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The Effect of Extreme Markets on the Benefits of International Portfolio Diversification

Daniella Acker*University of Bristol, U.K.

Nigel W. DuckUniversity of Bristol, U.K.

We investigate the effects of bull and bear markets on correlations betweendeveloped and emerging country equity returns, and on the benefits ofcombining international markets in a portfolio. Contrary to most other studieswe find that correlations fall in both bull and bear markets, although far morein the former; that emerging markets provide both additional diversificationbenefits for investors in developed markets and, especially, some protectionduring bear markets.(JEL: F3, G1, G10, G11, G15)

Keywords: International equity markets, correlations, portfolio choice.

I. Introduction

Portfolio diversification allows investors to increase returns withoutincreasing risk, and, all else equal, the benefits of diversification aregreater the lower the correlation between the portfolio’s assets. Cross-country portfolio diversification should therefore be morebeneficial the lower the degree of correlation between the markets ofdifferent countries. Recently, two strands of the finance literature havesuggested that (a) emerging markets have improved the scope fordiversification (for example, Goetzmann et al (2002)); and (b)cross-country returns are more highly correlated - and hence the benefits

*Daniella Acker gratefully acknowledges support from the ESRC, grant Number RES000-21-0298. We are indebted to David Ashton, Lawrence Kryzanowski and participants at the 13th Annual Multinational Finance Society Edinburgh meeting for useful suggestions. All errors in this manuscript are, of course, our own.

(Multinational Finance Journal, 2009, vol. 13, no. 3/4, pp. 155–188)© Multinational Finance Society, a nonprofit corporation. All rights reserved. DOI: 10.17578/13-3/4-1

Multinational Finance Journal156

of diversification are lower - when markets are volatile, particularly inbear markets (see for example, Ang and Bekaert (2002), Campbell et al(2002) and Erb et al (1994)).

Using weekly returns data from 44 countries from July 1994 toOctober 2003 we present in this paper evidence on both these issues. Specifically, we address the following questions:

Are cross-country returns of developed markets more or lesscorrelated with each other in bull and bear markets than they areoverall? Is the same true of correlations between the returns ofdeveloped and emerging markets?

Are there clear potential benefits to holding diversified portfoliosconsisting of pairs of developed markets (DEV/DEV pairs) in bull, bearand normal markets? Are any such benefits greater or less for portfoliosconsisting of pairs of developed and emerging markets (DEV/EMpairs)?1

Do such benefits in bull and bear markets depend upon investorsforeseeing the changes in the means, the standard deviation of returnsand the correlation between them in such markets, and adjusting theirportfolios accordingly? Or would they largely accrue anyway to aninvestor holding a portfolio appropriately diversified for a normalmarket?

Our results suggest the following.First, in contrast to most other studies, we find that international

equity correlations tend to fall in both bull and bear markets, though thesize of the fall is noticeably greater in bull markets. We also find thatDEV/DEV correlations are generally higher than DEV/EM correlations,although the former tend to fall more than the latter in both bull andbear markets.

Secondly, cross-country diversification is worthwhile in normalmarket conditions, increasing the certainty-equivalent rate of return byan amount roughly equal to the risk-free rate of interest (for a quadraticutility investor with relative risk aversion rate equal to 2). Thesebenefits are higher for DEV/EM pairs than for DEV/DEV pairs. In bull

1. In what follows we use the term ‘diversification’ to mean a combination of a risk-freeasset and only two risky assets, rather than a multi-asset portfolio. However, we examinedthese issues both for pairs of markets and for larger groups of markets. While in the case ofthe larger portfolios there appears to be little to choose between emerging and developedmarkets during normal market conditions, our central conclusions reported below aboutemerging markets providing more protection in bear markets remained qualitatively unalteredfor the larger portfolios. Because of this we report only the results of testing pairs of markets.

157International Portfolio Diversification

or bear markets that have not been foreseen by the investor, DEV/DEVportfolios lose the benefits of diversification (in fact, the investor mayactually lose by diversifying), while DEV/EM portfolios do not. So,emerging markets provide not only additional diversification benefitsfor investors in developed markets under normal market conditions, butthose benefits are maintained during unforeseen bull markets andenhanced during unforeseen bear markets. However, these benefits aresmall relative to the other effects of truncation on portfolioperformance.

Finally, a portfolio that is optimal in normal market conditions willmiss out on a large proportion of the gains that might be made fromcorrectly-adjusted portfolios in bull markets, and will lead to heavylosses in bear markets.

It is often the convention in the literature on extreme markets to terma set of especially low (high) returns as a bear (bull) market rather thanto adopt the more common definition of a bear (bull) market as a periodof time during which returns are particularly low (high) - see, forexample, Butler and Joaquin (BJ 2002) and Longin and Solnik (2001). We shall follow this convention and will therefore refer to bull and bearmarkets as ‘truncated’, since they represent tails of the distribution ofreturns, and use ‘normal’ to describe markets that are not truncated. Weexplain below precisely how we define a truncated distribution.

The paper proceeds as follows. The next section describes ourgeneral methodology, in particular how we extend the work of BJ(2002) combined with that of Levy and Sarnat (1970) to obtain ameasure of portfolio performance; section 3 explains our data anddiscusses some empirical issues; section 4 presents descriptive statisticsand results relating to some broad averages of countries. Section 5presents the results of formal tests of whether the effects that bull andbear markets have on correlations between DEV/DEV pairs andDEV/EM pairs are different and whether their effects on the benefits ofDEV/DEV and DEV/EM diversification are different. It also presentstests of the effects of bull and bear markets on the performance ofportfolios involving DEV/DEV pairs and DEV/EM pairs. Section 6concludes.

II. Methodology

Our framework is a standard model of portfolio selection in which the


investor selects among three assets, two of which are risky. Thisstandard analysis usually assumes the risky assets’ returns to bebivariate normal, but the analysis is valid for any distribution of returnsif the investor has a quadratic utility function. Since we shall beanalysing portfolio selection in truncated markets where bivariatenormality clearly does not apply, this is the utility function we shallassume.

In the spirit of BJ (2002)2 combined with Levy and Sarnat (1970)3,we can derive an (expected-utility-maximising) optimum portfoliowhich depends upon the investor’s utility function and degree of riskaversion, and on the risk-free rate, the standard deviation of eachasset’s return, their means, and the correlation between them. We canalso derive other portfolios which appear optimal to an investor giventhe (possibly incorrect) assessment that she makes of those six latterparameters.

Associated with each portfolio and assumed degree of risk aversionis an expected level of utility. From each such expected level of utilityit is possible to derive a certainty-equivalent rate of return defined as theriskless rate of return which would deliver to the investor that samelevel of expected utility. Our measures of both the benefits ofdiversification and of portfolio performance are in terms of the excesscertainty-equivalent rate of return (CERR) over and above the actualrisk-free rate of return.4

To assess the benefits of diversification we first calculate thefollowing CERRs for diversified portfolios.

RNN = the CERR that would yield the same expected utility thatcould optimally be achieved in a normal market.

RTT = the CERR that would yield the same expected utility that couldoptimally be achieved in a truncated market.

RNT = the CERR that would yield the same expected utility that

2. BJ (2002) investigate the loss of returns from a portfolio invested equally in each ofa pair of (developed) markets during a bear market. They quantify the loss as the differencebetween the return achievable from a bivariate normal distribution with the same parametersas the observed distributions of returns, and the observed portfolio returns.

3. They use standard portfolio theory to determine the optimal mix of assets in theportfolio and measure the performance of portfolios in utility per dollar invested rather thanas raw returns.

4. We have not used the Sharpe or Sortino ratios as performance measures since theirmeaning is not clear in cases of negative returns (see, for example, McLeod and van Vuuren,2004).


would be achieved in a truncated market by an investor who hadwrongly assumed that the market characteristics were those of thenormal rather than the truncated market.

For each of these we then define a ‘plain vanilla’ equivalent – i.e.the CERR from a portfolio which consists of the risk-free asset and onlyone risky asset. We denote these equivalents respectively by VRNN, VRTT

and VRNT. The differences between each CERR and its plain vanillaequivalent, denoted DRNN, DRTT and DRNT respectively, provide ameasure of the potential benefits of diversification in a normal market,in a truncated market that is foreseen, and in a truncated market that isnot foreseen.

To assess the impact of bull and bear markets on the performance ofa diversified portfolio, we first calculate ΔM, the difference betweenRNN and RTT, the maximum gain to be made in a bull market, or theminimum loss in a bear market. We next calculate ΔA, the differencebetween RTT and RNT. Since any such difference results from the failureof the investor to realise the true nature of market conditions we termthis the avoidable effect of operating in a truncated market.

Before presenting results on the interaction of international equitycorrelations and portfolio performance we analyse certaincharacteristics of the correlations themselves. We first define thevariable COR as the correlation between the returns of two marketsunder normal conditions, and test whether COR varies systematicallyaccording to the nature of the countries that are paired. We then assessthe impact of bull and bear markets on these correlations, definingΔCOR as the change in correlation between two assets when themarkets are truncated.

We start by presenting estimates of COR, ΔCOR, VRNN/RNN,VRTT/RTT, VRNT/RNT, ΔM and ΔA, for different broad categories of pairsof markets, for markets truncated at successively higher thresholds inabsolute terms. These give an overall view of the behaviour ofcorrelations, of the benefits of diversification, and of how such benefitschange in increasingly extreme markets.

We then present a set of regressions from the coefficients of whichwe assess whether the differences between correlations or CERRs varyaccording to the investor’s home country, or differ for emerging anddeveloped country pairs, and whether they are significantly affected bythe value of the threshold itself. Formally we estimate the followingsets of regressions:


, ,Model 1: i j k k i jk

a d THRλ ε= + +∑

3

, ,2

Model 2: i j i i k k i ji k

a b LD d THRλ ε=

= + + +∑ ∑

, , ,Model 3: i j k k k k j i jk k

a d THR e DEVTHRλ ε= + + +∑ ∑

3 3

, ,2 2

, ,

Model 4: i j i i i i j k ki i k

k k j i jk

a b LD c LDDEV d THR

e DEVTHR

λ

ε

= == + + +

+ +

∑ ∑ ∑

∑

Where i denotes the first country in the pair and j the second;

5, , , , , , , ,, , , , ;i j i j TT i j NT i j i j i jCOR DR DR M or Aλ = Δ Δ Δ

LDi are dummies for three selected ‘lead’ or ‘home’ countries which aremore fully explained below; i = 1,…,3. LDi takes the value 1 if the leadcountry is the US and is omitted from the regression in models 2 and 4since the US is the ‘baseline’ country; i = 2 denotes the UK and i = 3Australia;THRk is a dummy that takes the value 1 if the threshold at which the tailis truncated equals k, where k = –1, –0.5, –0, +0, +0.5, +1, +1.5 standarddeviations from the mean (with the –1.5 threshold forming the‘baseline’);DEVj is a dummy that takes the value 1 if the second country in the pairis a developed market;

, equals ; andk j k jDEVTHR THR DEV×

5. When ΔMij is the dependent variable the models are estimated for positive thresholdsonly. In almost all cases the optimum decision in a bear market, at any level of truncation,is to invest in the risk-free asset. This means that the reduction in the maximum CERRachievable equals the maximum itself, regardless of the values of the independent variables.


, equals .i j i jLDDEV LD DEV×

We also estimate the following models for the two variables that areunaffected by truncation:

3

, ,2

Model 2a: i j i i i ji

a b LDλ ε=

= + +∑

, ,Model 3a: i j j i ja eDEVλ ε= + +

3 3

, , ,2 1

Model 4a: i j i i i i j i ji i

a b LD c LDDEVλ ε= =

= + + +∑ ∑

, , , ,Where or .i j NN i j i jDR CORλ =

All these tests require a precise empirical definition of a truncatedmarket. We discuss this issue and our data in the next section.

III. Data Availability And Empirical Issues

Because of timing issues there are problems when using daily returnsdata on international markets. However, the use of monthly data wouldseverely limit the number of observations. We therefore base all ourresults on weekly returns.

We select four ‘lead’ countries, US, UK, Japan and Australia, onefrom each of the main trading areas, and pair these with each other andwith the non-lead (‘subsidiary’) countries for which we have data. The44 countries available are shown in table 1.

For each country we obtain weekly US$-denominated log returnsfrom Datastream, using Datastream code ‘TOTMKT’. The returns areadjusted for re-invested dividends (Datastream item ‘RI’). In our testswe classified non-lead countries into three main regions: Latin America,Asia (which consists of S.E. Asia, the Far East and India), and Europe(S. and N. Europe, Scandinavia, Russia and Turkey).

Our proxy for the risk-free rate of interest is the three-month USTreasury bill weekly yield. Since we are using dollar-denominated


returns we need a dollar interest rate, and under interest parity weshould get the same result whether we use US interest rates, or domesticinterest rates adjusted for exchange rate movements.6

The ‘youngest’ market in our sample is Brazil, which came intoexistence in July 1994, so we restrict our samples to the period fromJuly 1994 to October 2003, a total of 484 observations.

Subject to a qualification concerning Japan discussed below, weassume that this sample provides an accurate representation of thecomplete distribution of returns. It therefore allows us to calculate

TABLE 1. Countries available

Emerging Developed

Region Country Region Country

Latin America Argentina N. America CanadaBrazil US (Lead country)Chile Far East Hong KongMexico Japan (Lead country)Peru SE Asia SingaporeVenezuela Scandinavia Denmark

Far East China FinlandKorea NorwayTaiwan Sweden

SE Asia Malaysia S. Europe SpainPhilippines GreeceThailand Italy

N. Europe Czech PortugalRepublicHungary N. Europe GermanyPoland Belgium

Europe Russia FranceTurkey Ireland

Asia India LuxemburgOther Israel Netherlands

S. Africa AustriaSwitzerlandUK (Lead country)

Australasia Australia (Lead country)New Zealand

Total: 20 countries 24 countries

6. Interest parity does not always hold but variations in interest rates are small incomparison with the other parameters.


conventionally the means and standard deviations of any pair of assetreturns and the correlations between them in normal market conditions. And from these, again conventionally, we can calculate for any pair theportfolio that would maximise expected utility.7

To measure the equivalent parameters of pairs of markets in extremeconditions we need to decide (a) whether to condition on one or both ofthe asset returns when truncating the distributions; and (b) how thethresholds should be expressed (in absolute terms or in terms ofstandard deviations) and how high they should go.

A. Conditioning

Some researchers condition on both returns - double truncation - but aninvestor is likely to be interested in the behaviour of a foreign marketwhen the behaviour of the domestic market is extreme, rather than in thebehaviour of the two markets when they are both extreme. Consequentlywe set our thresholds in terms of only one return (single truncation),using the lead market as the conditioning variable. So, for example, forthe US/Argentina pair, observations used to estimate the portfolioparameters are all those US observations that lie in the appropriate tailand the associated Argentinean observations.

B. Thresholds

We set our thresholds at 1.5, 1, 0.5 and 0 standard deviations around themean (in terms of weekly returns of the lead market). We do not go tohigher extremes because the number of observations would then be sosmall that any estimates derived for them would, as noted by otherauthors such as Bae et al (2003), be unreliable, and also of rather limitedpractical importance.

Table 2 shows the numbers of observations used for estimation atdifferent degrees of truncation. This table shows that there is someskewness in the distributions, with more observations above the mean(threshold +0), than below it (threshold –0), except for Japan, which, wewill see below, has many other unusual characteristics.

7. In doing so we are, of course, abstracting from the practical problems ofimplementing any particular investment strategy, such as cost or the absence of suitableinvestment vehicles, both of which might be especially acute in emerging markets.


IV. Descriptive Statistics; Correlations and PortfolioPerformance in Normal and Truncated Markets

Table 3 shows dollar-denominated means, medians and standarddeviations for weekly returns of the whole sample of country marketsand for the upper and lower halves of the distributions. The data for thefour lead countries are shown separately, while, to save space, data forthe remaining countries are grouped into regions and a simple averagecalculated.

Of the lead countries, Japan was in a recession throughout thesample period. Furthermore, its median return is considerably lowerthan its mean, while all developed regions and most emerging ones havethe opposite relationship. Whilst this is useful in that it presents us withdata on unusual markets, it does question our assumption that thesample period represents the complete distribution of returns. Wetherefore deal with Japan separately in all the statistics presented belowand exclude it from our regressions.

For all the countries, standard deviations in the tails are lower thanoverall standard deviations. For all but Japan and Asian emergingmarkets the standard deviation of the top half of the distribution is lowerthan that in the lower half.

Table 4 shows the correlations between the weekly returns of eachlead country and each of the other three, and the average of correlationsbetween each of the four lead countries and selected other groups ofcountries. Correlations are shown for the whole sample and for theupper and lower tails of the distribution. They suggest, very broadly,that correlations between emerging markets and the developed ones arelower than correlations between developed markets (although againJapan is something of an exception); and that correlations in both tailsare lower than the overall correlation, a phenomenon that we exploremore fully below.

TABLE 2. Average number of observations in the tails

Threshold in terms of standard deviations around mean

–1.5 –1 –0.05 –0 +0 0.5 1 1.5Lead countryUS 29 68 127 225 259 138 61 24Japan 26 62 148 249 235 124 70 36UK 29 66 125 223 261 144 64 26Australia 27 63 144 236 248 142 69 31


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Table 5 presents estimates of average weekly CERRs generated byplain vanilla and diversified portfolios in normal markets, unexpectedlytruncated markets and correctly predicted bull markets:8 RNN and VRNN; RNT and VRNT; and RTT and VRTT. In the table Japan is treated separatelybut other lead countries are grouped together, so the results presentedthere give only a very broad picture of the benefits of diversification. They are also calculated for a particular degree of risk aversionparameter, viz. 2, though we have repeated all the tests and summariesfor parameter values 0.5, 1, 1.5, 2.5 and 3 and there were no qualitativedifferences.9

The first column of table 5 suggests that combining two internationalmarkets in a diversified portfolio under normal market conditions yieldssignificant but modest benefits. The average weekly risk-free rate overthe sample period was in the region of 0.075%. So, for lead countriesother than Japan, domestic diversification (investing in a single market)yielded approximately double this in CERR terms for an investor withrelative risk aversion of 2, while combining two markets added an extra0.05% - 0.07% on average. Note that a positive CERR is achievablewhen holding Japan as the only risky asset, even though Japan was inrecession over the sample period, because the optimum mix involvesshorting the market to invest in the risk-free asset. Combining Japanwith other countries generates the highest CERR in a normal marketbecause of the low correlation between Japan and the other leadmarkets, combined with the ability to short Japan.

The CERR figures in the last four columns suggest that in correctlyanticipated bull markets there are still rewards to diversification, butthat they are very small in relation to the overall returns. It is worthpointing out that the very high figures that appear here are caused byshort-selling. Clearly, an investor who knows that the market is aboutto enter a bull period will borrow heavily (short the risk-free asset) andinvest in the market; if the investor is correct, as assumed in thesecolumns, high rewards will ensue. An interesting extension of thispaper would be to investigate how a restriction on short-selling wouldaffect the results.

8. For our data and sample period, correctly predicted bear markets always generatezero CERRs, since, as mentioned above, the optimal decision is to invest only in the risk-freeasset for all pairs and at all levels of truncation.

9. The CERRs at different levels of risk aversion are inversely proportionate toδ/λ/2(1+λ), where λ is the rate of relative risk aversion (RRA). So, for example, the CERRswith RRA 0.5 are twice those with RRA of 2. Therefore regression results at all levels of riskaversion have the same standard errors, although the coefficient values vary proportionately.


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Ove

rall

C

ER

R %

CE

RR

in a

ntic

ipat

ed tr

unca

ted

mar

ket (

%)

VR

NN

or R

NN

VR

TT o

r R

TT

+0

+0.

5+

1+

1.5

Lea

d co

untr

ies

othe

r th

an J

apan

1. A

lone

0.14

77 5

6.98

3685

.568

810

2.67

7911

6.31

672.

Pai

red

wit

h Ja

pan

0.45

6857

.777

586

.436

210

3.02

2111

6.41

903.

Pai

red

wit

h ot

her

lead

cou

ntri

es0.

1988

57.3

204

86.2

380

103.

1368

116.

6708

4. P

aire

d w

ith

non-

lead

s0.

2164

57.3

395

86.1

350

103.

1241

117.

1133

Japa

n5.

Alo

ne0.

1501

45.7

665

77.6

148

96.3

523

105.

0492

6. P

aire

d w

ith

othe

r le

ad c

ount

ries

0.45

6846

.345

178

.638

596

.775

710

6.41

097.

Pai

red

wit

h no

n-le

ads

0.42

2146

.061

778

.536

597

.115

710

5.84

19

Not

e: T

he ta

ble

show

s th

e ex

cess

CE

RR

s ge

nera

ted

by v

ario

us p

ortf

olio

s. T

he c

olum

n he

aded

‘ov

eral

l’ C

ER

R s

how

s th

e m

axim

um C

ER

Rav

aila

ble

unde

r nor

mal

mar

ket c

ondi

tion

s, V

RN

N w

ith

a ‘p

lain

van

illa

’ por

tfol

io a

nd R

NN w

ith

a di

vers

ifie

d on

e. T

he o

ther

col

umns

sho

w th

e C

ER

Rge

nera

ted

whe

n th

e m

arke

t is

trun

cate

d as

sho

wn,

wit

h tr

unca

tion

thre

shol

ds in

term

s of

sta

ndar

d de

viat

ions

of

lead

cou

ntry

ret

urns

aro

und

thei

rm

ean.

VR

NT a

nd R

NT a

re C

ER

Rs

gene

rate

d by

the

port

foli

o th

at is

app

ropr

iate

for n

orm

al m

arke

t con

diti

ons;

VR

TT a

nd R

TT a

re C

ER

Rs

gene

rate

d by

the

port

foli

o th

at is

opt

imal

for

the

trun

cate

d m

arke

t. O

nly

posi

tive

thre

shol

ds a

re s

how

n in

this

cas

e, a

s th

e op

tim

um p

ortf

olio

in a

bea

r m

arke

tis

alw

ays

100%

in th

e ri

sk-f

ree

asse

t, ge

nera

ting

zer

o C

ER

Rs.

The

fig

ures

in li

nes

1- 4

, 6 a

nd 7

are

mea

ns a

cros

s th

e ca

tego

ries

sho

wn.


TA

BL

E 6

.E

ffec

ts o

f tr

unca

tion

on

CE

RR

s (r

isk

aver

sion

par

amet

er 2

); l

ead

coun

trie

s ot

her

than

Jap

an

All

in %

Eff

ect o

f tr

unca

tion

: opt

imal

out

com

e‘A

void

able

’ lo

ss c

ause

d by

Tot

al C

ER

Rsu

b-op

tim

al p

ortf

olio

Bes

t CE

RR

ach

ieva

ble

Max

gai

n /

Bes

t CE

RR

ach

ieva

ble

in

(Tab

le 5

col

8)

in n

orm

al m

arke

t (R

NN)

Min

loss

trun

cate

d m

arke

t (R

TT)

ΔA

RN

T

(ΔM

)

A. T

hres

hold

1 s

tand

ard

devi

atio

n ab

ove

the

mea

n

Pai

red

wit

h Ja

pan

Mea

n0.

4568

102.

5654

103.

0222

–92.

3350

10.6

872

Pai

red

wit

h ot

her

lead

sM

ean

0.19

8910

2.93

7910

3.13

68–9

2.91

2510

.224

3M

edia

n0.

2095

102.

6926

102.

8861

–93.

1188

Std

dev

0.03

352.

2379

2.22

463.

8401

Oth

er p

airs

Num

ber

120

120

120

120

Mea

n0.

2164

102.

9077

103.

1241

–92.

8205

10.3

036

Med

ian

0.20

4510

2.51

3310

2.71

85–9

3.09

89S

td d

ev0.

1045

2.28

792.

2482

3.79

27

( C

onti

nued

)


TA

BL

E 6

.(C

onti

nued

)

Eff

ect o

f tr

unca

tion

: opt

imal

out

com

e‘A

void

able

’ lo

ss c

ause

d by

Tot

al C

ER

Rsu

b-op

tim

al p

ortf

olio

Bes

t CE

RR

ach

ieva

ble

Max

gai

n /

Bes

t CE

RR

ach

ieva

ble

in

(Tab

le 5

col

3)

in n

orm

al m

arke

t (R

NN)

Min

loss

trun

cate

d m

arke

t (R

TT)

ΔA

RN

T

(ΔM

)

B. T

hres

hold

1 s

tand

ard

devi

atio

n be

low

the

mea

n

Pai

red

wit

h Ja

pan

Mea

n0.

4568

–0.4

568

0.00

00–9

.860

9–9

.860

9P

aire

d w

ith

othe

r le

ads

Mea

n0.

1988

–0.1

988

0.00

00–1

0.82

33–1

0.82

33M

edia

n0.

2095

–0.2

095

0.00

00–1

0.11

94S

td d

ev0.

0335

0.03

350.

0000

1.52

39O

ther

pai

rsN

umbe

r12

012

012

012

0M

ean

0.21

64–0

.216

40.

0000

–10.

5922

–10.

5922

Med

ian

0.20

45–0

.204

50.

0000

–9.9

649

Std

dev

0.10

450.

1045

0.00

001.

5627

Not

e: T

he ta

ble

show

s be

nefi

cial

(+

) an

d ha

rmfu

l (–)

eff

ects

of

trun

cati

on o

n th

e C

ER

R a

chie

ved

in b

ull a

nd b

ear

mar

kets

. T

he f

irst

thre

eco

lum

ns s

how

how

the

best

ach

ieva

ble

CE

RR

in n

orm

al m

arke

t con

diti

ons

(RN

N)

wou

ld b

e in

crea

sed

in a

bul

l mar

ket (

Pan

el A

) or

dec

reas

ed in

abe

ar m

arke

t (P

anel

B)

by a

n in

vest

or h

oldi

ng th

e po

rtfo

lio

that

is o

ptim

al f

or th

e tr

unca

ted

mar

ket (

RT

T).

Col

umn

4 sh

ows

how

this

opt

imum

isre

duce

d by

mis

-pre

dict

ing

the

mar

ket a

nd th

eref

ore

mis

take

nly

hold

ing

a po

rtfo

lio

base

d on

par

amet

ers

of th

e co

mpl

ete

dist

ribu

tion

(ΔA

). C

olum

n5

repe

ats

figu

res

in c

olum

ns 8

and

3 o

f ta

ble

5, f

or c

lari

ty, s

how

ing

the

brea

kdow

n of

thes

e fi

gure

s, n

amel

y R

TT+ΔA

.


Finally, when the lead market is unexpectedly truncated so that theinvestor is holding the portfolio which is appropriate for a normalmarket, table 5 suggests that the benefits of diversification are lessclear-cut for both bear and bull markets: the CERR on a diversifiedportfolio is generally higher on average than the CERR on a ‘plainvanilla’ portfolio but this is by no means always the case.10 However, inall cases the benefits of diversification per se are very small relative tothe overall returns.

These results suggest that, in general, cross-country diversificationis worthwhile in normal markets, but that it may not provide much extraprotection nor offer greater opportunities in periods of marketturbulence. On the other hand, it is not clear from these very generalresults whether benefits of diversification are actually lost during bullor bear markets. The tests below address this issue formally.

Panels A and B of table 6 focus on the effect of truncation ondiversified portfolios, elaborating on some of the figures in table 5. Forthe sake of space we show only figures for one standard deviation aboveand below the mean. The figures for other tails had similar patterns. Panel A refers to a bull market, panel B to a bear market. The topleft-hand figure in panel A (0.46%) is the CERR for an optimal portfoliothat combines the risk-free asset, Japan, and a lead country other thanJapan, in normal market conditions. The figure immediately to its rightshows that if the market were a bull market then the optimal portfolioin such a market would increase that CERR by 102.57% to 103.02%,the figure in the third column. However, of this additional 102.57%,92.33% (column 4) would be lost if the portfolio were not adjusted totake account of market conditions, resulting in a final CERR of 10.69%(column 5).

The equivalent figures for the bear market are shown in row one ofpanel B. Here the CERR for an optimal portfolio in normal marketconditions is 0.46% as before. The maximum achievable CERR in thetruncated market is now zero, since with almost any degree of truncationthe optimal portfolio in a bear market consists entirely of the risk-freeasset. The minimum loss resulting from the market truncation istherefore 0.46%. The additional loss that would result from notre-arranging the portfolio given the market conditions is shown incolumn 4 as –9.86%.

Overall, the results in table 6 indicate that appropriate

10. With Japan-led portfolios, the optimum portfolio mix under normal conditionsinvolves short-selling Japan so that when it is in a deeper recession than expected, the CERRsincrease, and the opposite applies in a boom.


re-arrangement of portfolios is required to achieve the large potentialgains offered by bull markets and to avoid the large losses in bearmarkets: holding a portfolio that is optimally diversified for normalmarket conditions will do neither.

V. Formal Tests

A. Correlations

Table 7 presents the results of estimating models 2(a) – 4(a) with λi,j =CORi,j and models 1-4 with λi,j = ΔCORi,j and figure 1 illustrates someof the results graphically, using the predicted values from the estimatesof models 3(a) and 3.11 Estimates of models 2(a)-4(a) suggest that, asone might expect, DEV/DEV correlations are significantly higher (byabout 0.2) than DEV/EM pairs, though this varies somewhat with thelead country. Estimates of models 1-4 suggest a marked and significanttendency for correlations to decline as the bull or bear market becomesmore extreme. The base case in these columns is the most extreme bearmarket, which has a strongly significant negative coefficient. All otherjoint coefficients (that is, base case + appropriate dummy) are negative. The last two columns of coefficients suggest that this tendency issignificantly more marked in DEV/DEV pairs. In fact, figure 1emphasises that, although the reduction in correlations is greater forDEV/DEV pairs, the overall correlation for such pairs is sufficientlyhigh to mean that DEV/DEV correlations are still higher than DEV/EMones in truncated markets. The fall in correlations as the absolute valueof the threshold increases is contrary to the findings of other studies (forexample, Longin and Solnik (2001)), most of which suggest thatinternational correlations increase with the severity of the bear market.Our results suggest that this is not true of our data period for any of thelead countries.12

B. Benefits of International Diversification

Table 8 and table 9 present the results of the regressions involvinginternational diversification benefits in normal markets and in truncated

11. As explained above, from this point onwards data relating to Japan are omitted.

12. To check whether our results differ from other researchers’ because we are usingsingle truncation, we examined correlations in tails of doubly-truncated distributions. Ourresults were qualitatively unaltered.


TA

BL

E 7

.A

naly

sis

of c

orre

lati

ons

Dep

var

: Cor

i,j (

over

all c

orre

l)D

ep v

ar: Δ

Cor

i,j (

corr

elat

ion

chan

ge)

Mod

el:

2a3a

4a1

23

4

Con

stan

t0.

3826

0.30

660.

2977

–0.1

202

–0.1

320

–0.0

759

–0.1

044

(16.

83)*

*(2

0.08

)**

(11.

60)*

*(–

9.82

)**

(–10

.05)

**(–

4.46

)**

(–5.

77)*

*L

DU

K0.

0477

0.00

05–0

.029

30.

0000

(1.4

8)(0

.02)

(–2.

88)*

*(0

.00)

LD

Au

0.00

390.

0263

0.06

440.

0855

(0.1

2)(0

.72)

(6.3

3)**

(6.1

0)**

DE

V0.

1779

(8.4

3)**

LD

DE

VU

S0.

1621

(4.5

7)**

LD

DE

VU

K0.

2520

–0.0

559

(7.1

1)**

(–2.

89)*

*L

DD

EV

Au

0.11

95–0

.040

2(3

.37)

**(–

2.08

)*–1

0.03

450.

0345

0.05

020.

0502

(2.0

0)*

(2.0

8)*

(2.0

9)*

(2.1

9)*

–0.5

0.05

810.

0581

0.05

290.

0529

(3.3

6)**

(3.5

0)**

(2.2

0)*

(2.3

1)*

–00.

0739

0.07

390.

0536

0.05

36(4

.27)

**(4

.45)

**(2

.23)

*(2

.34)

*

( C

onti

nued

)


TA

BL

E 7

.(C

onti

nued

)

Dep

var

: Cor

i,j (

over

all c

orre

l)D

ep v

ar: Δ

Cor

i,j (

corr

elat

ion

chan

ge)

Mod

el:

2a3a

4a1

23

4

+0

–0.0

715

–0.0

715

–0.0

792

–0.0

792

(–4.

13)*

*(–

4.31

)**

(–3.

29)*

*(–

3.46

)**

+0.

5–0

.141

9–0

.141

9–0

.138

3–0

.138

3(–

8.20

)**

(–8.

54)*

*(–

5.75

)**

(–6.

04)*

*+

1–0

.156

4–0

.156

4–0

.167

6–0

.167

6(–

9.03

)**

(–9.

42)*

*(–

6.97

)**

(–7.

32)*

*+

1.5

–0.2

055

–0.2

055

–0.2

030

–0.2

030

(–11

.87)

**(–

12.3

8)**

(–8.

44)*

*(–

8.87

)**

–1.5

DE

V–0

.084

7–0

.052

7(–

3.61

)**

(–2.

11)*

–1D

EV

–0.1

146

–0.0

825

(–4.

88)*

*(–

3.30

)**

–0.5

DE

V–0

.074

7–0

.042

6(–

3.18

)**

(–1.

70)

–0D

EV

–0.0

459

–0.0

138

(–1.

95)

(–0.

55)

+0D

EV

–0.0

702

–0.0

381

(–2.

99)*

*(–

1.52

)+

0.5D

EV

–0.0

915

–0.0

595

(–3.

89)*

*(–

2.38

)*

( C

onti

nued

)


TA

BL

E 7

.(C

onti

nued

)

Dep

var

: Cor

i,j (

over

all c

orre

l)D

ep v

ar: Δ

Cor

i,j (

corr

elat

ion

chan

ge)

Mod

el:

2a3a

4a1

23

4

+1D

EV

–0.0

633

–0.0

313

(–2.

69)*

*(–

1.25

)+

1.5D

EV

–0.0

896

–0.0

575

(–3.

81)*

*(–

2.30

)*A

djus

ted

R s

q0.

0056

0.35

930.

3969

0.34

660.

3988

0.39

980.

4564

NO

BS

126

126

126

1,00

81,

008

1,00

81,

008

Not

e: T

he ta

ble

show

s th

e re

sult

s of

est

imat

ing

the

foll

owin

g re

gres

sion

equ

atio

ns.

See

mod

el 2

a, m

odel

3a,

mod

el 4

a, m

odel

1, m

odel

2, m

odel

3, m

odel

4 o

n te

xt.

whe

re λ

i,j =

CO

Ri,j f

or m

odel

s 2a

-4a

and ΔC

OR

i,j f

or m

odel

s 1-

4;

ΔCO

Ri,j =

the

corr

elat

ion

in th

e re

leva

nt ta

il m

inus

the

over

all c

orre

lati

on;

LD

i are

lead

cou

ntry

dum

mie

s di

stin

guis

hing

bet

wee

n th

e U

S (

i = 1

), U

K (

i = 2

) an

d A

ustr

alia

(i =

3);

TH

Rk i

s a

dum

my

that

take

s th

e va

lue

1 if

the

thre

shol

d eq

uals

k, k

= –

1, –

0.5,

–0,

+0,

+0.

5, +

1, +

1.5

stan

dard

dev

iati

ons

arou

nd th

e le

ad c

ount

ry’s

mea

n;D

EV

j is

a du

mm

y th

at ta

kes

the

valu

e 1

if th

e se

cond

cou

ntry

in th

e pa

ir is

a d

evel

oped

mar

ket;

DE

VT

HR

k,j e

qual

s T

HR

k × D

EV

j; a

nd

LD

DE

Vi,j e

qual

s L

Di ×

DE

Vj

t-st

atis

tics

are

sho

wn

in p

aren

thes

es a

nd in

dica

te s

tati

stic

al s

igni

fica

nce

at 5

% (

*) a

nd 1

% (

**),

two-

tail

ed te

sts.


Emerging, truncated

KEY

Emerging, normal mkt

Developed, normal mkt

Developed, truncated

FIGURE 1.— Correlations in Normal and Truncated Markets Note: The figure shows the joint coefficients from the regression results of models 3 and3a in table 7.

markets, both predicted and unpredicted. Table 8 shows the results ofestimating models 2(a)-4(a) with λi,j = DRNN,i,j (diversification withnormal markets), and table 9 the results of estimating models 1-4 withλi,j = DRTT,i,j or DRNT,i,j (diversification with truncated markets). Figure2 uses the results from estimates of model 3(a) and model 3 to illustratetheir overall pattern graphically.

The constant in model 2(a) in table 8 confirms our earlier suggestionthat the benefits of diversification in normal markets are roughly equalto a doubling of the risk-free rate of interest (for an investor withrelative risk aversion of 2). But models 3(a) and 4(a) suggest that thebenefits for portfolios involving DEV/DEV pairs are about half that ofDEV/EM pairs, with US-led pairs suffering the most. The results intable 9, which are illustrated in the left-hand section of figure 2, suggestthat in unexpectedly truncated markets DEV/DEV portfolios lose the


benefits of diversification, while DEV/EM portfolios do not. ForDEV/DEV portfolios the benefits fall with the degree of truncation (bothin bull and bear markets); indeed they fall to such an extent that theyrapidly become negative. For DEV/EM portfolios, diversification inbull markets yields much the same benefit as in normal markets, whilethe benefits tend to increase in bear markets. However, as noted earlier,the benefits in truncated markets are minor when compared to the othereffects of truncation.

Finally, if a bull market is correctly predicted (right-hand section ofof table 9),13 benefits of diversification are higher than in normal

TABLE 8. Benefits of diversification in normal market (DRNN) (risk aversion 2)

Model: 2a 3a 4a

Constant 0.0636 0.0884 0.0922(12.44)** (21.13)** (12.74)**

LDUK 0.0017 –0.0135(0.23) (–1.32)

LDAu 0.0111 0.0023(1.54) (0.22)

DEV –0.0393(–6.79)**

LDDEVUS –0.0546(–5.46)**

LDDEVUK –0.0256(–2.56)*

LDDEVAu –0.0377(–3.77)**

Adj R sq 0.0008 0.0429 0.0459NOBS 1,008 1,008 1,008

Note: The table shows the results of estimating the following regression equations.See model 2a, model 3a, model 4a on text.where λi,j = DRNN,i,j ;LDi are lead country dummies distinguishing between the US (i = 1), UK (i = 2) and Australia(i = 3);THRk is a dummy that takes the value 1 if the threshold equals k, k = –1, –0.5, –0, +0, +0.5,+1, +1.5 standard deviations around the lead country’s mean;DEVj is a dummy that takes the value 1 if the second country in the pair is a developedmarket;DEVTHRk,j equals THRk × DEVj; and LDDEVi,j equals LDi × DEVj

T-statistics are shown in parentheses and indicate statistical significance at 5% (*) and 1%(**), two-tailed tests.

13. See also footnote 5.


TA

BL

E 9

.B

enef

its

of d

iver

sifi

cati

on in

tru

ncat

ed m

arke

ts (

risk

ave

rsio

n 2)

Unp

redi

cted

trun

cate

d m

arke

t (de

p va

r D

RN

T)

Pre

dict

ed tr

unca

ted

mar

ket (

dep

var

DR

TT)

Mod

el:

12

34

12

34

Con

stan

t0.

1047

0.14

030.

3437

0.40

290.

0710

0.56

540.

2411

0.48

76(1

.92)

(2.3

0)*

(4.5

0)**

(4.7

3)**

(3.5

4)**

(7.6

3)**

(2.7

0)**

(4.5

8)**

LD

UK

–0.0

800

–0.1

556

–0.2

815

–0.4

340

(–1.

70)

(–2.

36)*

(–3.

80)*

*(–

4.08

)**

LD

Au

–0.0

268

–0.0

222

–0.3

496

–0.3

057

(–0.

57)

(–0.

34)

(–4.

72)*

*(–

2.87

)**

LD

DE

VU

K0.

1443

0.29

11(1

.58)

(1.9

8)*

LD

DE

VA

u–0

.008

8–0

.083

9(–

0.10

)(–

0.57

)–1

–0.0

690

–0.0

690

–0.1

136

–0.1

136

(–0.

90)

(–0.

90)

(–1.

05)

(–1.

05)

–0.5

–0.0

646

–0.0

646

–0.1

732

–0.1

732

(–0.

84)

(–0.

84)

(–1.

60)

(–1.

61)

–0–0

.069

8–0

.069

8–0

.299

9–0

.299

9(–

0.91

)(–

0.91

)(–

2.78

)**

(–2.

78)*

*+

0–0

.003

5–0

.003

5–0

.209

6–0

.209

6(–

0.05

)(–

0.05

)(–

1.94

)(–

1.94

)

( C

onti

nued

)


TA

BL

E 9

.(C

onti

nued

)

Unp

redi

cted

trun

cate

d m

arke

t (de

p va

r D

RN

T)

Pre

dict

ed tr

unca

ted

mar

ket (

dep

var

DR

TT)

Mod

el:

12

34

12

34

+0.

5–0

.054

9–0

.054

9–0

.242

3–0

.242

30.

5001

0.21

610.

1954

0.19

54(–

0.71

)(–

0.71

)(–

2.24

)*(–

2.25

)*(1

0.19

)**

(2.5

3)*

(1.5

5)(1

.59)

+1

–0.1

719

–0.1

723

–0.2

657

–0.2

657

0.37

590.

0919

0.23

540.

2354

(–2.

23)*

(–2.

23)*

(–2.

46)*

(–2.

46)*

(7.6

6)**

(1.0

7)(1

.86)

(1.9

2)+

1.5

–0.3

307

–0.3

307

–0.2

520

–0.2

520

0.70

450.

4205

0.51

050.

5105

(–4.

29)*

*(–

4.29

)**

(–2.

33)*

(–2.

34)*

(14.

35)*

*(4

.91)

**(4

.04)

**(4

.16)

**–1

.5D

EV

–0.4

563

–0.5

014

(–4.

33)*

*(–

4.26

)**

–1D

EV

–0.3

710

–0.4

162

(–3.

52)*

*(–

3.53

)**

–0.5

DE

V–0

.249

0–0

.294

1(–

2.36

)*(–

2.50

)*–0

DE

V–0

.017

1–0

.062

3(–

0.16

)(–

0.53

)+

0DE

V–0

.062

8–0

.108

00.

2175

0.14

84(–

0.60

)(–

0.92

)(1

.76)

(1.0

1)+

0.5D

EV

–0.0

984

–0.1

435

0.25

720.

1881

(–0.

93)

(–1.

22)

(2.0

8)*

(1.2

8)

( C

onti

nued

)


TA

BL

E 9

.(C

onti

nued

)

Unp

redi

cted

trun

cate

d m

arke

t (de

p va

r D

RN

T)

Pre

dict

ed tr

unca

ted

mar

ket (

dep

var

DR

TT)

Mod

el:

12

34

12

34

+1D

EV

–0.2

774

–0.3

226

–0.0

566

–0.1

257

(–2.

63)*

*(–

2.74

)**

(–0.

46)

(–0.

85)

+1.

5DE

V–0

.606

5–0

.651

70.

0458

3–0

.023

4(–

5.75

)**

(–5.

53)*

*(0

.37)

(–0.

16)

Adj

R s

q 0.

0203

0.02

130.

0843

0.08

680.

2197

0.08

570.

0508

0.10

26N

OB

S1,

008

1,00

81,

008

1,00

81,

008

504

504

504

Not

e: T

he ta

ble

show

s th

e re

sult

s of

est

imat

ing

the

foll

owin

g re

gres

sion

equ

atio

ns.

See

mod

el 1

, mod

el 2

, mod

el 3

, mod

el 4

on

text

.w

here

λi,j =

DR

NT

,i,j o

r D

RT

T,i,

j ;

LD

i are

lead

cou

ntry

dum

mie

s di

stin

guis

hing

bet

wee

n th

e U

S (

i = 1

), U

K (

i = 2

) an

d A

ustr

alia

(i =

3);

TH

Rk i

s a

dum

my

that

take

s th

e va

lue

1 if

the

thre

shol

d eq

uals

k, k

= –

1, –

0.5,

–0,

+0,

+0.

5, +

1, +

1.5

stan

dard

dev

iati

ons

arou

nd th

e le

ad c

ount

ry’s

mea

n;D

EV

j is

a du

mm

y th

at ta

kes

the

valu

e 1

if th

e se

cond

cou

ntry

in th

e pa

ir is

a d

evel

oped

mar

ket;

DE

VT

HR

k,j e

qual

s T

HR

k ×

DE

Vj;

and

L

DD

EV

i,j e

qual

s L

Di ×

DE

Vj

T-s

tati

stic

s ar

e sh

own

in p

aren

thes

es a

nd in

dica

te s

tati

stic

al s

igni

fica

nce

at 5

% (

*) a

nd 1

% (

**),

two-

tail

ed te

sts.


-0.60

-0.40

-0.20

0.00

0.20

0.40

-1.5 -1 -0.5 0 0.5 1 1.5

CE

RR

%

0.0

0.2

0.4

0.6

0.8

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

CE

RR

%

Unpredicted truncated market vs Predicted truncated marketnormal market (upper tails) vs normal market

Emerging, truncated

KEY

Emerging, normal mkt

Developed, normal mkt

Developed, truncated

FIGURE 2.— Diversification Benefits (risk aversion 2)Note: The figures show the diversification benefits achievable in normal markets and intruncated markets, in terms of the change in CERRs produced by diversifyinginternationally. They are constructed from the joint coefficients of the regression results ofmodels 3 and 3a in tables 8 and 9. The left-hand panel shows the results of regressionswith DRNT as the dependent variable and the right- hand panel shows the results ofregressions with DRTT as the dependent variable.

markets, and increase with truncation. Other than at a threshold 0.5standard deviations above the mean, which has a significant coefficienton the +0.5DEV dummy, there is no significant difference betweenDEV/DEV and DEV/EM pairs in this respect.

C. Effects of Truncation on Internationally Diversified Portfolios

Table 10 shows the results of estimating models 1-4 for λi,j = ΔAi,j andtable 11 shows the results of ΔMi,j. In the case of ΔAi,j, the ‘avoidable’loss caused by holding a sub-optimal portfolio in a truncated market, wepresent separate estimates for the upper and lower tails because of thehighly skewed nature of the distribution, as explained in the discussionof table 6. In the case of ΔMi,j we present estimates only for the uppertail, i.e., for the maximum gain achievable in a bull market (see note 5).

The results for ΔAi,j in table 10 suggest first that the failure to predict


TA

BL

E 1

0.R

egre

ssio

n te

sts

of e

ffec

t of

tru

ncat

ion

on C

ER

R o

f di

vers

ifie

d po

rtfo

lios

in u

npre

dict

ed t

runc

ated

mar

ket

(ris

k av

ersi

on 2

)

ΔA, u

pper

tail

sΔA

, low

er ta

ils

Mod

el:

12

34

12

34

Con

stan

t–1

03.6

869

–100

.524

0–1

03.3

453

–100

.171

3–1

4.25

48–1

6.06

53–1

4.01

58–1

5.82

62(–

334.

41)*

*(–

526.

51)*

*(–

229.

48)*

*(–

362.

53)*

*(–

105.

60)*

*(–

183.

11)*

*(–

71.7

6)**

(–12

6.36

)**

LD

UK

–7.1

907

–7.1

513

2.71

062.

6726

(–37

.66)

**(–

25.8

8)**

(30.

90)*

*(2

1.34

)**

LD

Au

–2.2

980

–2.3

705

2.72

102.

7587

(–12

.04)

**(–

8.57

)**

(31.

01)*

*(2

2.03

)**

LD

DE

VU

K–0

.075

10.

0726

(–0.

20)

(0.4

2)L

DD

EV

Au

0.13

83–0

.072

1(0

.36)

(–0.

42)

-13.

6516

3.65

163.

6070

3.60

70(1

9.13

)**

(36.

04)*

*(1

3.06

)**

(24.

94)*

*-0

.56.

6101

6.61

016.

5016

6.50

16(3

4.62

)**

(65.

25)*

*(2

3.54

)**

(44.

95)*

*-0

9.24

879.

2487

9.01

879.

0187

(48.

45)*

*(9

1.29

)**

(32.

65)*

*(6

2.36

)**

+0

51.3

733

51.3

733

51.1

785

51.1

785

(117

.16)

**(2

33.0

3)**

(80.

36)*

*(1

60.4

0)**

+0.

525

.086

125

.086

124

.930

724

.930

7(5

7.21

)**

(113

.79)

**(3

9.15

)**

(78.

14)*

*

( C

onti

nued

)


TA

BL

E 1

0.(C

onti

nued

)

ΔA, u

pper

tail

sΔA

, low

er ta

ils

Mod

el:

12

34

12

34

+1

10.8

620

10.8

620

10.6

361

10.6

361

(24.

77)*

*(4

9.27

)**

(16.

70)*

*(3

3.34

)**

–1.5

DE

V–0

.456

3–0

.456

4(–

1.69

)(–

2.64

)**

–1D

EV

–0.3

710

–0.3

712

(–1.

37)

(–2.

14)*

–0.5

DE

V–0

.249

0–0

.249

1(–

0.92

)(–

1.44

)–0

DE

V–0

.017

1–0

.017

3(–

0.06

)(–

0.10

)+

0DE

V–0

.280

3–0

.301

4(–

0.45

)(–

0.79

)+

0.5D

EV

–0.3

555

–0.3

766

(–0.

57)

(–0.

99)

+1D

EV

–0.2

208

–0.2

419

(–0.

35)

(–0.

63)

+1.

5DE

V–0

.652

2–0

.673

3(–

1.05

)(–

1.76

)A

dj R

sq

0.96

840.

9920

0.96

820.

9920

0.83

780.

9543

0.83

830.

9557

NO

BS

504

504

504

504

504

504

504

504

( C

onti

nued

)


TA

BL

E 1

0.(C

onti

nued

)

Not

e: T

he ta

ble

show

s th

e re

sult

s of

est

imat

ing

the

foll

owin

g re

gres

sion

equ

atio

ns.

See

mod

el 1

, mod

el 2

, mod

el 3

, mod

el 4

on

text

.w

here

λi,j =

ΔA

i,j;

LD

i are

lead

cou

ntry

dum

mie

s di

stin

guis

hing

bet

wee

n th

e U

S (

i = 1

), U

K (

i = 2

) an

d A

ustr

alia

(i =

3);

TH

Rk i

s a

dum

my

that

take

s th

e va

lue

1 if

the

thre

shol

d eq

uals

k, k

= –

1, –

0.5,

–0,

+0,

+0.

5, +

1, +

1.5

stan

dard

dev

iati

ons

arou

nd th

e le

ad c

ount

ry’s

mea

n;D

EV

j is

a du

mm

y th

at ta

kes

the

valu

e 1

if th

e se

cond

cou

ntry

in th

e pa

ir is

a d

evel

oped

mar

ket;

DE

VT

HR

k,j e

qual

s T

HR

k × D

EV

j; a

nd

LD

DE

Vi,j e

qual

s L

Di ×

DE

Vj

T-s

tati

stic

s ar

e sh

own

in p

aren

thes

es a

nd in

dica

te s

tati

stic

al s

igni

fica

nce

at 5

% (

*) a

nd 1

% (

**),

two-

tail

ed te

sts.


TABLE 11. Regression tests of effect of truncation on CERR of diversifiedportfolios in predicted truncated market (risk aversion 2)

ΔM (Upper tails only)

Model: 1 2 3 4

Constant 11.2522 55.8970 56.9885 55.7906(15.48)** (330.74)** (181.83)** (227.19)**

LDUK 3.8471 3.7097(22.76)** (15.11)**

LDAu –0.1691 –0.1163(–1.00) (–0.47)

LDDEVUK 0.2621(0.77)

LDDEVAu –0.1007(–0.30)

+0.5 74.6722 28.8014 28.7806 28.7806(41.93)** (147.59)** (64.93)** (101.50)**

+1 91.6570 45.7862 45.9298 45.9298(51.47)** (234.62)** (103.62)** (161.98)**

+1.5 105.6245 59.7537 59.8437 59.8437(59.31)** (306.20)** (135.01)** (211.04)**

+0DEV 0.2568 0.2030(0.59) (0.60)

+0.5DEV 0.2965 0.2427(0.68) (0.72)

+1DEV –0.0173 –0.0711(–0.04) (–0.21)

+1.5DEV 0.0850 0.0312(0.20) (0.09)

Adj R sq 0.8565 0.9952 0.9883 0.9952NOBS 1,008 504 504 504

Note: The table shows the results of estimating the following regression equations.See model 1, model 2, model 3, model 4 on text.where λi,j = ΔMi,j; LDi are lead country dummies distinguishing between the US (i = 1), UK (i = 2) and Australia(i = 3);THRk is a dummy that takes the value 1 if the threshold equals k, k = –1, –0.5, –0, +0, +0.5,+1, +1.5 standard deviations around the lead country’s mean;DEVj is a dummy that takes the value 1 if the second country in the pair is a developedmarket;DEVTHRk,j equals THRk × DEVj; and LDDEVi,j equals LDi × DEVj

T-statistics are shown in parentheses and indicate statistical significance at5% (*) and 1% (**), two-tailed tests.


the nature of the market and appropriately change one’s diversifiedportfolio imposes heavy opportunity costs on investors, costs which interms of CERRs range from around 50 to 100 percentage points in a bullmarket (for example, the joint coefficient on the +0 dummy in model 1is –103.69 + 51.37 = –52.32) and 4 to 16 percentage points in a bearmarket (for investors with risk aversion 2). These clearly dwarf anylosses or benefits from holding a plain vanilla rather than diversifiedportfolio that we have discussed so far. The size of these losses appearsto be largely independent of whether the portfolio involves DEV/DEVor DEV/EM pairs of assets.

The results for ΔMi,j in table 11 confirm the large potential gainsfrom a positively truncated market and that they are negligibly affectedby whether the portfolio involves DEV/DEV or DEV/EM pairs of assets.

VI. Conclusions

In this paper we have used weekly returns data from 44 countriesbetween July 1994 and October 2003 to examine the effects of bull andbear markets on certain market variables and portfolio characteristics. In particular, we have investigated the behaviour of cross-countrycorrelations, benefits of international diversification and the effects oftruncation on the performance of diversified portfolios.

Our conclusions are as follows.Correlations between pairs of developed countries (DEV/DEV pairs)

are significantly higher (by about 0.2) than correlations between pairsof developed and emerging countries (DEV/EM pairs). Contrary toother work in this field we find that for all types of portfoliocorrelations tend to fall in both bull and bear markets, although they fallconsiderably more in bull markets. The fall in correlations is greater forDEV/DEV pairs, but the overall correlation for such pairs is sufficientlyhigh to mean that DEV/DEV correlations are still higher than DEV/EMones in truncated markets.

Cross-country diversification is worthwhile in normal markets,increasing the certainty-equivalent rate of return by an amount roughlyequal to the risk-free rate of interest (for an investor with relative riskaversion of 2). The benefits for an investor in a developed market ofdiversifying into an emerging market are higher than this, while thebenefits of diversifying into a developed market are somewhat lower.Furthermore, in unexpectedly truncated markets DEV/DEV portfolioslose the benefits of diversification, while DEV/EM portfolios do not.For DEV/DEV portfolios the benefits fall with the degree of truncation(both in bull and bear markets); indeed they fall to such an extent that


they rapidly become negative. For DEV/EM portfolios, diversificationin bull markets yields much the same benefit as in normal markets,while the benefits tend to increase in bear markets. So emergingmarkets not only provide additional diversification benefits, but thebenefits are not eroded in bull markets and are enhanced in bearmarkets. Nevertheless, the benefits in truncated markets are relativelysmall compared with the other effects of truncation.

As discussed above, our results abstract from certain practicalproblems, such as the unavailability of index futures, options andExchange Traded Funds for certain emerging markets which makes theassumption of the possibility of short-selling in all stocks at all levelsproblematic. The thinness of markets might also put practical limits onan investor’s ability to engage in DEV/EM diversification. Furtheruseful research would consider the extent to which the potential benefitsof DEV/EM diversification that we have identified are reduced by suchpractical difficulties.

Accepted by: Prof. R. Taffler, Guest Editor, January 2008 Prof. P. Theodossiou, Editor-in-Chief, January 2008

References

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Butler, K. C., and Joaquin, D. C., 2002. Are the gains from international portfolio diversification exaggerated? The influence of downside risk in bear markets, Journal of International Money and Finance, 21: 981-1011.

Campbell, R.; Koedijk, K.; and Kofman, P., 2002. Increased correlation in bearmarkets, Financial Analysts Journal, 58(1): 87-94

Erb, C. E.; Harvey, C. R.; and Viskanta, T. E., 1994. Forecasting internationalequity correlations, Financial Analysts Journal, 50(6): 32-45

Goetzmann, W. N.; Li, L.; and Rouwenhorst, K. G., 2002. Long-term globalmarket correlations, Yale ICF Working Paper 00-60; AFA 2003Washington, DC meetings

Levy, H., and Sarnat, M., 1970. International diversification of investmentportfolios, American Economic Review, 60(4): 668-675

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