the equity risk premium - university of texas at...

Topic One:

Expected Returns & Measuring the Risk Premium

Some Thoughts Related to Expected Returns:

Expected Return = E(R) = RF + (Risk Premium) - Ways to Measure E(R):

Historical Average Returns for a Specific Asset Benchmark Returns (e.g., S&P 500 for U.S. Equity) Peer Group Returns Risk-factor Model (e.g., CAPM, Fama-French 3-, 4-, or 5-Factor)

Expected returns are used in investment management for a number of reasons, from forecasting to measuring a manager’s value-added skills:

Actual Return = Expected Return + “Alpha”

or: Alpha = (Actual Return) – (Expected Return)

The expected return (i.e., E(R)) of an investment has a number of alternative names: discount rate, cost of capital, cost of equity, yield to maturity. It can also be expressed:

k = (Nominal RF) + (Risk Premium) = [(Real RF) + E(Inflation)] + (Risk Premium) where: Risk Premium = f(business risk, liquidity risk, political risk, financial risk)

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Some Thoughts Related to Expected Returns (cont.):

More formally, the relationship between asset returns and the risk premium can be expressed as follows:

Rt = (1 + RFt)(1 + RPt) – 1 = (1 + Inft) (1 + RRFt) (1 + RPt) – 1

where: Rt = return on asset class for year t, Inft = inflation rate RFt = nominal risk free rate RRFt = real risk free rate RPt = risk premium so that:

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Developing Expected Return Assumptions With the Risk Premium Approach

T bills

Real Interest

Rate

Inflation

Term Premium

Credit Risk

Premium

T notes

CorpBonds

USEquities

Equity Risk

Premium

3.00%

1.00%

1.40%

1.25%

1.5% to 2.0%

4.00%

5.40%6.65%

8.15%to

8.65%T bills

Real Interest

Rate

Real Interest

Rate

InflationInflation

Term Premium

Term Premium

Credit Risk

Premium

Credit Risk

Premium

T notes

CorpBonds

USEquities

Equity Risk

Premium

Equity Risk

Premium

3.00%

1.00%

1.40%

1.25%

1.5% to 2.0%

4.00%

5.40%6.65%

8.15%to

8.65%

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Methods for Estimating the Equity Risk Premium

1. Historical Evidence 2. Fundamental Estimates 3. Economic Estimates 4. Surveys

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Estimating the Equity Risk Premium

1. Historical Evidence: Representative Work

– Morningstar/Ibbotson Associates – US Markets (2015) – Fidelity Investments - Global Markets (2008) – Jorion and Goetzmann (Journal of Finance, 1999) – Dimson, Marsh, and Staunton (ICFA Monograph, 2011) – Credit Suisse – Global Markets (2016)

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Morningstar/Ibbotson Return & Risk Data: 1926 - 2015

Historical U.S. Nominal Asset Class Returns & Inflation:

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Stocks:

Bonds:

T-Bills:

Inflation:

1926-2015: Avg. Return 11.95% 6.30% 3.45% 3.00% Std. Deviation 19.99% 8.42% 3.12% 4.09% 1991-2015: Avg. Return 11.43 8.37 2.75 2.32 Std. Deviation 18.13 8.54 2.19 1.00 2006-2015: Avg. Return 9.14 6.79 1.10 1.85 Std. Deviation 18.97 8.05 1.91 1.27

2011-2015: Avg. Return 13.11 7.56 0.04 1.53 Std. Deviation 12.64 11.18 0.02 0.97 Source: Morningstar/Ibbotson Associates

Historical U.S. Real Asset Class Returns & Equity Risk Premia:

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U.S. Equity Risk Premium Histogram (vs. U.S. T-bills) There has been a wide disparity in annual realized risk premia over time and the

values are frequently negative

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Illustrating the U.S. Equity Risk Premium: 1935 - 2015 (10-yr rolling avg. vs. Bills)

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-10.00

-5.00

0.00

5.00

10.00

15.00

20.00

25.0019

3519

3719

3919

4119

4319

4519

4719

4919

5119

5319

5519

5719

5919

6119

6319

6519

6719

6919

7119

7319

7519

7719

7919

8119

8319

8519

8719

8919

9119

9319

9519

9719

9920

0120

0320

0520

0720

0920

1120

1320

15

Rolling 10-yr Avg USRisk PremiumLong-Term Avg

Historical Real Returns, 1951-2008: The Global Experience

Chile: Returns 1/83-7/08 Source: Global Financial Data

0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

Austra

lia

Belgium

Canad

aChil

e

Denmark

France

German

y

Irelan

dIta

lyJa

pan

Netherl

ands

New Zea

land

Norway

Spain

Sweden

Switzerl

and

United

Kingdo

m

United

States

Ann

ual C

ompo

und

Rea

l Ret

urn

EquityBond

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Historical Risk Premia, 1951-2008

-2%

0%

2%

4%

6%

8%

10%

12%

14%

Austra

lia

Belgium

Canad

aChil

e

Denmark

France

German

y

Irelan

dIta

lyJa

pan

Netherl

ands

New Zea

land

Norway

Spain

Sweden

Switzerl

and

United

Kingdo

m

United

States

Ris

k Pr

emia

(Geo

met

ric)

Equity-CashBond-Cash


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Historical Volatility Measures, 1951-2008

0%

5%

10%

15%

20%

25%

Austra

lia

Belgium

Canad

aChil

e

Denmark

France

German

y

Irelan

dIta

lyJa

pan

Netherl

ands

New Zea

land

Norway

Spain

Sweden

Switzerl

and

United

Kingdo

m

United

States

Ann

ual S

tand

ard

Dev

iatio

n

EquityBond


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Historical Global Equity Risk Premiums: 1900-2010

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Illustrating the United Kingdom Equity Risk Premium (10-yr rolling avg. vs. Bills)

Source: Elroy Dimson, London Business School

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Historical Global Equity Risk Premia: 1900 - 2015

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Estimating the Equity Risk Premium (cont.)

2. Fundamental Estimates: Representative Work

– Fama and French (University of Chicago, 2000) – Ibbotson and Chen (Yale University, 2001) – Claus and Thomas (Journal of Finance, 2001) – Arnott and Bernstein (Financial Analysts Journal, 2002) – Mehra and Prescott (Hnbk Econ Fin, 2003) – Heaton and Lucas (Hnbk ERP, 2008) – Bloomberg Consensus Forecasts (2016)

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Fundamental Risk Premium Estimates: An Overview

One potential problem with using historical averages to estimate future expected returns is that there is no way to control for the possibility that the past data sample you selected produced averages that are “abnormal” (i.e., too high or too low) in some way.

Another problem we have seen is that historical average returns tend to be fairly unstable (i.e., they are extremely sensitive to the time period chosen in the analysis).

Fundamental risk premium estimates attempt to objectively forecast

the expected returns that would normally occur, given the fundamental relationships that tend to exist in the capital markets. - In other words, fundamental forecasts attempt to link return expectations to

the economic conditions likely to pertain in the market during the forecast interval.

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Fama and French: The Equity Risk Premium

Main Idea: Use dividend and earnings growth rates to measure the expected rate of capital gains for equity investments. This process creates two ways of then estimating real (i.e., inflation-adjusted) expected equity returns: - E(R) = E(Div Yld) + E(Real Growth Rate of Dividends) = RD - E(R) = E(Div Yld) + E(Real Growth Rate of Earnings) = RY

Notice that the intuition behind this approach is simply that it is possible to compensated investors in two ways: cash flow and capital gain. This is sometimes referred to as a demand-side approach to estimating the risk premium

Real Equity Risk Premium can then be estimated by subtracting short-term commercial paper yields from RD and RY, which leaves RXD and RXY, respectively

Main Result: Using data from the period 1951 to 2000 for the US market (i.e., S&P

500), they find that: - RXD = 2.55% - RXY = 4.32%

Notice that both of these fundamental risk premium estimates are well below the

average historical risk premium during the period (i.e., 7.43%), leading the authors that future expected returns to equity investments are unlikely to match the high levels of the recent past

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Fama and French: The Equity Risk Premium (cont.)

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Claus and Thomas: Equity Risk Premia in US and International Markets

Main Idea: Based on the notion that the fundamental value of an equity investment can be described by its book value plus the present value of future abnormal earnings

This valuation can be estimated by a modified version of the multi-stage growth model:

where the discount rate k (= rf + rp) is the equity expected return

Main Results: Using observed market data (e.g., p, bv) and analyst

forecasts (e.g., g) for the other inputs over 1985-1998, the authors calculate the values of the equity risk premium (rp) that solve the model:

- US: 3.40% - Japan: 0.21% - UK: 2.81% - France: 2.60% - Canada: 2.23%

∑∞

=

++

++=

1t

t00 rp) rf (1

)gae(1 bv p

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Claus and Thomas: Estimates of Equity Risk Premia for US Markets

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Arnott and Bernstein: What Risk Premium is “Normal”?

Main Idea: The risk premium for stocks relative to bonds can be forecast as the difference between the expected real stock return and the expected real bond return. This is sometimes called a supply-side estimation process.

The real return to stocks consists of three components: - Dividend yield - Growth rate in the real dividend - Change in equity valuation level (e.g., change in market P/E)

The real return to bonds consists of three components:

- Nominal yield - Inflation - Change in yield times duration (i.e., reinvestment)

Main Conclusions:

- Historical real stock returns and the excess return for stocks relative to bonds over the past century have extraordinarily high (due to rising valuation multiples) and unlikely to be repeated in the future. The fundamental expected risk premium estimate over this past period would have been 2.4%

- Future expectations should be based on tractable fundamental relationships and indicate a real risk premium of near 0%

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Arnott and Bernstein: What Risk Premium is “Normal”? (cont.)

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Arnott and Bernstein: What Risk Premium is “Normal”? (cont.) Source: A. Ilmanen, Expected Returns on Major Asset Classes, CFA Institute, 2012

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Bloomberg Global Risk Premium Forecasts – July 2016

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Bloomberg Risk Premium Forecasts: 2014-2016 – United States

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Bloomberg Risk Premium Forecasts: 2014-2016 – Chile

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3. Economic Estimates: Representative Work

– Black and Litterman (1992, 2016) – Asset Class-Specific Risk Premia

– Aon Hewitt (2010, 2012)

– Damodaran (2015) – Country-Specific Risk Premia

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Implied Returns and the Black-Litterman Forecasting Process

The Black-Litterman (BL) model uses a quantitative technique known as reverse optimization to determine the implied returns for a series of asset classes that comprise the investment universe.

The main insight of the BL model is that if the global capital markets are in equilibrium, then the prevailing market capitalizations of these asset classes suggest the investment weights of an efficient portfolio with the highest Sharpe Ratio (i.e., risk premium per unit of risk) possible.

These investment weights can then be used, along with information about asset class standard deviations and correlations, to transform the user’s forecast of the global risk premium into asset class-specific risk premia (and expected returns) that are consistent with a capital market that is in equilibrium.

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4. Implied Expected Returns, Optimization, and TAA in the Black-Litterman Forecasting Process

The Black-Litterman (BL) model uses a quantitative technique known as reverse optimization to determine the implied returns for a series of asset classes that comprise the investment universe.

The main insight of the BL model is that if the global capital markets are in equilibrium, then the prevailing market capitalizations of these asset classes suggest the investment weights of an efficient portfolio with the highest Sharpe Ratio (i.e., risk premium per unit of risk) possible.

These investment weights can then be used, along with information about asset class standard deviations and correlations, to transform the user’s forecast of the global risk premium into asset class-specific risk premia (and expected returns) that are consistent with a capital market that is in equilibrium.

These equilibrium expected returns for the asset classes can then be used as inputs in a mean-variance portfolio optimization process or adjusted further given the user’s tactical views on asset class performance.

The Black-Litterman Process: An Example

Consider an investable universe consisting of the following five asset classes: - US Bonds - Global Bonds-ex US - US Equity - Global Equity-ex US - Emerging Market Equity

As of May 2016, these asset classes had the following market capitalizations (in USD millions):

- US Bonds $19,982,690 (22.16%) - Global Bonds-ex US 24,680,102 (27.36%) - US Equity 20,131,204 (22.32%) - Global Equity-ex US 21,322,124 (23.64%) - Emerging Market Equity 4,078,236 ( 4.52%) Total: $90,194,356

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Black-Litterman Example (cont.)

Consider also the following historical return standard deviations (January 1999 – April 2016): σusb = 3.51% σgb = 8.47% σuss = 15.14%

σgs = 17.61% σems = 23.00%

The historical correlation matrix, measured using all available pairwise historical return data: ρusb,gb = 0.5175 ρgb,gs = 0.4026

ρusb,uss = -0.0501 ρgb,ems = 0.2896

ρusb,gs = -0.0290 ρuss,gs = 0.8463

ρusb,ems = -0.0468 ρuss,ems = 0.7463

ρgb,uss = 0.1738 ρgs,ems = 0.8656 33


The remaining inputs that the user must specify are: (i) the global risk premium of the investment universe, and (ii) the risk-free rate. Using current market data we have:

- Global Risk Premium: 4.41% (10-yr Global Balanced) - Risk-Free Rate: 1.81% (10-yr US Treasury)

The heart of the BL process is to then calculate the implied

excess return for each asset class, using the following (stylized) formula:

[Risk Aversion Parameter] x [Covariance Matrix] x [Market Cap Weight Vector]

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The risk aversion parameter is the rate at which more return is required as compensation for more risk. It is calculated as:

RAP = [Global Risk Premium] / [Market Portfolio Variance]

It can be shown in this example that the market portfolio variance is (9.25%)2 = 0.856%, so that:

RAP = (0.0441)/(0.00856) = 5.15

The covariance between two asset classes (Y and Z) is given by the formula:

Cov(Y,Z) = ρy,z x σy x σz

For instance, the covariance between US Equity and Global Equity-ex US is: (0.8463) x (15.14%) x (17.61%) = 0.023

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The implied excess return (IER) for US Equity can then be computed as follows:

IERuss = (RAP) x {[Cov(uss,usb) x wusb] + [Cov(uss,gb) x wgb] +

… + [Cov(uss,ems) x wems]}

= (5.15) x {(0.000)(.2216) + … + (0.026)(.0452)} = 6.27% More formally, the solution for the entire asset class implied excess return

vector is given by:

0.30% 0.001 0.002 0.000 0.000 0.000 22.16% 2.31% 0.002 0.007 0.002 0.006 0.006 27.36% 6.27% = (5.15) x 0.000 0.002 0.023 0.022 0.026 x 22.32% 8.02% 0.000 0.006 0.023 0.031 0.035 23.64% 9.24% 0.000 0.006 0.026 0.035 0.053 4.52%

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The total expected return for US Equity is then simply the

IER plus the risk-free rate: 1.81% + 6.27% = 8.08%

The excess and total expected returns for the five asset

classes in this example are:

Excess Total - US Bonds: 0.30% 2.11% - Global Bonds: 2.31% 4.12% - US Equity: 6.27% 8.08% - Global Equity: 8.02% 9.83% - Emerging Equity: 9.24% 11.05%

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Black-Litterman Example: Excel Spreadsheet

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Black-Litterman Example: Proprietary Software (Zephyr Associates)

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Aon Hewitt (AON)

Historically, AON has used a similar process to the BL methodology in that they develop asset class expected return forecasts that are grounded in the notion that the global capital markets are in equilibrium

Specifically, AON estimates asset class expected returns to be consistent with a global Capital Asset Pricing Model (CAPM). Two expected return “anchors” are used as a starting point: - US Equity = 7.0%: Total return is divided into three components:

dividend yield (1.8%), nominal growth rate of corporate earnings (5.2%), and change in valuation levels (0.0%)

- US Bonds = 4.6%: Based on two components: current yield and simulated future changes in yields (based on forecasts of expected inflation, inflation risk premium, and real yields)

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AON Forecasts – March 2012

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Country-Specific Equity Risk Premium Estimates

Using a “link relative” process similar to that just described for different asset classes, Damodaran has shown how the risk premium for any country can be established relative to that of a benchmark sovereignty (e.g., United States)

Specifically, the equity risk premium for Country F can be given as:

so that the country premium for Country F is: 1 - 42

) StdDev / (StdDev x ERP ERP USFUSF =

ERP - ERP RPCountry USFF =

Country-Specific Equity Risk Premium Estimates (cont.)

For example, over a recent two-year period, we observed the following data in the US and Chilean equity markets:

- ERPUS = 5.80% - StdDevUS = 17.67% - StdDevChile = 14.14%

So, for Chile:

and:

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4.64% 17.67%) / (14.14% x 5.80% ERPChile ==

1.16%- 5.80% - 4.64% RPCountry Chile ==

Country-Specific Equity Risk Premium Estimates (cont.)

For various countries in Latin America as February 2015, Damodaran reports the following figures:

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4. Surveys: Representative Work

– Graham and Harvey (Duke University, 2014) – Aon Hewitt : Managers & Consultants (2009) – Teacher Retirement System of Texas (2014) – Fernandez, Ortiz, Arcin (IESE Business School, 2016) – Bloomberg Consensus Forecasts (2016)

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Graham-Harvey Survey of Corporate CFOs – April 2014

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Graham-Harvey Survey – April 2014 (cont.)

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Fernandez et al Global Analyst Survey – May 2016

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Fernandez et al Global Analyst Survey – May 2016 (cont.)

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Long-Term Expected Return & Volatility Forecasts: June 2014 (Texas Teacher Retirement System)

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Long-Term Risk Premium Forecasts: June 2014 (Texas Teacher Retirement System)

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Bloomberg Consensus Forecasts – United States July 2016

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Bloomberg Consensus Forecasts – Euro Region July 2016

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Bloomberg Consensus Forecasts – Chile July 2016

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The Equity Risk Premium: Some Concluding Thoughts The equity risk premium represents the crucial component to predicting

expected returns for stockholders, which impact everything from forecasting future market conditions to security valuation to measuring portfolio performance

There is no clear-cut best way to forecast equity risk premia - Extrapolating historical trends, forming an economically justifiable prediction, and

surveying other market participants are all used frequently in practice

There is a big disparity between the theoretical and historical levels of the equity risk premium - This gap between what theory predicts and what the actual data have shown is

called the equity premium puzzle, which has been the subject a substantial research literature attempting to explain it

Measured equity risk premia vary widely across different economies as well

as over time within any particular economy - This makes relying on a single point estimate at a specific point in time challenging

Equity risk premia throughout the world have been negative for the most

recent historical rolling-average periods, meaning that this data seems to be of relatively little use in helping us understand what to expect in the future

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the equity risk premium - university of texas at...

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