DISSECTING RISK PREMIUMSAmerican Society of Appraisers

Washington, DC, Metro Area Chapter

Presented: March 14, 2012

Zachary C. Reichenbach, CPA

Michael B. Lawrence

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

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

Cost of Equity (cont.)• Two Methods to Calculate the Cost of Equity• Both Methods Quantify Risk – “Building Blocks”

Build Up Method

Risk Free Rate

Equity Risk Premium

Size Premium

Industry Risk Premium

Specific Company Risk Premium

Modified CAPM

Risk Free Rate

(β x ERP)

Size Premium

Specific Company Risk Premium

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. Treasury Bond

GE Stock

Yield: 4% Yield: 15%

Difference in Yield = RP

RP = 11%

Risk Premiums on Various SecuritiesSecurity 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

Ibbotson’s ERP Data

Ibbotson

• Calculating the Historical ERP• Stock Market Benchmark• Risk-Free Asset• Arithmetic or Geometric Average• Time Period for Measurement

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

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

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)

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

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

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

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

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

Plotting Survivorship

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Real ReturnVolatilityLinear (Volatility)

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

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

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)

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

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)

Duff & Phelps’ ERP Data

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

Size and Risk Comparison

Size Study – 8 Measures

• Market Value of Equity• Book Value of Equity• 5-Year Average Net

Income• Market Value of Invested

Capital• Total Assets• 5-Year Average EBITDA• LTM Sales• No. of Employees

Risk Study – 3 Measures

• Operating Margin• Coefficient of Variation in

Operating Margin• Coefficient of Variation in

Return on Equity

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)

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

Build-Up Method – No Regression

• ERP Adjustment = User’s ERP – Historical ERP• Difference between user’s forward looking ERP and

D&P’s historical ERP (4.4%)

COE = Rf + RPm+s + RPu + ERPadj

Rf Risk Free Rate

RPm+s Market & Size Premium

RPu Specific Co. Risk

ERPadj ERP Adjustment

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

Equity Risk PremiumActual

Criteria ($mils.) Constant Slope Log PremiumLTM book value of common equity 0.500 17.48% -2.84% -0.301 18.33%5-year average net income 0.050 12.73% -2.15% -1.301 15.53%Most recent period total assets 0.600 19.32% -3.02% -0.222 19.99%5-year average EBITDA 0.080 16.71% -2.99% -1.097 19.99%LTM Sales 2.000 17.22% -2.34% 0.301 16.51%

Average 18.71%

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”

CAPM Method

• Beta – Compare with S&P 500• D&P – Recommended ERP is 5.5%

COE = Rf + (β x ERP) + RPs + RPu

Rf Risk Free Rate

β Beta

ERP Equity Risk Premium

RPs Beta Adjusted Size Premium

RPu Specific Co. Risk

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

RiskOperating

MarginRiskVariability

of Earnings

Build-Up Method

• ERP Adjustment = Difference between user’s forward looking ERP and D&P’s historical ERP (4.4%)

• Build Up Method Only (no CAPM)

COE = Rf + RPm+u + ERPadj

Rf Risk Free Rate

RPm+u Market & Specific Co. Risk Premium

ERPadj ERP Adjustment

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

Economic Challenges and the Impact on the Cost of Equity Components

Economic Challenges - 2008 & 2012

2008

• Securitization and Subprime Crisis

• Lack of Liquidity and Available Credit

• Housing Market Collapse• Extreme Volatility• Government Bailouts

2012

• Slow Global Growth• Housing Market Remains

Depressed• European Debt Crisis• Downgrades of Debt• High Unemployment• Low Interest Rate Levels

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

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

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

Conditional ERP at Trough of Stock Market Cycle

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

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

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 implemented1. 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?

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?

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…”

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

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)

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

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

U.S. Government Bond Yields

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

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

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

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14.0%Recent ERP Trends

ERP

Risk Free Rate

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

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

Questions?