3. In this issue of Horizon, we continue our focus on the new Barra Integrated Model.
In the Autumn 2002 Horizon, Dan Stefek, Barra’s senior vice president of Research
and Data, outlined the methodology for constructing the three asset-class models—
Global Equities, Global Fixed Income and Currencies— that comprise the integrated
Model. In this issue, Dan continues with a more detailed exploration of the structure
of each asset class.
The Barra Integrated Model is at the heart of many exciting new developments at
Barra. This multi-asset-class model forecasts equity, bond and currency risk at the
asset and portfolio level and is the basis for BarraOne, our new web-based product.
In our “Applications” section, Brad Thilges, Barra’s Director of Product Strategy,
builds on the theoretical discussion of the Integrated Model with a practical, hands-on
exploration of BarraOne. This case study shows how BarraOne’s easy-to-use, browser-
based interface uses the comprehensive coverage of the Integrated Model to analyze
risk in a very powerful and flexible way. The on-line, ASP model for delivering BarraOne
is a major departure for Barra and, in conjunction with the Integrated Model, demon-
strates a unique commitment to innovation.
As always, we offer the solution to the previous Barra Brainteaser and another
perplexing challenge for our readers. A complete listing of Barra’s educational and
industry events is also included.
Barra Horizon is also available on the Web at http://www.barra.com/horizon.
Aamir Sheikh, President, Barra Inc.
Welcome to Barra Horizon.
4. HORIZON•THEBARRANEWSLETTER•SPRING2003
2
n the Autumn 2002 edition of Horizon, we
introduced our new framework for global risk
analysis, the Barra Integrated Model. This
multi asset class framework was developed
with two goals in mind: breadth of coverage
and in-depth analysis. Risk analysis using the
Integrated Model allows investment profes-
sionals to capture the detail available with
local market models while retaining the broad
perspective of a global, multi asset class
model.
To achieve these objectives, we first build
models for three separate asset classes: global
equities, global bonds and currencies. The
general methodology for constructing these
models was described in Part One. In this
article, we more fully specify the structure for
each asset class.
Global Equities
Our approach to modeling global equities
consists of building a set of local risk models
and establishing linkages between them. We
customize the models for local markets to best
capture the forces explaining return and risk
in those markets. Then, to quantify the cross-
market risk in a global portfolio, we model the
relationship between local factors in different
markets. Not surprisingly, a smaller set of global
influences or factors explains much of the co-
movement of factors across markets.
Our new approach to modeling global equities
differs markedly from that of most global equity
models, which use a single set of factors to
characterize the risk of equities throughout the
world. Those models assume that all equities
are driven by exactly one parsimonious set of
factors, implying that returns due to industries
and styles move in lockstep across markets.
Table 1, shown on the following page, presents
evidence supporting our view. The table shows
the average pair-wise correlation between the
same factors (e.g., US size, UK size) in nine
major markets.1
We find that there is some
commonality in the behavior of both industries
I N S I G H T S
I
The Barra
Integrated
Model
Part Two
Dan Stefek
Senior Vice President,
Research and Data
1
The nine markets are: Australia, Canada, France, Germany, Italy, Japan, Switzerland, UK and US.
Our new approach to modeling
global equities differs markedly from
that of most global equity models.
5. and risk indices across countries. Despite this
correlation, it is clear that these factors behave
significantly differently from market to market.
Global Equity Factors
The global factors that we have chosen to
explain covariances of equity factors across
local models are:
■ A world factor
■ Country factors
■ Global industry factors
■ Global style factors:
Price Momentum, Size, Value and Volatility2
The world factor captures the global market
return, while the industry and country factors
reflect the return to global industry and country
influences net of other factors.3
These factors
were selected based on their ability to capture
common fluctuations across local equity factor
returns.
Local Equity Factor Average Correlation
Materials 0.42
Finance 0.43
Information Technology 0.46
Momentum 0.34
Size 0.18
Volatility 0.43
Exposures of Local Equity Factors
to Global Equity Factors
To determine the covariance of all the local
factors, we attribute a portion of each local
factor return to global factors, as follows:
The portion that is unexplained, , is
purely local and not correlated across markets.
We pre-specify the exposures of local equity
factors to global factors as follows. Each local
industry factor has unit exposure to the world
factor, , its own country factor, , and the
global industry to which it belongs, ; it has
no other global exposures.4
Each local style
factor (or risk index) corresponding to one of
the four global styles has unit exposure to that
style, , and no exposure to other factors. The
other local styles have no global exposure.
Estimating Returns to Global Equity Factors
We compiled a history of returns to global
equity factors by fitting the structural model
in the equations above to monthly local factor
returns. The global factor returns were esti-
mated using cross sectional weighted least
squares regression subject to constraints.5,6
The time period covered by this estimation
was January 1984 to the present. Many of the
country factor returns had incomplete histories
because models for these markets did not exist
gri
gind
gcntygwld
φ φind riand
f g Y g Y g
f g
ind wld cnty cnty ind ind ind
ri ri ri
= + + +
= +
φ
φ
I N S I G H T S
HORIZON•THEBARRANEWSLETTER•SPRING2003
3
Table 1
Local equity factor correlation
in nine major markets
January 1990 to April 2002
2
A list of global factors is available in the Appendix.
3
Both the industry factors and the country factors render the world factor redundant, creating what is known as an identification
problem. To resolve this, we follow the standard practice of requiring both a weighted combination of the countries, and of the
industry factor returns, to sum to zero.
4
A local industry factor may, in some cases, be exposed to more than one global industry factor with fractional weights in each.
5
Each local industry factor’s weight was roughly the sum of the square roots of the capitalization of the assets in the estimation universe
exposed to that factor. Each local style factor was given a weight proportional to the square root of capitalization of the assets in the
estimation universe of the corresponding local model.
6
See footnote 9 for a description of the constraints.
6. I N S I G H T S
HORIZON•THEBARRANEWSLETTER•SPRING2003
4
until some time after 1984. Where possible, we
constructed proxies for these missing returns
using country index returns.
Computing Covariances
of Global Equity Factors
We computed the covariance matrix of the
global equity factors, , from historical
estimates of the returns to these factors. To
account for changing relationships among
these factors, we placed greater weight on
more recent returns when constructing the
covariance matrix. In particular, we used an
exponentially weighted scheme with a half-life
of 48 months, in other words, weighting this
month’s factor return twice as much as one
four years ago. To cope with missing data, we
used the EM algorithm.7
The covariance matrix
of the purely local part of equity factor returns,
, was computed in a similar manner using a
half-life of 48 months.
The final step is to apply the scaling procedure
to make the covariance block for each local
market match that of the corresponding local
model. The result is a model for global equities
that provides analyses consistent with the local
equity models and, at the same time, forecasts
cross-market risk.
Global Bonds
Our approach to building a global bond model
parallels our work on equities.8
We start by
building factor models for each of the local
bond markets. The factors at work in these
local markets include shift, twist and butterfly
term structure movements (STB) and a swap
spread. Four markets—the US, the UK, Japan
and the euro zone—have more detailed credit
factors that explain the spread over swap on
the basis of sector or sector by rating classifi-
cations.9
In addition, emerging market bonds
denominated in an external currency have
country dependent spreads—one spread for
all bonds from each emerging market—that
enable us to include them in our model.
Altogether, there are over 270 local factors.
Global Bond Factors
In the previous section, we described how we
build the factor model that links local equity
models by pre-specifying local equity factors’
exposures to global factors and estimating the
returns to these global factors. In contrast, our
approach in building the factor model that
links local bond models is to pre-specify the
returns to global factors and estimate the
exposures of each local bond factor to these
global factors through time-series regressions.
In this section, we describe the global factors
we use and how their returns are calculated.
The global factors that we have included in the
model to capture covariances in bond factors
across different local markets are:
ΦE
GE
7
The EM algorithm ensures the creation of a positive semi-definite factor covariance matrix even when some of the factors have
incomplete histories. See Dempster, Laird and Rubin, “Maximum Likelihood Estimation from Incomplete Data Using the EM
Algorithm,” Journal of the Royal Statistical Society, 39 (Series B), 1-38, 1977, for a detailed description of the algorithm.
8
For further details, see O. Cheyette, “Global Credit Risk Modeling,” Barra Research Insights, 2002.
9
For the purposes of modeling corporate bonds, we have a single euro-credit model that spans twelve markets. The structure of this
model is similar to that of the other markets, so it makes no real difference for our exposition whether we consider the euro zone to
be one market or twelve individual markets—we will think of it as one.
We find that credit spreads are
strongly correlated within each of
the US, UK, Japan and euro-zone
markets.
7. ■ The STB factors from each of the local
markets
■ The swap spread factor from each local
market
■ An average credit spread factor for each
of the US, UK, Japan and the euro zone
■ An average emerging market credit spread
factor
■ An average US muni factor
■ Shift and, where applicable, twist factors for
real interest rates in the US, UK, Canada and
the euro zone
Period Shift Twist Butterfly Swap
Jan 1993 to Apr 2002
Average Correlation 0.42 0.22 0.02 0.09
% Significantly Positive 80% 50% 3% 22%
Jan 1993 to Dec 1996
Average Correlation 0.40 0.16 0.02 0.07
% Significantly Positive 55% 15% 4% 14%
Jan 1997 to Apr 2002
Average Correlation 0.45 0.27 0.04 0.12
% Significantly Positive 72% 51% 9% 26%
AAA AA A BBB
0.94 0.83 0.77 0.72 AAA
0.88 0.89 0.85 AA
0.95 0.92 A
0.96 BBB
AAA AA A BBB
0.73 0.59 0.39 0.15 AAA
0.63 0.59 0.39 AA
0.64 0.62 A
0.78 BBB
Note that the local term structure and swap
factors are themselves global factors as well.
This simply means that we do not use any
other factors as proxies for them in estimating
their covariance with the other local factors.
We decided to do this because some of these
variables are significantly correlated across
markets and the gain from proxying them with
a reduced set of variables was small.
Table 2 provides some support for this decision,
giving the average pair-wise correlations be-
tween each of the STB and swap factors across
markets (thus, it looks at all shift pairs, twist
pairs, etc.) and the percentage of significant
positive correlations over different time periods.
Clearly, shift and twist, and to some extent
swaps, are correlated significantly across
markets. Turning to credit spreads, we find
that these factors are strongly correlated
within each of the US, UK, Japan and euro-zone
markets. We illustrate the magnitude of this
correlation in Tables 3A and 3B, using the UK
and euro-zone credit spreads, respectively.
The return to this factor is defined as:
where k ∈ local credit factors and each factor’s
weight, , is inversely proportional to its
volatility. We selected these weights, in part, to
mitigate the influence of the lower quality credit
factors that tend to have substantially higher
volatilities.
We use emerging market bond spreads as
additional factors to explain the risk of emerging
market debt issues denominated in external
currencies. We find that these spreads are
wk
I N S I G H T S
HORIZON•THEBARRANEWSLETTER•SPRING2003
5
10
Each cell in the table is the average correlation of spread factors, either for a single rating category or between two
rating categories, but across different sectors. This is why the diagonals, the average correlation within a rating category,
do not equal one.
11
Omitting the month surrounding the Russian default, August 1998, reduces this correlation to 0.23, which is still substantial.
Table 2
Average pairwise factor correlation
across markets
Table 3A
Average correlation of
UK credit spread factors,
May 1999 to April 2002
10
Table 3B
Average correlation of euro
zone credit spread factors,
June 1999 to April 2002
8. strongly correlated. Over the period from
January 1998 to April 2002, the average corre-
lation between these factors was 0.38.11
As with
the credit spreads for US, UK, Japan and euro-
zone, we formed an average emerging market
credit factor that reflects the common behavior
of these markets, defining it to be:
where k ∈ emerging market credit factors and
the weight on each factor is inversely propor-
tional to its volatility.
The risk of US municipal bonds (“munis”) is
captured in the local US bond model using
muni key rate factors. We calculate the average
US muni factor as the equally-weighted mean
of all key rate factors—that is, the muni global
interest rate factor corresponds to a parallel
shift of interest rates calculated as an equal-
weighted average of the key rate changes.
Municipal bonds may additionally be exposed
to a credit spread factor. However, there is no
global factor for muni credit spreads.
Exposures of Local Bond Factors
to Global Bond Factors
The exposures of local bond factors to the
global bond factors are defined as follows:
■ The local shift, twist, butterfly and swap
factors each have unit exposure to the cor-
responding global factors.
■ The local credit spread factors in the US, UK,
Japan and euro markets are exposed to the
average credit and global swap factors corre-
sponding to their market. The exposures are
the regression coefficients obtained from
regressing the time series of local credit
spread factors simultaneously on the average
credit and global swap factors.
■ The local emerging market credit spread
factors are exposed to the average emerging
market credit spread factor. The exposures
are the regression coefficients obtained from
regressing the time series of the local factors
returns on this global factor.
■ The local US muni key rate factors are
exposed to the average US muni factor.
The exposures are calculated by running a
regression of each local factor on this global
factor.
Computing Covariances
of Global Bond Factors
As with equities, we need to estimate and
for bonds. We estimate these from the
global and purely local factor returns using an
exponential weighting scheme with a half-life
of 24 months. We use the EM algorithm to
cope with missing data.
After scaling in the local factor covariance
blocks, as with global equities, we obtain a
global bond model that is consistent with the
local bond models, and can also be used for
risk analysis of portfolios of global bonds.
The Currency Model
The global investor is interested in the risk of
and return to his portfolio from a particular
currency or numeraire perspective. For model-
ing purposes, we decompose the excess return
in the numeraire currency into a part due to
ΦB
GB
Average emerging market credit spread
= ∑ w fk kk
I N S I G H T S
HORIZON•THEBARRANEWSLETTER•SPRING2003
6
We define the currency return to be the excess
return to an investment in a foreign instrument
yielding the short-term rate.
9. currency fluctuations and a part due to local
equity. Consider the excess return from a US
dollar perspective of an investment in Sony
Corp on the Tokyo Stock Exchange, .
We can write this as:
where
We define the currency return to be the excess
return to an investment in a foreign instrument
yielding the short-term rate.
We regard the currency returns as local factors.
Cash holdings have unit exposure to the
appropriate currency factor. Since there are
substantially fewer currencies than equity or
bond factors, we do not model the covariance
of currencies with a smaller set of variables.
However, for ease of exposition later, it is useful
to put currencies in the same framework as
equities and bonds. We treat currencies as
both local (to the currency asset class) and
global factors (like the bond term structure
factors).
Thus, we can formally write:
where
We construct the currency covariance matrix by
estimating currency volatilities and correlations
separately.12
Currency volatilities are estimated
from daily returns using GARCH (1,1) models
while correlations are estimated from weekly
data using an exponential weighting scheme
with a 17-month half-life.
Summary
The core components of our integrated risk
model are these three global asset class risk
models. The results make up a global equity
model based upon 42 local equity models
covering 56 markets, a global fixed income
model covering 49 countries, and a currency
risk model for 56 currencies.
We based each global asset class model on
local market models, which are unique for each
market. Separate local market models allow us
to perform in-depth analysis within the broader
integrated model. However, separate models for
each market requires us to estimate numerous
covariance terms. We can estimate these cross-
market factor relationships best with structural
models. This approach enables investment pro-
fessionals to perform cross-market risk analysis
for global or regional analyses for equities and
bonds.
In future editions of Horizon, we will link the
asset class models together to form a multi
asset class, integrated risk model.
f
g
Y
G
C
C
C
C
=
=
=
=
a vector of local currency returns
a vector of global currency returns
the identity matrix
the currency covariance matrix
f Y g
F Y G Y
C C C
C C C C
=
= ′
and
r
rf
rf
ex
sony
usa
jpn
=
=
=
=
local return to Sony
US risk free rate
Japanese risk free rate
exchange return to an investment in
yen from a dollar perspective
¥ / $
r rf ex r rf
r rf ex rf rf
sony usa sony usa
sony jpn jpn usa
/$ /$
/$
¥
¥
− = +( ) +( ) +( )
≈ − + + −
1 1 1
local excess currency return
return
−
rSony/$
I N S I G H T S
HORIZON•THEBARRANEWSLETTER•SPRING2003
7
12
For details of the currency risk model, see L. Goldberg and J. Kremer, “Forecasting Currency Return Volatility,” Barra, 2001.
10. Appendix: Global Factors
Global Equity Factors
World Style Industry Country
1. World 1. Price Momentum 1. Alcohol 1. Argentina 29. Mexico
2. Size 2. Autos 2. Australia 30. Morocco
3. Value 3. Conglomerates 3. Austria 31. Netherlands
4. Volatility 4. Construction 4. Bahrain 32. New Zealand
5. Electrical 5. Belgium 33. Nigeria
6. Energy 6. Brazil 34. Norway
7. Financials 7. Canada 35. Oman
8. Food 8. Chile 36. Pakistan
9. Health 9. China 37. Peru
10. Heavy Machinery 10. Colombia 38. Philippines
11. Insurance 11. Czech Republic 39. Poland
12. Light Machinery 12. Denmark 40. Portugal
13. Materials 13. Egypt 41. Russia
14. Media 14. Finland 42. Saudi Arabia
15. Mining 15. France 43. Singapore
16. Pharmaceutical 16. Germany 44. Slovakia
17. Precious Metals 17. Greece 45. South Africa
18. Property 18. Hong Kong 46. Spain
19. Telecom 19. Hungary 47. Sri Lanka
20. Textiles 20. India 48. Sweden
21. Tobacco 21. Indonesia 49. Switzerland
22. Transportation 22. Ireland 50. Taiwan
23. Travel 23. Israel 51. Thailand
24. Utilities 24. Italy 52. Turkey
25. Japan 53. UK
26. Jordan 54. United States
27. Korea 55. Venezuela
28. Malaysia 56. Zimbabwe
I N S I G H T S
HORIZON•THEBARRANEWSLETTER•SPRING2003
8
11. Global Bond Factors
Australia ■ ■
Austria ■
Belgium ■
Canada ■ ■ ■
Denmark ■ ■
Emerging Markets ■
Euro ■ ■ ■ ■
Finland ■
France ■
Germany ■
Greece ■
Ireland ■
Italy ■
Japan ■ ■ ■
Netherlands ■
New Zealand ■ ■
Norway ■ ■
Poland ■ ■
Portugal ■
Singapore ■ ■
South Africa ■ ■
Spain ■
Sweden ■ ■
Switzerland ■ ■
United Kingdom ■ ■ ■ ■ ■
United States ■ ■ ■ ■ ■ ■
Market
SovereignTerm
StructureShift,TwistandButterfly
SwapSpreadShift
Inflation-ProtectedTermStructureShift
Inflation-ProtectedTermStructureTwist
CreditSpread
MuniFactor
I N S I G H T S
HORIZON•THEBARRANEWSLETTER•SPRING2003
9
12. HORIZON•THEBARRANEWSLETTER•SPRING2003
10
...
arra recently released BarraOne, a new
on-line risk management system. This case
study focuses on some of the features that make
BarraOne an innovation in risk management
technology.
BarraOne is a secure1
, web-based platform that
enables you to view risk along the dimensions
you choose. It provides flexible risk reporting
and a detailed, customized breakdown of
portfolio risk in a familiar browser interface.
BarraOne is a centrally hosted ASP solution
that is accessible from standard Internet
connections. No software installation or
maintenance is required.
You can use BarraOne to find unintended
bets in your portfolio, to identify the factors
contributing most to your portfolio’s risk, and
to investigate “what-if” trade scenarios to view
the effects of potential trades. Click-through
hyperlinks allow easy navigation and enable
quick examination of specific portions of the
portfolio.
BarraOne uses Barra’s new multi-asset class
Integrated Model for risk forecasting on equity-
only, fixed-income-only or balanced portfolios.
For a complete list of the 56 equity and 49
fixed income markets covered in the Integrated
Model, see the companion article in this edition
of Horizon.
The Scenario
Our aim is to demonstrate how BarraOne and
the Integrated Model can help investment
professionals better understand portfolio risk
and how this risk relates directly to the invest-
ment process. Our point of view will be that
of a US-based global equity portfolio manager,
Ms. Z. She regularly reviews the portfolio with
BarraOne to ensure the sources of portfolio risk
match her investment strategy. Proper allocation
of the risk budget is a high priority.
Ms. Z establishes regional and sector positions
using a top-down, macro-economic model,
selecting stocks based upon Price/Earnings
ratios. Her benchmark is the MSCI World index.
A team of analysts follows stocks from the
index and supplies her with recommendations.
Ms. Z usually holds 125 of these stocks. The
client mandate stipulates that active risk should
be about 4.50%.
Ms. Z is bullish on European equities and will
A P P L I C A T I O N S
BBrad Thilges
Director,
Equity Product Strategy
Spending the
Risk Budget
Wisely
1
Use of BarraOne is subject to the BarraOne Security Statement and the BarraOne Privacy Statement, which can be viewed at
http://www.barra.com/products/barraone.asp.
13. A P P L I C A T I O N S
HORIZON•THEBARRANEWSLETTER•SPRING2003
11
maintain her overweight position there. She also
does not wish to change her sector allocations,
so trades should be made within sector.
Global equity analyses require the use of both
the equity and currency components of Barra’s
Integrated Model. In this example, the fixed
income portion of the Integrated Model will
not be used.
Barra Traditional Risk Decomposition
The equity portion of the Barra Integrated
Model subsumes Barra’s local market models.
Ms. Z can therefore view portfolio risk in a famil-
iar common factor/selection risk2
framework.
Figure 1 contains an active risk decomposition
of the portfolio versus the MSCI World bench-
mark.
The annualized active risk forecast is 4.73%,
slightly higher than the target of 4.50%.
Approximately twice as much of the active risk
arises from active tilts on local market common
factors as from security selection bets3
. Local
market common factors include industries and
styles fitted to each market.
The portfolio has a relatively small amount
of active currency risk. The interaction of the
currency and equity markets produces a net
diversifying effect in this portfolio, lowering
the overall risk.
Figure 2 shows the common factor/selection
risk breakdown by region or Local Market
group. Current levels of active risk arising from
each region are consistent with Ms. Z’s strategy.
She believes euro area stocks will outperform
and has allocated her risk budget to reflect
this. Risk from euro area stocks contribute near-
ly 60% to the portfolio’s active risk.
Ms. Z intends to apply her strategy consistently
in each region. This means the common factor
risk within each region should be twice that of
selection risk. However, selection risk is too high
in North America and too low in the euro zone.
Flexible Risk Reporting
Ms. Z manages the portfolio along three key
dimensions: regions, MSCI/S&P GICS Sectors
and Price/Earnings ranges. Flexible reporting in
BarraOne allows her to translate a standard
Barra risk decomposition into a risk report
organized along the dimensions most relevant
to her investment process.
Figure 3 shows Ms. Z’s portfolio grouped by
Regions that match her investment process.
Ms. Z customizes this portfolio view and sum-
marizes portfolio information such as weights
and P/E ratios by region. She holds too many
low P/E stocks within the euro region and will
rebalance to change this.
Figure 4 shows active sector weights and
Contribution to Active Risk4
(%CAR) by sector5
.
Sector active weights do not deviate far from
Ms. Z’s expectations. However, contribution to
active risk for Consumer Staples is significantly
larger than the active weight would warrant.
Ms. Z holds a neutral view on this sector. She
does not want to waste her risk budget on
sectors she does not expect will out-perform.
2
Selection risk is also known as specific risk.
3
The proportion of risk arising from common factors is 68% versus 37% from selection. These do not add up to 100% due to currency
risk and interaction effects.
4
Percent contribution to active risk (%CAR) identifies the amount of risk arising from an asset or an individual risk source
(e.g., sector or region). Specifically, for every asset i in a risk source g:
5
Ms. Z must report using MSCI/S&P GICS Sectors. However, in certain markets, e.g., the UK, she prefers to follow local market
practices. BarraOne allows the user to view the portfolio using any industry scheme.
% %, .CAR MCARg
active
i active i
i
h= ⋅( ) ( )
∑ ×
1
100
σ
14. A P P L I C A T I O N S
HORIZON•THEBARRANEWSLETTER•SPRING2003
12
Figure 1
Risk decomposition
Figure 2
Local Market active risk
breakdown percentages
grouped by region
Finally, Ms. Z views the portfolio along P/E
ranges (Figure 5). The range breakpoints are set
to match her investment process. For example,
companies with a P/E ratio less than zero are
categorized as Distressed. Ms. Z selects stocks
by P/E ratio, preferring to hold Medium P/E
and High P/E stocks. Active weights and
portfolio risk in Distressed companies have
increased recently due to unfavorable earnings
announcements. Due to several such mis-
alignments, she decides to rebalance her
portfolio.
15. A P P L I C A T I O N S
HORIZON•THEBARRANEWSLETTER•SPRING2003
13
Case Study Assessment
Before using BarraOne to rebalance the port-
folio, let’s summarize what Ms. Z learned from
the analysis of the portfolio.
Active risk of 4.73% is higher than the target
of 4.50%. Therefore, Ms. Z prefers risk-reducing
trades.
The proportion of active risk coming from
common factors (industries and styles) and
security selection is not consistent across
regions. North America has too much selection
risk; the euro area has proportionally too little.
Ms. Z holds a neutral view on the Consumer
Staples sector; however, it contributes nearly
20% to the active risk of 4.73%.
She will trade into more diversifying stocks
within the sector.
Active weights and contribution to active risk
for Distressed companies are too high, but too
low for medium and high P/E stocks.
Rebalancing
Ms. Z can rebalance her portfolio knowing
which active weights need changing and which
sources of active risk need adjustment. She will
focus on risk-reducing trades to lower the port-
folio active risk level towards the target.
Ranking all securities by Contribution to Active
Risk (Figure 6), Ms. Z identifies trade candidates.
Danone is the largest contributor to active risk.
It is a member of the Consumer Staples sector
and has a negative P/E ratio, fitting our defini-
tion of Distressed companies. Her research
indicates Danone is a Sell. Ms. Z has a trade
candidate.
Ms. Z uses Trade Scenario in BarraOne to
identify the impact of trades on active risk. She
proposes a trade of Danone for Papastratos, a
Greek Consumer Staples company. Ms. Z’s
analyst rates Papastratos a Buy.
The P/E ratio of Papastratos falls in the Medium
P/E range, her area of expertise. Purchasing it
decreases exposure to Distressed companies
while keeping sector weights constant.
Figure 7 shows how active risk changes as
Danone’s portfolio weight changes. The most
risk-reducing trade lowers the weight in Danone
to 2.40% from 4.51%. Papastratos was not held
in the portfolio so its proposed weight is 2.11%.
With this trade the portfolio active risk falls to
4.58% from 4.73%. Ms. Z saves the trade. She is
now ready to propose further trades or re-
Figure 4
Positions grouped by
MSCI/S&P GICS sectors
Figure 5
Contribution to risk by
Price/Earnings ranges
Figure 3
Risk report grouped by region
16. A P P L I C A T I O N S
HORIZON•THEBARRANEWSLETTER•SPRING2003
14
examine the portfolio characteristics as she did
before trading.
Conclusion
This case study demonstrated the power of
BarraOne. Traditional (Barra) risk reporting and
flexible reporting can be combined to ensure
that sources of portfolio risk are completely
consistent with the investment strategy, effec-
tively allocating the risk budget.
Figure 6
Positions report ordered by
Contribution to Active Risk
Figure 7
Trade Scenario —
Papastratos for Danone
17. Barra Educational Events and Tradeshows
ril 2003 May 2003 June 2003 July 2003 April 2003 May 2003 June 2003 July 2003 April 2003 May
2003 July 2003 April 2003 May 2003 June 2003 July 2003 April 2003 May 2003 June 2003 July 2
ston Chicago Hong Kong Kuala Lumpur London New York Paris Pebble Beach Phoenix San Francis
oenix San Francisco Boston Chicago Hong Kong Kuala Lumpur London New York Paris Pebble Bea
18. Barra
Educational Events
NORTH AMERICA
Aegis Portfolio Manager Workshop:
Equity Risk Analysis
Level: Introductory
April 8 | Chicago, Illinois
April 22 | San Francisco, California
May 6 | New York, New York
June 3 | Boston, Massachusetts
June 17 | New York, New York
Whether you are a new Aegis user or looking for a refresher, this
interactive workshop will help you gain insight into using equity
multiple factor models and related risk analytics to broaden your
ability to make more informed investment decisions. This one-day
workshop begins with a general theory session and concludes with
the practical application of new concepts.
Aegis Portfolio Manager Workshop:
Equity Performance Analysis
Level: Introductory
April 9 | Chicago, Illinois
April 23 | San Francisco, California
June 4 | Boston, Massachusetts
June 18 | New York, New York
This one-day workshop features Aegis Performance Analyst, the
market-leading equity performance analysis tool. Use case studies
to work through practical exercises and learn how to identify
sources of return and risk in your portfolio over time.
27th Annual Research Seminar
Level: Advanced
June 8–11 | Pebble Beach, California
This annual seminar presents Barra’s latest findings in both
equity and fixed income research. Topics will include credit risk
modeling, hedge funds, risk and the investment horizon and
new approaches to global investment strategies. Speakers from
Barra's Research group will be featured, as well as noted
academics and practitioners as guest speakers.
INTERNATIONAL
Aegis Portfolio Management Workshop:
Equity Risk Analysis
Level: Introductory
April 8 | London, United Kingdom (Europe Model)
April 15 | Hong Kong
May 7 | London, United Kingdom (UK Model)
June 3 | London, United Kingdom (Europe Model)
Whether you are a new Aegis user or looking for a refresher, this
interactive workshop will help you gain insight into using equity
multiple factor models and related risk analytics to broaden your
ability to make more informed investment decisions. The half-day
workshop begins with a general theory session and concludes
with the practical application of new concepts. Class size has
been limited to ensure a low student to instructor ratio.
Aegis Portfolio Management Workshop:
Equity Portfolio Construction and Optimisation
Level: Introductory
April 9 | London, United Kingdom
May 15 | Hong Kong
June 4 | London, United Kingdom
July 22 | Hong Kong
This interactive workshop will help you construct mean-variance
efficient portfolios that meet your return or risk requirements.
We begin with a general theory session and conclude with a
practical session to apply new concepts. Class size has been
limited to ensure a low student to instructor ratio.
Cosmos Fixed Income Workshop
Level: Introductory
April 15–16 | London, United Kingdom
This two-day workshop focuses on fixed income risk analysis,
forecasting and optimisation using the Barra Cosmos System.
19. Aegis Portfolio Manager Workshop:
Equity Performance Analysis
Level: Introductory
May 8 | London, United Kingdom
June 17 | Hong Kong
This half-day workshop features Aegis Performance Analyst.
We use case studies and practical exercises to learn how to
identify sources of return and risk in your portfolio over time.
Equity Portfolio Management Seminar
Level: Introductory
May 12–14 | London, United Kingdom
This seminar focuses on an introduction to the investment
and statistical concepts that underlie Barra’s equity portfolio
management products. An optional day of applied theory and
one-on-one consultation is offered in addition to the program.
Aegis Portfolio Management Workshop:
Advanced Optimisation
Level: Introductory
May 22 | Hong Kong
This workshop uses a fund manager case study to demon-
strate the application of Aegis Portfolio Manager and Aegis
Performance Analyst in a real life situation. It also shows the
advanced application of the optimization function in Aegis.
CONTACT INFORMATION
For more information or to register for any of the Barra
seminars or workshops listed, please visit our web site at:
www.barra.com
Tradeshows
Look for Barra’s booth and speakers
at these events:
Risk 2003 Europe
April 7–10 | Paris, France
Sponsored By: RISK
CNIT La Défence
Paris, France
2003 AIMR Annual Conference
May 11–13 | Phoenix, Arizona
Sponsored By: AIMR
Barra Speakers: Vinod Chandrashekaran
Arizona Biltmore
Phoenix, Arizona
Fund Management Conference
June 4–5 | Kuala Lumpur, Malaysia
Sponsored By: ABF
Barra Speakers: Damien Laker
JW Marriot Hotel
Kuala Lumpur, Malaysia
Risk 2003 USA
June 10–12 | Boston, Massachusetts
Sponsored By: RISK
Barra Speaker: Lisa Goldberg
Seaport Hotel at the World Trade Center
Boston, Massachusetts
2003 SIA Technology Expo
June 17–19 | New York, New York
Sponsored By: SIA
New York Hilton
New York, New York
20. Calendar
of Barra Educational Events
APRIL
8 Aegis Portfolio Management Workshop
Equity Risk Analysis (Europe Model)
London, United Kingdom
8 Aegis Portfolio Management Workshop
Equity Risk Analysis
Chicago, Illinois
9 Aegis Portfolio Management Workshop
Equity Portfolio Construction and Optimisation
London, United Kingdom
9 Aegis Portfolio Management Workshop
Equity Performance Analysis
Chicago, Illinois
15 Aegis Portfolio Management Workshop
Equity Risk Analysis
Hong Kong
15–16 Cosmos Fixed Income Workshop
London, United Kingdom
22 Aegis Portfolio Management Workshop
Equity Risk Analysis
San Francisco, California
23 Aegis Portfolio Management Workshop
Equity Performance Analysis
San Francisco, California
MAY
6 Aegis Portfolio Management Workshop
Equity Risk Analysis
New York, New York
7 Aegis Portfolio Management Workshop
Equity Risk Analysis (UK Model)
London, United Kingdom
8 Aegis Portfolio Management Workshop
Equity Performance Analysis
London, United Kingdom
12–14 Equity Portfolio Management Seminar
London, United Kingdom
15 Aegis Portfolio Management Workshop
Equity Portfolio Construction and Optimisation
Hong Kong
22 Aegis Portfolio Management Workshop
Advanced Optimisation
Hong Kong
JUNE
3 Aegis Portfolio Management Workshop
Equity Risk Analysis (Europe Model)
London, United Kingdom
3 Aegis Portfolio Management Workshop
Equity Risk Analysis
Boston, Massachusetts
4 Aegis Portfolio Management Workshop
Equity Portfolio Construction and Optimisation
London, United Kingdom
4 Aegis Portfolio Management Workshop
Equity Performance Analysis
Boston, Massachusetts
8–11 27th Annual Research Seminar
Pebble Beach, California
17 Aegis Portfolio Management Workshop
Equity Performance Analysis
Hong Kong
17 Aegis Portfolio Management Workshop
Equity Risk Analysis
New York, New York
18 Aegis Portfolio Management Workshop
Equity Performance Analysis
New York, New York
JULY
3 Aegis Portfolio Management Workshop
Equity Risk Analysis (Global Equity Model)
Hong Kong
22 Aegis Portfolio Management Workshop
Equity Portfolio Construction and Optimisation
Hong Kong
21. 15
HORIZON•THEBARRANEWSLETTER•SPRING2003
...
problem has come to the trading desk
of Combinatorial Liberty Investments. One of
Combinatorial’s star strategists, known to be
brilliant but unstable, claims to have discov-
ered a portfolio selection scheme based on
observed market reactions to Combinatorial’s
trade signaling. It is supposed to be an absolute
winner. This particular strategist has made so
much money in the past that no matter how
strange, the desk knows it should execute his
instructions without fail. But the instructions
present peculiar difficulties.
Over the next several trading days, the strate-
gist would like to take and liquidate positions
in three different assets, so that all possible
portfolio combinations are held at least once:
[NNN], [LNN], [NLN], [NNL), [NLL], [LNL], [LLN],
and [LLL], where N denotes a neutral position
and L a long position. A portfolio combination
is always traded into on one day, held over-
night (or over the weekend), and traded out of
on the next trading day.
An absolutely crucial element of the strategy is
that each of the single-asset trades connecting
a portfolio with its nearest neighbors (the near-
est neighbors of [NNN] are [LNN], [NLN], and
[NNL], for example) be performed once and
only once. There are 12 of these “neighbor”
trades to do, since neighbor trades should
never be undone. That is, if the desk has traded
from [NNN] to [NNL], it must not trade from
[NNL] to [NNN]. The manager understands that
occasionally the portfolio may “get stuck,” and
require simultaneous trades in two or even
three of the assets to make another neighbor
trade possible. These multiple-asset trades are
particularly expensive, and the desk must keep
their number to a minimum.
In fact, trading is so expensive that if more than
two multiple-asset trades need to be perform-
ed, the strategy will fail—it was conceived
without considering trading costs. The desk
has warned the strategist about cost levels,
and determined the limit of two multi-trades in
consultation with him.
Since the consultation, the desk has not been
able to find a way to execute the strategist’s
request with fewer than three multiple-asset
trades. The traders need to discover a more
efficient trading sequence, or to prove beyond
doubt that no more efficient sequence exists.
They have referred the problem back to the
strategist, but he has locked himself in his
office with a Barra Brainteaser about four-
dimensional cheese, and refuses to pick up the
phone.
It’s little wonder that the traders are swilling a
popular pink antacid as if it were soda pop.
Can you help them?
B R A I N T E A S E R
AGuy Miller
Senior Consultant,
Research
Brain
Barra
You may send solutions
to the Barra Brainteaser
to Ben Walsh. E-mail
ben.walsh@barra.com,
fax 510.704.0862, or mail to
Barra, 2100 Milvia Street
Berkeley, CA 94704-1113
United States.
teaser
22. B R A I N T E A S E R
HORIZON•THEBARRANEWSLETTER•SPRING2003
16
Brainteaser from Last Issue
A group of bond traders, flush with a recent
success, decides to celebrate with an extrava-
gant dinner on the company’s account. After a
sumptuous entrée, the cheese cart is brought
over.
Sensing that this group will have nothing but
the finest, the fromagier fetches a cube of
exceedingly rare Epoisses cubique affiné au
marc de Bourgogne. To insure equitable
division of the cheese, the cube is placed with
three edges along the positive x, y, and z axes
and sliced along the planes x=y, y=z, and z=x.
There is then exactly one piece of cheese for
each diner.
■ How many diners were there?
One month later, having not yet been fired due
to an inexplicable oversight in the accounting
department, these same traders bring the entire
trading desk to the same restaurant. After a
sumptuous entrée, the fromagier brings out
an even rarer hyper-cube of four-dimensional
cheese.
A lively debate ensues between diners and staff
concerning what sort of knife will be needed,
inquiries as to the health consequences of the
consumption of high-dimensional food, and
whether such a piece of cheese might actually
exist at all.
Assured that it will be just the thing to comple-
ment a bottle of 1947 Petrus, the group agrees
that this is truly a unique dining opportunity.
The cheese is placed with four edges along
the positive w, x, y, and z axes, and it is sliced
along the hyper-planes w=x, x=y, y=z, z=w,
x=z, and w=y. As before, there is then exactly
one piece of cheese for each diner.
■ How many diners were there?
At each dinner, the issue was raised that the
partitioning of cheese might not be perfectly
equitable, with half of the diners complaining
about “left-handed” cheese.
■ Did the pieces of cheese in each case have
exactly the same size?
By “same size” we mean equal 3- (or 4-)
dimensional volume.
■ Did the pieces of cheese in each case have
exactly the same shape?
By “same shape” we mean differing only by
an orientation-preserving rigid motion, so in
particular an object and its mirror image may
not have the same shape.
The Solution
Consider the n-cube sliced by the hyper-
planes The inequalities
determine (the interior of)
one of the sets of the partition. The sets of the
partition are in one-to-one correspondence
with the permutations of the variables in this
string of inequalities. So there are n! pieces of
cheese, settling the first two questions.
For each n, all n! pieces have the same volume,
which is therefore . In general, the shape
question is more interesting, and the answer is
rather surprising. Provided all
pieces have the same shape. Provided
half of the pieces are mirror images
of the others, and are not all congruent in an
orientation-preserving sense. So for the easily
pictured case the pieces are indistinguish-
able, but half of our diners both times did in
fact get observably “left-handed” cheese.
It’s not hard to draw a picture for the case.
A single piece has edges of lengths
In this case, the left-handed pieces are distin-
guished from the right-handed pieces according
as the edges of these lengths meeting at a
1 2 3, .and
n = 3
n = 2
3 mod 4,
n ≡ 0 or
n ≡ 1or 2 mod 4,
1 n!
1 01 2
> > > > >x x xnL
x x i j ni j= ≤ < ≤for 1 .
0 1,[ ]n
Greg Anderson
Senior Consultant,
Fixed Income Research
Brainteaser Winners
Each winner will receive
a prize for solving the
Barra Brainteaser.
Dr. Qiang Liu
Highbridge Capital
Management
New York
23. 17
B R A I N T E A S E R
HORIZON•THEBARRANEWSLETTER•SPRING2003
given vertex occur in clockwise or counter-
clockwise fashion.
The remainder of this column is a proof of the
volume and handedness assertions presented
for completeness. We recommend consulting it
only for ideas, since the details tend to obscure
the big picture.
Let be the group of permutations of n letters,
so is the permutation Let be
the piece of cheese determined by
, and generally is the piece deter-
mined by
Take to be the permutation matrix associated
to so the ij entry is In other words, is
mostly 0 with one 1 in each row and each col-
umn as determined by The effect of as a
linear transformation is simply to permute the
variables, so in par-
ticular It is well-known (and easily
verified) that is orthogonal, so it preserves
volume, so all pieces of cheese are the same
size.
It is also well-known (and easily verified) that the
determinant of is the sign is a
product of an even number of transpositions,
and -1 if odd. Thus when is even, has the
same shape and orientation as . Similarly, all
for odd have the same shape and orienta-
tion. It remains to determine whether the two
types of pieces have the same or opposite
orientation.
Suppose for a moment that is odd, and that
and have the same shape, i.e., that there
is an orientation-preserving Euclidean isometry
sending onto . Since is odd, we already
know that is an orientation-reversing Euclid-
ean isometry sending onto . Composing
the two maps, we find that if all the pieces have
the same shape, then there is an orientation-
reversing isometry of onto itself. Conversely,
if there is an orientation-reversing isometry of
onto itself, composing this with (for odd
) gives an orientation-preserving Euclidean
isometry of onto .
Our plan now is to exhibit all Euclidean isome-
tries of onto itself and inspect them. As in the
previous paragraph, there is left-handed cheese
if and only if all such maps are orientation-
preserving. We will establish below that the only
such map other than the identity is given by
where is the vector of 1's and A has -1's on
the anti-diagonal and 0's elsewhere. We leave
r
1
f x f x
Ax
x x x x xn n n
r
r r
K K( )= ( )= −( )
= +
− − −−1 1 2 1
1
1
1 1 1, , , , , ,
C1
CσC1
σ
LσC1
C1
CσC1
Lσ
σC1
Cσ
CσC1
σ
σCσ
C1
Cσσ
σ σ, i.e., if+ 1Lσ
Lσ
L C Cσ σ1( )= .
L x x x xn nσ σ σ1 1
, , ,K K( )= ( )( ) ( )
Lσσ.
Lσδσ i( ).σ,
Lσ
1 1
> > >( ) ( )x x nσ σ
L .
Cσ0> >xnL
1 1 2
> > >x x
C1
i ia σ ( ).σ ∈Sn
Sn
24. B R A I N T E A S E R
HORIZON•THEBARRANEWSLETTER•SPRING2003
18
it as an exercise that the determinant of A is 1
if and -1 otherwise, thus estab-
lishing our previous claims.
Now suppose that is a Euclidean
isometry taking onto itself. As a preliminary
observation, note that f must either fix or inter-
change the origin and , the vector of 1's. This
is because the segment between these points is
the longest in the cube, hence the longest in .
A refinement of this observation gives the
results we seek. There is another distinguished
path from which must also be preserved
or reversed, namely the unique broken line path
along the edges of the original cube that lie on
. The vertices of the cube are the points
with coordinates either 0 or 1, and it is clear
that exactly of them satisfy the inequalities
defining the closure of .
Adjacent vertices, meaning those connected by
an edge, are characterized by being distance 1
apart, and there is evidently exactly one way to
get from via adjacent vertices in with
no backtracking. (This is also true of , so
another way to count the pieces is to count the
paths of length n along the edges from .)
Returning to the determination of f, the piece
has distinguished vertices and an order-
ing of them which can be recovered from the
Euclidean distance function. Thus f must either
preserve or reverse this itinerary of vertices,
which is If
preserves this, clearly f is the identity,
and so f preserves as well. If f reverses it, then
and the n requirements for A are
so A has -1’s on the anti-diagonal and 0’s else-
where. Thus there is only one nontrivial candi-
date for f, and it is easy to check that f does in
fact send onto itself.C1
A
A
A
10 0 0 0 0 0 1
110 0 0 0 1 1
1110 0 1 1 1
, , , , , , ,
, , , , , , ,
, , , , , , ,
K K
K K
K K
M
( )= −( )
( )= − −( )
( )= − − −( )
f b
r r r
0 1( )= =
C1
Ax b
r r
+
f x
r
( )=0 0 0 10 0 110, , , , , , , , , , , ,K K K K( ) ( ) ( )
n + 1C1
r r
0 1to
Cσ
C1
r r
0 1to
C1
1 01
≥ ≥ ≥ ≥x xnL
n + 1
2n
C1
r r
0 1to
C1
r
1
C1
f x Ax b
r r r
( )= +
n ≡ 0 or 3 mod 4
25. Research Seminar
Pebble Beach, California June 8—11, 2003
➔
27th Annual
Hedge Fund Transparency
Sources of Return in Global Investing
Does Corporate Governance Matter?
Optimization with Errors— Fact and Fallacy
Insider Trading and Earnings Quality
Flexible Risk Decomposition
Do Credit Risk Models Work?
26. Hedge Fund Transparency Sources of Risk in Global Investing Does Corporate Governa
on with Errors — Fact or Fallacyy Insider Trading and Earnings Qualityr y Flexible Risk Decom
Credit Risk Models Workk ? Hedge Fund Transparencyy Sources of Risk in Global Investing Does Corporate Governance M
➔ For information, or to register, visit us online at www.barra.com/education
27. Berkeley
2100 Milvia Street
Berkeley, CA 94704 -1113
United States
tel 510.548.5442
fax 510.548.4374
Cape Town
Barra International, Ltd.
2nd Floor Kildare House
Fedsure Oval, 1 Oakdale Road
Newlands 7700
South Africa
tel 21.683.3245
fax 21.683.3267
Frankfurt
Barra International, Ltd.
Goethestraße 5
D-60313 Frankfurt am Main
Germany
tel 069.133.859.0
fax 069.283.700
Hong Kong
Barra International, Ltd.
Suites 1910–1916, Jardine House
1 Connaught Place
Central, Hong Kong
tel 2536.2935
fax 2537.1375
London
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75 King William Street
London EC4N 7BE
United Kingdom
tel 0207.283.2255
fax 0207.220.7555
New York
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New York, NY 10005 -1801
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tel 212.785.9630
fax 212.785.9639
Rio de Janeiro
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Sala 310, Edificio Barra Trade I
Rio de Janeiro, RJ
Brazil CEP 22775-050
tel 21.2430.9515
fax 21.2430.9587
Sydney
Barra International, Ltd.
Level 14, 9 Castlereagh Street
Sydney, N.S.W. 2000
G.P.O. Box 4505, Sydney, N.S.W. 2001
Australia
tel 2.9223.9333
fax 2.9233.1666
Tokyo
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Sumitomo Hamamatsucho Building 7F
1-18-16 Hamamatsucho Minato-ku
Tokyo, 105-0013, Japan
tel 03.5402.4153
fax 03.5402.4154
Barra, Inc.
2100 Milvia Street
Berkeley, California 94704-1113
U.S.A.
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R E T U R N
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R E Q U E S T E D
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