Tail Dependence in REITs Returns

Kridsda NimmanuntaNIDA Business School, Thailand

Kanak PatelUniversity of Cambridge, UK

SEC Working Paper Forum #922nd October 2015

Overview

Nimmanunta & Patel2

Research QuestionsExisting LiteratureThe Generic Models and Data DescriptionsResults and Discussions

Marginal Distributions of REITsConditional CopulasTail Dependence of REITs with t Copula

Conclusions

Resea

rch Qu

estion

s

Nimma

nunta&

Patel

3Non-n

ormalit

y of as

set ret

urn dis

tributio

n (Mills

(1927)

)No

n-norm

ality o

f asset

return

s Joint

distribu

tionSee

e.g. Lo

nginand

Solnik

(2001)

, Ang

and Ch

en (20

02)A f

all in v

alues o

f asset

s beyon

d some

thresh

olds ca

n trigge

r a fall

in valu

es of ot

her ass

ets tha

t are in

itially w

eakly c

orrelat

ed wit

h the

former

Evidenc

e of ta

il depe

ndence

and a

symme

tric de

penden

ce stru

cture c

an be

found

in almo

st ever

y mark

etInte

rnation

al equi

ty mark

ets (Lo

nginand

Solnik

(2001)

)Equ

ity and

bond

marke

ts in G

-5 coun

tries (H

artmann

et al. (

2004))

Curre

ncy ex

change

marke

ts (Pat

ton (20

06))

Asian

develo

ped fut

ure ma

rkets (

Xuand

Li (20

09))

The US

and E

uropea

n CDS

marke

ts (Co

uderta

nd Ge

x(2008

))

Resea

rch Qu

estion

s

Nimma

nunta&

Patel

4In Real

Estate

marke

t,Kni

ght et

al. (200

5) the

poten

tial be

nefits

of diver

sificatio

n bet

ween re

al estat

e and e

quity m

arkets

during

down

turns

disappe

ars.

Real Es

tate Bo

om-Bu

rstDu

ring the

past t

en yea

rs, real

estate

assets

have te

nded to

mo

ve close

ly toge

ther

Tail De

penden

ce betw

een dif

ferent s

ectors

of rea

l estate

Tail de

penden

ceAsy

mmetr

y

Exist

ing Li

teratu

re Nimma

nunta&

Patel

5Time-v

arying

Condi

tional C

opula (

Patton

(2002)

), exten

ding C

opula (

Sklar(1

959))

The de

penden

ce stru

cture o

f asset

s dynam

ically o

ver tim

e by co

ndition

al on th

e past

informa

tionToo

many

copulas

to cho

ose ->

The co

pula w

ith the

highes

t loglik

elihood

value

Patton

(2006)

finds t

he dep

endenc

e betw

een De

utsche

Mark-

USD an

d Yen-U

SDhigh

ly asym

metric

in one

direct

ion be

fore the

introd

uction

of eur

o curr

ency

margin

ally asy

mmetr

ic in the

other d

irection

therea

fter

Jondea

uand

Rockin

ger(20

06) inv

estigat

e the d

epende

nce am

ong ma

jor sto

ck ma

rkets

Depen

dency b

etween

Europ

ean ma

rkets i

ncreas

es over

the sam

ple pe

riod

Goora

h(2007

) exam

ines th

e depe

ndence

struct

ure be

tween

US and

UK list

ed rea

l estate

com

panies

and RE

ITsSym

meter

isedJoe

-Clayto

n (SJC)

copul

a -bes

t fit to

the da

ily data

from 1

990Q1

to 200

7Q1

Lower t

ail depe

ndence

is gene

rally st

ronger

than th

e uppe

r one

In our p

aper, w

e exam

ine the

tail de

penden

ce withi

n US R

EITs

The G

eneri

c Mod

el

Nimma

nunta&

Patel

6Copul

a-base

d AR, G

JR-t-GA

RCH M

odel

The mo

del co

nsists o

f two c

ompon

ents: M

arginal

sand C

opula

are use

d to cap

ture th

e serial

corre

lation

Gloste

n-Jagan

nathan

-Runkl

e(GJR)

-t-GAR

CH can

captur

e three

feat

ures

Volatil

ity clus

tering

Excess

kurto

sis of t

he retu

rn distr

ibution

Levera

ge effec

tCo

ndition

al Copu

la to d

eal wit

h (asym

metric

) tail d

epende

nceGau

ssian, S

tudent

t, Gum

bel, Fr

ank, Cl

ayton, S

JC

The G

eneri

c Mod

el

Nimma

nunta&

Patel

7Specific

ation o

f the M

arginal

Distri

bution

s

The G

eneri

c Mod

el

Nimma

nunta&

Patel

8Specific

ation o

f the C

onditio

nal Co

pula

The G

eneri

c Mod

el

Nimma

nunta&

Patel

9Specific

ation o

f the C

onditio

nal Co

pula

The G

eneri

c Mod

el

Nimma

nunta&

Patel

10The Est

imation

of Par

amete

rs : Two

-step M

LUsi

ng the

exten

sion of

Sklarth

eorem

(Patto

n (2006

))

Hence

, the lo

g-likeli

hood fu

nction

can be

expre

ssed a

s

Data

Descr

iption

s

Nimma

nunta&

Patel

11Daily r

eturns

of the

U.S. eq

uity RE

ITs fro

m 2000

to 201

1:Ind

ustrial

& Office

, Reside

ntial, R

etail an

d Hote

l & Lod

gingTot

al Retu

rn Indi

ces of

FTSE/N

AREIT

North

Americ

a (Base d

ate 1st

Jan 200

0 at

1,000)

Data

Descr

iption

s

Nimma

nunta&

Patel

12Daily r

eturns

of the

U.S. eq

uity RE

ITs fro

m 2000

to 201

1:Ind

ustrial

& Office

, Reside

ntial, R

etail an

d Hote

l & Lod

ging

Data

Descr

iption

s

Nimma

nunta&

Patel

13 Data

Descr

iption

s

Nimma

nunta&

Patel

14

Margi

nal D

istrib

ution

s of R

EITs

Nimma

nunta&

Patel

15AR ter

ms bec

ome in

significa

nt after

includ

ing GA

RCH t

erms

GARC

H(1,2)

for Re

sidentia

l REIT

GARC

H(2,1)

for Ind

ustrial

& Office

REIT a

nd Ret

ail REIT

GARC

H(1,1)

for Ho

tel & L

odging

REIT

In cont

rast to

Cotter

& Stev

enson

(2007)

Levera

ge effec

t is fou

nd for

all four

REITs

Indust

rial &

Office

REIT h

as the

highest

levera

ge effec

tSign

ificant S

tudent

tdegr

ee of f

reedom

Implyin

g the e

xcess k

urtosis

of all f

our RE

ITs

Margi

nal D

istrib

ution

s of R

EITs

Nimma

nunta&

Patel

16

Margi

nal D

istrib

ution

s of R

EITs

Nimma

nunta&

Patel

17Condi

tional V

olatilit

y for ea

ch err

or ter

m of RE

ITs ret

urns

Cond

itiona

l Cop

ulas

Nimma

nunta&

Patel

18

Cond

itiona

l Cop

ulas

Nimma

nunta&

Patel

19 Cond

itiona

l Cop

ulas

Nimma

nunta&

Patel

20

Cond

itiona

l Cop

ulas

Nimma

nunta&

Patel

21 Cond

itiona

l Cop

ulas

Nimma

nunta&

Patel

22

Cond

itiona

l Cop

ulas

Nimma

nunta&

Patel

23 Cond

itiona

l Cop

ulas -

Summ

ary

Nimma

nunta&

Patel

24TV-Stu

dent tc

opula, w

hich ha

s symm

etric t

ail depe

ndence

, provi

des

the hig

hest lo

g-likeli

hood v

alue, A

IC, BIC

in all c

ases.

Hence

, the p

air-wis

e cont

empor

aneous

depen

dence

structu

res of

REITs No

t signif

icantly

asymm

etric

Unlike

other s

tudies

in vario

us asse

t mark

ets tha

t find th

e asym

metric

dep

endenc

e struc

ture

The sam

ple inc

ludes b

oth the

boom

and b

urst in

which

REITs

moved

togeth

er close

ly. As

REITs

are hig

hly cor

related

The gen

eral sh

ape of

the de

penden

ce stru

cture b

ecome

s more

imp

ortant

Cond

itiona

l Cop

ulas

Nimma

nunta&

Patel

25The sha

pe of t

he dep

endenc

e struc

ture o

f REITs

is close

r to tha

t of Stu

dent ta

nd Gu

assian

copulas

.Sca

tter Plo

ts of th

e Actu

al Prob

ability

Integra

l Value

and th

e Simu

lated Va

lue fro

m Six

Copul

as: Re

sidentia

l REIT v

s Indus

trial &

Office

REIT

Tail D

epend

ence

of RE

ITs

Nimma

nunta&

Patel

27

Linear

Corre

lation

of RE

ITs

Nimma

nunta&

Patel

28 Conc

lusion

s

Nimma

nunta&

Patel

29Using

daily d

ata of f

our U.S

. equity

REITs

(Jan 2

000 -D

ec 201

1)Lev

erage e

ffects f

ound in

every s

eries

Tail de

penden

ce wit

hin U.S

. REITs

is not s

ignifica

ntly

asymm

etric

The fea

ture fo

und in

REITs

over o

ur sam

ple pe

riod is t

he tail

depen

dence

during

both th

e uptu

rn and

downtu

rn.Ho

wever, t

he co-

movem

ents in

down

turn a

re clear

ly stro

nger

due to

leverag

e effec

ts

Q & A

Nimma

nunta &

Patel

30Conta

ct:Kr

idsda

Nimm

anun

taEm

ail: k

ridsda

.nim@

nida.a

c.th

Or Dr

Kana

k Pate

lEm

ail: k

p100

05@c

am.ac

.uk