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7/27/2019 Equity Chapter2
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RETURN CONCEPTS
PresenterVenueDate
7/27/2019 Equity Chapter2
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WHY FOCUS ON RETURN CONCEPTS?
To evaluate expectedand past performance
To understand riskpremiums
To estimate discountrates for valuation
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HOLDING PERIOD RETURN
0
0
0 0
1H H
HH
D Pr
P
P PDrP P
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OTHER RETURN CONCEPTS
RequiredReturn
Return fromConvergence
of Price toIntrinsicValue
DiscountRate
Internal Rateof Return
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EQUITY RISK PREMIUM
Currentexpectedrisk-freereturn
Equityrisk
premium
Requiredreturn on
equity
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EQUITY RISK PREMIUM ESTIMATES
Historical Estimates
Forward-Looking Estimates
-Gordon growth model estimates
-Macroeconomic model estimates
-Survey estimates
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ISSUES FOR USING HISTORICAL EQUITY
RISK PREMIUM ESTIMATES
Length of Sample Period
- Balancing long-term and short-term considerations
Geometric vs. Arithmetic Mean
- Geometric more accurately reflects future value
Choice of Risk-Free Return
- On-the-run long-term Treasuries
Survivorship Bias
- Using returns from surviving firms artificially inflates estimates of return
Strings of Unusual Events
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HISTORICAL EQUITY RISK PREMIUM ESTIMATES
1
4
1
6
4
1
1% to
2%
2% to
3%
3% to
4%
4% to
5%
5% to
6%
6% to
7%
NumberofMarkets
Equity Risk Premiums
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FORWARD-LOOKING EQUITY
RISK PREMIUM ESTIMATES
Gordongrowth
model riskpremium
Dividendyield
Earningsgrowth rate
Governmentbond yield
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FORWARD-LOOKING EQUITY
RISK PREMIUM ESTIMATES
Macroeconomic Model Equity Risk Premium (ERP)
ERP (1 EINFL)(1 EGREPS)(1 EGPE) 1 EINC F
R
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EXAMPLE:
FORWARD-LOOKING EQUITY RISK PREMIUM
Yield on treasury bonds 3.8%
Yield on Treasury inflation-protected securities 1.8%
Expected growth in labor productivity 1.5%
Expected growth in labor supply 1.0%
Expected growth in the P/E 0.0%
Expected dividend yield 2.7%
Return from reinvestment of income 0.1%
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EXAMPLE:
FORWARD-LOOKING EQUITY RISK PREMIUM
1 Treasury Bond YieldExpected Inflation
1 TIPS Yield
1 0.038Expected Inflation 1 2.0%
1 0.018
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EXAMPLE:
FORWARD-LOOKING EQUITY RISK PREMIUM
Real earnings growth Labor productivity Labor supply growth
1.5% 1.0%
2.5%
Expected income Dividend yield Reinvestment return
2.7% 0.1%
2.8%
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EXAMPLE:
FORWARD-LOOKING EQUITY RISK PREMIUM
Macroeconomic model equity risk premium
=
ERP (1 EINFL)(1 EGREPS)(1 EGPE) 1 EINC
(1 0.02)(1 0.025)(1 0) 1.0 0.028 0.038
3.5%
F
R
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ESTIMATING THE REQUIRED RETURN ON
AN EQUITY INVESTMENT
Capital Asset PricingModel
Multifactor Models FamaFrench model
PastorStambaugh model
Macroeconomic models
Statistical models
Build-Up Method
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CAPITAL ASSET PRICING MODEL
(CAPM)
Where
- E(Ri) = Required return on equity for security i
- RF= Current expected risk-free return
- i= Beta of security i
- E(RM) = Expected return on the market portfolio
- E(RM)RF= Equity risk premium
Assumptions- Investors are risk averse
- Investment is based on meanvariance optimization
- Relevant risk is systematic risk
( ) [ ( ) ], i F i M F E R R E R R
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BETA ESTIMATION ISSUES
S&P 500 and NYSE Composite arecommon choices in the United States
Choice of MarketIndex
Five years of monthly data is mostcommon choice
Length &Frequency of Data
Betas move towards 1.0 over timeAdjusted Betas
Adjust comparable betas for leverageThinly Traded andPrivate Firms
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MULTIFACTOR MODELS:
FAMAFRENCH MODEL
Required
Returnon
Equity
ValuePremium
SizePremium
MarketRisk
Premium
Risk-Free
Return
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FAMAFRENCH MODEL
where- SMB = The return to small stocks minus the return to large stocks
-size= The sensitivity of security ito movements in small stocks
- HML = The return to value stocks minus the return to growth stocks
- value= The sensitivity of security ito movements in value stocks
PASTORSTAMBAUGH MODEL
where
- LIQ = The return to illiquid stocks minus the return to liquid stocks
- liq= The sensitivity of security ito movements in illiquid stocks
mkt size value RMRF SMB HML, i F i i i
r R
mkt size value liq RMRF SMB HML LIQ, i F i i i i
r R
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EXAMPLE:
FAMAFRENCH MODEL
Risk-free rate 3.0%
Equity risk premium 5.0%
Beta 1.20
Size premium 2.2%
Size beta 0.12
Value premium 3.8%
Value beta 0.34
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EXAMPLE:
FAMAFRENCH MODEL
mkt size value RMRF SMB HML
3% 1.20(5%) 0.12(2.2%) 0.34(3.8%)10.56%
i F i i ir R
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BUILD-UP METHODS
For Private Firms
- Typical risk premiums
- size
- firm-specific risk
- Other risk premiums
- marketability
- control
Bond Yield plus RiskPremium Method
- Useful if firm has publicdebt
- YTM on long-term debt +risk premium
Required Returnon Equity
Risk-FreeRate
Equity
RiskPremium
Other
RiskPremiums
Other
RiskDiscounts
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INTERNATIONAL CONSIDERATIONS FOR
REQUIRED RETURNS
Exchange Rates
Emerging Markets
Country spread model
Country risk ratingmodel
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WEIGHTED AVERAGE COST OF CAPITAL
WeightedAverage
Cost of Capital
Debt
Cost of DebtMarket Value
of DebtTax Rate
Equity
Cost of EquityMarket Value
of Equity
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WEIGHTED AVERAGE COST OF CAPITAL
Where- MVD = Current market value of debt
- MVCE = Current market value of common equity
- rd= Before-tax cost of debt (which is transformed into the after-tax cost by
multiplying it by 1Tax rate)
- re= Cost of equity
MVD MVCE(1 Tax Rate) ,
MVD MVCE MVD MVCE
d e
r r
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EXAMPLE:
WEIGHTED AVERAGE COST OF CAPITAL
Risk-free rate 3 .0%
Equity risk premium 5 .0%
Beta 1 .20
YTM of long-term bond 6 .1%
Long-term debt/Total capital at market value 40 %
Tax rate 30 %
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EXAMPLE: WEIGHTED AVERAGE COST OF
CAPITAL
MVD MVCEWACC (1 Tax Rate)MVD MVCE MVD MVCE
0.40(6.1%)(1 0.30) 0.60(9.0%)7.11%
d er r
[ ( ) ]3% 1.2(5%) 9.0%
e F i m F
e
r R E R R
r
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CHOICE OF DISCOUNT RATE
WACCCash Flowsto the Firm
Required return on equityCash Flows
to Equity
Nominal discount ratesNominal
Cash Flows
Real discount ratesReal CashFlows
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SUMMARY
Holding period return, realized return, expected return,required return, discount rate, return from convergence ofprice to intrinsic value, and IRR
Return Concepts
= Required return on equityRisk-free return
Historical estimates
Issues in estimation: Sample period length, geometric vs.
arithmetic mean, risk-free return choice, survivorship bias,strings of unusual events
Forward-looking estimates: Gordon growth model estimates,macroeconomic model estimates, survey estimates
Equity Risk Premium
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SUMMARY
Capital asset pricing model
Multifactor models
FamaFrench model
PastorStambaugh model
Macroeconomic models
Statistical models Build-up method
Models for the Required Return on Equity
Choice of market index Length and frequency of data
Adjusted betas
Thinly traded and private firms
Beta Estimation Issues
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SUMMARY
Exchange rates
Emerging markets
International Considerations for Required
Returns
Use market values, marginal tax rates, current bond YTM,and equity required return
Weighted Average Cost of Capital
Use WACC for firm cash flows
Use equity required return for equity cash flows
Use nominal rates for nominal cash flows
Choice of Discount Rate