Second Investment Course

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Second Investment Course November 2005

• Topic One
• Expected Returns Measuring the Risk Premium

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Some Important Concepts Involving Expected
Investment Returns

• 1. Investors perform two functions for capital
  markets
• - Commit Financial Capital
• - Assume Risk
• so,
• E(R) (Risk-Free Rate) (Risk Premium)
• 2. The expected return (i.e., E(R)) of an
  investment has a number of alternative names
  e.g., discount rate, cost of capital, cost of
  equity, yield to maturity. It can also be
  expressed as
• k (Nominal RF) (Risk Premium)
• (Real RF) E(Inflation) (Risk Premium)
• where
• Risk Premium f(business risk, liquidity risk,
  political risk, financial risk)
• 3. Investors can be compensated in two ways
• - Period Cash Flows

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Measuring Expected Returns Overview
Risk Premium
Rt (1 Rft) (1 RPt) 1 or Rt (1 Inft) (1
RRft) (1 RPt) 1 where Rt return on asset
class for year t, Inft inflation rate Rft
risk free rate RRft real risk free rate RPt
risk premium RPt where RRt real asset class
return
1 Rt
1 RRt
- 1
- 1
1 RRft
1 Rft
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Developing Expected Return Assumptions With the
Risk Premium Approach
March, 2005
18
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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
• Ibbotson Associates US Markets (2004)
• Fidelity Investments - Global Markets (2004)
• Jorion and Goetzmann (Journal of Finance, 1999)
• Siegel (Financial Analysts Journal, 1992)
• Dimson, Marsh and Staunton (Business Strategy
  Review, 2000)

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Ibbotson Associates U.S. Return Risk Data 1926
- 2004
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Historical Returns and Risk for Various U.S.
Asset Classes
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Historical Global Stock Market Volatility
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More on Historical Asset Class Returns U.S.
Experience
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Historical Risk Premia vs. T-bills U.S.
Experience
Stocks Bonds Stock - Bond Difference
1926-2004 8.63 2.43 6.20
1980-2004 8.64 4.96 3.68
1995-2004 10.08 5.53 4.55
2000-2004 -3.42 7.20 -10.62
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Data for Historical Global Analysis
Series Starting Dates
Source Global Financial Data
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Historical Real Returns, 1954-2003 The Global
Experience
Chile Returns 1/54 6/03 Chile Returns 1/54
12/71 1/76 6/03 Source Global Financial Data
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Global Historical Volatility Measures, 1954-2003
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Global Historical Risk Premia, 1954-2003
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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)

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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.
• 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., SP 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

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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
• 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 yeld
• 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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Estimating the Equity Risk Premium (cont.)

• 3. Economic Estimates Representative Work
• Black and Litterman (1992)
• Asset Class-Specific Risk Premia
• Ennis Knupp Associates (2005)

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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
  users 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 users tactical views
  on asset class performance.

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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 September 2005, these asset classes had the
  following market capitalizations (in USD
  millions)
• US Bonds 8,607,149 (17.71)
• Global Bonds-ex US 12,426,562 (25.57)
• US Equity 13,776,249 (28.35)
• Global Equity-ex US 12,266,988 (25.24)
• Emerging Market Equity 1,521,275 ( 3.13)
• Total 48,598,223

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Black-Litterman Example (cont.)

• Consider also the following historical return
  standard deviations (October 2000 September
  2005)
• susb 4.02 sgb 8.81 suss 15.62
• sgs 15.35 sems 21.29
• The historical correlation matrix, measured using
  all available pairwise historical return data
• rusb,gb 0.41 rgb,gs 0.21
• rusb,uss -0.14 rgb,ems -0.00
• rusb,gs -0.16 russ,gs 0.65
• rusb,ems -0.20 russ,ems 0.69
• rgb,uss -0.02 rgs,ems 0.73

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Black-Litterman Example (cont.)

• 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 3.55 (10-yr Global
  Balanced)
• Risk-Free Rate 4.30 (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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Black-Litterman Example (cont.)

• 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 (8.57)2 0.734, so that
• RAP (0.0355)/(0.0073) 4.84
• The covariance between two asset classes (Y and
  Z) is given by the formula
• Cov(Y,Z) ry,z x sy x sz
• For instance, the covariance between US Equity
  and Global Equity-ex US is (15.62) x (15.35) x
  (0.65) 0.016

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Black-Litterman Example (cont.)

• 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
• (4.84) x (-0.001)(.1771)
  (0.023)(.0313) 5.49
• More formally, the solution for the entire asset
  class implied excess return vector is given by

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Black-Litterman Example (cont.)

• The total expected return for US Equity is then
  simply the IER plus the risk-free rate
• 4.30 5.49 9.79
• The excess and total expected returns for the
  other asset classes in this example are
• Excess Total
• US Bonds 0.05 4.35
• Global Bonds 1.39 5.69
• Global Equity 5.64 9.94
• Emerging Equity 6.59 10.89

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Black-Litterman Example Excel Spreadsheet
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Black-Litterman Example Proprietary Software
(Zephyr Associates)
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Ennis Knupp Associates (EKA) July 2005

• EKA uses 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, EKA 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 9.1 Total return is divided into
  three components dividend yield (1.7), nominal
  growth rate of corporate earnings (7.4), and
  change in valuation levels (0)
• US Bonds 5.4 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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EKA Fundamental Expected Return Estimates (cont.)

• Other asset class expected returns are then
  estimated relative to these anchors using the
  global CAPM. Specifically, expected returns on
  the various asset classes are proportional to
  their systematic risk levels relative to the
  global market portfolio, shown at the right.

• For example, the ratio of the US Bonds beta
  (0.40) to the US Equity beta (1.71) is 0.23.
  This implies that the ratio of US Bond risk
  premium to US Equity risk premium should also be
  23.
• Therefore
• (5.4 RF)/(9.1 RF) 0.23
• which results in an implied risk-free rate of
  4.3. The risk premium of each asset class is
  then calculated so that it is directly
  proportional to its systematic risk, given these
  two anchors

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EKA Fundamental Expected Return Estimates (cont.)
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Estimating the Equity Risk Premium (cont.)

• 4. Surveys Representative Work
• Graham and Harvey (Duke University, 2005)
• UTIMCO (2005)
• Ennis Knupp Managers Consultants (2005)
• Burr (Pensions and Investments, 1998)
• Welch (Journal of Business, 2000)

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Campbell-Harvey Survey of Corporate CFOs June
2005
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Survey of Asset Class Return Risk
ExpectationsUTIMCO Staff External Expert
Opinions March 2005
March, 2005
20
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Survey of Asset Class Return Risk Expectations
(cont.)UTIMCO Staff External Expert Opinions
March 2005
March, 2005
21
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Ennis Knupp Associates Survey Spring 2005