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CAPM MagicUse & Abuse of the Rabbit

Susan H. Glass, MBA, CA, CPA, FCBVNational Leader, KPMG Valuations

June 2018

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Specific Risk5 min

Risk-Free Rate<5 min

CAPM Model<5 min

Beta25 min

Size Premium5 min

Agenda

Market Equity Risk Premium

10 min

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Capital Asset Pricing Model OverviewCost of Equity Models

CoE = RFR + ß X ERP + Size + CRP Pure CAPM CoE = RFR + ß X ERP + Size + CRP + SRP Modified CAPMCoE = RFR + ERP + Size + CRP + SRP + IRP Build-up Approach

Glossary

CoE: Cost of Equity Size: Size PremiumRFR: Risk-Free Rate CRP: Country Risk Premium (if applicable)ß: Beta SRP: Specific Risk PremiumERP: Market Equity Risk Premium IRP: Industry Risk Premium (if applicable)

Applicability of CAPM

Public vs. private company valuations Extent of specific risk premium Issues arising with beta – address or use build-up approach (private companies)

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Term Long-term

10-year, 20-year, 30-year, over 10-year (Canada)…

Consistency with market equity risk premium (ERP)

Consistency with term of projections

Currency Consistent with cash flow

projections

Mature vs. emerging markets

Emerging markets:

1) Local cash flow and discount rate

2) Mature market cash flow and discount rate

• Cash flows s/b translated using forward rates (not spot or future rates)

3) Real cash flow and discount rate

Risk-Free Rate

Spot v. Normalized Assumption that current risk-

free rates are below sustainable levels

Support for both spot and normalized

Personal preference is spot

1) Opportunity cost

2) What if rates were abnormally high?

3) More flexible / easier to support (albeit not the deciding factor)

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Beta: Introduction

A measure of relative market risk

Common description:

─ A beta of 1.0 means the company is of similar risk to the overall market, while a beta of more (or less) than 1.0 indicates more (or less) risk relative to the overall market

What is Beta?

• Beta does not measure all risks.

• Beta only captures market risks, which are risks borne by all companies

─ Systematic risks

─ Non-diversifiable risks

• Each company bears market risks to a greater or lesser degree, which is the element captured by beta

• Beta does not capture risks specific to any particular company─ Non-systematic risks─ Diversifiable risks

Market vs. Specific Risksß = ρ(s,m) x σ (stock)

σ (market)

ρ (Rho): Correlation coefficient (─1 to +1) Effective range is 0 to 1 since negative

correlation is rare for stocks

σ (Sigma) = standard deviation Relative Volatility (RV) = σ (s) ÷ σ (m)

Beta of 1.0 might result from: 1.0 (RV) x 100% (ρ) 4.0 (RV) x 25% (ρ) etc. …

Relative Volatility & Correlation

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Relative Volatility & Correlation

Implications

─ Daily betas

─ Betas for thinly-traded shares

─ Foreign listings

─ Understanding beta

─ Betas for private companies

Beta = Covariance (s, m)Variance (m)

Cov (s,m) = Correlation coefficient (s,m) x σ(s) x σ(m)

Beta = Correlation coefficient (s,m) x σ(s) x σ(m)σ(m) x σ(m)

= Correlation coefficient (s,m) x σ(s)σ(m)

Beta = Correlation (s,m) x Relative Volatility = ρ (s,m) x σ(s) ÷ σ(m)

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Market Index

Direct v. Indirect

Other Issues &

Other Betas

BETA (OLS)

Factors Impacting Beta

Leverage & Cash

Period & Return Interval

Direct only relevant for pubcos

5-yr, 2-yr, etc.

Monthly, Weekly, Daily…

Canada, U.S., Mature Markets,

Emerging Markets

• Month-end or end-of week returns vs. average

• Sum beta, Total beta

• FIB, IRP, Liquidity

Net debt vs. gross debt with cash

adjustment

1.1 1.3

1.7

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Direct vs. Indirect Approach

Factors supporting direct approach Subject’s shares are actively traded Peer co’s/betas are only semi-comparable

Factors supporting indirect approach Private company valuation (necessary) Thin trading and/or comparable peers High standard error of single betas Date (staleness) issues in certain cases

Reliance on beta for subject company (direct) vs. reliance on betas of peer companies (indirect)

Factors influencing beta:

1) To aid in selecting peers, or 2) To aid in understanding betas

Business mix and changes over time Type of business and sensitivity to economic

conditions (discretionary vs. non-discret’y; brand strength; client mix; cyclicality; etc.)

Age and stage of maturity Operating leverage: inherent in business vs.

business model (outsource vs. insource; subcontracting)

High growth Prior-noted issues (t-test, liquidity) Volatility vs. correlation Unusually high specific risk issues can result

in temporary instability in beta Random vs. explainable issues

Selecting peer companies and betas: Issues arising in trading multiple analysis Beta comparability issues (see blue box) Length of time since IPO Statistically valid (t-test ≥ 1.96)

─ t-test = beta ÷ standard error Liquidity of peer company stock

─ betas of illiquid shares are understated

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S&P/TSX Composite• Benchmark Canadian index

• ~ 250 companies

• ~ 70% of market cap of TSE

S&P 500• Benchmark U.S. Index

• 500 of the largest pubcos listed in the U.S.

Consistency• With ERP – not with listing

exchange (i.e., don’t use NASDAQ for NASDAQ-listed stocks)

Local Stock Markets Exercise caution Correlation with ERP base Consistency of beta

Other Issues If consistency is not violated Number of co’s; market

weighting, broad base

MSCI World Index If the company and its peers

operate globally and are based in various countries

Market Index

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Estimation Period & Return IntervalEstimation Period:# of Years

Long: More observations, but might not capture current dynamics of company

Long period preferable for companies if relatively stable over time; shorter period is preferable if company/industry has undergone recent significant or structural changes

Shorter also prefer for companies growing rapidly

Return Interval

Monthly, weekly, daily

Shorter intervals will increase the number of observations, but may lessen reliability

Match return interval and # of years: need sufficient data points for beta to be relevant

Monthly Betas

For a standard monthly beta, you likely need five years to obtain sufficient observations, which is often too long given the rate of change of most companies

Alternative might lie in the approach used to calculate monthly returns – EOM only vs. daily (monthly returns as at 1st, 2nd, 3rd, etc.)

Daily Betas

Daily data contains a lot of noise that will dampen the relationship between a stock and the market, which will underestimate beta

Non-trading (or non-synchronous trading) on the asset during a return period will reduce the measured correlation with the market index, thus reducing beta

Will show a lower standard error, which is of no consequence.

Two-year weekly betas tend to be the most common

Benefit from more data, but don’t suffer detriments of a lengthy period or noise

End of week (Friday standard) vs. every Monday, Tuesday…?

Weekly Betas

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Beta by Weekday: 2YW (S&P500)

0.50

0.70

0.90

1.10

1.30

1.50

1.70

1/1/2016 7/1/2016 1/1/2017 7/1/2017

Expedia Beta

Mon Tue Wed Thr Fri

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

1.90

2.00

1/1/2016 7/1/2016 1/1/2017 7/1/2017

Booking Beta

Mon Tue Wed Thr Fri

Ramazan Gencay, Faruk Selcuk, Brandon Whitcher, Systematic Risk and Time Scales, March 2002 In the Matter of Shanda Games Limited, Grand Court of the Cayman Islands, 25 April 2017

Mon Tue Wed Thr Fri Min Max Avg

Booking 1.97 1.61 1.66 1.69 1.77 1.61 1.97 1.74 Expedia 1.40 1.33 1.12 0.67 1.15 0.67 1.40 1.13 Trip Advisor 1.61 1.44 1.49 0.62 0.97 0.62 1.61 1.22

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Beta by Weekday: 5YM (S&P500)

-

0.50

1.00

1.50

2.00

2.50

12/9/2017 12/19/2017 12/29/2017

Monthly Betas Calculated Each Day

Booking Expedia Trip Advisor

What if we were to calculate monthly returns for each day of the month?

─ Nov 1 to Dec 1

─ Nov 2 to Dec 2 … etc. …

• Determine beta using these returns

• What if we were to adopt the same approach using weekly returns?

Beta StERR1.37 6%1.01 7%1.61 11%

Each Day

2Y Wkly Beta StERRBooking 1.77 23%Expedia 1.15 28%Trip Advisor 0.97 38%

FridayBeta StERR1.75 10%1.12 12%1.22 17%

Each Day

Min Max Avg EOM

Booking 1.00 1.69 1.38 1.39 Expedia 0.63 1.64 1.01 0.89 Trip Advisor 1.00 2.34 1.61 2.34

5Y Mthly Beta StERRBooking 1.39 33%Expedia 0.89 36%Trip Advisor 2.34 52%

EOM

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Leverage & Cash

• Significant difference if cash balances are high or net debt is negative

• Gross debt with cash adjustment is preferred, but net debt is acceptable if difference is not material

Low Cash High Cash

Gross Debt 35.0% 35.0%

Cash 5.0% 30.0%

Net Debt 30.0% 5.0%

Tax Rate 25.0% 25.0%

Unlevered beta 1.55 1.55

Use Net Debt 1.27 1.49

Use Gross Debt / Cash 1.29 1.75

• Re-lever using D/E ratio used in discount rate (cash adjustment not necessary)

Two Alternatives:

1) D/E ratio based on net debt

2) D/E ratio based on gross debt with separate cash adjustment

1) D/E ratio used to un-lever betas

• Based on market values

• Typically MV of debt is assumed to equal book & MV of equity is based on market cap

• Over same term as beta (2 year, 5 year, etc.)

• Quarterly vs. daily?

2) Cash ratio

• Should be consistent with D/E ratio approach

3) Income tax rate used to un-lever betas

• Marginal vs. effective

4) D/E ratio and tax rate used to re-lever betas

• Consistent with assumptions used for WACC (if an unlevered approach is used)

• Consistent with cash flow projections on a market basis (if a levered approach is used)

• Market value based on FMV (not trading or book)

Levered Beta = Unlevered Beta x [1 + (1 – Tax Rate) x D/E Ratio]

Cash-Adjusted Beta = Unlevered beta / (1 – Cash Ratio), where

Cash Ratio = Cash / (Market Value of Equity + Market Value of Debt)

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Sum Beta

Based on a multiple regression.

Regress stock returns for a given week (month) against: (1) market returns for the same week (month); and (2) market returns for the prior week (month)

Beta is the sum of the two regression coefficients

To account for the lag in stock price reactions to market events, especially in smaller companies

Difference between sum beta and regression (OLS) beta tends to expand as the size of the company decreases

Issues: Data availability; whether use of a sum beta might double count size premium; complexity; relative to average weekly/monthly

Sum Beta

Other Betas

Total Beta

Discussed by Professor Damodaran

Beta (OLS) = Relative Volatility (s,m) x Correlation (s,m)

In effect, the presence of the correlation coefficient restricts risks to market risks only

By removing the correlation co-efficient, we obtain a measure of total risks –systematic and non-systematic

─ Viewed as an option for valuing private companies

Total beta = Relative Volatility (s,m) = StD(s) ÷ StD(m)

Issues: Much of pubco share price volatility is unrelated to fundamentals or underlying risk; can result in nonsensical results; over-reliance on statistics

Total Beta

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Liquidity

Full Information Betas & Industry Risk Premiums (D&P) Full information beta (FIB)

─ Based on multiple regressions involving beta and sales of companies engaged in multiple businesses

─ Consider if dealing with private companies involved in niche businesses Industry Risk Premiums

─ Based on FIB and ERP (historical, supply-side and D&P recommended)

FIB & IRP

Betas for Illiquid Securities are Systematically Understated Liquidity tests

─ Number of no-trade days (preferably none)─ Bid-ask spread (% and $)─ Annual trading volume as a % of free float─ Number of daily trades

Case law (Dell – SC of Delaware; Shanda – Cayman); MI 61-101

Other Beta Issues

Beta Calculation Tips Columns with market returns and stock returns for each company being analysed

for each relevant date (i.e., every Friday over a two-year period) Beta = SLOPE (Stock Data Range, Market Data Range) Correlation = CORREL (Stock Data Range, Market Data Range) Std. Dev = STDEV.P (Stock Data Range) and STDEV.P (Market Data Range) Relative Volatility = STDEV.P (Stock Data Range) ÷ STDEV.P (Market Data Range) R-squared = Correlation ^ 2

Math

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I Equity Risk Premium: ERP

Historical Supply-Side Implied

Equity Risk Premium

ERP

Expected average annual return on market equity less risk-free rate

Market portfolio:– S&P/TSX (Canada)– S&P 500 (U.S.) – Mature/emerging

Issues– How measured?– Arithmetic vs.

geometric?

Historical ERP

Average difference between actual historical equity rates of return and risk-free rates

Issues:

– Pros and cons of longer vs. shorter periods

– Review data for Canada

Supply Side ERP

Historical ERP adjusted to remove P/E expansion

Logic: P/E expansion not likely to continue indefinitely into the future

Issues:

– Data availability outside of U.S.

Implied ERP

Estimated ERP based on current stock prices, expected future cash flow and growth

Dr. Damodaran

Issues:

– Assumptions in the analysis

– Only calculated for U.S. markets

– Various versions, only two of which are relevant

Practice

Industry Practice

ERPs drawn from experience, along with internal or external studies and discussions

Issues:

– Subjective

– Ability to defend (should not be deciding factor)

– Strong market support

– Often assessed after considering various options

Definition

Approaches & Issues

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ERP: Canadian Data Arithmetic and geometric averages are presented, but arithmetic

average is preferred when developing a discount rate

Longest (82-year) and shortest (20-year) periods support ERP of ~5.5%, while 30-50 year periods support an ERP of 4.0% to 4.5%

Multiple 10-year periods and 20-year periods support an ERP in the 4.3% to 5.7% range (based on all 10-year and 20-year periods beginning in 1935 and forward)

Industry practice: Canada 5.0% & U.S. 6.0%

# of Yrs Arithmetic Geometric

1935-2016 82 (91) 5.6% 4.4%1967-2016 50 3.9% 2.6%1977-2016 40 4.5% 3.3%1987-2016 30 4.1% 2.9%1997-2016 20 5.4% 3.9%[1] Per data obtained from Duff & Phelps International

Valuation Handbook, Report on Canadian Economic Statistics 1936 - 2000 (Canadian Institute of Actuaries)and S&P/TSX

Canada [1]Date Range 10-Yr 20-Yr

Minimum -2.9% -0.3%Maximum 16.0% 12.5%Average 5.7% 5.5%Median 5.4% 4.3%{1] As sourced in prior table

1935 to 2016 [1]

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Arithmetic is a simple average, while geometric is a compound average

Arithmetic will always be higher than geometric (unless returns are identical)

The difference between the arithmetic and geometric average will increase as the volatility of returns increases (higher standard deviation)

Some sources, including Duff & Phelps (and before them Morningstar, and before them Ibbotson) recommend the arithmetic average

Others recommend geometric

Logical Analysis Geometric only considers the endpoints and

is unaffected by all other data points. Focuses on the destination, not the route

Higher volatility will increase the arithmetic average, but not the geometric

Arithmetic vs. Geometric

Simple two-stage model. Annual return will be either a gain of 12% or a loss of 4%.

Arithmetic average would be 4.0%, which (if compounded) would produce an ending balance of $108.16

Geometric average is 3.69%

CompoundRate of Return

100 x 1.12 x 0.96 = $107.52 3.69% 100 x 0.96 x 1.12 = $107.52 3.69%100 x 1.12 x 1.12 = $125.44100 x 0.96 x 0.96 = $92.16

Average of the above four results = $108.16 Same result will arise in cases more

realistic than a simple two-stage model Compare to future possibilities arising for

projected cash flows – risks that actuals might differ from projections

Mathematical Analysis

Arithmetic vs. Geometric

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Size PremiumRelative Risks

Small companies are higher risk → return Maintain/increase market share Endure economic downturns

For & Against

Academic Studies

Dr. Rolf Banz 1981 (pre-81 data) Later studies focus on data for 1982-1997 Duff & Phelps: Returns on small-cap co’s

in 80’s were lower; trends since reversed Not clear why – perhaps due to increase

in new Pubcos in 80s/90s (Duff & Phelps)

Approach

Against: Academic studies show market data does not support higher premiums

For: Academic studies show market data supports higher premiums

Alleged double count of liquidity issues

Three potential approaches to quantify:─ Specific deciles (1 to 10a…)─ Categories: mid, low, micro─ Risk Premium Report Study (RPRS)

Impact of size on trading multiples Professional community (i.e., rating agencies) Delaware Courts: Merion Capital (2013),

Orchard Enterprises (2012); Just Care (2012); Shanda (2016; Cayman Islands)

Exposure to competitive threats Exposure to changes in business climate Access to capital

Potential issues with deciles 10b or lower(distressed, start-ups, liquidity, etc.)

Removed in RPRS Match size premium to beta (OLS vs. sum)

D&P: All combinations of monthly start andend dates from Jan 1926 to Dec 2017

92 years x 12 months = 1,104 months 1,104 x 1,105 ÷ 2 = 609,960 periods Small cap > returns in 514,465 periods (84%) High proportion of low returns arose in 1980s

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Specific Risk Premium

Public vs. Private

More easily supported in a private company scenario than in the valuation of a

public company

Nature of Purchaser

Individual or small/mid-market vs. public company

or large well-diversified fund/corporate acquirer

Levels of Diversification

Public company investor vs. large well-diversified fund

Global vs. domestic

Purpose of Valuation

Litigation, income tax, financial reporting, IPO,

expected transaction, etc.

List of Factors

List of positives & negatives plus a conclusion. Good first

step, but hard to support.

Standard Ranges

Low, High, Moderate. Industry wide for use with

CAPM; otherwise build-up? Something to think about…

Total Beta

Beta = Relative Volatility x Correlation

Total beta: Remove correlation (Damodaran)

Relative to Beta

Review beta premium for market risks. Compare to nature of specific risks.

Proportionate Basis

Determine cost of equity prior to SRP and add a further premium on a

percentage basis.

• Should a specific risk premium be included if using CAPM?• If so, how is it best determined and supported?

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Questions ?

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Thank you

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