EQ: Return Concepts

Realized alpha (ex post) =

= actual holding period return - contemporaneous required return

BIRR model (Burmeister, Roll, and Ross)

Macro economic factor models 1. confidence risk 2. time horizon risk 3. inflation risk 4. business cycle risk 5. market timing risk

Equity risk premium

The equity risk premium is the incremental return (premium) that investors require for holding equities rather than a risk-free asset. Thus, it is the difference between the required return on equities and a specified expected risk-free rate of return.

2 discount rates for finding the present value of stocks: required return on equity and firm's cost of capital

nominal required return on equity for when cashflows are available to common shareholders nominal after-tax WACC when the cashflows are those available to all the company's capital providers.

With means to estimate the equity risk premium, what are 3 ways to estimates the required return on equity

- CAPM - multi-factor models (Fama-French) - build-up method, such as the bond yield plus risk premium method

CAPM key insights

- an equation for the required return - should hold in equilibrium - assumes investors are risk averse and they make decisions based on the mean return and variance of returns of their total portfolio - The chief insight of the model is that investors evaluate the risk of an asset in terms of the asset's contribution to the systematic risk of their total portfolio

2 factors that influence unadjusted, raw beta

- choice of index used to represent market portfolio - length of data period and frequency of observations (5 yrs monthly, 60 obs, most common practice for calculating beta i.e. 5 yr beta estimate)

WACC

- marginal tax rate, not the effective tax rate that can reflect nonrecurring items, is better at reflecting the future costs of raising funds - target weights are used to approximate the capital structure of firms when the current weight misrepresent the normal cap. structure.

Build up method estimates of the required return on equity

- widely used for private businesses - estimates the RR based on the sum of the risk-free rate and a set of risk premia (no betas)

2 additional issues related to the required return estimate for private companies include

1. consideration of the relative values of controlling v. minority interest in share value 2. the effect on share value of the lack of ready marketability for a small equity interest in a private company

2. Return Concepts

2.1 holding period return 2.2 realized and expected return 2.3 required return 2.4 expected return estimates from intrinsic value estimates 2.5 discount rate 2.6 internal rate of return

3. The Equity Risk Premium

3.1 Historical Estimates 3.2 Forward-Looking Estimates

4. The Required Return on Equity

4.1 CAPM 4.2 Multifactor models 4.3 Build-up method 4.4 Required Return on Equity

Expected alpha (ex ante) =

= expected return - required return

Adjusted Beta (by Blume)

Adjusted beta = (2/3)(Unadjusted beta) + (1/3)(1.0) Because valuation is forward looking, it is logical to adjust the raw beta so it more accurately predicts a future beta. The most commonly used adjustment was introduced by Blume

Which is larger the geometric or arithmetic mean?

Arithmetic mean is always larger than geometric, except when they equal.

CAPM vs. APT models

CAPM adds a single risk premium to the risk-free rate. While Arbitrage Pricing Theory (APT) models are based on multiple factors representing drivers of return.

Macroeconomic model estimates: Ibbotson and Chen, supply side analysis, the four components of total return to equity. The Ibbotson-Chen formula estimates the equity risk premium.

Equity risk premium = { [(1+EINFL)(1+EGREPS)(1+EGPE)−1.0] +EINC}−Expected risk-free return - expected inflation: EINFL; - expected growth rate in real earnings per share: EGREPS; - expected growth rate in the P/E ratio (the ratio of share price to earnings per share): EGPE; and - expected income component (including return from reinvestment of income): EINC.

Estimate of required return premium for emerging market equity

Equity risk premium estimate = Equity risk premium for a developed market + Country premium Country premium is estimated as the yield on emerging market bonds (denominated in the currency of the developed market) minus the yield on develop market govt. bonds.

Gordon growth model (GGM) equity risk premium estimate is: Useful for mature developed equity markets, based on the assumption that earning growth is at a stable rate and markets are efficient.

GGM equity risk premium estimate = Dividend yield on the index based on year-ahead aggregate forecasted dividends and aggregate market value + Consensus long-term earnings growth rate − Current long-term government bond yield

Forward Looking Estimates

Gordon Growth Model Estimates Macroeconomic model estimates Survey Estimates

Adjustments to Historical estimates

One type of adjustment is made to offset the effect of biases (survivorship-bias, back-filling returns) in the data series being used to estimate the equity risk premium. A second type of adjustment is made to favorable or unfavorable historic market conditions and adjust estimates based on forward-looking models. In both cases the adjustment could be upward or downward.

Fama-French Model factors: (includes equity market factor, size premium, and value premium)

RMRF - means market return minus risk-free return (1 mo. T-bill rate) This factor is shared with CAPM. SMB - Small minus big. Average of 3 small and large-cap portfolios. Represents a small-cap premium. HML - high minus low. Avg. of 2 high and low book-to-market portfolios. HML represents a value premium.

CAPM Equation

Required return on share i = Current expected risk-free return + β1(Equity risk premium)

Beta estimate for a nonpublic company

Steps: 1) select the benchmark (comparable) 2) Estimate benchmark's beta 3) Unlever the benchmark's beta 4) Lever the beta to reflect the subject company's financial leverage benchmark beta: Bu = [1 / (1+D/E)]Be subject company's equity beta: Be = [1+D'/E']Bu

Survey Estimates

Survey estimates of the equity risk premium involve asking a sample of people—frequently, experts—about their expectations for it, or for capital market expectations from which the premium can be inferred.

Internal Rate of Return (IRR)

The internal rate of return (IRR) on an investment is the discount rate that equates the present value of the asset's expected future cash flows to the asset's price—i.e., the amount of money needed today to purchase a right to those cash flows.

cost of equity and cost of debt

The required rate of return on common stock and debt are also known as the cost of equity and cost of debt, respectively, taking the perspective of the issuer. It's therefore the issuer's marginal cost for raising additional capital offered by similarly risky securities.

unadjusted or "raw" historical beta

The simplest estimate of beta results from an ordinary least squares regression of the return on the stock on the return on the market. The result is often called an unadjusted or "raw" historical beta

Local vs. worldwide CAPM can produce different required returns

Typically, equity risk premium is based on a national equity market index largely determined by local investors. The opposite assumption is that all investors worldwide participate equally in setting prices (perfectly integrated markets). That assumption results in the international CAPM (or world CAPM) in which the risk premium is relative to a world market portfolio.

WACC equals

WACC = Wd(rd)(1-t) + We(re)

Fourth factor, LIQ

an average liquidity equity should have a liquidity beta of 0, with no impact on required return. Below-average liquidity (positive beta) and above-average liquidity (negative beta).

Bond Yield plus risk premium (BYPRP) Formula BYPRP

companies with publicly traded debt can use this method to estimate the cost of equity. BYPRP cost of equity = YTM on the company's LT debt + risk premium

a consequence of the GGM's assumption of a constant dividend payout ratio and efficient markets is that

earnings, dividends, and prices are expected to grow at dividend growth rate, so that the P/E ratio is constant. The analyst may believe, however, that the P/E ratio will expand or contract.

Discount rate

is a general term for any rate used in finding the present value of a future cash flow. generally assumed to equal the risk-free rate—and required compensation for the risk of the cash flow.

The required rate of return...

is the minimum level of expected return that an investor requires in order to invest in the asset over a specified time period, given the asset's riskiness. It represents the opportunity cost for investing in the asset—the highest level of expected return available elsewhere from investments of similar risk.

APT model formula

r = Rf + (risk premium)1 + (risk premium) 2 + (risk premium)k where (risk premium) = (factor sensitivity x Factor risk premium) Each factor sensitivity is standalone, holding all other factors constant.

Build up method formula

require return = risk-free rate + equity risk premium + size premium + company specific risk premium

Fama-French Model equation estimate

required return = Risk-free rate +Bmkt(Rm-Rf) +Bsize(SMB) +Bvalue(HML)

In statistical factor models

statistical methods are applied to historical returns to determine portfolios of securities (serving as factors) that explain those return in various senses.

Beta Estimation for Thinly Traded Stocks and Nonpublic Companies

the analyst can estimate indirectly the beta of the nonpublic company on the basis of the public peer's beta.

A geometric mean equity risk premium estimate equal to

the compound annual excess return of equities over the risk-free return. The choice when estimating a required return in a multi-period context. The geometric mean return of a sample represents the compound rate of growth that equates the beginning value to the ending value of one unit of money initially invested in an asset.

In macroeconomic factor models

the factors are economic variables that affect the expected future cash flows companies and/or the discount rate that is appropriate to determining their present values

A historical equity risk premium estimate is usually calculated as

the mean value of the differences between broad-based equity-market-index returns and government debt returns over some selected sample period.

weighted average cost of capital (WACC)

the overall required rate of return of a company's suppliers of capital is usually referred to as the company's cost of capital. The cost of capital is most commonly estimated using the company's after-tax weighted average cost of capital.

risk-free rate is...

the rate of return on an asset that produces the same, known rate of return in all future economic states.

annualizing holding period returns, when the holding period is a fraction of a year, is unrealistic when

the reinvestment rate is not an actual, available reinvestment rate.

analyst decisions when developing a historical equity risk premium estimate

the selection of: - the equity index to represent equity market returns - the time period for computing the estimate (greater period = greater precision) - the type of mean calculated (geometric or arithmetic) - the proxy for the risk free return (either long or short-term govt bond return)

An arithmetic mean equity risk premium estimate equal to

the sum of the annual return differences divided by the number of observations in the sample. The arithmetic mean return as the average one-period return best represents the mean return in a single period.

How did Pastor and Stambaugh extend the FFM?

they extended the FFM to encompass compensation for the degree of liquidity of an equity investment. fourth factor, LIQ, represents the excess returns to a portfolio that invests the proceeds from shorting high liquidity stock in a portfolio of low liquidity stocks.