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Ibbotson Risk Premia: Under the Microscope
Michael W. BaradIbbotson AssociatesASA/CICBV 5th Joint Business Valuation ConferenceOrlando, FloridaOctober 24, 2002
Copyright © 2002 Ibbotson Associates, Inc. Page 2
Overview
Cost of Capital / Cost of Equity
– Equity Risk Premium
– Size Premium
– Industry Premium
Copyright © 2002 Ibbotson Associates, Inc. Page 3
Cost of Capital
The cost of capital is the discount rate that should be used to derive the present value of an asset’s future cash flows.The weighted average cost of capital (WACC) is the average required rate of return of all the company’s financing, equity, debt, and preferred stock, weighted in proportion to the company’s total invested capital.
WACC = WDkD(1-t) + WEkE
WD, WE = Weights of debt and equity respectively for the firm
kD = Cost of Debt
kE = Cost of Equity (can be estimated by Buildup Method or CAPM)
t = tax rate
Copyright © 2002 Ibbotson Associates, Inc. Page 4
Cost of Equity
Buildup MethodRisk Free Rate
+ Equity Risk Premium+ Size Premium+ Industry Premium+ Other Factors?
Cost of Equity
Capital Asset Pricing Model (CAPM)Cost of Equity = Rf + β (ERP) + SP
Copyright © 2002 Ibbotson Associates, Inc. Page 5
Equity Risk Premium
Definition– The expected equity risk premium is defined as the additional
return an investor expects to receive to compensate for the additional risk associated with investing in equities as opposed to investing in riskless assets
– Excess return of stocks over bonds
Ibbotson Calculation– ERP = (arithmetic mean total return of stocks) - (arithmetic mean
income return of a risk-free asset)
Copyright © 2002 Ibbotson Associates, Inc. Page 6
Issues with Calculating ERP
Stock Market Benchmark and Risk-Free Asset– S&P 500– 20 Year Government Bond
Arithmetic verses Geometric Average
Time period for measurement
Copyright © 2002 Ibbotson Associates, Inc. Page 7
Equity Risk PremiumRealized Annual ERP
-60%
-40%
-20%
0%
20%
40%
60%
1926
1929
1932
1935
1938
1941
1944
1947
1950
1953
1956
1959
1962
1965
1968
1971
1974
1977
1980
1983
1986
1989
1992
1995
1998
2001
Equi
ty R
isk
Prem
ium
Copyright © 2002 Ibbotson Associates, Inc. Page 8
Equity Risk PremiumDifferent Starting Dates
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
1926
1929
1932
1935
1938
1941
1944
1947
1950
1953
1956
1959
1962
1965
1968
1971
1974
1977
1980
1983
1986
1989
1992
1995
Ave
rage
ER
P th
roug
h 20
01
Copyright © 2002 Ibbotson Associates, Inc. Page 9
Equity Risk PremiumAlternative Calculation Techniques
Survey Results
Supply-Side
Demand-Side
Exponential Weighting
Copyright © 2002 Ibbotson Associates, Inc. Page 10
Size PremiumCost of Equity Models
Buildup MethodRisk Free Rate
+ Equity Risk Premium+ Size Premium+ Industry Premium+ Other Factors?
Cost of Equity
Capital Asset Pricing Model (CAPM)Cost of Equity = Rf + β (ERP) + SP
Copyright © 2002 Ibbotson Associates, Inc. Page 11
Size PremiumExplanation of Terms
Size Premium (beta-adjusted)– The return on small company stocks in excess of that predicted by
the CAPM. It is the additional return that cannot be explained by the betas of small companies.
Small Stock Premium (non-beta-adjusted)– The excess return of small company stocks over large company
stocks.
Copyright © 2002 Ibbotson Associates, Inc. Page 12
Size Premium
Steps to identifying an appropriate size premium:Classify your company– Public vs. Private– Market Cap or Equivalent
Which decile does the company fit into?
Locate a size premium for the corresponding decile
Copyright © 2002 Ibbotson Associates, Inc. Page 13
Size PremiumPrivate company market capitalization equivalent
Companies Without Market Capitalization Data– Market Capitalization Equivalent
• Financial Ratios– Example with the Price/Sales ratio for a company in the food stores
industry, SIC 54• Sales for Company A are $200 million• The P/S ratio for SIC 54 is 0.40• 0.40 x $200 million = $80 million
– Example with P/CF ratio for the same company• The Cash Flow is $10 million• The average P/CF for SIC 54 is 18.0• 18.0 x $10 million = $180 million
200
= 40.0P
= 18.0.10P
Copyright © 2002 Ibbotson Associates, Inc. Page 14
Size-Decile BreakpointsFrom the SBBI Valuation Edition 2001 Yearbook
Market Cap of Largest
Decile Company (in thousands)
1 - Largest $524,351,578
2 10,343,765
3 4,143,902
4 2,177,448
5 1,327,582
6 840,000
7 537,693
8 333,442
9 192,598
10 - Smallest 84,521
Mid-Cap, 3-5 Capitalization between $840 and $4,144million
Low-Cap, 6-8 Capitalization between $192 and $840 million
Micro-Cap, 9-10 Capitalization below $192 million
Market Cap of LargestDecile Company (in thousands)10a 84,52110b 48,345
Copyright © 2002 Ibbotson Associates, Inc. Page 15
Size PremiumCalculation
Return in Excess of CAPM
ks = rf + β (ERP)
– Run a CAPM regression to determine the beta of each size decile
– CAPM estimates that smaller stocks will have higher returns to go along with their higher betas
• Smaller stocks should and do have higher returns • CAPM estimates vs. historical returns
– Smaller stocks have had returns that are not fully explained by their higher betas
Copyright © 2002 Ibbotson Associates, Inc. Page 16
Size Premium TableFrom the SBBI Valuation Edition 2001 Yearbook
Realized Estimated Size PremReturn in Return in (Return in
Arithmetic Excess of Excess of Excess ofDecile Beta Mean Return Riskless Rate Riskless Rate CAPM)1-Largest 0.91 12.06% 6.84% 7.03% -0.20%2 1.04 13.58% 8.36% 8.05% 0.31%3 1.09 14.16% 8.93% 8.47% 0.47%4 1.13 14.60% 9.38% 8.75% 0.62%5 1.16 15.18% 9.95% 9.03% 0.93%6 1.18 15.48% 10.26% 9.18% 1.08%7 1.24 15.68% 10.46% 9.58% 0.88%8 1.28 16.60% 11.38% 9.91% 1.47%9 1.34 17.39% 12. 17% 10.43% 1.74%10-Smallest 1.42 20.90% 15.67% 11.05% 4.63%
1.12 14.46% 9.23% 8.65% 0.58%1.22 15.75% 10.52% 9.45% 1.07%1.36 18.41% 13.18% 10.56% 2.62%
Mid-Cap, 3-5Low-Cap, 6-8Micro-Cap, 9-10
Copyright © 2002 Ibbotson Associates, Inc. Page 17
Derivation of the Size Premium
Realized Estimated Size PremReturn in Return in (Return in
Arithmetic Excess of Excess of Excess ofDecile Beta Mean Return Riskless Rate Riskless Rate
CAPM)Realized -
Historical Return Return - Riskless Rate Beta x ERPEstimated(20.90%) (20.90% - 5.22%) (1.42 x 7.76)
15.67% - 11.05% = 4.63%
10-Smallest 1.42 20.90% 15.67% 11.05%4.63%
Riskless Rate = Arithmetic mean income return on the U.S. LT Gvt Bond (5.22%)
ERP = Arithmetic mean total return of the S&P 500 (12.98%) minus the arithmetic mean income return on the U.S. LT Gvt Bond (5.22%) = 7.76%
Copyright © 2002 Ibbotson Associates, Inc. Page 18
Size PremiumGraphical Representation
0%
5%
10%
15%
20%
25%
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Riskless Rate
S&P 5001
2 3 4 56 78
9
10
Arith
met
ic M
ean
Ret
urn
Beta
Security Market Line versus Size-Decile Portfolios of the NYSE/AMEX/NASDAQ
Amount by which actualreturns have outperformedwhat a pure CAPM wouldestimate
Copyright © 2002 Ibbotson Associates, Inc. Page 19
Size Premium ComparisonBeta-adjusted vs. non-beta-adjusted
Ibbotson provided non-beta-adjusted size premia up through the Stocks, Bonds, Bills, and Inflation 1994 Yearbook– (small stock return - large stock return)– Also referred to as small stock premium
Ibbotson has provided beta-adjusted size premia starting in the SBBI 1995 Yearbook through the present– Return in excess of CAPM
Copyright © 2002 Ibbotson Associates, Inc. Page 20
Size Premium
Non-Beta-Adjusted– Using a non-beta-adjusted size premium assumes that
the company being valued has the same systematic risk (or beta) as the portfolio of small stocks used in the calculation of the size premium
– Different industries tend to have different levels of systematic risk
• Companies within the food stores industry tend to have less systematic risk than the market. By using the historical returnon small stocks to develop a non-beta-adjusted size premium you would be assuming that a small food stores company has the same risk as the portfolio of all small stocks across any industry
Copyright © 2002 Ibbotson Associates, Inc. Page 21
Size Premium
Beta-Adjusted– A beta-adjusted size premium isolates the excess
return due to size, so it can be applied to a company without making any assumptions regarding the company’s systematic risk
– Adding a size premium independent of systematic risk allows the addition of other factors that do account for risk without overlap
• Buildup Method– An industry premium can be added to account for industry specific
risk
• CAPM– The beta used in a CAPM can account for certain risk factors inherent
to the company itself or the industry of its peers
Copyright © 2002 Ibbotson Associates, Inc. Page 22
Industry Risk Premia
Ibbotson Associates calculates industry premia for almost 300 industries
– For use in the buildup method• Same as using an industry beta, but in the context of the
buildup
– Many are negative
– Full information approach is used (FI beta)• IRP = (RI x ERP) - ERP
– RI = the risk index for a particular industry (FI Beta)– ERP = the expected equity risk premium– Example for the food stores industry, SIC 54
• IRP = (0.36 x 7.8) - 7.8 = -5.0%
Copyright © 2002 Ibbotson Associates, Inc. Page 23
Industry PremiumRange of premia presented in the SBBI Valuation Edition Yearbook
0
10
20
30
40
50
60
70
80
90
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
12%
14%
16%
Industry Premium
# of
Indu
strie
s W
ithin
Eac
h R
ange
Copyright © 2002 Ibbotson Associates, Inc. Page 24
Industry PremiumFull information example - household appliance industry
Company Name
Sales to SIC 363
($Mil)
Total Company
Sales ($Mil)
% of Industry Sales to Total
Company Sales
% of Sales to SIC 363
Pure Play Member
Full Information
MemberAPPLICA INC 715$ 715$ 100.0% 2.7% Yes YesHMI INDUSTRIES INC 32$ 32$ 100.0% 0.1% Yes YesNATIONAL PRESTO INDS INC 117$ 117$ 100.0% 0.4% Yes YesSALTON INC 792$ 792$ 100.0% 3.0% Yes YesWHIRLPOOL CORP 10,343$ 10,343$ 100.0% 39.1% Yes YesROYAL APPLIANCE MFG CO 407$ 428$ 94.9% 1.5% Yes YesMAYTAG CORP 4,094$ 4,324$ 94.7% 15.5% Yes YesMARTIN INDUSTRIES INC/DE 21$ 64$ 32.8% 0.1% NO YesSMITH (A O) CORP 349$ 1,151$ 30.3% 1.3% NO YesNACCO INDUSTRIES -CL A 650$ 2,970$ 21.9% 2.5% NO YesGILLETTE CO 1,657$ 9,295$ 17.8% 6.3% NO YesILLINOIS TOOL WORKS 483$ 10,404$ 4.6% 1.8% NO YesGENERAL ELECTRIC CO 5,806$ 127,376$ 4.6% 22.0% NO YesBERKSHIRE HATHAWAY -CL A 963$ 27,347$ 3.5% 3.6% NO Yes
26,427$ 100%
Copyright © 2002 Ibbotson Associates, Inc. Page 25
Michael W. Barad
IbbotsonAssociates225 N. Michigan AvenueSuite 700Chicago, IL 60601-7676
312-616-1620 Phone312-616-0404 [email protected]