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