T H E
B A R R A
N E W S L E T T E R
HORIZON
99
Estimation of the European Equity Model
by Gregory Connor and Nick Herbert
R
E
S
SPECIAL SECTION
E
European
Monetary Union
A
RESEARCH
C
Estimation of the
European Equity Model
H
European Bond and
Currency Markets in
Anticipation of Monetary
Union
EQUITY ANALYTICS
Volatile Markets and
BARRA Models
MARKET NEUTRAL
Part One: The Case
for Market Neutral
SPECIAL
ANNOUNCEMENT
BARRA announces
new managing director
of research
R
T
his report introduces the European
Equity Model and describes the results
from the estimation of this new model.
Section 2 discusses the construction of the
risk indices and the estimation of the factor
model. Section 3 presents the specific risk
model. Section 4 shows the results from
performance testing of the risk forecasts
from the model. Section 5 analyzes the predicted betas from the model and compares
them to historically estimated betas.
Section 6 concludes the report.
1. Introduction
The integration movement in Western
Europe is one of the most important political-economic developments of our time.
Its basic objective is the creation of an integrated super-state in which the member
states retain some individual economic and
political identity. It is not surprising that
Western European equity markets have
responded over recent decades by becoming increasingly homogeneous (see for
example Beckers, Connor and Curds
(1996) or Freimann (1998)).
As various analysts have noted, the entity
being created in Western Europe, particu-
larly within the single currency region, is
in many ways unprecedented. BARRA
has, accordingly, created a new type of
equity risk model, the European Equity
Model (EEM). The new model sits
halfway between BARRA’s Global Equity
Model (GEM) and its family of single
country equity models. Like the GEM,
the European Equity Model contains
country, industry and risk index factors.
Unlike the GEM, all the factors are estimated simultaneously rather than country factors first. This allows the regional
influences to fully exert their explanatory
power.
When we started the research for this new
model, we expected to find a significant distinction between the “Ins” (those countries
adopting the Euro currency in 1999) and
the “Outs.” Empirical evidence, however,
indicated otherwise - many Outs, such as
Switzerland, for example, are well integrated into the equity factor structure of continental Europe. Rather, we discovered that
the key distinction was between the UK and
everyone else. For this reason the European
equity model includes separate industry
factors for the UK, and makes no modeling
distinction between the Ins and
c o nt i nu e d o n p g . 1 6
W I N T E R
1 9 9 9
P U B L I C A T I O N
N U M B E R
1 6 9
T H E
B A R R A
N E W S L E T T E R
HORIZON
Managing Editor
Sherri Roberson
EDITORIAL BOARD
B e r ke l ey
99
Andrew Rudd
Nicolo G. Torre
London
Andrew Cauldwell
S yd n ey
Peter Ritchie
M o n t re a l
Pierre Brodeur
C
Yo ko h a m a
Yoshio Mizoroki
O
N
SPECIAL SECTION
T
European Monetary Union
C o n t r i bu t i n g E d i t o rs
Nick Baturin
Gregory Connor
Mark J. Ferrari
Neil Gilfedder
Lisa Goldberg
Nick Herbert
Anton Honikman
Kenneth Hui
Jason Lejonvarn
Claes Lekander
Eugene Reznik
E
N
RESEARCH (COVER ARTICLE)
T
Estimation of the European
Equity Model
S
BRAINTEASER
by Gregory Connor, Nick Herbert .....
Monica Edler
C i rc u l a t i o n
by Lisa Goldberg,
Anton Honikman...........................
BARRA, Inc.
2100 Milvia Street
Berkeley, CA 94704-1113
tel: 510.548.5442
fax: 510.548.1709
A subscription can also be
obtained by visiting BARRA’s
website at www.barra.com,
or by calling any of BARRA’s
offices located worldwide.
Copyright © BARRA 1999.
All rights reserved.
28
Solution to the Fall 1998
Brainteaser
by Eugene Reznik, Nick Baturin . . .
29
3
Sherri Roberson
The Horizon Newsletter is published
quarterly by BARRA, Inc. from its
headquarters in Berkeley, California.
Please send all address changes and
requests for subscriptions to:
The BARRA Brainteaser
for Winter 1999
by Mark Ferrari . . . . . . . . . . . . . .
European Bond and Currency
Markets in Anticipation of
Monetary Union
D e s i g n & P ro d u c t i o n A r t s
1
E Q U I T Y A N A LY T I C S
Volatile Markets
and BARRA Models
SPECIAL ANNOUNCEMENT
BARRA announces new
managing director of research
by Andrew Rudd .........................
by Neil Gilfedder, Kenneth Hui . . . .
27
31
MARKET NEUTRAL
Part One: The Case
for Market Neutral
by Jason Lejonvarn, Claes Lekander . .
33
E U R O P E A N
M O N E TA R Y
U N I O N
European Bond and Currency Markets
in Anticipation of Monetary Union
by Lisa R. Goldberg and Anton Honikman
R
Portions of this article appeared in the December 1998 issue of Euro Magazine.
E
Lisa Goldberg is manager of
S
International Fixed Income
E
Research in Berkeley.
A
R
C
Anton Honikman is a
product manager in BARRA’s
Institutional Analytics
group in Berkeley.
H
Introduction
When European Monetary Union took
effect on January 1, 1999, eleven currencies
collapsed into one and a common monetary policy for eleven countries came under
the authority of a single central bank.
Europe now has a reserve currency that
competes with the U.S. dollar. As a result,
business and financial transactions across
European borders will become increasingly
fluid, and markets will behave in new ways
that are difficult to predict.
Developing EMU-compatible investment
tools presented a unique challenge. Some
required features were known in advance for example, new settlement and accrual
rules and dual currency reporting capabilities could be incorporated into existing
models ahead of time. Modification of valuation and risk models was a trickier problem and there was no “right way” to handle
it. Would EMU sovereign bond markets
collapse into a single homogenous market?
How could Euro volatility forecasts be
generated early in January with no data
Figure 1
Spreads of 5-Year Sovereign Spot Rates
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THE
BARRA
NEWSLETTER
3
Figure 2a
Forward Swap Curves for EMU
Markets: January 1, 1999 as seen from
July 1, 1997
Figure 2b
Forward Swap Curves for EMU
Markets: January 1, 1999 as seen from
July 1, 1998
history? How should models be modified
to handle markets exiting and entering
EMU?
This article answers these questions by
examining the ways in which bond and
currency markets anticipated monetary
union. The information revealed by this
examination was used by BARRA to design
EMU-compatible fixed income valuation
and risk models that should perform well
no matter what the Euro brings.
Term Structures
At the core of any fixed income valuation
4
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1999
THE
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model is a term structure of interest rates.
This is the curve that comprises lending
rates for terms of different length. There
are different term structures for different
markets such as French sovereign bonds,
Japanese AA bonds, or GNMA 30-year
mortgages.
, however, is at best a
loosely defined term. Candidate attributes
used to characterize a market include its
currency of denomination, credit level, liquidity, the nature of the issuing entity and
other factors.
Market
Should one continue to differentiate
between EMU markets based on country of
issue? Fluctuating exchange rates have
Figure 3a
Forward Sovereign Curves for EMU
Markets: January 1, 1999 as seen from
July 1, 1997
Figure 3b
Forward Sovereign Curves for EMU
Markets: January 1, 1999 as seen from
July 1, 1998
historically enabled the term structures of
EMU markets, as defined by their principal
currency, to move with relative independence. figure 1 shows a time series of
French and Italian 5-year sovereign spreads
over Germany. These spreads were quite
large, especially for Italy, until November
1997. In the past year, however, these markets have become more uniform. Will they
eventually collapse into a single market?
calculator which was used to forecast the
likelihood of markets joining the EMU.
The curve in figure 2a is derived from
the July 1, 1997 while the curve in figure
2b is as of July 1, 1998. The convergence is
dramatic. The forward curves in figure
2b practically coincide. This is encouraging, since the existence of a single EMU
central bank implies that there will be a
single swap curve for all EMU markets
once the Euro is launched.
figures 2a and 2b show implied forward
swap curves beginning with the inception
of the Euro on January 1, 1999. Curves of
this type formed the basis of the now
defunct J. P. Morgan implied probability
HORIZON · WINTER
1999
A similar analysis made for sovereign
markets shows a similar but less dramatic
trend. The results are displayed in
figures 3a and 3b.
THE
BARRA
NEWSLETTER
5
While sovereign term structures have converged, spreads as high as 75 basis points
remain. The existence of these spreads indicates the market’s perception of the creditworthiness of the issuing sovereign. While
liquidity and supply do affect bond prices,
credit quality is the overriding means by
which market participants differentiate
between sovereign issuers within EMU.
What are the model implications? Creditworthiness characterizes markets in EMU.
Global models therefore need to account
for the credit spreads between legacy markets. A single sovereign EMU term structure will not give sufficiently accurate
model values since the differences between
legacy markets are significant. More evidence for this conclusion is given below.
BARRA’s EMU Term Structure
What is the right benchmark against which
to measure sovereign term structures in
EMU markets? The most obvious candidates are the German sovereign term structure and the EMU swap curve. While both
candidates have been adopted by analysts
and market commentators, neither is perfect. Germany is the dominant EMU mar-
ket in the sense that it has the largest GDP,
the least credit risk, and the greatest supply.
The Germany term structure, however,
does not reflect “average” EMU behavior.
The second choice, the EMU swap curve, is
more appealing since it belongs to all EMU
markets. However, the swap curve prices
debt issued by commercial financial institutions, not sovereigns. Part of the spread
between the EMU swap curve and an EMU
sovereign curve results from the fact that a
bank is more likely to default than a government. The swap curve does not provide
a basis for comparing markets which have
sovereign credit qualities.
An ideal approach is to estimate an EMU
sovereign term structure from a pool of
sovereign bonds belonging to EMU markets. A convenient pool is provided by the
leading European sovereign indices: the J. P.
Morgan EMU Bond Index and the
Salomon Smith Barney EMU Government
Bond Index (EGBI).
figure 4 displays BARRA’s Benchmark
EMU term structure, estimated from the
J. P. Morgan EMU Bond Index comprising
bonds from all the EMU markets except
Luxembourg.1
Figure 4
Sovereign Term Structures for EMU
Markets and Euro: July 1, 1998
1 There are many ways to estimate a term structure of interest rates. The curve displayed in this document uses
the same estimation procedure as in all BARRA fixed income models. We solve for rates that minimize relative
pricing error. In this example, the Gross Domestic Products of the sovereign issuers weight bonds in the estimation universe.
6
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Figure 5
figure 5 displays the GDP weights used
GDP Weights
in the estimation
Although we
use the broader spectrum of EMU member
markets in the estimation universe, GDP
weights dictate that the combination of
France, Germany and Italy will dominate
the outcome.
procedure.2
Market
Weight
AUT
.0330
BEL
.0386
FIN
.0189
FRA
.2209
GER
.3350
IRE
.0210
ITA
.1828
NET
.0575
POR
.0160
SPA
.0853
figure 6 shows a less cluttered picture of
the EMU term structure plotted with the
three dominant markets: Germany, France
and Italy.
Despite contributing over 18% of the estimation weight, Italy trades at a significant
positive spread over the EMU baseline. The
market is clearly pricing Italian sovereign
debt differently from that of other markets
in the currency union. There is a premium
for perceived extra credit risk and potential
departure from EMU.
Italy and Portugal the least.
The EMU sovereign term structure is a natural choice of benchmark. It elucidates the
differences between the member markets.
But how accurately does it value bonds?
figure 8 shows a table of root mean
square pricing errors for the universes used
to estimate EMU and legacy term structures.
When valued off the EMU term structure,
the typical pricing error for the universe of
EMU sovereign bonds is 80 basis points.
The analogous pricing error, if legacy market term structures are used, is roughly
nine basis points. Hence, a typical EMU
bond will have a much larger pricing error
relative to the EMU term structure than to
a legacy term structure. This further supports the conclusion that legacy sovereign
term structures should continue after the
introduction of the Euro. They do a much
better job of pricing debt issued by their
own sovereign entity.
figure 7 gives a more detailed look at
these spreads. It provides a cross-sectional
view of member markets forward spreads
relative to the EMU term structure at the
5- and 10-year vertices.
Term Structure Movements
France and Germany are clearly perceived
as having the greatest credit-worthiness,
The dominant source of risk for sovereign
and investment grade corporate bonds in a
Figure 6
Sovereign Term Structure for
Dominant EMU Markets and Euro:
July 1, 1998
2 As remarked in “Weight Problem” on page 80 of the November 6, 1998 Economist, bond indexes suffer from
the “perverse logic” of heavily weighting countries with large debt, even though these countries may be “borrowing their way into trouble.” GDP weighting ensures that BARRA’s EMU term structure is dominated by
the strongest markets rather than those markets with the largest debt.
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THE
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7
Figure 7
Implied 5- and 10-Year Forward
Spreads for EMU Markets: January 1,
1999 as seen from July 1, 1998
Figure 8
Root Mean Square Pricing Errors,
Term Structure Estimation: July 1,
1998
Market
RMSE
AUT
.08
BEL
.04
FIN
.02
GER
.08
IRE
.09
ITA
.09
NET
.07
POR
.13
SPA
.06
EMU
.80
single market is change in term structure.3
Moreover, the dominant component of
term structure change is a shift in level of
rates.
importance to more recent data, market
stability through July end has a greater
effect on the volatility estimates, dragging
them downwards.
figure 9a looks at EMU market shift
figures 10a and 10b display correlations
between EMU market term structure
shifts. figure 10a shows correlations by
date, while figure 10b shows correlations
as of July 1, 1998 as a function of half-life.
These results are intuitive. Correlations
tend to increase as monetary union
approaches and as halflife shortens.
volatilities at July 1, 1997 and July 1, 1998.
In all cases, volatility decreased by roughly
10-15%. figure 9b displays volatility
forecasts for EMU markets as of July 1,
1998 as a function of half-life.4 Data were
weighted exponentially with half-lives of 6,
12 and 24 months. As one would expect,
volatility decreases with half-life uniformly
across EMU members. As we give greater
On the other hand, these markets are still
3 Typically, a term structure is specified by rates at a set of key maturities or vertices, together with an interpolating rule to determine rates between vertices. The term structure specification suggests a risk model specification, which is a key rate model whose factors are changes in key interest rates. Empirical studies show that a
key rate model forecasts risk effectively within a single market.
Nevertheless, a collection of key rate models is not the ideal design for a global model. Accurate valuation
requires a term structure to have roughly 10 vertices. Even without considering credit or currency risk, a global model covering 20 markets with 10 interest rate factors per market results 200 risk factors. A history of at
least 200 data points is needed in order to estimate the model parameters in a meaningful fashion. If the
model has a monthly horizon, data from 17 years before the analysis date must be incorporated into the
model. On the other hand, economic models benefit only from recent data. Old data tend to corrupt rather
than improve economic forecasts. Fortunately, many of the key rate factors are redundant. Changes in interest
rates within a single market are highly correlated, and a shift in interest rates accounts for more than 75% of
term structure volatility in most developed markets. This fact enables us to compare market moves by looking
at their shift volatilities and correlations.
4 For many economic time series, statistical parameters such as mean and standard deviation change over time.
In these cases, parameter estimates should count recent information more heavily than old information. A
simple, effective way to accomplish this is with an exponential weighting scheme. The scheme depends on a
weight lbetween 0 and 1. The ith oldest data point is multiplied by a constant times li. The constant is chosen
so that the resulting estimates are unbiased. The most intuitive way to understand a weighting scheme is in
terms of its half-life, -log 2/ log l. The data point x(j - hl) counts roughly half as much as x(j).
8
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Figure 9a
Shift Volatility of EMU Markets
Figure 9b
Shift Volatilities of EMU Markets:
July 1, 1998
imperfectly correlated. The July 1, 1998
shift correlation between Germany and
Italy estimated with a halflife of 6 months is
.55. The analogous estimates for Germany
and Italy shift volatilities differ by more
than 25 basis points. Separate risk factors
for legacy markets still carry important,
non-redundant information.
Currencies
Risk management systems will require Euro
risk forecasts after the first trading date of
monetary union, January 4, 1999. Since
there is no history for the Euro, a proxy history is required to generate these forecasts.
Natural candidates for the proxy are the
HORIZON · WINTER
1999
Deutschmark or a weighted basket of EMU
markets.
In the absence of Euro data, it is hard to
imagine a test that would identify the best
scheme. It turns out, however, that such a
test is unnecessary since EMU currencies
are already behaving as a single currency.
figure 11 shows a time series of daily
returns for EMU currencies from a U.S.
dollar perspective for the months of August
and September. The data points are virtually on top of one another despite market
turbulence throughout this period.
figure 12 displays monthly volatility forecasts for EMU currencies for January
THE
BARRA
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9
Figure 10a
Shift Correlations Between Pairs of
EMU Markets
Figure 10b
Shift Correlations Between Pairs
of EMU Markets: July 1, 1998
Figure 11
Daily Currency Returns in European
Markets
10
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Figure 12
Volatilities of European Currencies
Figure 13
Correlations of EMU Currencies with
the Deutschmark
through September 1998. At the end of
September, all EMU currency volatilities
were approximately 9.4%. From August
end to September end, volatility increased
significantly. The only outlier is the Irish
Punt which had a September end volatility
forecast of 9.9%. figure 13 shows the correlation of the Deutschmark with other
EMU currencies. By August end, all currencies other than the Irish Punt were perfectly correlated with the Deutschmark. The
latest Deutschmark-Punt correlation is .92.
Is the U.K. an Island?
Our attention now turns to the most
intriguing of the “Outs”5 - the United
Kingdom. Among Outs, the UK has by far
the largest economy. It has deep-rooted
trade links with all EMU members and
presided over the European Union while
most of the EMU convergence took place.6
Since the economies and policies of the UK
and EMU markets are so closely linked, one
would expect their bond markets and cur-
5 The term “Outs” commonly refers to countries that are eligible for inclusion in EMU by virtue of the fact that
they are members of the European Union, but have either not satisfied the inclusion criteria or have voluntarily excluded themselves.
6 The United Kingdom held the presidency of the European Union from January 1, through June 30, 1998.
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11
rencies to exhibit similar behavior. This
section superimposes an analysis of the UK
onto analyses already performed for EMU
members. This puts some of our previous
results in context.
Recall that market volatility7 decreased as a
function of a reduction in half-life. In figure 14 we observe that while the market
volatility in the UK has also decreased, it
does so at a more constant rate than in
EMU markets.
Contrary to initial expectations, the UK
market exhibits lower correlation with
Figure 14
Shift Volatilities of EMU Markets
and the UK: July 1, 1998
Figure 15
Shift Correlations Between EMU
Markets and UK: July 1, 1998
7 As expressed by shift volatility.
12
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EMU members as one weights recent data
more heavily. figure 15 shows shift correlation between the UK and EMU members
as a function of half-life. In every case the
use of a 6-month half-life significantly
decreases the correlation.
Interestingly, the correlation with France
(0.31) and Germany (0.38) are low, and are
even lower than the correlations of the U.S.
with those markets: France (0.41) and
Germany (.54).
figure 16 shows how the volatilities of
EMU currencies are virtually identical to
Figure 16
Volatilities of European Markets
Figure 17
Correlations of EMU Currencies
and Sterling with Deutschmark
one another while Sterling volatility is
about 100bps lower. Similarly, the SterlingDeutschmark correlation diminished during 1998. Earlier in 1998, Sterling exhibited
a profile similar to the Irish Punt - both
had a correlation coefficient of just under
.7 with Deutschmark. As of September end,
the Punt-Deutschmark correlation was .92
while the Sterling-Deutschmark was less
than 0.6. By contrast, all EMU currencies
with the exception of Punt were perfectly
correlated with Deutschmark. This information is displayed in figure 17.
Further disparities between the UK and the
EMU markets are found in their term
HORIZON · WINTER
1999
structures of interest rates. Forward curves
beginning January 1, 1998 implied by
July 1, 1998 term structures are shown in
figure 18 . The EMU markets have
upwardly sloping curves, and offer similar
yields to maturity. The UK has an inverted
yield curve whose rates bear no resemblance to those of the EMU.
The behavior of the bond and currency
markets of the United Kingdom in this
context attests to the homogeneity of EMU
members. Despite economic and geographic ties with the European continent,
the United Kingdom is most definitely an
island.
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13
Figure 18
Forward Sovereign Curves for EMU
Markets and UK: January 1, 1999 as
seen from July 1, 1997
Figure 19
Sovereign 5-Year Forward Spreads
of European Markets Over EMU:
January 1, 1999
Conclusion
Severe turmoil has prevailed in world markets since we started this study. The crash
of the ruble at the end of August and the
subsequent Asian and Brazilian currency
crises have had serious repercussions in
more developed markets. These events and
the ensuing market volatility have raised
the specter of default in the minds of
investors, who are sacrificing expected
return in favor of lower risk and flocking to
the most conservative securities. As a
result, spreads of all kinds have widened.
How much has worldwide volatility shaken
up the EMU? Implied sovereign forward 5-
14
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year EMU spreads widened significantly
between July 1, 1998 and October 16, 1998.
Several of these spreads are depicted in
figure 19.
By contrast, swap spreads have remained
tight. figure 20 displays forward swap
curves for January 1, 1999 implied by
October 16, 1998. It is instructive to compare figure 20 and figure 2b. With the
exception of Ireland, long end swap spreads
were as tight on October 16 as they were on
July 1. Short end spreads have narrowed
significantly. This is reassuring insofar as
monetary union mandates a single swap
curve for all EMU markets beginning in
January.
figure 17 depicts a dramatic increase in
EMU currency volatility for the month of
September during which forecasts rose by
roughly 150 basis points. Nevertheless, the
EMU currencies continued to behave in
unison. Excluding the Punt, the largest
September end volatility spread was
between the Belgian Franc and the
Deutschmark at 21 basis points and the
lowest September end correlation was
between the Lira and the Deutschmark at
.982. Furthermore, correlations between
pairs of EMU currencies remained perfect
in the face of high volatility.
Clearly, currency and swap markets have
converged. But the evidence given above
confirms the hypothesis that perceptions of
creditworthiness differentiate between
markets in EMU. Good models need to
support this distinction. ■
Figure 20
Implied Forward Swap Curves:
January 1, 1999 as seen from
October 16, 1999
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15
E U R O P E A N
M O N E TA R Y
U N I O N
Estimation of the European
Equity Model
2. Construction of the Risk Indices
and the Factor Model Regressions
els. The Blue Chip Membership risk index
is designed to capture the common movement of the top-tier equities. It is a dummy
variable whose value is one if the stock is
among the top 100 capitalization stocks in
the universe at the beginning of the month,
and zero otherwise. table 1 shows the risk
indices and the descriptors contained in
them.
The European Equity Model has six risk
indices: Value, Size, Momentum, Volatility,
Yield, and Blue Chip Membership. The first
five of these are standard BARRA risk
indices that have been applied successfully
in a large number of our equity risk mod-
All descriptors are filtered for errors using
the skipped Huber method, that is, values
which are greater than 5.2 median absolute
deviations from the median are set to this
limit value. The risk index exposures are
standardized to have a capitalization-
continued from cover page
Outs except the obvious one in their currency covariances.
Gregory Connor is
director of research,
BARRA International.
Nick Herbert is a
research consultant for
BARRA International.
Table 1
Size — The size index is based on market capitalization. It differentiates large stocks
from small stocks. The size index has been a major determinant of performance over
the years, and is an important source of risk as well.
The Risk Indices and their Underlying
Descriptors
+
Log of Capitalization
Momentum — The momentum index identifies stocks that have been recently successful based on price behavior in the market, measured by twelve-month cumulative
excess returns.
+
Log rate of excess return over the last twelve months
Value — This index captures the extent to which a company’s ongoing business is
priced inexpensively in the marketplace by looking at earnings to price and book to
price. It is an important source of performance and also one of the most important
sources of common factor risk.
+
+
Book to Price Ratio
Earnings to Price Ratio
Volatility — This risk index is a predictor of the volatility of a stock based on its historical price behavior.
+
Historical Sigma
Yield — This risk index measures the company’s current dividend yield.
+
Current Yield
Bluechip — This risk index equals 1 if the stock is currently a member of the top 100
stocks in the European Market by capitalization, and zero otherwise.
16
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weighted mean of zero and an equally
weighted standard deviation1 of 1.0 each
month.
Table 2
The Industry Categories Used in EUE1
Chemical
Basic resources
Media
Retail
Auto
Consumer Cyclical
Pharmaceutical
Food / Beverage
Consumer non-Cyclical
Energy
Banking
Insurance
Financial Services
Conglomerate
Construction
Industrial
Technology
Telecom
Utility
Table 3
The Countries Used in EUE1
Austria
Belgium
Denmark
Finland
France
Germany
Greece
Ireland
Italy
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
UK
We have chosen to use the Stoxx2 industry
classifications for the model. table 2 lists
the industry classifications and their cover-
Market Percentage by
Number of Share Issues
Market Percentage
by Capitalization
2.6
3.8
3.2
3.9
2.5
7.9
0.3
5.2
4.9
1.7
4.6
3.2
14.6
1.5
7.0
19.3
10.2
0.4
2.9
3.2
2.4
2.8
3.5
2.8
2.8
7.8
4.4
5.9
7.4
14.4
8.8
5.4
1.8
2.7
7.8
6.3
4.7
5.2
Market Percentage by
Number of Share Issues
Market Percentage
by Capitalization
2.0
2.0
4.7
1.1
6.9
8.9
6.1
0.6
5.3
3.6
2.7
2.0
2.2
6.8
6.5
38.6
0.5
2.3
1.4
1.1
11.8
13.2
0.6
0.7
5.6
7.8
1.1
0.8
3.6
4.5
10.1
35.0
1 The standard deviation is calculated around the cap-weighted mean not the equally-weighted mean. The
standardization is Europe-wide not country-by-country.
2 STOXX is a registered trademark of STOXX Ltd. a joint partnership between SBF- Bourse de Paris, Deutsche
Börse AG, Swiss Exchange SWX and Dow Jones & Company Inc.
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
17
age across the sixteen countries, both in
terms of number of issues and percentage
capitalization. The model also includes
country dummies for each of the sixteen
countries in the model. The countries are
listed in table 3 along with number of
issues and percentage capitalization in
each. The UK market is by far the largest by
either criterion.
Unlike the GEM, the EEM estimates all the
factor returns including the country factors
simultaneously, rather than estimating the
country factor returns first and then all
other factor returns on the first-stage residuals. The simultaneous presence of both
industry dummies and country dummies
creates a singularity in the matrix of independent variables. To adjust for this, we
impose a linear restriction on the country
factor returns. The weighted sum of country factor returns is constrained to equal
zero. The weight for each security is the
square root of its market capitalization.
Details are shown in the Appendix.
In our preliminary empirical work we
found that the industry factors estimated
Europe-wide fit poorly on the UK subset.
This lack of integration between UK and
continental equities cannot be attributed
solely to the UK’s opt-out from the single
currency. Sweden, Denmark, Norway and
Switzerland are not joining the single currency either and yet their equity returns are
well explained by the Europe-wide industry factor returns. It does however conform
to anecdotal and empirical findings that
UK equities behave distinctly differently
from continental equities.3 To account for
the lack of integration of UK and continental markets, we include a second set of
industry factor for the UK only. All continental4 stocks have zero exposure to the
UK industries and all UK stocks have zero
exposure to the continental industries.
The UK and continental industry dummies
(2 x 19 industries) plus sixteen country
dummies plus six risk index exposures
of all assets at time t constitute a 60 x nt
matrix Xt where nt is the number of assets
in the cross-section at time t. Let Rt denote
the nt vector of asset excess returns at time
t. The factor model regressions are performed using excess returns in local currency for each security. This means that the
factor returns are measured from a “fully
hedged” perspective. We estimate the 60vector of factor returns by cross-sectional
weighted least squares regression:
Rt = Xt Ft + et
(1)
Ft is the 60-vector of industry, country and
risk index factor returns and et is the ntvector of asset-specific returns.
table 4 shows the square-root-cap-weighted adjusted R2s for each of the cross-sectional regressions (1). The cross-sectional
regressions are run over the sixty-nine
month period April 1992 to December
1997. table 4 also shows the number of
country, industry, and risk index factors
that are significant each month. Since these
are risk factors, we do not expect them all
to have a significant effect on the cross-section of returns every month. Each month,
some of the factors have significant
returns. Each factor has a significant return
at least occasionally. The adjusted R2 of the
regression varies from 9.6% to 56.3% with
a time-series average of 30.2%. This means
that in a typical month, 30.2% of the
return to a typical stock comes from common return and the rest from asset-specific return. By the nature of a risk model, the
R2 varies widely between a low value in very
quiet months to a high value in months
with large market-wide moves. Note that
the proportion of factor return in a broadbased portfolio will be much higher than in
3 It is interesting to note that our fixed income research team has found a parallel result working independently.
As remarked by Goldberg (1998), when it comes to regional modeling of the European fixed income market
“the UK is an island.”
4 Including Ireland as a continental country.
18
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
Table 4
Date
Adjusted
R2
No. of sig.
country factors
(out of 16)
No. of sig. continental industry
factors (out of 19)
No. of sig. UK
industry factors
(out of 19)
No. of sig. risk
index factors
(out of 6)
1992-04
1992-05
1992-06
1992-07
1992-08
1992-09
1992-10
1992-11
1992-12
1993-01
1993-02
1993-03
1993-04
1993-05
1993-06
1993-07
1993-08
1993-09
1993-10
1993-11
1993-12
1994-01
1994-02
1994-03
1994-04
1994-05
1994-06
1994-07
1994-08
1994-09
1994-10
1994-11
1994-12
1995-01
1995-02
1995-03
1995-04
1995-05
1995-06
1995-07
1995-08
1995-09
1995-10
1995-11
1995-12
1996-01
1996-02
1996-03
1996-04
1996-05
1996-06
1996-07
1996-08
1996-09
1996-10
1996-11
1996-12
1997-01
1997-02
1997-03
1997-04
1997-05
1997-06
1997-07
1997-08
1997-09
1997-10
1997-11
1997-12
Average
49.9
14.7
54.5
56.3
50.6
41.3
42.0
37.8
26.7
28.2
36.7
24.5
25.3
20.4
22.4
36.4
46.7
19.5
40.7
20.0
52.7
50.8
27.9
43.0
33.1
40.8
36.9
40.0
31.5
49.0
17.7
12.7
11.9
28.9
12.5
36.1
34.1
29.2
16.2
28.2
9.6
18.3
19.8
19.7
15.1
31.3
14.1
16.2
37.0
10.7
14.2
32.4
27.6
19.8
12.3
32.6
18.6
46.5
31.3
14.7
20.2
26.1
37.5
45.1
42.4
45.0
45.2
18.3
36.6
30.2
11
8
9
9
12
13
9
8
11
9
10
12
11
11
11
12
12
12
11
10
9
11
7
8
11
11
11
10
9
10
12
9
9
10
9
14
12
9
9
11
5
8
12
8
6
9
9
8
9
7
10
11
11
6
7
10
7
8
9
7
8
5
11
11
10
12
8
8
9
9.58
15
6
16
16
15
5
7
7
10
5
14
8
6
7
16
14
15
13
15
5
16
16
15
13
5
16
16
15
9
16
4
9
1
14
5
12
16
16
5
16
4
5
5
8
10
15
4
7
14
8
7
14
16
14
4
13
14
15
12
3
10
15
16
16
16
16
16
11
11
11.14
15
5
17
19
18
9
7
6
11
8
15
12
9
7
17
18
15
15
18
7
16
17
15
11
12
17
18
17
7
15
9
5
4
16
6
7
18
16
5
13
8
5
13
11
10
15
5
8
11
5
6
15
15
12
7
12
12
16
15
8
8
17
18
17
18
18
18
9
12
12.12
4
3
4
4
4
4
4
4
5
6
4
3
4
3
3
3
5
3
3
2
4
3
2
1
2
5
2
5
1
2
3
2
2
3
2
4
3
0
3
2
3
2
2
4
3
1
4
2
3
2
3
2
3
4
3
2
3
3
1
3
4
4
3
3
5
2
4
2
3
3.03
Adjusted R-squareds
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
19
Table 5
Risk Factor
Individual factors: Percentage of
months significant and market betas
Size
Momentum
Value
Volatility
Yield
Bluechip
Chemical
Basic resources
Media
Retail
Auto
Consumer Cyclical
Pharmaceutical
Food / Beverage
Consumer non-Cyclical
Energy
Banking
Insurance
Financial Services
Conglomerate
Construction
Industrial
Technology
Telecom
Utility
Chemical – UK
Basic resources – UK
Media –UK
Retail – UK
Auto – UK
Consumer Cyclical – UK
Pharmaceutical –UK
Food / Beverage – UK
Consumer non-Cyclical – UK
Energy –UK
Banking – UK
Insurance – UK
Financial Services – UK
Conglomerate – UK
Construction – UK
Industrial – UK
Technology – UK
Telecom – UK
Utility – UK
Austria
Belgium
Denmark
Finland
France
Germany
Greece
Ireland
Italy
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
UK
20
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
Percentage of
Months Significant
65.2
69.6
30.4
71.0
31.9
34.8
63.8
79.7
62.3
66.7
63.8
71.0
55.1
66.7
76.8
62.3
79.7
76.8
69.6
68.1
73.9
78.3
71.0
72.5
68.1
53.6
53.6
62.3
60.9
55.1
65.2
60.9
72.5
65.2
60.9
72.5
65.2
73.9
46.4
71.0
75.4
69.6
60.9
66.7
44.9
52.2
46.4
65.2
72.5
66.7
78.3
29.0
87.0
47.8
56.5
44.9
68.1
60.9
58.0
79.7
Beta of factor returns
against market
T-stat
for Beta
0.39
-0.05
0.02
-0.13
-0.03
0.00
0.98
1.14
1.02
0.92
1.26
0.99
0.83
0.86
0.97
0.98
1.06
1.09
1.11
1.03
1.12
1.10
1.07
1.17
0.87
1.00
0.88
0.94
0.87
1.21
1.12
0.59
1.00
0.81
0.88
1.16
1.02
1.37
0.77
1.20
1.12
0.94
0.72
1.02
0.01
-0.01
-0.10
0.42
0.05
-0.08
-0.01
0.03
0.03
0.05
0.14
-0.03
0.19
0.04
-0.10
-0.05
8.49
-1.87
1.79
3.73
-2.55
0.03
16.16
12.73
14.97
12.92
12.07
16.58
10.50
18.53
17.54
13.24
17.48
14.04
21.15
14.86
18.92
19.87
18.18
7.25
13.06
11.04
7.66
11.03
12.86
9.04
15.90
3.77
13.97
10.07
9.48
9.80
9.64
19.20
7.18
11.48
20.62
12.28
5.54
6.39
0.10
-0.10
-1.18
2.22
0.75
-1.16
-0.04
0.28
0.15
0.69
1.21
-0.24
1.67
0.25
-1.42
-0.57
a typical stock, due to the effect of diversification on asset-specific return.
estimated using exponential smoothing
with a 48-month half-life.
table 5 shows the percentage of months
3. The Specific Risk Model
for which the t-statistic for each factor
return from the cross-sectional regression
(1) is significant. This indicates which factor returns are most frequently important
in explaining cross-sectional returns. All
six risk factors have good-to-excellent
explanatory power by this measure. The
same applies to the industry and country
factors. table 5 also shows the market
betas of each of the factors and t-statistics
for these betas. These measure the extent to
which the different risk factors have market
risk exposure or are purely extra-market
sources of risk. The size factor has a large
positive beta of 0.39. The betas of the country factors are generally near zero and often
negative. This reflects the presence of the
industry factors and the linear constraint
placed upon the country factors. The “general market move” is by construction
placed in the industry factors rather than in
the country factors.
The currency covariance matrix is constructed from a Euro-perspective using the
Deutschmark as historical proxy for the
Euro. The ten Euro In countries in the
model have zero currency volatility from
this perspective. The covariance matrix has
nonzero variances and covariances for the
other six currencies, those for Denmark,
Greece, Norway, Sweden, Switzerland and
the UK. There are also non-zero covariances of these currency returns with the 60
risk factors. The factor covariance matrix is
Table 6
Empirical Ratio for CapitalisationRanked Decile Portfolios
HORIZON · WINTER
1999
The specific risk model uses the standard
BARRA methodology. Let eit denote the
asset-specific return to security i in month
t from the factor model regressions. Let πit
denote the relative absolute specific return
of asset i in month t:
pit = (|eit| - St)/St
where St is the square-root-cap-weighted average of |eit|, i=1,...,nt, in month t. As
explanatory variables for πit we use a set of
descriptors which includes all the industry
and country dummies. Let Zit-1 denote the
vector of descriptors for asset i at time t-1.
We stack the time-series/cross-sectional
sample of πit and regress them against Zit-1:
pit = b¢Zit-1 + uit i=1,..nt t=1,...,T,
where b are the estimated regression coefficients and uit are the regression residuals.
St is forecast using an equally-weighted
moving average of the past six months’
realized St. The product of the one-monthahead forecasts for pit and St are the forecast absolute specific returns. The standard
BARRA technology is to scale these forecasts to make them specific risk forecasts by
multiplying them by the empirical ratio of
mean absolute specific return to standard
deviation of specific return. We found that
this ratio differs by capitalization class.
Decile
Empirical Ratio
1 (bottom 10% cap)
2
3
4
5
6
7
8
9
10 (top 10% cap)
1.466
1.396
1.400
1.346
1.308
1.318
1.321
1.283
1.261
1.277
THE
BARRA
NEWSLETTER
21
Table 7
Tilt
Total
Active
0.98
1.03
0.81
0.98
0.83
1.05
1.09
0.91
1.07
0.98
1.06
0.68
1.08
1.28
0.96
0.97
1.05
1.10
1.02
1.07
1.13
1.12
1.12
1.21
1.08
1.13
0.92
1.10
1.04
1.15
0.84
0.98
1.04
0.99
0.89
0.86
0.97
0.81
1.03
0.83
0.83
0.83
1.04
1.00
0.86
1.11
0.91
0.87
0.91
1.01
0.87
0.93
1.03
0.92
1.09
1.13
0.95
1.03
1.06
1.17
1.06
0.79
0.76
0.76
0.62
1.02
1.04
0.87
1.18
1.30
0.92
1.13
1.21
1.08
0.84
0.79
1.07
1.02
1.10
1.07
1.02
1.07
0.80
1.03
0.97
1.07
0.95
0.79
1.18
0.91
1.15
0.95
1.05
0.72
1.03
0.90
1.16
0.68
0.90
0.83
1.04
0.97
1.05
0.94
0.82
0.72
0.94
0.96
0.88
0.94
0.86
0.79
1.14
0.88
1.00
0.85
0.86
0.75
0.77
0.66
0.82
0.94
0.99
0.56
0.88
0.95
0.90
1.07
0.73
0.76
0.76
0.61
1.02
0.89
Bias Test Results
1-10th biggest
11-50th biggest
negative size
positive size
negative momentum
positive momentum
negative value
positive value
negative volatility
positive volatility
negative yield
positive yield
Bluechip
coind 1 : Chemicals
coind 2 : Basic Resources
coind 3 : Media
coind 4 : Retail
coind 5: Auto
coind 6: Consumer Cyclical
coind 7: Pharmaceutical
coind 8: Food Beverage
coind 9: Consumer Non Cyclical
coind 10: Energy
coind 11: Bank
coind 12: Insurance
coind 13: Financial Services
coind 14: Conglomerate
coind 15: Construction
coind 16: Industrial
coind 17: Technology
coind 18: Telecom
coind 19: Utility
ukind 1 : Chemicals
ukind 2 : Basic Resources
ukind 3 : Media
ukind 4 : Retail
ukind 5: Auto
ukind 6: Consumer Cyclical
ukind 7: Pharmaceutical
ukind 8: Food Beverage
ukind 9: Consumer Non Cyclical
ukind 10: Energy
ukind 11: Bank
ukind 12: Insurance
ukind 13: Financial Services
ukind 14: Conglomerate
ukind 15: Construction
ukind 16: Industrial
ukind 17: Technology
ukind 18: Telecom
ukind 19: Utility
country 1 : Austria
country 2 : Belgium
country 3 : Finland
country 4 : France
country 5: Germany
country 6: Ireland
country 7: Italy
country 8: Netherlands
country 9: Portugal
country 10: Spain
country 11: Denmark
country 12: Greece
country 13: Norway
country 14: Sweden
country 15: Switzerland
country 16: UK
22
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
table 6 shows the empirical ratio for capranked decile portfolios (each portfolio
contains 10% of total capitalisation).
To account for this, we divided securities
into those in the top 50% of total cap and
those in the bottom 50% and calculated the
ratio separately. The two ratios used in the
model are 1.3 for the top 50% of capitalization and 1.47 for the bottom 50%.
4. Risk Forecasting Performance of
the Model
The performance of the equity model is
tested by generating risk forecasts for a
variety of portfolios and then observing
whether the magnitude of realized returns
on the portfolios is consistent with the risk
forecasts. Define a standardized outcome as
the realized return on a portfolio divided
by its ex-ante predicted risk. If the risk
forecast is accurate, then the time series of
standardized outcomes should have a sample standard deviation close to 1.0.
table 7 shows the sample standard deviations of standardized outcomes for a variety of portfolios. For these tests, we use
fully hedged returns and all the portfolios
are cap-weighted. We use the fifty-six
month test period January 1994 to August
1998 for table 7.
The first portfolio consists of the top 10
stocks by capitalization, and the second
portfolio the next 40 (stocks 11 - 50). The
next 11 portfolios consist of all securities in
the top and bottom deciles (as percent of
Table 8
Statistic
capitalization) of exposure for each risk
index exposure. The exception to this rule
is the Blue Chip Membership risk index,
where we use a portfolio of all assets with
unit exposure. The next 38 portfolios consist of all stocks in each of the industries
(19 continental and 19 UK). The final sixteen portfolios consist of all securities in
each country.
The risk forecasting bias test is performed
for both total and active risk forecasts. The
active risks use the cap-weighted universe
portfolio as benchmark. The results are
generally excellent, with the test values
tightly clustered around 1.0.
5. Analysis of the Factor Model
Predicted Betas
The next two tables compare the performance of time-series estimated betas
(called historical betas) and betas estimated using the BARRA factor model (called
predicted betas).
Let STS denote the n x n time-series sample
covariance matrix of asset excess returns.
Let SFM denote the n x n covariance matrix
estimated from BARRA’s factor model. Let
m denote the n-vector of market portfolio
weights (the cap-weighted portfolio of all
stocks in the model). The linear algebraic
formulas for the n-vectors of historic and
predicted betas are:
bhistoric = (m¢STSm)-1 STSm
Historical Beta
Predicted Beta
Distribution of Market Betas
Mean
Standard Deviation
Skewness
Kurtosis
Range
Inter-quartile range
Maximum
Upper Quartile
Median
Lower Quartile
Minimum
HORIZON · WINTER
1999
0.680
0.537
0.0134
1.662
7.467
0.708
4.020
1.028
0.675
0.320
-3.447
THE
0.716
0.241
0.071
0.293
1.806
0.312
1.684
0.871
0.715
0.558
-0.123
BARRA
NEWSLETTER
23
Table 9
Panel A: Bottom 10 Securities Sorted by Historical Beta
Rank
1
2
3
4
5
6
7
8
9
10
BARRA-ID
SWIAJE1
UKIFFG1
SWIAGY2
SWIAAH2
GREACO1
SWIANG1
SWIANC2
UKIFFD1
SWIAFK2
DENAGL1
Name
CI COM B
DRUID GROUP
OMNIUM GENEVE B 500
ASCOM HOLDING R100
ASPIS PRONIA GEN I GR
HELVETIA PATRIA N
BON APPETIT N
THISTLE HOTELS
ZEHNDER HOLDING PC
NATIONAL INDUSTRI -B
HBeta
-3.450
-1.500
-1.226
-1.220
-1.180
-1.160
-1.044
-1.022
-0.973
-0.953
PredBeta
0.310
0.768
0.210
-0.013
1.164
0.731
0.481
0.822
0.359
0.562
Panel B: Top 10 Securities Sorted by Historical Beta
Rank
1
2
3
4
5
6
7
8
9
10
BARRA-ID
NETAKI1
GERAEI2
FRACOR1
GERADK1
SWIAKC3
GREAGE2
NORABD1
BELAEL2
NETAHA1
SPAABW1
Name
ASM LITHOGRAPHY HL NL
GLUNZ STA
CIPE FRANCE
DT. BABCOCK STA
MBO-BAHN N
AEGEK SA PRF GRD600
NCL HOLDING
TUBIZE –B
VERTO
HORNOS IBERICOS AL
HBeta
4.020
2.616
2.593
2.591
2.520
2.423
2.314
2.289
2.282
2.215
PredBeta
1.212
0.799
0.932
0.852
0.614
0.641
1.000
0.868
0.458
1.076
Panel C: Bottom 10 Securities Sorted by Predicted Beta
Rank
1
2
3
4
5
6
7
8
9
10
BARRA-ID
SWIAKE2
SWIAKE1
SWIAHH1
SWIAHS2
SWIAHH3
GERAEP1
SWIAHS1
GREADX2
SWIAJY1
SWIAHH2
Name
NAVIGAT. LAC LEMAN B
NAVIGAT. LAC LEMAN
GARES FRIGORIFIQ. B100
VILLARS HOLDING R
GARES FRIGORIFIQ. PC
HAMBURGER GETR. VZA
VILLARS HOLDING B
VIAMYL (PREF)
LET HOLD. LEYSIN R
GARES FRIGORIFIQ. B20
HBeta
0.046
-0.141
-0.223
0.591
-0.359
0.205
0.587
0.011
0.939
-1.220
PredBeta
-0.121
-0.089
-0.084
-0.079
-0.074
-0.058
-0.028
-0.019
-0.014
-0.013
Panel D: Top 10 Securities Sorted by Predicted Beta
Rank
1
2
3
4
5
6
7
8
9
10
24
HORIZON · WINTER
1999
THE
BARRA
BARRA-ID
FINAAL4
FINAAL1
ITAADK1
ITAACY1
ITAAKJ2
ITAADK3
SPAACN1
FINAAS2
GERACM1
FINAAO2
NEWSLETTER
Name
NOKIA (AB) OY SER’A’F
NOKIA (AB) OY SER’K’F
FIAT
TELECOM ITALIA SPA
TELECOM ITAL MOBILE
FIAT PTC PREF
TELEFONICA SA (ESP500)
MERITA A
DAIMLER BENZ
UPM-KYMMENE CORP FIM1
HBeta
1.579
1.575
1.247
1.604
1.137
1.595
1.388
1.189
1.705
1.710
PredBeta
1.694
1.584
1.565
1.493
1.437
1.425
1.418
1.411
1.410
1.409
bpredicted = (m¢SFMm)-1 SFMm.
performance.
table 8 shows the cross-sectional distrib-
Appendix
ution statistics for the historic and predicted betas for December 1997. Note the toowide range for the historic betas. It is not
credible that any European equities have
betas as low as -3.447 or as high as 4.02.
This shows the weakness of historic betas they tend to have large measurement
errors. The predicted betas all lie in a more
reasonable interval: a maximum of 1.684
and a minimum of -0.123. table 9 sorts
securities using each type of beta and displays the top ten and bottom ten securities
with their associated betas.
6. Conclusion
The European Equity Model is an innovation for BARRA in that it takes a regional
rather than global or single-country perspective in modeling equity returns. It was
developed in response to the integration
movement in western Europe, in particular
the Economic and Monetary Union
(EMU) program of the European Union,
and the growing empirical evidence for
equity market integration in the region.
The development of the model is partly
motivated by the adoption of a single currency in eleven European countries.
However, we find that the single-currency
component of EMU is not definitive in
terms of European capital market integration. Some countries which are not joining
the currency are well integrated into the
regional capital market. For this reason, we
include all the Outs in the model’s estimation universe. A significantly lower level of
integration than the continental markets
distinguishes the UK equity market, which
is why we include separate industry factors
for the UK.
The model has very good fit both in terms
of explanatory power and risk forecasting
HORIZON · WINTER
1999
The Linear Constraints on Country and
Industry Factors
The factor model includes 16 country
dummies and 38 industry dummies. Each
asset has a unit exposure to one country
dummy and one industry dummy, and this
creates a singularity in the matrix of independent variables. To see the problem intuitively, consider adding 10% (or any arbitrary amount) to each of the 16 country
factor returns, and subtracting the same
amount from each of the 38 industry factor
returns. Since every asset has unit exposure
to exactly one industry factor and one
country factor, every asset has 10% added
and 10% subtracted from its explained
return - leaving every asset’s explained
return unchanged. We can, therefore, make
these arbitrary changes without affecting
the fit of the model - that is the nature of an
indeterminacy. We need to put a constraint
on the factor returns to “identify” them,
that is, to properly separate the country
factor returns from the industry factor
returns.
We resolve the indeterminacy by placing a
linear constraint on the country factor
returns. The weighted average country factor return is constrained to equal zero. We
use the square root of equity capitalization
of each security as weights. The linear constraint is therefore:
16
n
 Â(CAPi )1/2 d ijc f jc = 0
j =1i =1
(A1)
where CAPi is the market capitalization of
security i, dijc equals 1 if security i is in
country j and zero otherwise, fjc is country
factor return j, and n is the number of securities in the model.
If the model had only one set of industry
THE
BARRA
NEWSLETTER
25
factors then (A1) would fully resolve the
indeterminacy. However the presence of
two full sets of industry factors, one for the
UK and one for all other countries, means
that (A1) alone is not enough. We need to
ensure that the UK and continental industry factor returns capture the same overall
market move, so that the constraint (A1) is
binding. To do this, we constrain the
weighted sum of the differences between
the UK and continental industry factors to
equal zero:
19
n
UK + d Con )( f UK - f Con ) = 0
 Â(CAPi )1/2 (d ih
ih
h
h
h=1i =1
(A2)
where dihUK equals 1 if security i is in UK
industry h and zero otherwise, fhUK is UK
industry factor return h, and dihCon, fhCon are
defined the same for continental industries.
References
26
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
Beckers, Stan, Gregory Connor and Ross
Curds (1996) “National versus Global
Influences on Equity Returns,” Financial
Analysts Journal, vol. 52, no. 2, 31-39.
Chaumeton, Lucie, Gregory Connor and
Ross Curds (1996) “A Global Stock and
Bond Model,” Financial Analysts Journal,
vol. 52, no. 6, 65-74.
Freimann, Eckhard (1998) “Economic
Integration and Country Allocation in
Europe,” Financial Analysts Journal, vol. 54,
no. 5, 32-41.
Goldberg, Lisa (1998) “European Bond and
Currency Markets: Post EMU,” presentation at the Institute of Investment Research
Conference The Impact of the Euro on U.S.
Markets, New York City, September 25th,
1998.
Heston, Steven L. and K. Geert
Rouwenhorst (1994) “Does Industrial
Structure Explain the Benefits of
BARRA Announces New Managing Director of Research
S
P
E
C
I
A
L
A
N
A strong commitment to excellence in
quantitative research and analysis has
always been at the core of BARRA’s business. Since the departure of Ron Kahn, we
have searched for a replacement who
would strengthen our commitment, and
maintain a focus on investment issues of
practical concern. During this search, I
have acted as the company’s head of
Research. Now, I am very pleased to
announce that we have appointed Nicolo
Torre as BARRA’s new managing director
of Research.
N
O
U
N
C
E
M
E
N
Nicolo joined BARRA in 1990 after earning a Ph.D. from the University of
California at Berkeley. Initially Nicolo
worked primarily on client consulting projects, and in 1993 was appointed manager
of Special Projects. In this role, he conducted a range of advanced research projects for both the equity and fixed income
departments at BARRA, which included
leading the effort to adapt the US equity
model to the modern post-industrial econ-
omy. Nicolo was also involved in analyzing
the role of Treasury Inflation Protection
Securities (TIPS) in strategic asset allocation strategies, where he was able to assess
the risk characteristics of a novel asset class
which had no track history. Most recently,
Nicolo has led the effort to develop
BARRA’s Market Impact Model, which
provides a forecast of transaction costs
prior to trading. The range and scope of
these projects amply illustrate the depth
and creative insight which Nicolo has
brought to BARRA's research. He has a
clear appreciation of our clients’ viewpoint, and insight into how BARRA technology is practically applied.
Nicolo inherits a world-class research
team that draws on more than twenty
years of investment research experience.
Together they will continue to offer seasoned, innovative and practical insights
into the investment problems facing institutional investors. ■
T
Sincerely,
Andrew Rudd
Chairman and Chief Executive Officer
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
27
The BARRA Brainteaser: A Truly Global Market
by Mark J. Ferrari
B
Problem
R
A
I
N
T
E
A
S
E
You may send solutions to the
BARRA Brainteaser to Mark Ferrari.
E-mail: [email protected];
fax: 510.548.4374; mail: BARRA,
2100 Milvia Street, Berkeley, CA
94704-1333, United States.
Consider the post of Dealer A, who is sending out his robots in random directions in
search of counterparties. Because the other
dealers’ posts are small (for the purposes of
this problem you may assume they are
geometric points), the robots risk circumnavigating the planet many times before
blundering into one. Accordingly, they are
programmed with the following rule - the
post closest to the robot must at all times
be either Dealer A (its origin) or the post at
which it will arrive if it continues without
turning, which we will call Dealer B. If the
robot detects a third post (Dealer C) which
is closer than either of these - call this event
Mark J. Ferrari is the senior
manager of investment
strategies in the Research
group, Berkeley.
Paul Jung (cartoon artist)
is a consultant in the
Research group, Berkeley.
28
HORIZON · WINTER
R
The trading community is buzzing with the
rumor that the upcoming Star Wars movie
will offer a glimpse of the capital markets
that finance the Galactic Empire’s expansion. One scene reportedly takes place on
the floor of the Imperial Stock Exchange
(ISE), an oceanless planet whose entire surface has been covered with sturdy blue carpeting and fluorescent lighting. Scattered
randomly on the surface of this planet are
outposts of the galaxy’s various securities
firms which function as dealers; there are
no specialists on the ISE. Due to the complete lack of natural topography, any location on the planet is equally likely to be the
site of a dealer’s post. Dealers trade with
each other by dispatching order-carrying
robots. Trading electronically would be
much more efficient, but that would leave
the Hollywood special effects wizards with
little to depict.
1999
THE
BARRA
NEWSLETTER
a close encounter - it returns home to
Dealer A, registers Dealer B as an unacceptable destination to prevent other robots
from wasting their time on it, and sets off
for Dealer C. The effect of this rule is that
one dealer will trade with another if and
only if a robot traveling directly between
them would never find itself closer to a
third dealer than to the closer of the two.
Each dealer trades with several other dealers, the exact number of which depends on
how the posts happen to be arranged in his
neighborhood. If the posts are randomly
and independently situated, what is the
average number of counterparties with
whom each dealer trades? You may assume
that the average distance between dealers is
much smaller than the size of the planet, so
that the curvature of the planet may be
neglected. In other words, a flat map is an
adequate representation of any part of the
globe.
Bonus Questions
1. Imagine that Dealer A finds he has too
few counterparties to effectively work his
trades. He reprograms his robots so that
they ignore the first close encounter but
turn back upon the second. What happens
to his expected number of counterparties?
What if he allows his robots to ignore two
close encounters?
2. If trading took place in a three-dimensional space rather than on a two-dimensional
planetary surface, what would happen to the
expected number of counterparties? ■
Brainteaser from Fall 1998
by Eugene Reznik
Eugene Reznik is a consultant in BARRA’s Enterprise
Risk Management group in
Westborough, MA.
On the CBOE exchange, stock prices move
by exactly one tick from one trade to the
next, with a 50% probability of moving
either up or down. On average, after how
many trades will a stock on the CBOE
exchange have traded at N different levels
after opening? How is the answer affected if
the probabilities of the up and down moves
are p and q respectively?
Brainteaser Solution
by Eugene Reznik and Nick Baturin
Nick Baturin is a consultant
in the Research group,
Berkeley.
Let t(N) denote the expected number
of trades it takes for the stock to trade
at N distinct levels. The stock always
opens at some level and so t(1) = 0. Since
it always takes one trade to get to a
new level t(2) = 1. We can try to find a
recursive solution of the form t(N) =
F(t(N-1)).
Let the state (N,k) denote a situation in
which the stock has traded at N distinct
price levels (numbered 1 through N from
lowest to highest) and is currently at level
number k. Also, let M(N,k) be the time it
takes for the stock to reach a new high or
low starting from the state (N,k).
Now M(N,k) satisfies the following difference equation:
M(N , k) = 1 + pM(N , k + 1) + qM(N , k - 1) (1)
with boundary conditions
M(N , 0) = M(N , N + 1) = 0
(2)
The solution to equation (1) with bound-
ary conditions (2) is:
M(N , k) =
(1 - (q / p)k )( N + 1)
1
{k }
(q - p)
1 - (q / p)N +1
In the special case where p = q = 1/2, equation (1) with boundary conditions (2) is
solved by M(N,k) = k(N+1-k). Thus,
M(N,1) = M(N,N) = N. This implies that
t(N) = t(N-1) + (N-1) = (N-1)N/2 and we
have the answer to the first part of the
problem. Note that in the general case, the
formula is not symmetric, i.e., M(N,1) ≠
M(N,N). The solutions to (1) and (2)
above are derived from Feller1.
In the general case, we can say that:
t(N+1) = t(N) +
(1-H(N))M(N,1)
H(N)M(N,N)
+
where H(N) is the probability of being in
the state (N,N) conditioned on having just
covered a new level. In order to calculate
H(N) let’s define h(N,k) as the probability
of the stock price reaching a new high from
the state (N,k) before reaching a new low.
1 W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 1970.
HORIZON · WINTER
1999
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NEWSLETTER
29
Like M(N,k), h(N,k) satisfies a simple
difference equation:
(
h N,k
) = p h(N, k+1) + q h(N, k-1)
(3)
( ) = H(N-1) h(N-1,N-1) +
(1-H(N-1)) h(N-1,1)
H N
with boundary conditions
(
) = 0; h(N,N+1) = 1
h N,0
We can solve (3) and (4) to obtain
h(N , k) =
1 - (q / p)k
1 - (q / p)N +1
Figure 1
Number of trades required to cover N
different levels as a function of N and
probability of an up move p.
30
HORIZON · WINTER
1999
THE
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NEWSLETTER
To find H(N), note that H(2) = h(1,1) = p.
Note also that H(N) can be expressed
in terms of H(N-1), h(N-1,1) and
h(N-1,N) as:
(4)
This completes the solution as we now have
all the necessary pieces to recursively calculate t(N). figure 1 contains a plot of t
as a function of N and p. We can see that
t(N) = N(N-1)/2 in the special case where
p=1/2 and that t(N) = N-1 in the case
where p = 1. ■
Volatile Markets and BARRA Models
by Neil Gilfedder and Kenneth Hui
E
Neil Gilfedder is a
Q
consultant in BARRA’s
U
Equity Sales and Client
Relations group.
I
T
Y
Kenneth Hui is senior
manager in the Equity
A
Models Research group.
N
A
L
Y
T
I
C
S
The U.S. equity markets were sharply negative in August, 1998. That, perhaps, is the
bad news. The good news is that BARRA’s
US E-3 model performed remarkably well.
In this article, we will assess the scale of
August’s market movement, and then look
at how well the US E-3 model explained,
forecast, and reacted to it.
How unusual was August? The graph below
illustrates the distribution of monthly total
returns of the S&P 500 from January, 1973
through September, 1998. Over that period, the mean monthly return was 1.00%,
and the standard deviation was 4.47%. As a
result, August’s return of -14.4% was a 3.2standard-deviation (or 3.2-sigma) event.
The graph also shows that there have been
four 3-standard-deviation events since
1973. In other words, 3-sigma events
occurred 1.3% of the time during the 309month period considered.
If the S&P 500’s total returns followed a
normal distribution, we’d expect to see 3sigma events occurring 0.26% of the time.
The returns, in fact, are somewhat “fattailed” (or have positive kurtosis), implying
that big events occur more frequently than
they would under a normal distribution.
Active returns, however, do tend to follow a
normal distribution.
Given that August was a significant and
unusual month, how did the model do at
explaining its market movement? The
model uses 65 common factors (13 risk
indices and 52 industries) to explain asset
returns. The proportion of variance in
return explained by the variance in the common factors is measured by the R-squared.
In August, the R-squared was 80%, compared with a historical average of 32.8%.
The R-squared will tend to be higher when
there is major market movement, because
figure 1:
S&P 500 Returns, 1973-1998
HORIZON · WINTER
1999
THE
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NEWSLETTER
31
figure 2:
Factor Returns vs Beta, August 1998
the co-movement of stocks will dominate
the movement of stocks relative to other
stocks, and this co-movement is largely
explained by the model’s common factors.
The high R-squared is nevertheless an indication that the model’s factors provide a
good ex-post explanation of August’s events.
The predicted betas also performed well.
Predicted beta is a measure of the degree to
which assets co-vary with the market.
Assets with higher betas should decline
more when the market declines. In August,
this happened: the higher-beta risk indices
and industries had larger negative returns
than did lower-beta factors. This is illustrated in the following graph.
Finally, how unexpected was August’s market-movement? And how did the model
react? The model’s forecast of the S&P
500’s volatility is based on an extended
GARCH time-series regression. This
methodology results in a model that
responds quickly to large events in the
market. Hence, the forecasts better reflect
the historical observation that markets
tend to become more volatile after large
32
HORIZON · WINTER
1999
THE
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NEWSLETTER
downturns and less volatile after large
upturns. Going into August, the predicted
volatility was 14.76%. In other words, the
return was predicted to be in the range of ±
14.76% per year (or ± 4.26% per month)
with approximately a two-thirds probability. After August, the forecast volatility rose
to 17.33% in response to the downturn,
exhibiting the responsiveness of GARCH
models. As the markets became less turbulent in subsequent months, the forecast
volatility fell. Going into January, 1999, the
predicted volatility of the S&P 500 was
13.95%
Large-scale market movements are difficult
to predict, but investors who use BARRA’s
U.S. equity risk model have an advantage.
The model’s powerful common factors,
which explain much of the movement,
enable those investors to expose themselves
only to risks similar to their benchmark’s,
and hence, not to stray far from the benchmark’s returns. In addition, the model is
quick to react to changes in the market,
thus allowing investors to react swiftly and
take altered market conditions into
account. ■
Part I: The Case for Market Neutral
by Jason Lejonvarn and Claes Lekander
Next Issue: Part II: The Mechanics of Market Neutral in the BARRA Aegis System™ Suite
M
A
Jason Lejonvarn is a
product manager in the
R
Institutional Analytics
K
group in Berkeley.
E
T
Claes Lekander is a senior
managing director in the
N
Institutional Analytics
E
group in Berkeley.
U
T
R
A
L
The well-publicized reversal of fortune suffered by several prominent hedge funds has
moved many to fear any investment strategy that advertises the word “hedge.” Not all
hedge strategies deserve such a stigma.
Two recent examples highlight why
investors should understand the nuances
of and distinctions between different
hedge strategies. An article on Long-Term
Capital stated, “These bets required the
strategists to buy one thing and sell short
another, so that they maintained a Swisslike neutrality to the market.”1 In 1996,
David Shaw pointed out that his firm’s
proprietary strategies were “market neutral, meaning the goal is finding these little
profit pockets without actually betting on
the direction of the market.”2 Executives at
Bank of America may to this day be asking
themselves, “Was D.E. Shaw really market
neutral?”
This article discusses the merits of market
neutral hedge strategies, particularly as
they are practiced by institutional portfolio
managers.
Definitions
A hedge strategy involves the inclusion of
both long and short positions in a portfolio. The short positions allow the manager
to achieve leverage, which can also be
achieved through the use of derivatives.
Leverage is an absolute exposure to risky
assets which is greater than 100% of invested capital. A strategy’s leverage can be
expressed as a ratio; for example, a strategy
that is long two dollars and short one dollar for every dollar of invested capital has a
leverage of 3:1.
A market neutral hedge strategy takes
long and short positions in such a way that
the impact of the overall market is minimized. Market neutral can imply dollar
neutral, beta neutral or both. A dollar neutral strategy has zero net investment (i.e.,
equal dollar amounts in long and short
positions).
A beta neutral strategy targets a zero total
portfolio beta (i.e., the beta of the long side
equals the beta of the short side). Does dollar neutrality alone make a fund market
neutral? While dollar neutrality has the
virtue of simplicity, beta neutrality better
defines a strategy uncorrelated with the
market return.
To refer to hedge funds as a group is not
instructive since they do not conform to a
single definition. However, institutional
market neutral managers implement a
more or less standardized hedge strategy
that is often dollar and beta neutral with a
fixed 2:1 leverage. This strategy, for the
1 Michael Lewis, “How the Eggheads Cracked.” New York Times, January 24, 1999.
2 James Aley, “Wall Street’s King Quant,” Fortune, February 5, 1996.
HORIZON · WINTER
1999
THE
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NEWSLETTER
33
purposes of this article, will be referred to
as institutional market neutral.
Basic Theory
A review of portfolio theory further illustrates the differences between dollar neutral and beta neutral strategies. It also
emphasizes the theoretical underpinnings
of the market neutral approach and
describes its inherent advantages.
Notation:
r excess return
a residual return
m market return
h absolute fraction of invested capital
l
the long portfolio
s the short portfolio
p the total portfolio or l + s
In the general context of a hedge strategy,
equation 1 defines excess return. equation 2 separates out market related return
and residual return.
Graph 1
(1) rp = hl rl + hs rs
(2) rp = hl (bl m + al ) + hs(-bs m + as )
Correlation (al, as) and Risk
In the case of a dollar neutral strategy,
equation 1 can be reduced to equation
3. A dollar neutral strategy that fixes leverage at 2:1 is defined by equation 4.
(3) rp = hl (rl + rs)
(4) rp = (rl + rs)
The excess return of a beta neutral strategy
is given by equation 5. The condition bl =
-bs neutralizes the effect of the market,
leaving only residual returns. equation 6
defines a strategy that is both dollar and
beta neutral. Finally, if a strategy also
employs a fixed 2:1 leverage, as in the institutional market neutral strategy, then the
portfolio’s excess return can be expressed
by equation 7.
(5) rp = hl al + hs as
(6) rp = hl (al + as)
(7) rp = al + as
3 Assume h = h or dollar neutrality and s = s .
l
s
a1
as
34
HORIZON · WINTER
1999
THE
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NEWSLETTER
equation 7 is the “double-alpha” argument that institutional market neutral
managers frequently use to promote their
strategy. equation 8 extends equation
7 to the residual risk dimension. The more
general formula for the risk of hedge strategies is given by equation 9.
(8) sp = ( sa l2 + sas2 + 2 sa1sas ra1, as)1/2
(9) sp = (hl2 srl2 + hs2 srs2 + 2hl hs sr l, r s)1/2
Portfolio theory reinforces how one can
reduce risk by taking advantage of low
correlations among assets’ returns. In this
regard, the market neutral portfolio is similar to any other portfolio. What makes it
unique is the opportunity to exploit the
correlation between the longs and shorts.
This diversification benefit for the institutional market neutral manager is depicted
in graph 1.3 If the correlation ral, as is less
than 1, then the increase in residual risk is
less than the increase in residual return.
equation 10, by combining equation 7
and 8, defines the information ratio, IR, for
an institutional market neutral manager.
(10) IRp = E[ (al + as) ] / (sa12 + sas2 + 2
sa1sasra1, as)1/2
If E[al] = E[as] and sa1 = sas, then equation 11 demonstrates the improvement in
IR with the addition of the short side.
(11) IRp = IRl { 2 / (1 + ra1, as)}1/2
An institutional market neutral portfolio
with a high residual correlation between the
longs and shorts (ra1, as = 1) attains double
the return (al + as), but also double the risk
(2s). On the other hand, if the manager can
construct long and short portfolios with
uncorrelated residual returns (ra1, as = 0), as
illustrated in graph 1, then the return is
double but the risk increases by 1.4 ( 2 s).
Consequently, the effectiveness of the institutional market neutral strategy improves
by approximately 40%, as expressed in
equation 11.
Efficient Frontier Analysis
A picture is worth more than 11 equations.
graph 2 makes a succinct theoretical case
for market neutral by plotting three ex-ante
residual efficient frontiers:
Long =
Traditional long-only strategy
M/N =
Market neutral strategy with
unconstrained leverage
M/N (2:1) = Market neutral strategy
with leverage 2:1
All three strategies use the same information set. Random alphas for all stocks in the
S&P 500 were fed to the BARRA optimizer.
The area under each frontier represents
each strategy’s opportunity set. At low risk
levels, the frontiers are almost indistinguishable from one another. For example, a
market neutral fund with a risk of 1% does
not do much better than a long-only portfolio with the same risk.
For a risk level above 1%, the opportunity
set of the long-only strategy becomes
increasingly inferior to those of the market
neutral strategies. Beyond the 4% risk level,
the market neutral strategy with leverage of
2:1 starts to lose ground to its sibling with
unconstrained leverage.
How can one explain the divergence
between the efficient frontiers? The answer
lies in the strategies’ implicit constraints. As
is suggested by its name, a long-only portfolio consists only of long positions (and by
extension, has no leverage). The manager
therefore cannot take full advantage of
negative information. The most a longonly manager can under-weight a stock is
the stock’s weight in the benchmark. Even
worse, if the stock is not in the benchmark,
it cannot be under-weighted. In a low risk
strategy, which tends to hold the portfolio’s
weights close to those of the benchmark,
the efficiency loss is not great because the
optimal solution is largely unaffected by
the implicit lower asset bounds. For aggressive portfolios, however, the loss can be
substantial, as the efficient frontiers show.
With no implicit lower bound on asset
holdings, the market neutral manager can
fully exploit negative information and
more efficiently diversify risk. In the
unconstrained case (i.e. M/N), the highest
attainable information ratio can be infinitely leveraged with no change in the
composition of the portfolio. Therefore,
the straight-line frontier defines the upper
limit of all opportunity sets.
If leverage is constrained (i.e. M/N (2:1)),
then the market neutral manager cannot
maintain the same information ratio for all
levels of risk. At the point where maximum
leverage is reached, the optimizer can
increase expected return only by changing
Graph 2
Ex-Ante Risk/Return Frontier
HORIZON · WINTER
1999
THE
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35
the composition of the portfolio, which is
less efficient than leverage.
the managers must also estimate the
covariance matrix.
This theoretical efficient frontier analysis
supports market neutral strategies at intermediate and high levels of risk. In fact, the
analysis endorses leverage for aggressive
strategies. But recent hedge fund losses
highlight an important caveat — hedge
managers should ensure that their risks are
accurately measured and consistent with
the investor’s risk tolerance.
At the start of each simulation, 20 months
of data is available to estimate the required
parameters. Over the course of the simulation, the estimation errors gradually decline
as a longer history becomes available.
Monte Carlo
Theory is a good starting point, but does
the case for market neutral hold up in the
real world? While a Monte Carlo simulation does not entirely answer this question,
it does provide a significant intermediate
step between theory and practice.
A Monte Carlo study was done to compare
the performance of four strategies: institutional market neutral, long-only conservative, long-only moderate, and long-only
aggressive.4 Each strategy is emulated by
100 managers, all operating in the same
environment. The effectiveness of each
strategy is measured by the average “realized” residual information ratio.
In this study, optimal portfolios are formed
on a monthly basis given a set of alphas and
a covariance matrix, without controlling
for turnover or transaction costs. In the
first set of simulations, the managers know
the covariance matrix and need only to
estimate an IC for each asset. In the second,
Table 2
After 5 Years
Average Simulated Performance:
Estimation Error on IC
s
IR
Each manager’s signals (raw forecasts) are
drawn from a normal distribution ~N[0,1]
and are uncorrelated by design. Each manager possesses a different information coefficient (correlation between signal and
actual return) that is drawn from a uniform
distribution with a range of [0, .2] and a
mean of 0.105 for each asset. To produce
alphas, the manager scales the signals using
the fundamental law of active management.5
Results of the first set of simulations, presented in table 2, show that the institutional market neutral strategy comfortably
beats all three long-only strategies in the
case where the covariance matrix is known.
The risk levels chosen to define the strategies are shown in addition to the information ratios. While all strategies improve as
the simulation period is extended, their relative performance remains largely the
same. Notice that for the long strategies,
there is a strong inverse relationship
between the risk level and the information
ratio. This finding is consistent with the
preceding efficient frontier analysis.
table 3 shows the results of the second set
of simulations, where both IC and risk are
After 10 Years
After 20 Years
s
s
IR
IR
Inst. Market-Neutral
5.54 %
2.08
5.54 %
2.22
5.54 %
2.29
Long-Only Conservative
0.66 %
1.87
0.66 %
1.97
0.66 %
2.03
Long-Only Moderate
2.32 %
1.39
2.32 %
1.45
2.32 %
1.47
Long-Only Aggressive
8.80 %
0.42
8.80 %
0.48
8.80 %
0.52
4 Stan Beckers, “Manager Skill and Investment Performance: How Strong is the Link?,” presented at BARRA’s
European Research Seminar in 1997.
36
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
Table 3
After 5 Years
Average Simulated Performance:
Estimation Error on IC and s
s
IR
s
After 20 Years
s
IR
IR
Inst. Market-Neutral
8.92 %
1.34
7.34 %
1.65
6.46 %
1.96
Long Conservative
0.78 %
1.5
0.72 %
1.68
0.69 %
1.89
Long Moderate
2.48 %
1.2
2.39 %
1.31
2.38 %
1.45
Long Aggressive
8.34 %
0.45
8.69 %
0.48
8.75 %
0.53
unknown and must be estimated. Note that
the presence of estimation error on risk
impacts alphas as well as risk because
volatility is used in the scaling of the raw
signals. This scenario more closely emulates the realities of portfolio construction.
The introduction of estimation error on risk
impacts the market neutral strategy more
negatively than the long-only strategies. The
long-only conservative strategy outperforms
the market neutral strategy after 5 years, but
after 20 years, the risk estimation error is
sufficiently reduced that market neutral is
again the superior strategy. These results
reinforce the notion that market neutral
investing is difficult to justify at low levels of
risk but clearly outperforms when compared to aggressive long-only strategies.
Empirical Study
Ideally, the merits of a portfolio strategy
could be entirely defined by observed performance. Unfortunately performance data
can contain many biases, such as sample
bias, time period bias, and survivorship
bias. Furthermore, the short statistical history of investment funds and the nuances
between investment techniques often prevent the statistically significant identification of a superior strategy. Despite these
caveats, empirical comparisons can be
instructive, especially in light of the strong
theoretical arguments for market neutral.
5
After 10 Years
A study that compares the realized information ratios of institutional market neutral managers to several hundred institutional and mutual fund managers who represent long-only strategies is summarized
in table 4.6 The market neutral strategy is
represented by fourteen BARRA clients
who provided their performance histories.
In this study, the market neutral managers
out performed institutional and mutual
fund managers. Focusing on the skillful
managers, as represented by those in the
90th and 75th percentiles, the market neutral strategy shows a markedly superior IR
to both institutional and mutual fund
managers.
This performance gap could be due to sample and selection biases, but for two reasons, it is not a surprising result. First, the
inherent advantages of institutional market
neutral strategies, other things equal
(including skill), imply that they should do
better than long-only strategies. Second,
for its inherent advantages, skillful managers should gravitate toward market neutral strategies. Consequently, the skill level
of market neutral managers becomes higher than that of long-only managers.
This empirical comparison lends credence
to market neutral strategies and builds on
the already compelling theoretical case for
market neutral strategies.
ai = (signal)i (information coefficient)manager (volatility)i . See R. Grinold and R. Kahn, Active Portfolio
Management, 1995.
6 Andrew Rudd and Ron Kahn, “What’s the Market for Market Neutral,” presented at BARRA’s 1997 Research
Seminar. The study includes US equity funds only.
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
37
Drawbacks and Limitations
Market neutral strategies have steadily
increased in popularity over the past
decade.8 But surely there must be some
potential pitfalls otherwise every active
manager would be market neutral. Here are
some common arguments against market
neutral investing.
Transaction costs To maintain market
neutrality, frequent re-balancing is necessary as differential returns between the
long and short sides create an imbalance.
The “up-tick” rule also adds to the transaction cost on the short side. In addition, a
futures overlay (to regain a desired market
exposure) creates an additional source of
transaction cost that is incurred when contracts have to be rolled over.
Liquidity The short side of the market
contains a potential shortage of liquidity.
Every stock is not available to short. If a
stock is available, the quantity one can
obtain may be limited. The capacity of a
long-short strategy is clearly constrained
for this reason.
Unlimited downside risk The strategy can
conceivably lose more than its invested
capital, as proved recently by some hedge
funds. For strategies with fixed leverage,
beta neutrality and sound diversification,
this risk is not of practical significance.
Risk measurement As demonstrated in
the Monte Carlo study, optimized market
Table 4
Percentile
Realized information ratios
for different investment strategies.
14 MarketNeutral
1/90-12/90
neutral strategies tend to exploit estimation errors in risk forecasts. If the estimation errors are large, the true risk of the
portfolio could be substantially underestimated. The same bias could be present
even if an optimizer is not used, as long as
risk was a consideration in the portfolio
construction process.
Capacity to absorb capital If a market neutral fund doubles its capital, the fund may
accept large positions in thinly traded assets,
positions in assets with lower absolute
alphas or return the capital to investors for
lack of opportunities. If a long-only fund
doubles its capital, the fund may double its
positions and, purposely or inadvertently,
increase exposure to the market.
Conclusion
Contrast these pitfalls with the arguments
in favor of market neutral investing:
double alpha,
flexibility to diversify risk,
increased opportunity sets, and
superior information ratios.
The case for institutional market neutral
investing is supported by a clear and persuasive theoretical framework and empirical evidence. For low risk strategies, there is
little to gain from market neutral investing.
Aggressive, skillful managers, on the other
hand, should take a close look at market
neutral strategies. Are they discarding an
important opportunity to enhance their
performance? ■
Heuristic
Long Only
367 Institutional
Portfolios
Q4/93 – Q4/96
300 Mutual
Funds
10/88 – 9/94
90
1.45
1.00
1.01
1.08
75
1.24
0.50
0.48
0.58
8 The watershed market neutral event for institutions was the Internal Revenue Service’s private letter ruling
issued in 1988. On behalf of the Common Fund, this private letter clarified that short sales did not constituent
Unrelated Business Taxable Income (UBTI).
38
HORIZON · WINTER
1999
THE
BARRA
NEWSLETTER
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