Strategic Asset Allocation
session 1
Andrei Simonov
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Agenda
Introduction, Course Outline,
Requirements, Resources
 Reminder: SAA
 Definitions
 Historical Records of Returns on different
securities
 Crisis in Investment Industry

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Introduction

The field of Finance and Investments
– Individual agents making decisions to supply capital to
the markets
– Firms getting capital from the financial markets (when,
where, how?)
– Capital Markets acting as market clearing device.

Goal of the course:
– To familiarize you with ”real world” of investments.
– To give broad overview of modern investment issues. By
June one should know what does that mean to be
investment professional.
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Resources and requirements:


Course web page andreisimonov.com/NES
Articles (package+web site)





Provide deeper insight, latest developments
No econometrics, just general idea
Access to Internet, some Excel experience, basic
knowledge of econometrics
It is assumed that basic courses are still remembered
by you.
Groups of 2-3 (pls let TA know by the end of the
week)
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Cases

What case report is NOT:
– Not copy of textbook or article.
– Not exercise in history of economics or finance. I do not care (at least, in
that class) who got Nobel Prize for what...

Ideal case report is similar to consulting report:
–
–
–
–
–
–


Analysis of data that is in the case (preferrably statistical analysis)
Covering all relevant issues (pros and cons)
Take the position and defend it!
Case report is not War and Peace. Be brief!
Please understand what you are writing about.
Cases are due before the discussion session.
Do not spend more than 2 days on ANY case!
Class discussion is part of the case work.
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My assumptions about you:
You know and understand basic regression
analysis (what is R2, statistical significance,
etc.)
 You remember conditions of optimality from
Econ 101
 You remember basics from Finance I
 You are willing to learn...

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Agenda



Individual’s preferences, utility function
Measurement of risk by variance
Diversification
–
–
–
–


A bit of math
Industry diversification
International diversification
Latest evidence
Shortcut to math: Excel!
Risk accounting
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First Approximation Model of
Investors’ Behavior: Assumptions:
Single holding period
 Investors are risk-averse
 Investors are ”small”
 The information about asset payoffs is
common knowledge
 Assets are in unlimited supply
 Assets are perfectly divisible
 No transaction cost
 Wealth W is invested in assets

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Investors´ preferences




Attitude to risk
Time horizon (do
not confuse with
holding period)
Non-traded risks
(liabilities, labor
income, human
capital)
Constraints
Strategic Asset Allocation
Advisor & Investor Type:
Fidelity
Conservative
Moderate
Aggressive
Merrill Lynch
Conservative
Moderate
Aggressive
New York Times
Conservative
Moderate
Aggressive
Portfolio
Cash
Bond
Stock
Bonds/Stock
50
20
5
30
40
30
20
40
65
1.500
1.000
0.462
20
5
5
35
40
20
45
55
75
0.778
0.727
0.267
20
10
0
40
30
20
40
60
80
1.000
0.500
0.250
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Investor’s preferences:Meanvariance framework

Representation by utility function of wealth W
– u’(W)>0, u’’(W)<0

Taylor Expansion:
1
~
~
~ ~
~
~ ~
~
u (W )  u ( E (W ))  u ' ( E (W ))(W  E (W ))  u ' ' ( E (W ))(W  E (W )) 2  
2
Applying Expectations operator:
1
~
~
~
E u (W )  u ( E (W ))  u ' ' ( E (W ))s 2
2
 Simplest utility function is quadratic:u=W-0.5bW2





b
~
~ b
~
~ b
~
~
E u (W )  E (W )  E (W 2 )  E (W )  E (W ) 2  s 2  f ( E (W ))  s 2
2
2
2



Problem: satiation
Arbitrary preferences: Asset returns are distributed as
multivariate normal
A dominates B if E(rA) (>) E(rB) and sA <() sB
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Indifference curves


All portfolios on a given
indifference curve are
equally desirable
Any portfolio that is lying
on indifference curve that
is ”further North-west” is
more desirable than any
portfolio that is lying on
indifference curve that is
”less Northwest”
Different investors (e.g., in
risk aversion) have
different indifference
curves
Strategic Asset Allocation
Solid line, b=1, dashed line, b=2
1.8
1.7
1.6
Exp. return

1.5
1.4
1.3
1.2
1.1
1
0
1
2
3
Std. Dev.
4
5
6
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Measuring risk by variance

Variance
– definition: probability weighted squared deviations
from the expected value
– based on probability distribution

Any drawbacks of this measure?
– People do not behave that way (read Odean):



Overconfidence (“wrong” probability distribution)
Regret (distinguish “gains” from “losses”)
Should we use semi-variance?
– Particularly in case of delegated portfolio
management?
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How to live with risk?

Know and classify risks into
asset classes. On what basis?
 Price risk (Country (incl.
Political risk),
$17
Industry,statistical categories) $15
 Credit risk, counterparty risk
$13
 Tail risk or risk of ruin

Most important classification
concept: statistical correlation
 pitfalls of correlations
 quasi-arbitrage opportunities
(“convergence trades”):
LTCM and limits of arbitrage
(Shleifer &Visny)
Strategic Asset Allocation
Large vs. Small Cap: Total Return (01.1954=$1)
$11
Large Cap
Small Cap
Large Cap
Small Cap
$9
$7
HIGH CORRELATION
r =0.99
$5
LOW
CORRELATION
r =0.5
$3
$1
1954
1959
1964
1969
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The same story:
Nasdaq vs. S&P 500
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Henry Lowenfeld, 1909
“It is significant to see how entirely all the rest of the
Geographically Distributed stocks differ in their price
movements from the British stock. It is this individuality
of movement on the part of each security, included in a
well-distributed Investment List, which ensures the first
great essential of successful investment, namely, Capital
Stability.”
From: Investment and Exact Science, 1909.
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Globalization and Financial
Linkages

Common wisdom is that globalization and
integration of markets accentuates financial
linkages (correlations)
–
–
–
–
–

Business cycle synchronization
Policy coordination
Coordination of institutions
Decrease in “home bias” of investors
Globalization of firms
Globalization and integration also allows country
specialization
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What is the overall effect?






Decrease in expected returns
Higher correlation between asset markets
More markets for investment
Increase in the types of marketed securities
Potential synchronization of business cycles
Increased policy coordination
Net effect?
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International Diversification 2:
Time-Varying Correlations
1. Correlations between
countries are highly timevarying.
2. Result of Solnik can be due
to segmentation period
used.
3. There is striking similarities
between end of XIX and
XX centuries.
(Based on Goetzmann et. al.
NBER W8612)
Strategic Asset Allocation
1872-2000
UK
US
France
US
France
Germany
0.265
0.351
0.143
0.163
0.083
0.189
Average correlation =0.199
Integration, 18721914, 1972-2000
US
France
Germany
UK
0.345
0.467
0.369
US
0.301
0.284
France
0.520
Average correlation =0.381
Segmentation,
1914-1971
US
France
Germany
UK
0.193
0.311
0.097
US
0.101
0.041
France
0.135
Average correlation =0.146
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The Role of Emerging Markets

Expand the investment opportunity set

Are imperfectly correlated with existing
markets

What is the relative contribution of
changing correlations and evolution in the
investment opportunity set for
diversification benefits?
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Decomposing the Benefits of International Diversification
equally-weighted portfolio variance / average market variance
Ratio portfolio volatility / average market volatility
1.0
Core Countries (limited diversification)
0.8
Average four countries
All Countries (unlimited diversification)
0.6
0.4
0.2
0.0
1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
Bottom Line: International Diversification
Does Not Work as it Used to...
•Trade barriers disappear (NAFTA, EU, ASEAN, etc.)
•Globalization of Business Enterprises,
•Wave of intra-industry M&A (incl. cross-border M&A)
“…active portfolio managers will have increasing difficulty adding
value by using a top-down strategy through European country
allocation.” (Freiman, 1998)
 New Holy Graal: Industry Diversification
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Industry vs. International Diversification
APT-style estimation:
Ri=ai(t)+SdijbijNatlMarketIndexj+ Sd1ijgijGlobalIndustryIndex+ i
where dij (d1)=1 if firm i belongs to country (industry) j. This can be further
simlified as
Ri=ai(t)+Sdijbij(t)+ Sd1ikgik (t) + i
2-stage estimation as in Fama-McBeth procedure (time-series + cross-section)
gives us time-series of prices of national and industry risk. One can interpret
ai(t)+bij (t) is return on geographically diversified industry portfolio. ai(t)+gij(t)
is return on industry-diversified national portfolio.
Small Print: (a) We miss all “other” firm characteristics-size, b/m, dividend
payout ratio, leverage, etc. (b)We also assume that securities in country i have
same exposure to domestic and foreign factors. (c) We do not address Ericsson
problem. (d) Cavaglia et. al. (2001) consider 35 industries in 21 countries.
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Random diversification:
international vs. industrial
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Eiling, Gerard, Hillion & de Roon (2009)

Adding currency deposits to industry portfolios
is a winning recepie.
Our conditional results show that international equity returns are primarily
driven by industry and currency risk factors…The dominance of global
industry factors over country factors is in line with the seven developed
countries in our sample being among the most integrated equity markets in the
world. Finally, we find that currency returns significantly improve the meanvariance efficiency of country, industry and world market portfolio returns.
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K. Lewis: Breaks are country breaks
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K. Lewis 2

Firms correlations are determined by
markets’ integration, not vv.
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How non-diversifiable risk changes
with time (Campbell et al, 2000)?



It increases...
When before you
were OK with 10
stocks, now you
have to use 50.
Why?
– Younger
companies are on
the market
– Internal capital
markets are gone
– Competition
– Institutions
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Do you really have to go abroad to achieve
international diversification? (based on
Diermeier-Solnik 2001)
No, It is enough to invest into companies that do business abroad.
Ri=ai+biLocInd+SgijIndj+ SdijCurrencyj+ i
gij is “exposure” to foreign market risk, dij is “exposure” to foreign currency risk.
Exposure is explained well by
% of foreign sales,
gij =li+mijForSalesj
Adjusted R2
Strategic Asset Allocation
International
Market
Exposure
Country
France
0.13
Germany
0.31
Italy
0.40
Japan
0.22
Netherlands
0.49
Switzerland
0.32
UK
0.22
US
0.02
Foreign
Currency
Exposure
0.06
0.09
0.00
0.24
0.19
0
0.17
0.02 32
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Word of caution:
“Trust companies…have reckoned that
by a wide spreading of their investment
risk, a stable revenue position could be
maintained, as it was not to be
expected that all the world would go
wrong at the same time. But the
unexpected has happened, and every
part of the civilized world is in
trouble…”
Chairman of Alliance Trust Company
(1929)
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Non traded risks





Human capital and death insurance
Investment in residence
Other consumption needs: saving for
retirement and life insurance
Liabilities: B/S optimization
You must consider that these are part and
parcel of your portfolio, but with immutable
weights
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Human Capital






Most of the ”normal” individual wealth is in the form
of HUMAN CAPITAL.
Assume that human capital supply (willingness to
work) is flexible and tradeable. Value of future cash
flow decreases with time.
Share of stocks will go down with time
The higher is the riskiness of human capital, the less is
the willingness to invest in stock
Strong effect on portfolio decisions.
Real estate can amplify riskiness of human capital
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Normative multi-period AA: theory
One risk-free asset (return r) and n risky assets
with e=E[R] and var-covar matrix V.
 Investor’s consumption-investment problem:
 T  t

max EU Ct , Ct 1 ,...,CT   max E  d U C 

Ct , wt

Ct , wt
  t
~
' ~
s.t. Wt 1  Wt  Ct  1  w t 1r  w t R t 1



Constant relative risk aversion (CRRA) utility:
 C1g

, g  0, g  1
U (C )  1  g

 ln C , g  1
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Optimal dynamic portfolios:
C 

U
x H
w  AM  BH  
M


WU C
W C
W
W
C
CC
M  V 1 E R   r1,
H  V 1 ν, ν '  (s 1x ,...)
M is mean-variance portfolio
 H is hedge portfolio against changes in
variable x.
 H does not matter for non-stochastic
opportunity set or log –utility function.

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Constraints


Liquidity
Regulations: public or self imposed
 SEC
 Pension funds: Employee Retirement Income Security Act
(ERISA); European directives
 no more than 5% in any publicly traded company
 Mostly domestic assets
 Mutual funds:




No borrowing.
Association for Investment Management and Research (AIMR)
Taxes
Unique needs: internal restrictions
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Frontier with constraints
S&P500 (51.8%)
IA Small Stocks (7.5%)
MSCI Europe (19.7%)
S&P500 (20.0%)
MSCI Pacific TR (7.5%)
IA 5YR Gvt (4.5%)
IA Small Stocks (2.6%)
MSCI Europe (11.9%)
Real Estate (20.0%)
IA 1 Year Gvt (20.0%)
Real Estate (23.5%)
MSCI Pacific TR (10.2%)
Expected Return
19.0
18.0
IA Small Stocks
17.0
16.0
14.0
Source:Ibbotson Assoc.
Portfolios with s=20%
No short sales
B: 20% max
MSCI Pacific TR
CRSP MidCap
15.0
S&P500
MSCI Europe
13.0
12.0
Russell 2000
11.0
10.0
9.0
8.0
Real Estate
7.0
6.0
IA Corporate
IA 1 Year Gvt
IA 5YR Gvt
5.0
4.0
IA 20Yr Gvt
Non-US LT Gvt
30 Day TBILL
3.0
Gold
2.0
Strategic Asset Allocation
0.0
3.0
6.0
9.0
12.0
15.0
18.0
21.0
24.0
Standard Deviation (Risk)
27.0
30.0
33.0
36.0
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39.0
42.0
Time ”Diversification”

Can you reduce risk by
holding assets longer?
– Uncertainty in annual
rate of return goes down
– BUT!!! Uncertainty of
total returns goes up
Position 56
Return Percentiles
Position 56
Compound Annual Return
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
-10.0%
-20.0%
Nov
2001
Source: Ibbotson Assoc.
R=15%, s=20%
S&P500 (37.6%)
IA Small Stocks (23.2%)
95th Percentile
Dec
2005
Dec
2010
Time
Expected Value
Dec
2015
Nov
2020
5th Percentile
Wealth Percentiles
Position 56
Wealth (USD)
50
10
Real Estate (8.1%)
1
1
MSCI Pacific TR (12.5%)
MSCI Europe (18.7%)
Nov
2000
95th Percentile
Strategic Asset Allocation
Dec
2005
Expected Value
Dec
2010
Time
5th Percentile
Dec
2015
Nov
2020
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Practicality: Estimation Risk

Óptimization results are usually
suffering from:
– Huge short positions in many assets in
no-constraint case.
– “Corner” solutions with zero positions
in may assets if constraints are
imposed.
– Huge positions in obscure markets
with small cap
– Large shifts in positions when exp.
returns or covariances changes just a
bit…

All of those are coming from one
common cause: difficulties in
estimation of expected returns.
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Another example (GS 2003):

Here are forecasts
given by “Wall Street
Protagonist”
(Columns 1 and 2)
and set of portfolio
weights that are
generated by it.
RETURN STD DEV
Japanese Gov Bonds
4.7%
4.2%
EU Gov Bonds
5.1%
3.6%
US Gov Bonds
5.2%
4.6%
US Equities
5.4%
15.5%
Global Fixed income
6.0%
3.6%
EU Equities
6.1%
16.6%
US Inv Grade Corp Bonds 6.3%
5.4%
EAFE
8.0%
15.3%
Hedge Fund Portfolio
8.0%
5.2%
US High Yield
8.9%
7.3%
Private Equity
9.0%
28.9%
Emerging Debt
9.0%
17.6%
REITs
9.0%
13.0%
Japanese Equity
9.5%
19.6%
Emerging Equities
11.8%
23.4%
Portfolio ER
Portfolio Volatility
Asset Pricing Models
Unconstrained No Short
weights
Sales
-2.02
0.00
-3.21
0.00
-4.84
0.00
-0.11
0.00
14.93
0.00
-2.58
0.00
-3.86
0.00
3.14
0.00
0.58
0.55
-0.10
0.36
0.01
0.00
-0.29
0.00
0.04
0.08
-0.72
0.01
0.03
0.00
4.90%
18.20%
5.10%
8.40%
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Equilibrium and individual
asset’ expected return
One can expect that ERP is between 4 and
6% and is fairly stable with time (see later
in the course)
 One can make forecast for individual
assets that are different from long term
premium.
 But by forecasting one asset class, we are
implicitly making forecast for other asset
classes as well.

Asset Pricing Models
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Practicality: How to express
views?



Method is due to Black & Litterman (Goldman
Sachs). The core themes: equilibrium returns and
views.
Investors normally have views/preferences. They are
NOT incorporated into optimization process.
Views=mathematically expressed preferences of
individual investors.
Step Action
1
2
3
4
5
6
Calculate equilibrium returns
Define weight for news
Set target tracking error
Set target market exposure
Get portfolio weight
Examine risk distribution
Asset Pricing Models
Purpose
Set neutral reference point
Dampen impact of aggressive news
Control risk wrt benchmark
control directional effect
Find allocation that maximize performance
Is risk diversifies?
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Equilibrium optimal portfolio



Imagine that the investor thin
that US is still in recession.
Thus, stocks will perform badly,
and bonds will perform OK.
Mathematically, it is equivalent
to assuming that bonds will go
up 0.8%, and stocks will drop
2.5%
Result: see Table 8:
Asset Pricing Models
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Updating of discrete
probabilities
1. We have a probability estimate for event H:
prior probability P(H)
2. New information D is gained
3. Update the estimate using Bayes’ theorem:
posterior probability P(H|D)
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The Bayes’ theorem
The updating is done using the Bayes’
theorem:
P( D | H ) P( H )
P( H | D) 
P( D)
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Example: Using Bayes’
theorem
1,5 % of the population suffer from schizophrenia

P(S) = 0.015 (prior probability)
Brain atrophy is found in
– 30 % of the schizophrenic  P(A|S) = 0.3
– 2 % of normal people  P(A|S) = 0.02
If a person has brain atrophy, the probability that he is schizophrenic
(posterior probability) is:
P( A | S ) P( S )
P( S | A) 
P( A | S ) P( S )  P( A | S ) P( S )
0.3  0.015

 0.186
0.3  0.015  0.02  0.985
Picture: Clemen s. 250
Figure: Posterior probability with different
prior probabilities.
Asset Pricing Models
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Updating of continuous
distributions
Choose a theoretical distribution, P(X=x|),
for the physical process of interest.
Assess uncertainty about parameter :
prior distribution, f()
Note:
Uncertainty about
X has two parts:
Observe data x1
Update using Bayes’ theorem:
posterior distribution of , f(|x1)
Asset Pricing Models
1. Due to the
process itself,
P(X=x|).
2. Uncertainty
about , f(), later
updated to f(|x1).
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Updating of continuous
distributions
Bayes’ theorem for continuous  :
f ( | x1 ) 


f ( x1 |  ) f ( )
f ( x1 |  ) f ( )d



f(x1|) is called the likelihood function of  with a given
observed data x1.
In most cases the posterior distribution can not be
calculated analytically, but must be solved numerically.
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Normal distribution
1. The physical process of interest is normal distributed:
X ~ N(m, s2)
(s is assumed to be known)
2. Prior distribution for m:
m ~ N(m0, s20)
(notation: s20 = s2 / n0)
3. Observe a sample of the physical process:
– sample size: n1
– sample mean: x1
4. The posterior distribution, calculated using the Bayes’
theorem, gets reduced to:
m0s 2 n1  x1s 02 n0 m0  n1 x1
m* 

2
2
m ~ N(m*, s2*), where
s n1  s 0
n0  n1
s 02s 2 n1
s2
s * 2

2
s n1  s 0 n0  n1
2
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Expressing Views




Thus, one need to specify set of “views” and “precisions” of
views for each asset f(x|m).
“No views” is equivalent to having sx For this case
posterior=prior.
Model will deviate further for assets where views are stronger.
All assets are affected:
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Further risk control & results:




Minimize tracking error
Mkt. Exposure of the portfolio (b) (neutral should be 1)
Look at diversification (are all eggs in one basket?)
Results (according to GS, 95-97): (+103 bp, +83 bp, -26bp)
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Other uses:



Black-Litterman model is essentially Tactical Asset
Allocation model (provided that algorithm of selecting
“views” is specified).
But it can be used effectively in updating priors on the
distribution of the signals.
It can be used to bring in new asset classes for which
the recorded history is short or unreliable (venture
capital funds, hedge funds, emerging markets, etc.)
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What is expected risk premium?
Expected risk premium= Var(rM)/E[W/]
 Plays central role in any discussion about
the market
 What is that? How to measure it? What
will it tell us about mankind and economy
(or Asset Pricing Model)?

– Historical perspective
– Equilibrium perspective
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Asset Classes Returns: US History
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Asset Classes Returns: Swedish
History
1 SEK invested in 1900
1000000
100000
10000
DMS Global Sweden Bill TR
DMS Global Sweden Inflation
DMS Global Sweden Equity TR
DMS Global Sweden Bond TR
1000
100
10
1
1900
0.1
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1920
1940
1960
1980
2000
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Goetzmann&Jorion: International Evidence
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Goetzmann&Jorion: International Evidence
Median Market RR 0.75%
GDP-weighted RR 4%
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Estimates from historical data
Ibbotson & Sinquefield (76): Real ERP= 5%
 Ibbotson & Chen (2000)
4%
 Fama & French (2002) longer period 4.4%
 Jagannathan, McGrattan,Scherbina (2000)

– 1926-70 ERP=7%
– 1971-99 ERP=0.7%
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What is going on 2day?
Strategic Asset Allocation
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Equilibrium Approach: C-CAPM
Individuals have preferences over consumption
C described by CRRA u=-C1-g
 Certainty case: marginal utility of consumption
today =discounted marginal utility of
consumption tomorrow times teturn of asset ri:
C-gt[(1+ri)/(1+r)] C-gt+1
 In case of uncertainty
C-gtE[(1+ri)/(1+r)] C-gt+1
 Introducing consumption growth
g=C(t+1)/C(t)-1

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C-CAPM(2)
E 1  r 1  g    1  r
g
i
T aylorexpansion: 1  ri 1  g   1  ri  gg  ggri 
g
g (1  g )
2
g2
ApplyingExpectations operator:
r  Eri   gEg   g E ri Eg   covri , g  
g (1  g )
Eg   Varg 
2
If t is small, thenquadratic termscan be disregarded :
g (1  g )
r  Eri   gEg   g covri , g  
Varg 
2
T hiseq. should be true for both risky and riskless assets:
g (1  g )
r  rf  gE g  
Varg   Eri   rf  g covri , g 
2
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C-CAPM: Equity premium puzzle

Mehra&Prescott(85); Mankiv &Zeldes(91):
–
–
–
–
1890-1979[1948-88]: Risk premium=0.06 [.08]
Std of consumption growth =0.036 [0.014]
Std of market returns=0.167 [0.14]
Correlation between consumption growth and
market returns = 0.40 [0.45]
– 0.06=g*0.40*0.167*.036 => g=25 [90]
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Equity premium puzzle
Gamble: take 20% paycut if state of the
world is ”bad” (prob=1/2) and stay at your
current salary in good state, or agree on
permanent cut of X%:
 0.5*(0.81g+1)=x1g

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Equity premium puzzle
Gamble: take 20% paycut if state of the
world is ”bad” (prob=1/2) and stay at your
current salary in good state, or agree on
permanent cut of X%:
 0.5*(0.81g+1)=x1g
 If g=25 then x=17.7%
 Realistic estimate for gamma=3

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How can we solve it?

Habit formation u=-(Ct-lCt-1)1-g
– Increases demand for bonds, lower Rf
– “Keeping up with the Joneses”: instead C(t-1)
there is AVERAGE consumption in the
reference group.
Idiosynchratic labor risk
 Disaster states and survivorship bias.
 Liquidity premium
 Limited Participation

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