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RETURN CONCEPTS
PresenterVenueDate
WHY FOCUS ON RETURN CONCEPTS?
To evaluate expected and past performance
To understand risk premiums
To estimate discount rates for valuation
HOLDING PERIOD RETURN
0
0
0 0
1H H
HH
D Pr
P
P PDr
P P
OTHER RETURN CONCEPTS
Required Return
Return from Convergence
of Price to Intrinsic Value
Discount Rate
Internal Rate of Return
EQUITY RISK PREMIUM
Current expected risk-free return
Equity risk
premium
Required return on
equity
EQUITY RISK PREMIUM ESTIMATES
•Historical Estimates
•Forward-Looking Estimates
-Gordon growth model estimates
-Macroeconomic model estimates
-Survey estimates
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
HISTORICAL EQUITY RISK PREMIUM ESTIMATES
1% to 2%
2% to 3%
3% to 4%
4% to 5%
5% to 6%
6% to 7%
1
4
1
6
4
1
Equity Risk Premiums
Nu
mb
er o
f M
arke
ts
FORWARD-LOOKING EQUITY RISK PREMIUM ESTIMATES
Gordon growth
model risk premium
Dividend yield
Earnings growth rate
Government bond yield
FORWARD-LOOKING EQUITY RISK PREMIUM ESTIMATES
Macroeconomic Model Equity Risk Premium (ERP)
ERP (1 EINFL)(1 EGREPS)(1 EGPE) 1 EINC FR
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%
EXAMPLE: FORWARD-LOOKING EQUITY RISK PREMIUM
1 Treasury Bond YieldExpected Inflation
1 TIPS Yield
1 0.038Expected Inflation 1 2.0%
1 0.018
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%
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%
FR
ESTIMATING THE REQUIRED RETURN ON AN EQUITY INVESTMENT
Capital Asset Pricing Model
Multifactor Models• Fama–French model
• Pastor–Stambaugh model• Macroeconomic models
• Statistical models
Build-Up Method
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 mean–variance optimization
- Relevant risk is systematic risk
( ) [ ( ) ], i F i M FE R R E R R
BETA ESTIMATION ISSUES
• S&P 500 and NYSE Composite are common choices in the United States
Choice of Market Index
• Five years of monthly data is most common choice
Length & Frequency of Data
• Betas move towards 1.0 over timeAdjusted Betas
• Adjust comparable betas for leverageThinly Traded and Private Firms
MULTIFACTOR MODELS:FAMA–FRENCH MODEL
Required Return
on Equity
Value Premium
Size Premium
Market Risk
Premium
Risk-Free
Return
FAMA–FRENCH MODEL
• where
- SMB = The return to small stocks minus the return to large stocks
- βsize = The sensitivity of security i to movements in small stocks
- HML = The return to value stocks minus the return to growth stocks
- β value = The sensitivity of security i to movements in value stocks
PASTOR–STAMBAUGH MODEL
• where
- LIQ = The return to illiquid stocks minus the return to liquid stocks
- β liq = The sensitivity of security i to movements in illiquid stocks
mkt size valueβ RMRF β SMB β HML, i F i i ir R
mkt size value liqβ RMRF β SMB β HML β LIQ, i F i i i ir R
EXAMPLE: FAMA–FRENCH 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
EXAMPLE: FAMA–FRENCH MODEL
mkt size valueβ RMRF β SMB β HML
3% 1.20(5%) 0.12(2.2%) 0.34(3.8%)
10.56%
i F i i ir R
BUILD-UP METHODS
• For Private Firms
- Typical risk premiums
- size
- firm-specific risk
- Other risk premiums
- marketability
- control
• Bond Yield plus Risk Premium Method
- Useful if firm has public debt
- YTM on long-term debt + risk premium
Required Return on Equity
Risk-Free Rate
Equity Risk
Premium
Other Risk
Premiums
Other Risk
Discounts
INTERNATIONAL CONSIDERATIONS FOR REQUIRED RETURNS
Exchange Rates
Emerging Markets• Country spread model• Country risk rating
model
WEIGHTED AVERAGE COST OF CAPITAL
Weighted Average
Cost of Capital
Debt
Cost of Debt Market Value of Debt Tax Rate
Equity
Cost of Equity Market Value of Equity
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 1 – Tax rate)
- re = Cost of equity
MVD MVCE(1 Tax Rate) ,
MVD MVCE MVD MVCE
d er r
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%
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
CHOICE OF DISCOUNT RATE
• WACCCash Flows to the Firm
• Required return on equityCash Flows to Equity
• Nominal discount ratesNominal Cash Flows
• Real discount ratesReal Cash Flows
SUMMARY
• Holding period return, realized return, expected return, required return, discount rate, return from convergence of price to intrinsic value, and IRR
Return Concepts
• = Required return on equity – Risk-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
SUMMARY
• Capital asset pricing model• Multifactor models• Fama–French model• Pastor–Stambaugh 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
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