetzler
• If the firm makes zero net investments, RETt = 0 ∀ t
• Retention is zero, if and only if , i.e. zero nominal growth
• In this case, Gordon-Shapiro simplifies to
• Bradley and Jarrell (2003, 2008) obtain a different representation of the Gordon-Shapiro model under inflation
Under inflation there is no need to adjust the Gordon-Shapiro model in the special case of zero net investments
( )( ) 11g1 * =π++
KIncV 1
0 =
The Gordon-Shapiro model for zero net investments
Chair of Finance, 34 Prof. Dr. Bernhard Schwetzler
• We analyze an expansion of investment beyond the optimal scale and assume that the firm retains and additionally reinvests an amount of RET1 at its cost of capital K in t=1
• Again under positive net investments the absolute retention reflects the nominal growth in assets: RET1 = G´*BV0
• G´ denotes the nominal growth rate in assets under the sub-optimal investment program including the zero-NPV projects
• Linking retention and growth under the zero-NPV assumption requires an additional assumption ensuring that K = IRR = RoI is going to hold in any future period
• Except for the trivial case of a one period lifetime of the representative project, the condition RoI = IRR requires a special depreciation policy of the firm, the “IRR depreciation” for the representative investment that meets the requirement RoIt = IRR for t=1, ..., n
The Gordon-Shapiro model for zero net present value investments (1)
Chair of Finance, 35 Prof. Dr. Bernhard Schwetzler
• Under this assumption period t=2 income is:
• Income growth between t=1 and t=2 is then:
Thus finally the Zero – NPV net investment case also yields the GS valuation equation as the correct result:
KqIncIncRETRoIIncInc 11112 ⋅⋅+=⋅+=
´GKq1IncInc
1
2 =⋅=−
The Gordon-Shapiro model for zero net present value investments (2)
( )K
IncKqKq1IncV 11
0 =−
−=
( )Kq1Inc1 ⋅+=
Chair of Finance, 36 Prof. Dr. Bernhard Schwetzler
There is no need for adjustments of the valuation formula. The GS-valuation formula isbased on nominal future cash flows and nominal cost of capital and thus fully captures theimpact of inflation
Yes, inflation does have an impact upon firm value. This impact is highly firm-specific(ability to pass price increases to customers etc.) and reflected in estimates of future cash flows
No, inflation does not have an impact on the valuation formula
(Our) conclusion)*:
• Additional earnings / cash flows should only be caused by returns on newly acquired assets
• Writing up the book value of an asset should not have any impact on the firm‘s cash flows
• Accounting standards usually do not allow for appreciations above historic costs
* See: Friedl / Schwetzler (2008): „Terminal Value, Accounting Numbers and Inflation“
Some points against the logic of the BJ valuation formula
Chair of Finance, 37 Prof. Dr. Bernhard Schwetzler
1. Motivation
2. Conventional wisdom: The Gordon-Shapiro model
3. A challenge to conventional wisdom: The Bradley/Jarrell model
4. Analyzing growth and inflation
5. Bonus track: Beta stability
Agenda
Chair of Finance, 38 Prof. Dr. Bernhard Schwetzler
The predictability of stock returns and the link of returns and risk associated with stocks are issues of major interest among academics and practitioners in the area of finance
A systematic explanation of these relations has been made by Sharpe (1964) and Lintner (1965) with the development of the capital asset pricing model (CAPM)
An important aspect of the model is the consistency of the risk-measuring factor
beta
Practical applications of the CAPM implicitly assume beta-factor stability over
the whole period under consideration
Various CAPM tests have been conducted, fuelled by the many necessary assumptions the model builds on:
Empirical research on CAPM validity and beta-stability yields contradictory results
Until 1992, many studies affirmed the explanatory power of the CAPM
In 1992, Fama/French published their landmark study, opposing the CAPM
• e.g. Black/Jensen/ Scholes (1972), Blume/Friend (1973), Fama/MacBeth (1973
• Fama/French (1992) do not find beta to be an explanatory factor for average stock returns
• They find size & BE/ME-ratio more appropriate
Subsequently, the interest in research on CAPM validity and beta-factor stability has remained
Controversy of results among the numerous studies
• Finance researchershave been keenlyinterested in exploringthe stability charact-eristics of the beta-factor
• German studies: Sauer/ Murphy (1992) & Elsas/ El-Shaer/Theissen (2005) con-firmed validity of the CAPM, while Ebner/ Neumann (2005) disapproved
Chair of Finance, 39 Prof. Dr. Bernhard Schwetzler
Reliability of estimation Stability of estimation
„True“ betas can also change over time!
„True“ beta
Estimator
Instable
Stable
Stable
Instable
Reliable
Reliable
Unreliable
Unreliable
Only the estimatorcan be observed!
• Low beta stability is not necessarily a reason for a critique of the CAPM• During a „regime shift“ R2 decreases even if the model is true!
Stability of beta-factors (or rather of their estimators) is not necessarily a desirable attribute
Chair of Finance, 40 Prof. Dr. Bernhard Schwetzler
Pos
itive
rj
rm
. . . . . . .
. . .
. . . . .
. .. .
rj
rm
. . . . . . . .. .
. . . . .. .
Changes in betaC
hang
esin
R2
Positive NegativeN
egat
ive
• Low beta• Low R2
• High beta• High R2
• High beta• Low R2
• Low beta• High R2
• Low beta• High R2
• High beta• Low R2
• High beta• High R2
• Low beta• Low R2
rj
rm
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. . .
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. .. .
. . . . .. . .
rj
rm
. . . . . . . .. . .
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. .. .
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. . . . . . . .. .
. . . . .. .
rj
rm
. . . . .. . .
rj
rm
. . . . . . .. . .
Simultaneous changes of beta and R2 indicate a “regime shift”
There are four different types of changes and regime shifts
Type I Type II
Type IVType III
Chair of Finance, 41 Prof. Dr. Bernhard Schwetzler
Beta
R2
Automobile 200 days
Automobile 200 days
Regime Shift Type IV
Effects of the technology bubble:
between 1999 and 2001
Decreasing betas
Decreasing goodness of fit
Betas and goodness of fit are subject to significant changes even on industry level: E.g. automobile
Chair of Finance, 42 Prof. Dr. Bernhard Schwetzler
Beta
R2
Banks 200 days
Banks 200 days
Betas and goodness of fit are subject to significant changes even on industry level: E.g. banks
Regime Shift Type IV
Effects of the technology bubble:
between 1999 and 2001
Decreasing betas
Decreasing goodness of fit
Chair of Finance, 43 Prof. Dr. Bernhard Schwetzler
Beta
R2
Media 200 days
Media 200 days
Betas and goodness of fit are subject to significant changes even on industry level: E.g. media
Regime Shift Type I
Effects of the technology bubble:
between 1999 and 2001
Increasing betas
Increasing goodness of fit
Chair of Finance, 44 Prof. Dr. Bernhard Schwetzler
Beta
R2
Telco 200 days
Telco 200 days
Betas and goodness of fit are subject to significant changes even on industry level: E.g. telco
Regime Shift Type I
Effects of the technology bubble:
between 1999 and 2001
Increasing betas
Increasing goodness of fit