Second Investment Course – November 2005
Topic One:
Expected Returns & Measuring the Risk Premium
1-0
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
- Capital Gain
so,
E(R) = E(Cash Flow) + E(Capital Gain)
1-1
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 =
1 + Rt
1 + Rft
1 + RRt
-1=
1 + RRft
-1
where RRt = real asset class return
1-2
Developing Expected Return Assumptions With the Risk Premium Approach
1.5% to 2.0%
Equity
Risk
Premium
1.25%
Credit
Risk
Premium
1.40%
Term
Premium
1.00%
3.00%
March, 2005
Real
Interest
Rate
Inflation
T bills
4.00%
T notes
5.40%
Corp
Bonds
6.65%
US
Equities
8.15%
to
8.65%
1-3
18
Methods for Estimating the Equity Risk Premium
1. Historical Evidence
2. Fundamental Estimates
3. Economic Estimates
4. Surveys
1-4
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)
1-5
Ibbotson Associates U.S. Return & Risk Data: 1926 - 2004
1-6
Historical Returns and Risk for Various U.S. Asset Classes
1-7
Historical Global Stock Market Volatility
1-8
More on Historical Asset Class Returns: U.S. Experience
Stocks:
Bonds:
T-Bills:
Inflation:
1926-2004:
Avg. Return
Std. Deviation
12.39%
20.31%
6.19%
8.56%
3.76%
3.14%
3.13%
4.32%
1980-2004:
Avg. Return
Std. Deviation
14.73
16.33
11.05
11.51
6.09
3.26
3.75
2.43
1995-2004:
Avg. Return
Std. Deviation
14.00
21.09
9.45
9.32
3.92
1.90
2.49
0.81
2000-2004:
Avg. Return
Std. Deviation
-0.70
20.32
9.92
5.04
2.72
2.10
2.60
0.97
Source: Ibbotson Associates
1-9
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
1 - 10
Data for Historical Global Analysis
Series Starting Dates
Argentina
Australia
Austria
Belgium
Canada
Chile
Denmark
Finland
France
Germany
Greece
Ireland
Israel
Stocks
Bonds
Jan-1988
Nov-1882
Jan-1970
Jan-1951
Jan-1934
Feb-1927
Jan-1970
Jan-1962
Mar-1895
Jan-1870
Jan-1977
Jan-1988
Jan-1993
May-1991
Jan-1859
Aug-1945
Jul-1832
Sep-1855
Jan-1993
Jul-1821
Jan-1960
Mar-1800
Jan-1924
n/a
Jun-1928
Nov-1993
Italy
Japan
Mexico
Netherlands
New Zealand
Norway
Portugal
South Africa
Spain
Sweden
Switzerland
UK
USA
Stocks
Bonds
Jan-1925
Jan-1921
Jan-1970
Jan-1951
Aug-1986
Jan-1970
Jan-1988
Mar-1960
May-1940
Jan-1919
Mar-1966
Oct-1694
Mar-1871
Jan-1862
Dec-1870
Jan-1995
Nov-1915
Mar-1925
Dec-1876
Jan-1976
Dec-1860
Dec-1940
Jan-1922
Mar-1915
Aug-1700
Mar-1800
Source: Global Financial Data
1 - 11
Historical Real Returns, 1954-2003: The Global Experience
Historical Real Returns, 1954-2003
9%
8%
Annually Compounded Real Return, %
7%
6%
5%
Equities
Bonds
4%
3%
2%
1%
Ire
lan
d
Ze
ala
nd
No
rw
ay
So
uth
Af
r
Sw ica
itz
er
lan
d
Ne
w
ma
rk
De
n
e
Au
str
ia
Ch
il
ds
er
lan
US
A
Ne
th
e*
y
Chile: Returns 1/54 – 6/03
Chile*: Returns 1/54 – 12/71; 1/76 – 6/03
Source: Global Financial Data
Ch
il
rm
an
tra
lia
Ge
n
Au
s
Ja
pa
UK
ium
a
ad
Be
lg
in
ly
ce
Ca
n
Fr
an
Sp
a
Ita
Sw
ed
e
n
0%
1 - 12
rla
n
d
ric
a
wa
y
Af
tze
Sw
i
th
No
r
ala
nd
Ze
d
ar
k
Ire
lan
m
e
tri
a
Au
s
Ch
il
ds
US
A
e*
Ch
il
rla
n
he
So
u
Ne
w
lia
n
rm
an
y
De
n
Ne
t
Ge
tra
Au
s
pa
Ja
UK
ium
a
ce
in
ad
Be
lg
Ca
n
Fr
an
Sp
a
n
ly
Ita
Sw
ed
e
Annually Compounded Real Return, %
Global Historical Volatility Measures, 1954-2003
Historical Risk, 1954-2003
40%
35%
30%
25%
20%
Equities
Bonds
15%
10%
5%
0%
1 - 13
d
rla
n
d
ric
a
wa
y
Af
tze
th
Sw
i
So
u
No
r
ala
n
Ze
d
ar
k
Ire
lan
m
a
e
tri
Au
s
Ch
il
ds
US
A
rla
n
De
n
Ne
w
tra
an
UK
lia
rm
an
y
Ch
ile
*
he
Ne
t
Ge
a
ce
in
ium
Ja
p
Au
s
n
ly
ad
Be
lg
Ca
n
Fr
an
Sp
a
Ita
Sw
ed
e
Annually Compounded Real Return, %
Global Historical Risk Premia, 1954-2003
Risk Premia of Stocks and Bonds to Cash, 1954-2003
18%
16%
14%
12%
10%
8%
Equities-Cash
Bonds-Cash
6%
4%
2%
0%
-2%
1 - 14
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)
1 - 15
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.
1 - 16
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:
a.
b.
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., 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.
1 - 17
Fama and French: The Equity Risk Premium (cont.)
1 - 18
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:

 ae(1  g t ) 
p 0  bv 0   

t  1  (1  rf  rp) 
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:
Japan:
UK:
France:
Canada:
3.40%
0.21%
2.81%
2.60%
2.23%
1 - 19
Claus and Thomas: Estimates of Equity Risk Premia for US Markets
1 - 20
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:
-

The real return to bonds consists of three components:
-

Dividend yield
Growth rate in the real dividend
Change in equity valuation level (e.g., change in market P/E)
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%.
1 - 21
Arnott and Bernstein: What Risk Premium is “Normal”? (cont.)
1 - 22
Estimating the Equity Risk Premium (cont.)
3. Economic Estimates: Representative Work
–
Black and Litterman (1992)
– Asset Class-Specific Risk Premia
–
Ennis Knupp Associates (2005)
1 - 23
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.

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.
1 - 24
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
Global Bonds-ex US
US Equity
Global Equity-ex US
Emerging Market Equity
Total:
$ 8,607,149
12,426,562
13,776,249
12,266,988
1,521,275
$48,598,223
(17.71%)
(25.57%)
(28.35%)
(25.24%)
( 3.13%)
1 - 25
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
1 - 26
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:
Risk-Free Rate:
3.55% (10-yr Global Balanced)
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]
1 - 27
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 Equityex US is: (15.62%) x (15.35%) x (0.65) = 0.016
1 - 28
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:
0.05%
1.39%
5.49%
5.64%
6.59%
=
(4.84) x
0.002
0.001
-0.001
-0.001
-0.002
0.001
0.008
0.000
0.003
0.000
-0.001
0.000
0.024
0.016
0.023
-0.001
0.003
0.016
0.024
0.024
-0.002
0.000
0.023
0.024
0.045
17.71%
25.57%
x 28.35%
25.24%
3.13%
1 - 29
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
-
-
US Bonds:
Global Bonds:
Global Equity:
Emerging Equity:
0.05%
1.39%
5.64%
6.59%
Total
4.35%
5.69%
9.94%
10.89%
1 - 30
Black-Litterman Example: Excel Spreadsheet
1 - 31
Black-Litterman Example: Proprietary Software (Zephyr Associates)
1 - 32
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)
1 - 33
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
1 - 34
EKA Fundamental Expected Return Estimates (cont.)
1 - 35
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)
1 - 36
Campbell-Harvey Survey of Corporate CFOs – June 2005
1 - 37
Survey of Asset Class Return & Risk Expectations:
UTIMCO Staff & External Expert Opinions – March 2005
Asset Category
Cambridge
Associates
Goldman
Sachs
Wilshire
Associates
BridgeWater
EnnisKnupp
10 years
BGI
Citigroup
Consultant
Average
Historical
UTIMCO
2003
UTIMCO
2005
US Equity
Nominal Returns
Real Returns
Std Deviation
10.00%
7.00%
17.00%
8.00%
5.80%
17.30%
9.20%
6.95%
17.00%
7.90%
5.00%
15.50%
8.06%
6.06%
15.50%
8.80%
6.30%
17.00%
10.00%
7.50%
15.79%
8.85%
6.37%
16.44%
11.53%
6.86%
15.82%
8.50%
5.50%
17.00%
8.50%
5.50%
17.00%
Global Equity
Nominal Returns
Real Returns
Std Deviation
10.00%
7.00%
20.00%
7.70%
5.50%
17.40%
9.75%
7.50%
20.00%
7.60%
4.70%
14.50%
8.06%
6.06%
16.25%
NA
NA
19.00%
10.00%
7.50%
15.23%
8.85%
6.38%
17.48%
11.86%
7.19%
16.77%
8.50%
5.50%
19.00%
8.50%
5.50%
19.00%
Emerging Markets Equity
Nominal Returns
Real Returns
Std Deviation
13.00%
10.00%
28.00%
8.30%
6.10%
23.60%
11.40%
9.15%
27.00%
9.30%
6.40%
21.00%
9.14%
7.14%
25.00%
NA
NA
NA
10.90%
8.40%
24.22%
10.34%
7.86%
24.80%
15.04%
10.36%
23.25%
11.00%
8.00%
26.00%
10.50%
7.50%
26.00%
Absolute Return Hedge Funds
Nominal Returns
7.00%
Real Returns
4.00%
Std Deviation
9.00%
8.40%
6.20%
4.90%
6.82%
4.57%
8.00%
NA
NA
NA
NA
NA
NA
NA
NA
NA
5.40%
2.90%
4.06%
6.91%
4.42%
6.49%
10.79%
6.12%
6.15%
7.00%
4.00%
7.50%
7.00%
4.00%
7.50%
Directional Hedge Funds
Nominal Returns
Real Returns
Std Deviation
9.00%
6.00%
13.00%
8.40%
6.20%
4.90%
6.82%
4.57%
8.00%
NA
NA
NA
NA
NA
NA
NA
NA
NA
9.60%
7.10%
7.56%
8.46%
5.97%
8.37%
10.48%
5.81%
8.16%
8.00%
5.00%
11.00%
8.00%
5.00%
10.00%
Venture Capital
Nominal Returns
Real Returns
Std Deviation
15.00%
12.00%
28.00%
NA
NA
NA
15.25%
12.99%
30.00%
10.30%
7.40%
25.00%
NA
NA
NA
NA
NA
NA
16.40%
13.90%
43.50%
14.24%
11.57%
31.63%
15.16%
10.49%
18.78%
14.00%
11.00%
30.00%
14.00%
11.00%
30.00%
March, 2005
1 - 38
20
Survey of Asset Class Return & Risk Expectations (cont.):
UTIMCO Staff & External Expert Opinions – March 2005
Asset Category
Cambridge
Associates
Goldman
Sachs
Wilshire
Associates
BridgeWater
EnnisKnupp
10 years
BGI
Citigroup
Consultant
Average
Historical
UTIMCO
2003
UTIMCO
2005
Private Equity
Nominal Returns
Real Returns
Std Deviation
13.00%
10.00%
24.00%
10.70%
8.50%
29.10%
15.25%
12.99%
30.00%
10.30%
7.40%
25.00%
10.00%
8.00%
30.00%
NA
NA
31.40%
NA
NA
NA
11.85%
9.38%
28.25%
11.32%
6.65%
9.04%
11.50%
8.50%
20.00%
11.50%
8.50%
24.00%
REITs
Nominal Returns
Real Returns
Std Deviation
9.00%
6.00%
15.00%
5.60%
3.40%
13.90%
8.78%
6.52%
16.00%
7.50%
4.60%
14.00%
6.45%
4.45%
13.20%
NA
NA
11.50%
10.00%
7.50%
11.87%
7.89%
5.41%
13.64%
14.54%
9.87%
14.74%
7.50%
4.50%
15.00%
7.50%
4.50%
15.00%
Commodities (Financial)
Nominal Returns
Real Returns
Std Deviation
8.00%
5.00%
19.00%
4.50%
2.30%
18.40%
NA
NA
NA
6.70%
3.80%
18.00%
NA
NA
NA
NA
NA
NA
NA
NA
NA
6.40%
3.70%
18.47%
13.37%
8.70%
18.43%
5.00%
2.00%
18.00%
6.00%
3.00%
18.00%
Nominal Returns
Real Returns
Std Deviation
5.50%
2.50%
6.00%
NA
NA
NA
4.43%
2.17%
6.00%
5.50%
2.60%
6.00%
4.34%
2.34%
6.00%
NA
NA
NA
NA
NA
NA
4.94%
2.40%
6.00%
9.07%
4.39%
3.69%
5.50%
2.50%
6.00%
5.50%
2.50%
6.00%
Fixed Income
Nominal Returns
Real Returns
Std Deviation
6.00%
3.00%
7.00%
4.60%
2.40%
4.50%
4.63%
2.37%
5.00%
5.30%
2.40%
5.00%
4.86%
2.86%
5.50%
5.80%
3.30%
6.40%
5.10%
2.60%
4.00%
5.18%
2.70%
5.34%
8.80%
4.13%
6.02%
5.00%
2.00%
6.00%
5.75%
2.75%
7.00%
4.00%
1.00%
2.00%
2.70%
0.50%
0.00%
2.75%
0.50%
1.00%
4.00%
1.10%
0.30%
3.05%
1.05%
1.50%
NA
NA
NA
3.50%
1.00%
0.46%
3.33%
0.86%
0.88%
6.43%
1.75%
0.91%
4.00%
1.00%
1.00%
4.00%
1.00%
1.00%
3.00%
NA
2.20%
NA
2.25%
NA
2.90%
1.50%
2.00%
1.00%
2.50%
NA
2.50%
NA
2.48%
1.25%
4.67%
1.17%
3.00%
2.00%
3.00%
1.50%
TIPS
Cash
Nominal Returns
Real Returns
Std Deviation
Inflation
Returns
Std Deviation
March, 2005
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Ennis Knupp Associates Survey – Spring 2005
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