Barad ASA-Risk Premia

Ibbotson Risk Premia: Under the Microscope

Michael W. BaradIbbotson AssociatesASA/CICBV 5th Joint Business Valuation ConferenceOrlando, FloridaOctober 24, 2002

Copyright © 2002 Ibbotson Associates, Inc.

Overview

Cost of Capital / Cost of Equity

– Equity Risk Premium

– Size Premium

– Industry Premium


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


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


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)


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


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


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


Equity Risk PremiumAlternative Calculation Techniques

Survey Results

Supply-Side

Demand-Side

Exponential Weighting


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


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.


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


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


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


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


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


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%


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


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


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


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


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%


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


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%


Michael W. Barad

IbbotsonAssociates225 N. Michigan AvenueSuite 700Chicago, IL 60601-7676

312-616-1620 Phone312-616-0404 [email protected]

Barad ASA-Risk Premia

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