RETURN CONCEPTS Dr. David Krause AIM Program Marquette University

WHY FOCUS ON RETURN CONCEPTS? To evaluate expected and past performance To understand risk premiums To estimate discount rates for valuation

HOLDING PERIOD RETURN

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

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)

EXAMPLE: FORWARD-LOOKING EQUITY RISK PREMIUM Yield on treasury bonds3.8% Yield on Treasury inflation-protected securities1.8% Expected growth in labor productivity1.5% Expected growth in labor supply1.0% Expected growth in the P/E0.0% Expected dividend yield2.7% Return from reinvestment of income0.1%

EXAMPLE: FORWARD-LOOKING EQUITY RISK PREMIUM

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(R i ) = Required return on equity for security i -R F = Current expected risk-free return -  i = Beta of security i -E(R M ) = Expected return on the market portfolio -E(R M ) – R F = Equity risk premium Assumptions -Investors are risk averse -Investment is based on mean – variance optimization -Relevant risk is systematic risk

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 time Adjusted Betas Adjust comparable betas for leverage Thinly 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 -β size = 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

EXAMPLE: FAMA–FRENCH MODEL Risk-free rate3.0% Equity risk premium5.0% Beta1.20 Size premium2.2% Size beta0.12 Value premium3.8% Value beta0.34

EXAMPLE: FAMA–FRENCH MODEL

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 DebtCost of Debt Market Value of Debt Tax RateEquityCost 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 -r d = Before-tax cost of debt (which is transformed into the after-tax cost by multiplying it by 1 – Tax rate) -r e = Cost of equity

EXAMPLE: WEIGHTED AVERAGE COST OF CAPITAL Risk-free rate3.0% Equity risk premium5.0% Beta1.20 YTM of long-term bond6.1% Long-term debt/Total capital at market value40% Tax rate30%

EXAMPLE: WEIGHTED AVERAGE COST OF CAPITAL

CHOICE OF DISCOUNT RATE WACC Cash Flows to the Firm Required return on equity Cash Flows to Equity Nominal discount rates Nominal Cash Flows Real discount rates Real 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

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