1. DISSECTING RISK PREMIUMS
American Society of Appraisers
Washington, DC, Metro Area Chapter
Presented: March 14, 2012
Zachary C. Reichenbach, CPA
Michael B. Lawrence
2. Overview
• Introduction to the Cost of Equity
• Introduction of Risk Premium
• Ibbotson‟s Historical ERP
• Ibbotson‟s Supply Side ERP
• Duff & Phelps‟ ERP
• Current Economic Challenges
• Adjustments to ERP
• Adjustments to Risk Free Rate
• Use of Monthly ERP Data – Damadoran Online
• Conclusion/Questions
3. Introduction to the Cost of Equity
• Definition: The return a company theoretically pays to its
equity investors to compensate for the risk they undertake
by investing their capital
• Measures and Quantifies Risk
• Market Risk
• Size Risk
• Industry Risk
• Specific Company Risk
• Used to determine the WACC
• Two Components: Debt and Equity
• Primarily used for Income Approach methods of valuation
4. Cost of Equity (cont.)
• Two Methods to Calculate the Cost of Equity
• Both Methods Quantify Risk – “Building Blocks”
Build Up Method Modified CAPM
Risk Free Rate Risk Free Rate
Equity Risk Premium (β x ERP)
Size Premium Size Premium
Specific Company Risk
Industry Risk Premium
Premium
Specific Company Risk
Premium
5. Introduction to Risk Premium
• What is a Risk Premium?
• The return in excess of the risk-free rate of return that an
investment is expected to yield
• Gives investors incentives to invest in riskier securities
• The unknown – the possibility that an investor might lose his
initial investment
Example:
20-Year U.S.
Difference in Yield = RP GE Stock
Treasury Bond
Yield: 4% RP = 11% Yield: 15%
6. Risk Premiums on Various Securities
Security Risk Premiums
Treasury Bills Real Rate + Inflation
Treasury Notes Real Rate + Inflation + Duration Premium
Treasury Bonds Real Rate + Inflation + Duration Premium
Corporate Bonds Real Rate + Inflation + Duration Premium + Default
Premium
Large Cap Stocks Real Rate + Inflation + Equity Risk Premium
Small Cap Stocks Real Rate + Inflation + Equity Risk Premium + Size
Premium
8. Ibbotson
• Calculating the Historical ERP
• Stock Market Benchmark
• Risk-Free Asset
• Arithmetic or Geometric Average
• Time Period for Measurement
9. Ibbotson – Stock Market Benchmark
• Broad index that reflects the market as a whole
• S&P 500
• New York Stock Exchange Composite Index
• Dow Jones Industrial Average – inappropriate for
calculating ERP
• Too narrow
• Total return of large company stock index as the market
benchmark
• S&P 500 – large sample of companies over a large number of
industries
• 88 separate industry groups since December 31, 1993
• Most widely accepted
10. Ibbotson – Market Benchmark and Firm Size
• Valuation professionals usually value small companies
• Have different risk and return characteristics than large companies
• Adjustment if using large stock index to account for differences
• Based on size premium
• Smaller companies have higher returns on average than larger
ones
• Less liquid, higher cost of capital requires higher return
• Liquidity not directly observable
• Capitalization is measurable size can serve as a partial
measure of cost of capital
11. Ibbotson – Risk-Free Asset
• Short-Term Horizon 30-day Treasury Bill
• Intermediate-Term Horizon 5-year Treasury Bond
• Long-Term Horizon 20-year Treasury Bond
• Long-horizon equity risk premium is preferable for use in
most business-valuation settings
• Even if investor has a shorter time horizon
• Companies are entities that generally have no defined life span
• Important to use long-term discount rate; life of company infinite
• 20-Year versus 30-Year Treasuries
• 30-Year securities have only been issued over the recent past („77)
12. Ibbotson – Arithmetic versus Geometric Means
• Ibbotson utilizes arithmetic average risk premia
• Appropriate when discounting future cash flows
• The equity risk premium that should be employed is the equity risk
premium expected to be incurred over future time periods
• Applicable for CAPM or Build-Up Method
• Both CAPM and Build-Up Method are additive models
• Cost of capital is the sum of its parts
• Simple difference between arithmetic means of stock market
returns and riskless rates
• Geometric mean more appropriate for reporting past
performance
• Represents compound average return
13. Ibbotson – Appropriate Historical Time Period
• ERP can be estimated using any historical time period
• U.S. market data exists back to the late 1800s
• Ibbotson covers the time period from 1926 to present
• Original data source for the time series – Center for Research in
Security Prices (CRSP)
• Begins their analysis of market returns with 1926 for 2 reasons:
1. CRSP determined that the time period around 1926 was when quality
financial data became available
• Wanted to include extreme market volatility from the late twenties and early thirties
2. 1926 includes one full business cycle before the market crash of 1929
• Implicit in using history to forecast future, investors‟
expectations for future outcomes conform to past results
• “Future equals the past” assumption
14. Ibbotson – Appropriate Historical Time Period
• Prediction of economic environment of future
• Does the period account for too many “unusual” events?
• All periods contain unusual events
• Inflation of late 1970s
• October 1987 stock market crash
• Collapse of the high-yield bond market
• Major contraction of the thrift industry
• Collapse of the Soviet Union
• Development of the European Economic Community
• Attacks of September 11, 2001
• Liquidity crisis of 2008
• Long-term time period will smooth out volatility from certain market
conditions
15. Ibbotson – ERP Represent Minority or
Controlling Interest?
• Use of publicly traded company data to derive equity risk
premium – Is a minority discount implicit in this data?
• Both the S&P 500 and the NYSE include a preponderance of
companies that are minority held
• Does the Equity risk premium (or size premium) derived from this data
represent a minority interest premium?
• Application of a minority discount or control premium can have a material
impact on the indication of value – watch for “double dipping”
• Not correct to assume the risk premia derived from these return data
have a minority discount implicit within them
• Returns generated by the S&P 500 and the NYSE represent returns to
equity holders
• The ERP represents expected premiums that holders of securities of a similar
nature can expect to achieve on average in the future
• No distinction between minority owners and controlling owners
• Adjust cash flows, not discount rate
16. Issues with Ibbotson‟s Historical ERP
• Survivorship
• Premise: U.S. stock market is most successful stock
market in 20th Century
• Potential overstatement of ERP due to a higher-than-average
stock market
• Global capital markets have been systematically subject to
dramatic changes over the past century; the U.S. is the
exception as it has not been subject to dramatic changes
• Pollutes U.S. markets with more “winners” with “losers”
• U.S. real capital appreciation since 1926 is 4.3 percent
• Global capital markets average capital appreciation
since 1926 is 0.8 percent
18. Conclusion on Survivorship
• U.S. Markets haven‟t had drastic temporary or permanent
systematic disruptions
• Financial Crisis
• War/Invasion on home territory
• Hyperinflation
• Using U.S. markets does not capture all of the “losers” to
offset “winners” - U.S. is the exception to the average
• Conclusion: Historical ERP from Ibbotson is
approximately 60 basis points (0.6%) overstated
19. Issues with Ibbotson‟s Historical ERP
• Realized ERP vs. Expected ERP
• Arnott & Bernstein: Ibbotson Historical ERP Overstated
• Expected ERP in 1926 was above long-term premium
• Important non-recurring developments were not anticipated by
investors
• Fama & French: Ibbotson Historical ERP Overstated
• Unanticipated decline in discount rates
• McGrattan & Prescott
• Investors did not expect changes such as: decreases in marginal
tax rates and defined benefit and contributions plans
• Ibbotson & Chen
• Developed forward-looking, long-term sustainable expected ERP
20. Ibbotson – Supply Side Model
• Long-term expected equity returns can be forecasted with
supply side models
• Supply of stock market returns is generated by the productivity of
the corporations in the real economy
• Investors should not expect a much higher or lower return
• Over the long run, equity returns should be close to long-run supply
estimate
• Roger G. Ibbotson and Peng Chen forecast the ERP using
historical data
• Utilize an earnings model as the basis for their supply side estimate
• Historically, growth in corporate earnings = growth in overall economic
production
• Earnings model has four pieces
• Inflation
• Income return
• Growth in real earnings per share
• Growth in the P/E ratio (3 year average earnings)
21. Ibbotson
• Build-Up Method
• Utilizes various market rates of return and risk premiums
• Risk-Free Rate
• Long-Term Equity Risk Premium
• Specific Company Risk Premium
• Cost of Equity = Rf + ERP + SCs
• Rf = Risk-Free Rate
• ERP = Equity Risk Premium
• SCs = Specific Company Risk Premium
22. Ibbotson - ERP
• Data from Ibbotson Associates
“Stocks, Bonds, Bills and Inflation 2011
Yearbook” published by Morningstar®
• Market risk premium of 6.0 percent (supply side)
• Historical equity risk premium minus the P/E ratio
calculated using the 3 year average returns
• Small company premium
• Contingent on size of company
• Size decile based on market capitalization
• Size premium return in excess of CAPM
• Usually consider 10th decile (6.4 percent)
24. Duff and Phelps
• Built on the following two fundamentals:
• Stock returns can be predicted by measures of size other than market
capitalization
• Stock returns can be measured by fundamental risk measures based
on accounting data
• Premise: As size decreases, the returns tend to increase
• Small Cap stock higher risk/return potential than large cap stock
• Like Ibbotson: Dividing historical data by size
• Ibbotson: 10 deciles based on market capitalization
• Duff & Phelps: 25 deciles based on multiple measures
• Duff & Phelps – Ranking just by market capitalization
eliminates:
• Inherent bias
• “Guesstimating” the market capitalization for privately-held companies
25. Size and Risk Comparison
Size Study – 8 Measures Risk Study – 3 Measures
• Market Value of Equity • Operating Margin
• Book Value of Equity • Coefficient of Variation in
• 5-Year Average Net Operating Margin
Income • Coefficient of Variation in
• Market Value of Invested Return on Equity
Capital
• Total Assets
• 5-Year Average EBITDA
• LTM Sales
• No. of Employees
26. Size Study Overview
• Use 8 Factors:
• Eliminates bias
• Factors other than market capitalization may have
factor
• Eliminates the need to guess/estimate market
capitalization for privately-held companies
• More factors better than 1
• Use of two cost of equity methods:
• Build Up Method: Risk Premium Over Risk Free Rate
(“A” Exhibits)
• CAPM: Risk Premium over CAPM (“B” Exhibits)
27. Size Study - Risk Premium Over Risk
Free Rate
• Difference in historical return of equities over the risk free
rate
• Long-run average historical risk premium used as
indicator of expected risk premium for a typical investor
• Returns based on dividend and capital appreciation after
corporate taxes, but before shareholder taxes
• Difference between income from risk-free asset (20-Year
Treasury) and equity security represents size risk and
market risk
29. Use of Regression Equation
• When the subject company size measures do not exactly
match the average company size of the guideline
portfolios
• Exhibits provide method to interpolate the exact risk
premium
30. Size Study: Risk Premium Over CAPM
• Beta-adjusted size premium
• Unlike Risk Premium over Risk Free Rate, only the size
premium is considered
• CAPM uses beta which accounts for market risk
• Size Premium
• Portfolio Premium x (Portfolio beta x Realized Market Premium)
• “What actually happened” – “What CAPM predicted would happen”
32. D&P – Risk Study
• Risk Study analyzes the relationship between
fundamental risk measures and return
• Measure of earnings volatility can explain credit
ratings, predict insolvency and CAPM Beta
• Fundamental Risk Measures
• 5-Year Average Operating Income Margin
• Coefficient of Variation in Operating Income Margin
• Coefficient of Variation in Book Equity
Operating Variability
Risk Risk
Margin of Earnings
33. Build-Up Method
COE = Rf + RPm+u + ERPadj
Rf Risk Free Rate
RPm+u Market & Specific Co. Risk
Premium
ERPadj ERP Adjustment
• ERP Adjustment = Difference between user‟s
forward looking ERP and D&P‟s historical ERP
(4.4%)
• Build Up Method Only (no CAPM)
34. Using D&P and Ibbotson Collectively
• Use of Ibbotson IRP with Duff & Phelps
• Need to adjust the IRP for differences in the estimated ERP
• Difference between forward looking ERP and Ibbotson Historical
ERP
• Adjusted IRP = Ibbotson IRP x (Forward Looking ERP / Ibbotson ERP)
• Once Adjusted IRP has been determined, use them in a regular
build-up method
• Duff & Phelps cautions users that these adjustments might double
count the beta effect
• CAPM might be better solution
• Size premium use okay with CAPM and Build-up method
36. Economic Challenges - 2008 & 2012
2008 2012
• Securitization and • Slow Global Growth
Subprime Crisis • Housing Market Remains
• Lack of Liquidity and Depressed
Available Credit • European Debt Crisis
• Housing Market Collapse • Downgrades of Debt
• Extreme Volatility • High Unemployment
• Government Bailouts • Low Interest Rate Levels
37. Challenges to the Cost of Equity
• Economic conditions has presented historically uncommon
levels of risk/return levels
• Substantially changed interest rates
• Substantially changed risk premiums
• Today‟s economic climate not supported by historic data
• Changes in investor‟s expectations and behavior
• Changes to risk treatments
• Recent shift from risk retention to risk avoidance - “Flight to
Quality”
• Historically low interest rates
38. ERP During Periods of “Flight to Quality”
• Any estimate of ERP must be made in relation to a risk-
free security
• Expected return of a company‟s equity investors must be measured
in its relationship to the rate of return on a risk-free security
• Function of the holding period for the investment
• Short-term holding period U.S. Government short-term security
• Long-term holding period Long-term U.S. Government bond
• Valuing a business = long-term investment
39. Conditional Estimate of ERP and the Great Recession
• September 2008 – Economy plunges into crisis
• Long-term trend in large company stocks parallels ERP
estimate over time
• Stock market goes through cycles
• Decline from the long-term average (i.e. last half of 2008)
• Conditional ERP will be greater than the average for some time
• Average over the long-run to return to the average
• Below average for a period (losses during 2008)
• ERP will be higher to then get back to average
• As stock market declined and risk increased, implied ERP
estimates increased while realized risk premiums decreased
• Estimate ERP using a method just like “normal” times, estimate would
be flawed
41. Estimating ERP during Recession
• 2008 – 2010 not ordinary times
• Standard practice of practitioners utilizes “spot” yield
• 20-year U.S. government bonds
• Add to arithmetic average of realized risk premiums from
Ibbotson, etc. as the base of capital estimate
• Methodology has created many erroneous estimates
• December 2007 yield on 20-year U.S. Gov‟t Bonds = 4.5%
• December 2008 yield on 20-year U.S. Gov‟t Bonds = 3.0%
• Risk in economy increased
• Base cost of equity capital using risk premiums decreased
• Similar scenario in 2010
• European sovereign debt crisis causes base cost of equity to be
understated
42. Implied Volatility and the ERP
• Implied volatility is the market‟s best estimate of future
volatility over the term of the option
• Crisis begins in September 2008
• Stock market moves down
• Fear envelops the financial markets
• Implied volatilities increased in S&P 500 and long-term U.S. bonds
• Peaked in October – December 2008 period
• Concurrently, interest rates on U.S. bills and bonds decline
• Levels below those justified by the real rate of interest plus inflation
• Increased volatility in the expected interest rates
• Market questioned sustainability
• Uncertainty about the trajectory of economic and financial markets
43. Implied ERP Estimates and the Risk-Free Rate
• Actual risk-free rates versus normalized risk-free rates
• ERP against actual risk free rates ERP greater
• Risk-free rates are lower than one would expect given:
• Real rate of interest
• Inflation expectations
• Reinvestment risk
• Using a normalized risk-free rate and benchmarking one‟s estimate
of ERP against the normalized should be implemented
1. Any period in which the risk-free rate is reduced due to flight-to-quality,
one must re-estimate the ERP
2. Monthly re-estimate of ERP assumes that the implied ERP model is
accurate and that inputs are updated
3. Given that we are valuing an entire business, do the values of the
subject business actually change monthly?
44. Conclusion of Adjustments to ERP
• Normal ERP is a range reflecting the principle investor‟s
expectations are NOT homogeneous
• Different investors have different cash flow expectations
• Different future assessments of risk
• Estimating ERP is one of the most important issues in
Cost of Capital of a subject business
• Consider variety of sources
• Examine realized returns over various periods
• Employ forward looking estimates
• What is reasonable estimate of unconditional (long-range)
ERP?
45. Global GT LP and Global GT LTD v.
Golden Telecom, Inc.
• Del. Court of Chancery, April 23, 2010
• Golden‟s expert selected 7.1% long-term ERP
• Based on Ibbotson SBBI Valuation Yearbook
• Petitioner‟s expert selected ERP of 6.0%
• Based on teaching experience, relevant empirical literature, „supply
side‟ ERP reported in Ibbotson Yearbook
• Court rejected the use of the ERP based solely on
Ibbotson
• “…relevant professional community has mined additional data and
pondered the reliability of past practice and come, by a healthy
weight of reasoned opinion, to believe that a different practice
should become the norm…”
46. Risk-Free Rate
• Reflects three components:
1. Rental Rate – real return for lending funds over the investment
period
2. Inflation – expected rate of inflation over the term
3. Maturity Risk – (investment rate risk) risk that the investment‟s
principal market value will rise or fall during the period to maturity
due to changes in interest rates
• All three of these economic factors are embedded in the
yield to maturity for any given maturity length
47. Risk-Free Rate - Inflation
• Basic risk-free rate includes inflation expectations
• When projecting cost of capital to discount future net
cash flows; net cash flows should also reflect the
expected effect of inflation
• Building cost of capital in nominal terms v. real dollars
• Nominal = goal or approximation as opposed to real value
• Estimate long-term economic inflation forecast by taking
difference in yield in risk-free security and the yield on
TIPS (Treasury Inflation-Protected Securities)
48. Risk-Free Rate – “Going-Concern” Businesses
• Valuing “Going-Concern” Businesses
• Generally use long-term U.S. government bonds as risk-free
security
• Estimate ERP in relation to long-term U.S. government bonds
• Most business investments have long durations
• Suffer from a reinvestment risk comparable to long-term U.S.
government bonds
• As such, an ERP estimated relative to long-term bonds reflects the
investment horizon and risks confronting valuators
• Most use 20-year (constant maturity) U.S. government bond
yield to maturity as of the valuation date
• 10-year or 30-year may be applicable depending on each unique situation
49. Risk-Free Rate - Appropriateness
• Use of Risk-Free Rate as building block for Cost of Equity
Capital still appropriate?
• 2008 financial crisis
• U.S. government security yields declined
• Long-term U.S. government bond yields diminished to
abnormally low levels
• Thus, the typical benchmark used in Cost of Equity Capital
models became abnormally low
• Leads to inaccurate indications of value
51. Risk-Free Rate - Adjustment
• Market interest rate influenced by a “Flight to Quality”?
• “Flight of Quality” – the action of investors moving their capital away
from riskier investments to the safest possible investment vehicles
• Uncertainty in the financial or international markets
• U.S. Economic Recovery
• European Sovereign Debt Crisis
• QE (Quantitative Easing) Purchases
• Assess the changes in the market interest rates and other economic
indicators
• Flow of Funds
• Implied Volatility of Options
• Changes in Estimated Inflation
• If market rates prove abnormally low, use a build-up approach to normalize
• Consider historic averages
• Real rate of interest
• Inflation estimates
52. Damodaran Online
• Published by Aswath Damodaran – Professor of Finance
at the Stern School of Business at NYU
• Publishes Monthly Cost of Equity Component data online
• Assumption: When using historical ERP, we assume the
ERP will not change much over short periods of time and
revert back over time to historical averages
• Reasonable for mature equity markets?
• Example: Fall of Lehman Brothers and subsequent equity
collapse
• ERP on Oct 10: High of 6.6%, Low of 6.1%
• Might be better to look at data monthly, rather than annually
53. Damodaran Monthly Data
• Two Ways to View ERP Volatility
• Once crisis has passed, ERP will return to status quo
• Crisis should be ignored and move to ERP at status quo for
mature markets (i.e. ERP fixed near 5-6%)
• Once crisis has passed, ERP won‟t return to status quo
right away
• Crisis is a structural shift in markets and ERP should be modified
to reflect market changes
• Damodaran argues a combination of both
• ERP should be assessment of the Company, not purely the equity
markets
55. Monthly Data Calculation
• Data Sources:
• Value Line – For U.S. Data
• Capital IQ – For International Data
• Bloomberg – For International Data
• Uses a 2-stage model
• Projects expected distributions
• Dividends and stock buy-backs
• Based on average of analyst estimates for earnings growth for firms
comprising S&P 500
• Calculates for first 5 years
• Expects growth to equal risk-free rate thereafter
• Solves for expected return (discount rate)
• Equates distributions to current levels of S&P 500
• Benchmarks his implied ERP estimates
• Subtracts current yield on 10-year U.S. bonds from expected return of S&P
56. Incorporating it into Report?
• Good tool to estimate value for appraisal updates
• Helps better understand swings in market risks and
unsystematic risks
• Might assist in development of financial
forecasts/projections
• What does Damodaran think?
• Does not recommend data to be used in legal arena
• Experts should not put much weight into data
• Not transparent in how many of his data collections are calculated
• No authoritative support or evidence this would beat annual data
