RETURN, VOLATILITY AND LIQUIDITY SPILLOVERS:

THE CASE OF EQUITY AND COMMODITY MARKETS

Master Thesis

June 2007

Dalia Lasaite1

MSc in Finance

Supervised by:

Prof. Michael Rockinger

University of Lausanne

1 I am very grateful to my supervisor, Prof. Michael Rockinger, for his valuable support and patience. I would also like to thank Maria Khodorkovskaya, Mustafa Karaman, Ji Hyung Noh, Elzbieta Lukenskaite, and other fellow students for their valuable help, mind-blowing discussions, and entertainment. My sincerest gratitude goes to my family and Tomasz Sinicki, who supported me throughout the way. All the remaining errors are mine.

ABSTRACT

We investigate the interactions between equities and six commodity assets using vector

autoregression (VAR) and identification through heteroskedasticity (IH) techniques and find

evidence of spillovers within commodity markets, but also between equity, oil and precious

metals. Each commodity asset is mostly negatively auto-correlated in returns and positively in

volatility and liquidity, and the spillovers within commodity markets usually occur through the

latter channels. Spillovers between equities in commodities, however, are slightly different,

resulting in positive relationship in returns and liquidity between equities, precious metals and

oil. From equity investor point of view, precious metals and oil therefore are not the best

choice for diversification purposes, as they experience both return falls and liquidity squeezes

at the same time as the equity market does. Comparison of 1998-2001 and 2004-2007 periods

suggests increasing integration between metals, oil and equities, but the evidence is rather

weak. Inclusion of liquidity parameter versus return and volatility estimation does not alter the

picture dramatically, only slightly strengthening persistence in volatility. We were unable to

detect contemporaneous effects with the daily data either because of parameter instability, lack

of such interactions, or noise. The study has important implications for portfolio management

and diversification.

TABLE OF CONTENTS

1 INTRODUCTION................................................................................................................. 42 LITERATURE REVIEW .................................................................................................... 6

2.1 Market liquidity ........................................................................................................... 72.2 Liquidity spillovers ...................................................................................................... 92.3 Commodities as a portfolio investment ..................................................................... 10

3 METHODOLOGY ............................................................................................................. 113.1 Liquidity proxies........................................................................................................ 113.2 Vector Autoregression Model.................................................................................... 133.3 Identification through heteroskedasticity................................................................... 133.4 Implementation .......................................................................................................... 173.5 A note on methodology.............................................................................................. 173.6 Data ............................................................................................................................ 18

4 RESULTS ............................................................................................................................ 194.1 VAR: Single asset results........................................................................................... 19

4.1.1 Gold.................................................................................................................... 194.1.2 Silver .................................................................................................................. 194.1.3 Copper................................................................................................................ 194.1.4 Aluminium ......................................................................................................... 204.1.5 Zinc .................................................................................................................... 204.1.6 Oil ...................................................................................................................... 204.1.7 Equities .............................................................................................................. 20

4.2 VAR: Multiple asset results ....................................................................................... 214.2.1 Commodities ...................................................................................................... 214.2.2 Commodities and equities.................................................................................. 224.2.3 Time dependence ............................................................................................... 23

4.3 Identification through heteroskedasiticity: Commodity reaction to stock market..... 245 CONCLUDING REMARKS ............................................................................................. 266 REFERENCES.................................................................................................................... 28

1 INTRODUCTION

Diversification is at the heart of many portfolio management strategies. Investors, seeking for

diversification opportunities, have explored markets across the globe, and once highly

specialized investments, such as asset-backed securities or emerging market equities, have long

entered mainstream. There is some evidence, however, that as investors start chasing

diversification opportunities, correlations tend to increase and diversification gains diminish.

Indeed, recent decades have seen an increase in correlations among geographically distinct

equity markets (see Quinn & Voth (2006)). While globalization provides clear economic

reasons for this trend, alternative views suggest that the increase in correlations was caused by

either increasing inadequacy of benchmarks used (see Diermeier and Solnik, 2001) or by

endogenous reasons as portfolio holdings become more similar, resulting in liquidity-based

correlation (Acharya and Schaefer (2006)).The latter view is somewhat supported by evidence

of increasing correlations during periods of market stress, when fundamentally different assets

tend to move in-sync and liquidity dries up throughout diverse markets (see for instance

Longin and Solnik (2001)). Recent examples of such behaviour include the infamous Long

Term Capital Management collapse and, on a smaller scale, recent market corrections in May

2006 and February 2007.

Obviously, these trends are important when forming portfolio strategies. High correlation in

market crises hinders investor possibilities of realizing diversification gains if they are forced

to sell prematurely. It is particularly pronounced when investors are leveraged and face margin

calls or experience fund withdrawals if their performance falls below a threshold (see Vishny

and Shleifer (1997), Vayanos (2004)), thereby facing forced sales and propagating the crisis

further. Absolute majority of investors, however, are leveraged and/or performance-concerned,

which gives rise to self-enforcing mechanism of crises. This interrelation between correlation

risk and liquidity risk is well discussed in Acharya and Schaefer (2006). They suggest that

correlation shock depresses the collateral values of financial intermediaries’ assets, thereby

forcing them to sell their holdings across a variety of markets, which increases the correlation

further. Allen and Gale (1994) coined the term “cash-in-the-market” pricing to refer to such

situations. Therefore, if much of diversification benefits can be wiped out because of lack of

liquidity during volatile times, it is important to take these effects into account when estimating

the portfolio risk.

This paper sets out to explore this phenomenon by examining a special case: the co-behaviour

of equity and commodity markets. During recent years, commodities have come into fashion

and experienced substantial inflows from the financial sector. Increasing availability of

commodity index trackers gave more ways of investment that are available not only to highly

specialized investors but also to an average Joe. Major selling point of commodity investment

has been their low correlation to other asset classes, especially equities (outstanding

commodity returns after the technology boom also helped). Commodities generally represent

real assets with fixed supply, thereby conserving purchasing power. This perception has been

particularly evident in the case of gold, which traditionally has been a hedge against inflation

that harms both stocks and bonds, whereas oil is used to hedge against political instabilities in

oil producing regions. Since 1998, the value of OTC commodity derivatives grew 14-fold up to

$6.4 trillion (BIS Survey (2007)).

Fundamental factors of equity and commodity markets are not very related and are unlikely to

become more interrelated over time (contrary to the relation between developed and emerging

equity markets). This sets a good historical case for examining what is the interplay between

the two markets and how has it evolved over time. If the mechanism suggested by Acharya and

Schaefer (2006) is in place, one should also find that as more investors hold commodity assets,

the shocks are propagated much easier across the two markets and correlations should increase.

Consequently, the research questions of the paper are the following:

1. Are shocks to commodity markets transmitted to equities and vice versa? Has this

transmission been stable over time?

2. Can the liquidity effect explain some of the transmission in return and volatility

shocks?

We use vector autoregression (VAR) technique for estimation and test for stability of

parameters using identification through heteroskedasticity (IH) methodology by Rigobon

(2002), which circumvents simultaneity and omitted variable biases and takes advantage of

heteroscedasticity in the data. This procedure is superior to other contagion/shock propagation

estimation techniques, which use much more stringent assumptions regarding innovation

processes. To our knowledge, there has not been a study focusing on liquidity transmission

between commodities and equities.

Our results show that while volatility almost does not spill over between equities and

commodities, there is some evidence on return and liquidity spillovers between the two

markets, yet the extent is rather limited. Industrial metals experience more cross-movement in

volatility and liquidity, whereas lagged returns only influence the returns of the asset itself and

have a negative influence (i.e. there is return reversal behaviour in the data). The results are

rather distinct for precious metals, especially gold. Gold returns are positively influenced by

lagged equity returns, implying that a fall in equity prices also suggests a fall in gold prices and

vice versa. Liquidity spillovers are also persistent for gold and oil; therefore if the market dries

up in equities, it also tends to dry up in gold and oil markets. This suggests that the effective

diversification for equity portfolios is somewhat limited in gold and oil markets, and investors

should rather choose investments in aluminium or zinc, that do not exhibit such patterns.

Heteroskedasticity analysis shows no clear pattern, and, in all cases, strongly rejects the

hypothesis that parameters are stable. This may occur due to non-linearities in parameters or

violations of other assumptions. It may be the case that other shocks are not homoskedastic, as

required by the model, which may skew the results. Alternatively, it may well be the case that

the interaction between the markets is much more pronounced during crises, therefore the

parameters shift as the variance increases. This partially supports the ideas outlined in Acharya

and Schaefer (2006), who claim that the markets operate under different – liquidity and

illiquidity – regimes. Further research is clearly needed in this area and higher quality data on

liquidity indicators, such as bid ask spreads, volume, and order imbalances would be helpful.

The paper is organized in the following way. Section 2 describes theoretical literature and the

empirical studies in the field. Section 3 presents the methodological approach and the data

used. Section 4 presents the estimation results and analysis. Section 5 concludes.

2 LITERATURE REVIEW

This paper builds on numerous studies, related to several strands of academic research. Given

the nature of the study, we combine theoretical and empirical studies on liquidity, which have

been quite vast, and empirical studies on interrelation between commodities and equities,

which are emerging rapidly. The following sections will review each field in detail. Literature,

related to the methodological approach, is reviewed in the methodology section.

2.1 Market liquidity

Even though a substantial body of academic literature has accumulated on issues related to

liquidity, many issues still remain unresolved. There still is no unanimous definition of

liquidity and liquidity risk, and most studies adopt a somewhat loose concept of “the ease of

trading”, which we also use here. Research is also encumbered by the fact that liquidity is not

an observable variable, and proxies have to be estimated, while the data availability is rather

limited, especially for the less developed markets.

One approach of researching issues related to liquidity is to compare pairs of liquid and illiquid

assets with very similar remaining characteristics and see the difference in returns. A classic

example of the liquidity premium is the price behaviour of on-the-run Treasury securities (i.e.

issued in the most recent auction) and off-the-run Treasury securities (i.e. issued in the

previous auctions), which share very similar maturities and risk characteristics, yet trade at

different yields. The yield difference for two-year Treasury bills may rise up to 12 basis points

in volatile periods, such as autumn 1998 (see Furfine & Remonola (2002)). Silber (1991)

examines the discount of shares with trading restrictions as compared to freely traded shares

and finds that the illiquidity discount is on average 30%. Chan, Jain and Xia (2005) examine

closed-end single country funds and find that the fund premium is positively affected by the

target country market illiquidity. Chen and Xiong (2001) find that illiquidity discount for

Chinese restricted institutional shares, for which trading activity is highly regulated, is on

average 80%. Gagnon and Karolyi (2004) find that the price differences between ADRs and

their foreign listed primary securities can be explained by illiquidity in the U.S. and foreign

markets. Clearly, these results suggest that investors appreciate more liquid investments versus

the illiquid ones. Scholes (2000) has also suggested that liquid assets have embedded

optionality to raise cash in times of market turbulence, which illiquid assets do not have, and

therefore deserve a premium.

It is not trivial, however, what is the mechanism of incorporating liquidity to returns, and

several theoretical studies deal with this issue. Kyle (1985) has been one of the pioneers in the

literature, in his seminal work he uses a sequential auction model to show how liquidity

emerges in a dynamic setting with information asymmetry. In his model, liquidity is a result of

inventory risk as the market makers are dealing with asymmetric information.

Acharya and Pedersen (2001), also construct a general equilibrium model, where the relation

between illiquidity at individual security and market level as well as security and market

returns is investigated. They find that (1) covariance between the security illiquidity and

market illiquidity has positive effect on asset returns, (2) covariance between individual stock

returns and market illiquidity has negative effect on returns, (3) covariance between individual

security’s illiquidity and market return has negative effect on returns. In other words, investors

appreciate assets that are liquid when the market is illiquid, assets that have high returns when

market liquidity is low, and assets that have high liquidity when the market is down. Applying

their model to Center for Research in Security Prices data for the period 1964 – 2000, they find

empirical support for their results. Overall, annualized liquidity risk premium of holding

portfolio of illiquid securities against portfolio of most liquid stocks amounts to 1.1%, which is

statistically significant.

Another important contribution by Vayanos (2004) uses a general equilibrium model to show

that during volatile times, liquidity premium increases, investors become more risk averse,

assets’ pair-wise correlations may increase and illiquid assets’ market betas increase. The

defining characteristic of their model is that investors are fund managers and their clients are

withdrawing their funds if the performance falls below a threshold. This assumption is in-line

with the influential paper by Vishny and Schleifer (1997), who argue that certain asset price

misalignments cannot be arbitraged away, as the arbitrageurs, managing client portfolios and

involved in long-term arbitrage trades, face fund outflows when the misalignments deepen.

Kyle (2001) reaches similar conclusions by modelling the wealth effect of the arbitrageurs – as

the wealth of the arbitrageurs falls, they become reluctant to pursue the risky arbitrage strategy

further.

Allen and Gale (2004) developed a model, where in an incomplete-market setting, financial

intermediaries are forced to sell assets in order to obtain liquidity. As supply and demand for

liquidity may be inelastic in the short term, a small degree of aggregate uncertainty may cause

major fluctuations in the short run. This demand for liquidity is not met by the arbitrageurs,

since holding liquid assets entails significant opportunity costs, which can only be recovered

during crises. They conclude that financial crises in incomplete markets may occur purely

because of small liquidity shocks.

Acharya and Schaefer (2006) present a conceptual link between liquidity risk and correlation

risk, backed by a survey of risk managers. Their start with the observation that both liquidity

and correlation shocks are frequently preceded by a large negative asset price shock. This

shock reduces the net worth of financial intermediaries, thereby pushing them towards their

capital and collateral constraints. The intermediaries then sell their assets to meet these

constraints, which depresses asset prices and liquidity further. In this way, correlation between

seemingly unrelated assets increases and the asset prices do not reflect fundamentals anymore.

Finally, a study by Morris and Shin (2003) uses a three period model with a risky asset and two

types of traders (long horizon risk-averse traders and institutional traders) to examine the

phenomenon of sharp temporary fall in asset prices, known as liquidity black holes. They find

that as institutions impose stop-loss limits to traders, their trading horizons become shorter. If

the price falls towards the trading limits, which are commonly known, the incentives to sell

increase for all traders because of the expectation that others would sell as well. In essence, this

model is similar to the models of bank run, when withdrawals (sales) become mutually

reinforcing. Thereby, liquidity black holes come into existence.

These studies have far reaching implications for portfolio and risk management. As correlation

rises and liquidity dries up upon large negative shocks, diversification benefits decrease

substantially when they are most needed, and shocks during crises are transmitted across

otherwise uncorrelated asset classes. Also, even if asset prices do not fall during a crisis, lack

of liquidity across different markets may make them do so, thereby making it extremely

difficult to realise diversification benefits. We now turn to examine the literature on liquidity

spillovers across different assets and markets.

2.2 Liquidity spillovers

Academic work on liquidity spillovers is rather limited. Chordia, Sarkar & Subrahmanyam

(2006) examine liquidity spillovers across market-capitalisation based stock portfolios. They

use vector autoregression model and find that return and volatility spillovers persist even if

liquidity spillovers are accounted for. They also find that liquidity and volatility innovations in

small-cap portfolios are informative when predicting large-cap liquidity and vice versa.

Goyenko (2005) examines the joint dynamics of stock and bond market liquidity. Again, using

vector autoregression model, he finds that stock and bond market liquidity goes in both

directions, and is more dependent on returns than volatility. Liquidity and return innovations

are negatively correlated, and monetary policy has significant impact on bond market liquidity.

Tang and Yan (2006) analyze liquidity spillovers to credit default swap (CDS) markets. They

find significant liquidity spillovers from bond, stock, and option markets. Chordia, Roll and

Subrahmanyam (1999) find that there exists commonality in liquidity, i.e. that there exist

market-wide factors that affect the liquidity of all assets in the market. Newman and Rieson

(2004) find that in the European telecom sector illiquidity of newly issued bonds spills over to

other bonds in the sector. Overall, however, literature on interaction of liquidity among

different asset classes is quite scarce. We have not encountered a study which would focus on

liquidity spillovers between commodity and equities markets. The section below provides an

overview of literature on commodity markets and their role in portfolio diversification.

2.3 Commodities as a portfolio investment

Increasing importance of commodities has attracted more academic research into commodity-

related fields. There has been a wide debate on whether commodities are an asset class or not,

and some studies attempted to look at their historical returns. Erb and Harvey (2006) present

evidence that some features of commodities, such as term structure, may provide equity-like

returns over long term. Jensen et al (2002) suggests that if commodities are a hedge for

inflation, they should be correlated with monetary policy. They find that commodities provide

beneficial diversification opportunities during times of restrictive monetary policy, but not

during times of expansive monetary policy. Other studies mostly focus on commodity term

structure (see Lautier (2005)) or commodities in isolation, which are less relevant for our

study.

This study, in its spirit, is the most similar to Woelfle (2006). Woelfle measures the volatility

mechanism of information transmission between commodity and equity markets using

GARCH. They find no evidence of spillovers between equity and commodity markets, except

for energy sector, which is largely driven by the end-consumer side. Gold also stands out as a

hedge for energy crises; therefore its interdependence does not coincide with other metals, such

as silver or copper. Woelfe (2006), however, does not include liquidity factors in his analysis,

and therefore we would like to fill this gap in the literature.

Given the literature above, we combine insights both from liquidity and commodity research to

date. Commodity investments provide extremely interesting case study for the liquidity

literature. Investments in commodities have been emerging rapidly during recent years, while

research of correlation behaviour is mostly based on historical returns. If the link between

correlation and liquidity exists, as suggested by Acharya and Schaefer (2006), then spillovers

should increase as more investors enter the market. In addition, gold and oil should be more

interrelated to equity markets, due to their relative popularity as compared to industrial metals.

3 METHODOLOGY

3.1 Liquidity proxies

One harbinger in liquidity-related research is that liquidity is not an observable variable.

Numerous proxies have been suggested in the literature, many of them, however, are quite

data-intensive.

Quoted bid-ask spread. Bid-ask spread is the most readily available proxy for liquidity. It has

several flaws however, as some trades occur inside the quotes, which is not reflected in the

spread, thereby potentially underestimating illiquidity during crises. In their analysis, Chordia,

Sarkar and Subrahmanyam (2006) use quoted spread, defined as the difference between bid

and ask prices, and relative quoted spread, which is defined as quoted spread divided by the

midpoint of bid/ask prices, thereby eliminating the price level effects in the data. They also use

order imbalance indicator, which, unfortunately is not always available.

Effective spread proxies. Effective spread proxies aim to estimate the average cost of a round-

trip (buy and sell) transaction. Since bid-ask spreads do not always indicate the effective

transaction cost, academic literature has generally attempted to estimate the effective spread

from available data.

One measure of effective spread, developed in Roll (1984), is extremely simple, but relies on

several assumptions. The market is assumed to be informationally efficient and the observed

price changes have a stationary probability distribution. In addition, all customers trade

through a market marker, who maintains a constant spread. Finally, successive transactions are

sales or purchases with equal probability. Roll’s measure is estimated in the following way:

),(2 1 tt ppCovRM

Roll’s measure carries several limitations, for instance, it may underestimate illiquidity during

periods of market stress. In addition, the measure is undefined if the prices are serially

correlated. It is, however, widely used in the literature, and was shown to correlate well with

other high-frequency data liquidity measures (see Goyenko, Holden, Trzcinka and Lundblad

(2006)). Yet, as suggested by Bryant and Haigh (2007), it does not entirely fit commodity data

due to violations of the last assumption.

Another measure of effective spread was developed by Thompson and Waller (1988). It is

based on non-zero price change days and estimates the nominal spread. It is estimated in the

following way:

T

ttp

TTWM

1

1

The estimate, however, does not filter out the real price changes. Both estimates discussed

above are more appropriate when tick-by-tick data is available.

Price impact measures. Price impact measures aim to estimate the impact that a given trade has

on the price. The measure developed by Amihud (2002) is the most widely used in this class:

t

t

Volume

rAverageILLIQ

The ratio is calculated for positive volume days, since it is undefined for zero volume days.

This measure captures the illiquidity of the market and is designed to measure the daily price

response associated with one dollar of trading volume.

Several studies have compared the accuracy of various liquidity measures (see Goyenko,

Holden, Trzcinka and Lundblad (2006)). They have found that Amihud (2002) and Roll (1984)

perform well for monthly intervals. A more specific study, applying effective spread measures

to commodity markets, finds that Roll’s and other serial correlation based measures do not

perform well compared to absolute price change estimators, such as TWM (Bryant and Haigh

(2007)). Major problem, however, is that the microstructure data in commodity markets is

scarce and expensive, and the above mentioned estimates based on daily data can only be

obtained for monthly frequency, which dramatically reduces the sample size. With the above-

outlined caveats in mind, we will use quoted bid-ask spread in our analysis, since it is available

on a daily basis while other proxies are not.

3.2 Vector Autoregression Model

We first estimate Vector Autoregression Model (VAR), which is widely used in the literature.

VAR estimates the dynamics jointly, thereby showing the interactions between multiple

variables. The following functional form is specified:

tttt XLYLcY )()(

where tY is a vector consisting of endogenous parameters: CMt

CMt

CMt

STt

STt

STtt rrY ,,,,, .

r denotes daily log-returns, denotes volatility, estimated as the absolute value of daily log-

returns, and stands for the liquidity parameter, while superscripts ST and CM stand for stock

and commodity markets respectively. )(L is a lag operator, )(L is a lag operator with

contemporaneous variables, and tX stands for exogenous factors. We estimate this model for

stock and commodity markets, as well as for each asset separately.

While this model is useful to examine the lagged influence of one market on the other, it does

not capture the contemporaneous influence of endogenous variables. In addition, VAR does

not provide an opportunity to test the stability of parameters across different variance regimes.

In order to deal with this issue, we use identification through heteroskedasticity method by

Rigobon (2000) and specify an alternative model in the next section.

3.3 Identification through heteroskedasticity

Although widely applied, VAR models may miss out the contemporaneous influences between

the dependent variables. Since we use daily data in our estimations, and a trading day is a

sufficient period of time to transmit the shocks in one market to another, it is could be the case

that the contemporaneous influence is present. Contemporaneous interactions are infamously

hard to identify, and identification through heteroskedasticity solves this problem without

imposing restrictive assumptions. We will illustrate the methodology by the following

example.

Assume for now that the sole objective of the study is to investigate the reaction of commodity

returns to shocks in stock market. Mathematically, this could be defined in the following way:

tttt xsc

where c is daily commodity return, s is Standard & Poor’s 500 index daily return, x includes

lags of stock market returns and other observable control variables, and ε is the residual term.

Commodity market reaction to shocks in the equity market is then captured by variable β.

Alternatively, one can estimate the reaction function of the stock market to shocks in

commodity markets. This is represented in the following form:

tttt xcs

where the reaction of the stock market to shocks in commodities markets is represented by α.

The most obvious approach of estimating these effects is estimating each of the equations

separately. This approach, however, has two fundamental problems, which destroy the validity

of such estimates – simultaneity bias and omitted variables. Simultaneity bias arises from the

fact that not only stock prices influence commodity markets, but also commodities have an

influence on the stock prices. Therefore, the true relation should be written in the following

form:

tttt

tttt

xcs

xsc

The first difficulty with this estimation is that both equations are determined simultaneously,

which means that we cannot identify them in this form. There several ways of dealing with this

problem. One way used in the literature for dealing with endogeneity is imposing restrictions

on one of the coefficients. Since we are interested in estimating β, we can only imposed the

restriction of α = 0. This implicitly assumes that there is no reaction of stock prices to

commodity prices, which is unlikely. Another way of dealing with the endogeneity problem is

finding an instrumental variable which would be correlated with stock prices, but uncorrelated

with commodities. While in some cases this technique is very useful, it is difficult to find a

proper instrumental variable in this case, since both commodities and equities are influenced

by numerous economic factors, thus most variables that influence stock prices would likely

influence commodity prices as well. Therefore, none of these approaches work well in this

case.

The second potential bias is omitted variables. Omitted variables represent unobservable

factors, such as risk aversion or liquidity preference, which potentially affect stock prices

and/or commodities. This issue is difficult to deal with, since those factors are not observable,

and therefore their quantification requires proxies which are difficult to find. The third problem

may arise from heteroskedasticity, therefore using simple correlation measures between the

stock market and commodity returns is inappropriate and may bias correlation coefficients. The

bias could be corrected as proposed in Forbes and Rigobon (2002), yet the assumptions

required to make this correction are that there are no omitted variables, which is unlikely in this

case. In order to deal with heteroskedasticity, simultaneity and omitted variables biases,

Rigobon (2002) has proposed identification through heteroskedasticity.

The basic principle of identification through heteroskedasticity relies on the observation that in

a heteroskedastic data series, changes in their variance are related to changes their covariance

with the explanatory variable. In other words, when stock market has low variance, commodity

markets will explain less of the covariance between commodities and stock market. Therefore,

taking into account potential omitted variables bias, a new functional form is specified:

ttttt

ttttt

zxcs

zxsc

where z represents unobservable shocks such as liquidity preference and risk aversion.

Then, substituting expressions for c and s, a reduced form equation is obtained:

st

ct

tt

t

v

vx

s

c

where:

1

1 and

1

)1(1

)(

ttt

ttt

st

ct

z

z

v

v

This equation can be estimated with vector autoregressive approaches, but one obtains and

reduced form residuals only. In order to trace back the parameter of interest β, we will use the

fact that data exhibits heteroskedasticity over time. The variance-covariance matrix of the

residuals is the following:

22222

22222222

2 )1(.

))(1()(

)1(

1

я

zz

In the estimated matrix, we have three restrictions and six unknowns - 222 ,,,,, z.

Since the restrictions obtained from variance-covariance matrix are insufficient to identify all

parameters, it is useful to introduce heteroskedasticity in the model. Heteroskedasticty implies

that variance-covariance matrix is not constant over time, which helps to obtain additional

restrictions for the model. For that, one has to assume that there are certain regimes of variance

behaviour in stock markets and commodity markets.

The data is split into two subsamples: low variance and high variance. While the classification

is fairly arbitrary, it is more likely to fulfil the assumption of the homoskedasticity within a

subsample and yield useful results. The reduced form equation can be estimated for both

regimes separately. In this way two variance-covariance matrices are obtained, which bring

additional restrictions but also additional unknowns ( 222 ,, z for each subsample). In order

to identify the parameters, one needs to make assumptions regarding stability of the variances.

We therefore assume that commodity market shocks (ε) and unobservable shocks (z) are

homoskedastic and uncorrelated with the error term.

In this way, the matrices for each regime are denoted i for i=1..2, and the difference matrix

has the following form: 12 . Then the difference matrix is estimated as follows:

22222

22222222

212 )1(

))(1()(

)1(

1

z

zz

However, since we assume that 2z and 2

do not change throughout different variance regimes,

the differences of the terms are equal to zero and the difference matrix reduces to:

1)1(

2

2

2

Then, parameter can be estimated in two ways:

21

11ˆ

and 22

12ˆ

This additional restriction helps to test parameter stability, which we discuss together with the

results.

3.4 Implementation

Rigobon and Sack (2002) suggest a convenient instrumental variable interpretation for the

estimation of the following bivariate case:

ttttt

ttttt

zxcs

zxsc

Define two instrumental variables in the following way:

)()(1 LsHsw lh

)()(2 LcHcw lh

where H stands for high volatility subsample, and L for the low/usual volatility subsample.

Then, using the standard instrumental variable estimation procedure, estimators take the

following form:

)()(

),(),(

''

''')'(ˆ

11

11 lh

llhh

llhh

llhh

sVarsVar

csCovcsCov

ssss

cscscwsw

),(),(

)()(

''

''')'(ˆ

21

22 llhh

lh

llhh

llhh

csCovcsCov

cVarcVar

scsc

cccccwsw

These estimators are exactly the same as derived above, since estimators converge to the

variances and covariances that were developed above2. This instrumental variable methodology

makes identification through heteroskedasticity very convenient and easy to implement.

3.5 A note on methodology

Identification through heteroskedasticity is an innovative and useful methodology for

estimating various simultaneous problems. It has been successfully applied to a number of

cases, such as estimating stock market reaction to monetary policy (Rigobon and Sack (2002))

and war risk effects on financial markets (Rigobon and Sack (2003)). However, there are

2 More detailed derivations are available in Rigobon and Sack (2002) and Rigobon (2000).

several cautionary remarks that may make the procedure inapplicable. IH relies on the

following assumptions and if they are not fulfilled, the estimation would be incorrect:

- Parameters are stable throughout different regimes

- Unobservable shocks are homoskedastic and uncorrelated to the residual term

- Commodity market shocks are homoskedastic and uncorrelated to the residual term

These assumptions are less restrictive than the usual OLS or event study assumptions, but by

estimating the model we effectively put these assumptions to test. It is therefore crucial to

divide the subsamples in a way that fulfils the second and third assumptions, and yet there is no

way of testing whether the second and the third assumptions are fulfilled. We discuss this issue

further in the results section.

3.6 Data

The data used for the estimation is obtained from Reuters and Datastream and spans the time

frame of 1998 – 2007. We choose the Standard & Poor’s 500 index as a proxy for equities. In

commodities, the number of available contracts is vast, yet much of the contracts do not report

bid-ask spreads, therefore we apply data availability and liquidity criteria in order to determine

the proxies, which are summarized in the table below.

Commodity Contract maturity ExchangeGold Spot LMESilver Spot LMECopper 3M LMEAluminium 3M LMEZinc 3M LMEOil 1M NYMEX

Each asset has three data series for the whole sample period: log-return, volatility (absolute

return), and illiquidity parameter (relative bid-ask spread)3. The series are adjusted by

regressing them on weekday dummies and trend variables, in order to filter out the effects that

are not relevant to the study. Adjusted time series are used for all estimations. MATLAB codes

are available in the appendix4. The model is estimated with two lags.

3 Unfortunately, we were unable to retrieve liquidity parameters for oil; therefore only returns and volatility are used in the estimation4 Some MATLAB codes were taken from www.spatialeconometrics.com, to which we are grateful.

4 RESULTS

4.1 VAR: Single asset results

We first estimate the interplay between returns, volatility and illiquidity for single asset

markets. The results for each asset are discussed below.

4.1.1 Gold

Returns in gold are not persistent and do not spill over to volatility and illiquidity. Innovations

in illiquidity and volatility strongly Granger-cause each other, thereby confirming the intuition

that illiquidity periods tend to be succeeded by periods of high volatility, and vice versa.

Exclusion of illiquidity parameter gives similar results, the only persistent factor being

volatility.

4.1.2 Silver

Silver patterns are slightly distinct from other metals, for that returns are Granger-caused both

by lagged returns and volatility. In addition, returns, volatility and illiquidity play a role in

determining volatility. Higher lagged volatility results in higher volatility and higher returns,

while widening bid-ask spread results in higher volatility. In addition, model without illiquidity

parameter shows similar results, exhibiting substantial persistence in returns and volatility. The

results for gold and silver are summarized in the table below.

Table 1. Granger-causality F-test probabilities

Gold SilverReturns Volatility Illiquidity Returns Volatility Illiquidity

Returns 0,2537 0,9084 0,1677 0,0000 0,2214 0,3098Volatility 0,8804 0,0000 0,0180 0,0000 0,0000 0,0000Illiquidity 0,9073 0,0001 0,0000 0,3276 0,0761 0,3165N.B. Green (red) variable implies that the relationship is positive (negative)

4.1.3 Copper

VAR results suggest that returns are Granger-caused by return lags, and, to a lesser extent, by

lags in volatility; however, the R-squared is a meagre 0.03, therefore the links are rather weak.

Illiquidity plays almost no role in determining the return behaviour. Volatility exhibits

persistent behaviour and is Granger-caused both by volatility and illiquidity lags - higher bid-

ask spread suggests higher volatility in the next period. Illiquidity variable is significantly

determined by returns, volatility and illiquidity lags. The relationship is most pronounced for

illiquidity, thereby suggesting that illiquidity could behave in a regime-switching fashion. High

volatility results in higher bid ask spreads next periods, while positive returns result in

narrower bid-ask spreads. Exclusion of illiquidity parameter from the estimation does not alter

the results for returns and volatility significantly.

4.1.4 Aluminium

In the case of aluminium, all lagged variables tend to predict themselves, while their

interaction is much less significant. Returns appear to Ganger-cause illiquidity and the relation

between returns and bid-ask spread is, somewhat counter-intuitively, positive. Other variables

do not exert any significant effects. Inclusion of the illiquidity parameter, as compared to

returns and volatility only estimation, significantly alters the results and decreases the

persistence of returns and volatility.

4.1.5 Zinc

Zinc exhibits strong positive Granger-causality of volatility and bid-ask spreads in both

directions, implying that a liquidity squeeze is followed by market volatility, and market

volatility is followed by lower liquidity. Lagged returns play a role in explaining future returns

– positive returns Granger-cause negative returns, implying frequent price reversals. Again,

returns play no role in Granger-causing illiquidity or volatility.

Table 2. Granger-causality F-test probabilitiesCopper Aluminium Zinc

Returns Volatility Illiquidity Returns Volatility Illiquidity Returns Volatility IlliquidityReturns 0,0015 0,0020 0,2248 0,0362 0,2299 0,0000 0,1010 0,1341 0,7036

Volatility 0,4357 0,0000 0,0004 0,0000 0,0000 0,0000 0,1856 0,0000 0,0000Illiquidity 0,0106 0,0001 0,0000 0,4848 0,8600 0,6587 0,0891 0,0002 0,0000N.B. Green (red) variable implies that the relationship is positive (negative)

4.1.6 Oil

Since data for oil liquidity is not available, the results are quite limited for oil. Volatility seems

to negatively Granger-cause returns, i.e. following high volatility the returns are lower.

Volatility is also persistent and high (low) volatility tends to stay high (low).

4.1.7 Equities

In the case of equities, returns do not exhibit any persistence, and both volatility and illiquidity

do not play a role in return determination. Returns only Granger-cause volatility, implying that

negative returns give rise to high volatility. Both illiquidity and volatility are persistent, thus

high volatility (liquidity) today suggests high volatility (liquidity) tomorrow. Finally, volatility

has a surprising negative relation to illiquidity, but the relation is quite weak. Excluding

illiquidity variable from the estimation has no effect on return persistence, and only strengthens

the persistence in volatility.

Table 3. Granger-causality F-test probabilitiesEquities

Returns Volatility IlliquidityReturns 0,3687 0,4754 0,4008

Volatility 0,0000 0,0000 0,0288Illiquidity 0,9189 0,0055 0,0000

N.B. Green (red) variable implies that the relationship is positive (negative)

Overall, it seems that returns, volatility and illiquidity are more persistent in their own

domains, and the cross-relations are quite weak. Volatility and liquidity have somewhat

stronger interrelation patterns both for equities and commodities, and, as expected, higher

illiquidity results in higher volatility and the opposite. Exclusion of liquidity parameter

generally has no effect on returns, but somewhat strengthens the persistence in volatility, which

suggests that liquidity plays a role in volatility behaviour.

4.2 VAR: Multiple asset results

4.2.1 Commodities

In this estimation, we estimate the model for all five metals and oil jointly. In this way, one

may see whether returns, volatility and liquidity spill over across different assets. Due to high

space requirements, complete results are available upon request.

Return spillovers are not very persistent, most returns are Granger-caused by lagged own

returns, with the exceptions of copper (caused by aluminium) and gold (caused by silver).

Illiquidity and volatility generally do not play a role in return prediction. Illiquidity and

volatility exhibit more interdependence across different assets, yet the extent is rather limited.

Both parameters are rather persistent within the series of each assets, and more spillovers occur

in these variables than in returns. Copper volatility and liquidity spill over from all metals

except gold, similar pattern is observable for zinc. Silver is influenced only by own lags and

gold volatility, while gold is determined separately and does not experience Granger-causality

from any of the other metals except silver. Oil has no spillovers from other metals as well.

Table 4. Estimation results: CommoditiesAsset Code Significantly Granger-caused by*:Copper Returns CR CR(-), AR(+)Copper Volatility CV CV(+), CL(+), SV(+)Copper Illiquidity CL CV(+), CL(+), AV(-), ZL(+)Aluminium Returns AR AL(+)Aluminium Volatility AV AR(-), AV(+), AL(+)Aluminium Illiquidity ALZinc Returns ZRZinc Volatility ZV CV(+),CL(+), ZL(+), SL(+)Zinc Illiquidity ZL CV(+), CL(+), ZL(+)Silver Returns SR SR(-)Silver Volatility SV SR(-), SV(+), SL(+), GR(+), GVSilver Illiquidity SLGold Returns GRGold Volatility GV GV(+)Gold Illiquidity GL GV(+), GL(+)Oil Returns OR OV(-)Oil Volatility OV OV(+)

*At 1% level of significance

As seen from the table above, most spill overs occur through volatility, whereas illiquidity and

returns have slightly less persistent patterns. Illiquidity, however, shows much stronger

persistence than returns. Own returns tend to exhibit reversals and have negative relation to

their lags.

4.2.2 Commodities and equities

Inclusion of equities into the estimation does not change the interactions between the metals

dramatically, yet equities cause some interesting effects. Equity returns play a role in Granger-

causing copper, silver, and gold returns. Contrary to metal own lagged returns, when the

relation is negative (i.e. returns tend to reverse), equity returns have a positive influence on

metal returns, i.e. after a fall in stock prices, metals tend to fall as well. This effect is

particularly pronounced for the precious metals – gold and silver.

Table 5. Estimation results: Commodities and equitiesAsset Code Significantly Granger-caused by*:Copper Returns CR CR(-), AR, ER(+)Copper Volatility CV CL(+), ZV, SV(+)Copper Liquidity CL CV(+), CL(+), AV(-), ZL(+)Aluminium Returns AR AL(+)Aluminium Volatility AV AR(-), AV(+), AL(+)Aluminium Liquidity ALZinc Returns ZRZinc Volatility ZV CV(+),CL(+), SV(+)Zinc Liquidity ZL CV(+), CL(+), ZL(+)Silver Returns SR SR(-), ER(+)Silver Volatility SV SR(-), SV(+), SL(+), GR(+), GVSilver Liquidity SLGold Returns GR ER(+)Gold Volatility GV GV(+)Gold Liquidity GL GV(+), GL(+), EL(+)Oil Returns OR OV(-)Oil Volatility OV OV(+), EL(+)Equity Returns EREquity Volatility EV ER(-), EV(+)Equity Liqudity EL EL(+), GL(-)* Significant Granger-causality is set at the level of 1% or smaller

Equity volatility does not influence commodities at all, the only influence that it has is a lagged

positive effect on equity volatility, supporting the prior academic evidence on volatility

persistence. Equity liquidity, however, has a positive influence on gold liquidity and oil

volatility, thereby implying that after times of low liquidity in the equity markets, liqudity also

dries up in the gold market and volatility rises in the oil market. A speculative explanation

could be that since gold and oil markets are the most popular commodity investments5, a shock

in the equity markets is easily transmitted to these markets. Clearly, this effect is not

particularly desirable when considering diversification opportunities.

4.2.3 Time dependence

In order to capture the dynamic changes in the spillover patterns, we estimate the model for

two 3-year periods: 1998 – 2001 and 2004 – 2007. This allows to check whether the

interactions have changed over time. The results of the estimation point to strengthening

liquidity channel and increasing cross-autocorrelations among metals. Influence of equity

5 Crude oil and gold respectively have 93mn and 34.5mn futures contracts and 14.8mn and 2.9mn options contracts traded by financial market participants in 2005 (BIS survey (2007))

returns became more pronounced for copper liquidity and zinc returns, while equity liquidity

exerted impact on silver liquidity and oil volatility in the second period, but not in the first one.

Overall, there is a trend on more cross-relations and higher role of liquidity towards the second

sample, yet further research is needed in order to find a more conclusive result.

Table 6. Granger-causality: Time dependenceAsset Code 1998 – 2001 R-sq. 2004 – 2007 R-sq.Copper Returns CR 0.0933 0.0744Copper Volatility CV 0.0797 0.1260Copper Liquidity CL CL(+), ZL(+) 0.3003 CL(+), ER(-), AL(+) 0.1977Aluminium Returns AR AL(+) 0.3048 AL(+) 0.3063Aluminium Volatility AV 0.1029 CV(+), CL(+) 0.1331Aluminium Liquidity AL 0.0535 AV(-) 0.0858Zinc Returns ZR ZL(+) 0.0781 ER(+) 0.0716Zinc Volatility ZV 0.0702 CL(+) 0.1328Zinc Liquidity ZL CL(+), ZL(+) 0.3041 ZL(+), EL(-) 0.1625Silver Returns SR SV(+), ER(+) 0.0795 GR(-) 0.0860Silver Volatility SV 0.0780 SV(+) 0.1478Silver Liquidity SL EL(+) 0.1235 SL(+), EL(+) 0.1848Gold Returns GR 0.0636 GR(-) 0.0801Gold Volatility GV GV(+), GL(+) 0.1730 SV(+) 0.0914Gold Liquidity GL GV(+), GL(+) 0.2404 GL(+) 0.2052Oil Returns OR OV(-) 0.0748 0.0390Oil Volatility OV ER(+) 0.0795 EL(+) 0.0757Equity Returns ER 0.0617 0.0581Equity Volatility EV ER(-), EV(+) 0.1238 ER(+) 0.0816Equity Liquidity EL EL(+) 0.3839 EL(+) 0.2649

4.3 Identification through heteroskedasiticity: Commodity reaction to stock market

Vector autoregressive estimations are clearly useful, yet they do not capture the

contemporaneous interrelations between the endogenous variables. If contemporaneous

interactions between these markets are substantial, important effects may be hidden if one

relies on VAR method only. Therefore, now we estimate an alternative methodology,

identification through heteroskedasticity (IH).

The intuition behind IH is similar to event study approaches, except that IH assumptions are

much less stringent. In order to reach consistent estimate in the event study methodology, an

implicit assumption of variance of the shock in question being infinitely large compared to

other shocks has to be fulfilled (Rigobon and Sack (2002)). This assumption is dropped in IH

estimation, the only requirement is that the variance of the shock of interest would increase

while other shock variances stay the same. Since we are looking from the point of view of

investor who uses commodities as a tool to diversify his equity holdings, we are more

concerned with the reaction of commodity markets to shocks in the stock market. Therefore,

the primary interest of this section is the simultaneous reaction of commodities to the shocks in

the stock market.

In order to estimate IH, one first has to divide the sample into subsamples based on variance

behaviour, the key condition being that the stock market shocks would be homoskedastic in the

subsamples. The sample is divided based on implied volatility index (VIX) behaviour into high

volatility and low volatility6, since this index shows investor risk aversion and therefore is a

good proxy for stock market shocks. We then estimate the reduced form residuals for each

subsample, obtain variance-covariance matrices, and estimate the parameters using

instrumental variable approach. We estimate IH for each commodity paired with equity

market. The results of the estimation are summarized in the table below.

Table 7. Identification through heteroskedasticity resultsAsset Code Beta 1 T-stat Beta 2 T-statCopper Returns CR 0.9620 0.3381 5.7083 2.1511Copper Volatility CV -0.1804 -0.0452 30.4756 1.6006Copper Liquidity CL -0.0219 -0.0345 6.9185 0.0714Aluminium Returns AR 8.6527 1.6453 -22.2390 -48.8530Aluminium Volatility AV 9.9884 0.9968 50.1642 68.1388Aluminium Liquidity AL 21.1205 1.3696 1416.2517 110.8988Zinc Returns ZR 1.4070 1.1335 3.0931 4.2582Zinc Volatility ZV 1.2756 0.2272 16.0873 4.8237Zinc Liquidity ZL 0.2560 0.1344 490.1365 7.4429Silver Returns SR 0.8727 0.5573 3.0766 1.6329Silver Volatility SV 1.5886 0.2022 12.2599 2.3042Silver Liquidity SL 0.4109 0.7333 -5.1935 -1.4028Gold Returns GR -0.1345 -0.1466 -16.0532 -3.8669Gold Volatility GV 11.4232 2.6390 1.3982 6.3252Gold Liquidity GL 0.3345 1.2321 -4.9327 -4.6875Oil Returns OR -0.1056 -0.0240 -104.2781 -1.8047Oil Volatility OV -2.8243 -0.4385 7.5942 2.4017

Clearly, the table above suggests that either the parameters are unstable or some assumptions

of the model are violated. Beta 2 in absolute value is almost always larger than Beta 1,

therefore it is useful to recall how are both parameters estimated:

)()(

),(),(')'(ˆ

11

11 lh

llhh

sVarsVar

csCovcsCovcwsw

6 High volatility sub-sample includes the days when VIX changes by more one standard deviation from the mean, and low volatility is defined when analogous change occurs one deviation below the mean.

),(),(

)()(')'(ˆ

21

22 llhh

lh

csCovcsCov

cVarcVarcwsw

Examination of the intermediate estimation results suggests that although high and low

variance regimes are quite similar, the shift in commodity variance is substantial, while the

shift in covariances is not. This basically implies that the shocks in one market do not change

the correlation between the two markets, thereby making proper identification impossible and

parameters unstable. Intuitively, this situation resembles the case when in an event study the

event shocks are overwhelmed by usual market activity or shocks from other markets, thereby

decreasing the impact of the shocks. Therefore, we are unable to claim the stability of

parameters, interrelation remains inconclusive, and alternative specifications of variance

regimes could be employed in further research.

5 CONCLUDING REMARKS

The study is aimed to investigate the interaction between equity and commodity markets.

Empirical results suggest that shocks in equity and commodity markets are responding to

shocks in one another to a certain extent. While intra-commodity market effects are mostly

transferred through volatility and liquidity, relationship between equity and commodity

markets is transmitted through return and liquidity channels. These effects are more

pronounced for precious metals and oil. These transmission channels seem to be leaning

towards more interaction in recent years as compared to 1998-2001, however, the results are

not clear-cut and require caution when interpreting. It also seems that liquidity channel is

playing increasingly larger role, but this result has to be cross-checked with other proxies for

liquidity.

Determining simultaneous interactions between the two markets did not yield any consistent

results. It could be the case that the transmission parameters are unstable with regard to the

variance in the stock market, or additional shocks prevented estimation the contemporaneous

influences. This may also imply that the markets do not interact contemporaneously, as the

change in commodity market variance does not cause major shifts in correlation patterns

between the two markets. Therefore, interactions may not be substantial on a daily time frame,

but prevail in the longer term.

Inclusion of liquidity parameter into the estimation alters the results only slightly. Volatility is

still very persistent, which is in line with previous results in the literature, and returns are

negatively auto-correlated for some metals. Equity returns have a positive relationship with

gold, silver and copper, and equity liquidity positively Granger-causes volatility in the oil and

gold markets. This undermines the effectiveness of diversification in those markets, therefore

an investor willing to diversify her equity holdings should rather choose aluminium or zinc

investments.

Implications for further research include, first of all, search for better data and better liquidity

proxies for commodities, since the reported bid-ask spread is quite a noisy indicator. Research

on spillovers and their relationship to the share of financial speculator participation in

commodity markets would also be very interesting, and the liquidity channel effects clearly

deserve further study. In addition, effective diversification could be estimated for investors

who face funds withdrawals as the performance falls below a threshold based on the historical

data. Somewhat speculatively, these results suggest that in order to reap diversification

benefits, a leveraged investor should invest into markets which are liquid, but also, in which

most investors have different portfolios and different trading motives than the investor, such as,

for instance, hedging. This would minimize the risk of liquidity squeezes that occur

endogenously. All these issues merit further research, which would usefully complement the

literature on portfolio management in frictionless markets with insights from a more realistic

perspective.

6 REFERENCES

Acharya, V. and L. H. Pedersen, 2003. "Asset Pricing with Liquidity Risk" (February 2003). CEPR Discussion Paper No. 3749.

Acharya, V. and S. Schaefer, 2006. “Liquidity Risk and Correlation Risk: Implications for Risk Management”, Working Paper Series.

Allen, F. and D. Gale, 2004. "Financial Fragility, Liquidity and Asset Prices," Center for Financial Institutions Working Papers 01-37, Wharton School Center for Financial Institutions, University of Pennsylvania.

Allen, F. and D. Gale, 1991. "Limited Market Participation and Volatility of Asset Prices," Weiss Center Working Papers 14-91, Wharton School - Weiss Center for International Financial Research.

Amihud, Y., 2002. “Illiquidity and Stock Returns: Cross section and time-series effects.” Journal of Financial Markets 5, 31-56.

Bryant, H.L. and M. S. Haigh, 2007. „Bid-Ask Spreads in Commodity Futures Markets“, University of Maryland Working Paper.

Chan, J., R. Jain and Y. Xia, 2005. „Market Segmentation, Liquidity Spillover, and Closed-end Country Fund Discounts“, Working paper.

Chen, Z. and P. Xiong 2001, "Discounts On Illiquid Stocks: Evidence From China" (September 2001). Yale ICF Working Paper No. 00-56.

Chordia, T., R. Roll, and A. Subrahmanyam, 1999. "Commonality in Liquidity" (March 1999).

Chordia, T., A. Sarkar, and A. Subrahmanyam, 2005. "Liquidity Dynamics and Cross-Autocorrelations" (November 22, 2005). FRB NY Research Paper No. 207.

Diermeier J. and B. Solnik, 2001. “Global Pricing of Equity”, Financial Analysts Journal, Vol. 57, No. 3.

Domanski, D. and A. Heath, 2007. „Financial investors and commodity markets“, BIS Quarterly Review.

Ehrmanna, M., M. Fratzscherb and R. Rigobon, 2005. „Stocks, Bonds, Money Markets and Exchange Rates: Measuring International Financial Transmission“, Working paper.

Erb, C. B. And C. R. Harvey, 2006. „The Tactical and Strategic Value of Commodity Futures“, Working papers.

Forbes, K.J. and R. Rigobon, 2002. “No Contagion, Only Interdependence: MeasuringStock Market Comovements,” Journal of Finance, 57 (5), 2223–2261.

Furfine, C.H. and E. M. Remolona, 2002. „What’s behind the liquidity spread? On-the-run and off-the-run US Treasuries in autumn 1998“, BIS Quarterly Review, June 2002.

Gagnon, L. J. and G. A. Karolyi, 2004. "Multi-Market Trading and Arbitrage" (June 17, 2004). Dice Center No. 2004-9.

Goyenko, Ruslan, 2006. "Stock and Bond Pricing with Liquidity Risk" (March 2006). EFA 2005 Moscow Meetings.

Goyenko, R., C. W. Holden, C. A. Trzcinka, and C. T. Lundblad, 2006. „Horseraces of Monthly and Annual Liquidity Measures“, Working Paper.

Jensen, G.R., R.R. Johnson, and J.M. Mercer, 2002. “Tactical Asset Allocation and Commodity Futures,” Journal of Portfolio Management, 2002, 28 (4), 100–111.

Kyle, A.S., 1985. „Continuous Auctions and Insider Trading“, Econometrica, Vol. 53, No. 6. (Nov., 1985), pp. 1315-1335.

Kyle, A.S. and W. Xiong, 2001. „Contagion as a Wealth Effect“, The Journal of Finance, Vol. 56, No. 4, Papers and Proceedings of the Sixty-First Annual Meeting of the American Finance Association, New Orleans, Louisiana, January 5-7, 2001. (Aug., 2001), pp. 1401-1440.

Lautier D., 2005. „Term Structure Models of Commodity Prices: A Review“, Journal of Alternative Investments, Summer 2005.

Longin, F. and B. Solnik, 2001. „Extreme Correlation of International Equity Markets“, The Journal of Finance, Vol. 56, No. 2. (Apr., 2001), pp. 649-676.

Morris, S. And H. S. Shin, 2003. „Liquidity Black Holes“

Newman, Y. S., and M. A. Rierson, 2004. „Illiquidity Spillovers: Theory and Evidence From European Telecom Bond Issuance“

Quinn, D. and H.-J. Voth, 2006.“The Great Diversification Fata Morgana: Capital Account Openness and the Fall and Rise of Stock Market Correlations, 1890-2000”, Universitat Pompeu Fabra Working paper Series.

Rigobon, R., 2000. „A simple test for stability of linear models under heteroskedasticity, omitted variable, and endogenous variable problems.“

Rigobon, R. and B. Sack, 2001. "Measuring the Reaction of Monetary Policy to the Stock Market" (February 23, 2001). FEDS Working Paper No. 2001-14.

Rigobon, R. 2002. „Identification through Heteroskedasticity“. Sloan School of Management, MIT and NBER Working Papers.

Rigobon, R., 2002. „On the Measurement of the International Propagation of Shocks: Is the Transmission Stable?“

Rigobon, R. and B. P. Sack, 2003. "The Effects of War Risk on U.S. Financial Markets" (March 26, 2003). MIT Sloan Working Paper No. 4417-03.

Roll, R., 1984. „A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market“, The Journal of Finance, Vol. 39, No. 4. (Sep., 1984), pp. 1127-1139.

Scholes, M. S., 2000. „Crisis and Risk Management“, The American Economic Review, Vol. 90, No. 2, Papers and Proceedings of the One Hundred Twelfth Annual Meeting of the American Economic Association. (May, 2000), pp. 17-21.

Shleifer, A. and R. W. Vishny, 1997. „The Limits of Arbitrage“, The Journal of Finance, Vol. 52, No. 1. (Mar., 1997), pp. 35-55.

Silber, W. L., 1991, Discounts on restricted stock: The impact of illiquidity on stock prices,Financial Analysts Journal 47, 60-64.

Tangy, D.Y. and H. Yanz, 2006. „Liquidity, Liquidity Spillover, and Credit Default SwapSpreads“, Working Paper.

Vayanos, D., 2004. „Flight to Quality, Flight to Liquidity and the Pricing of Risk“, NBER Working Paper Series, No. 10327.

Wölfle, M., 2006. „Information Transmission among Commodities: A Volatility Approach to Input Markets“, Working Paper.

APPENDIX: MATLAB CODES

Implementation: VAR

close allclear allclc

CopperRaw = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\alle.xls', 'Copper');

CopperAdj = [];j=1;for j=1:3 Results = ols(CopperRaw(:,j),CopperRaw(:,4:end)); CopperAdj(:,j)=Results.resid;end

AlRaw = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\alle.xls', 'Aluminium');

AlAdj = [];j=1;for j=1:3 Results = ols(AlRaw(:,j),AlRaw(:,4:end)); AlAdj(:,j)=Results.resid;end

ZincRaw = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\alle.xls', 'Zinc');j=1;ZincAdj = [];

for j=1:3 Results = ols(ZincRaw(:,j),ZincRaw(:,4:end)); ZincAdj(:,j)=Results.resid;end

SilverRaw = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\alle.xls', 'Silver');

SilverAdj = [];j=1;for j=1:3 Results = ols(SilverRaw(:,j),SilverRaw(:,4:end)); SilverAdj(:,j)=Results.resid;end

GoldRaw = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\alle.xls', 'Gold');

GoldAdj = [];j=1;for j=1:3 Results = ols(GoldRaw(:,j),GoldRaw(:,4:end)); GoldAdj(:,j)=Results.resid;end

SPRaw = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\alle.xls', 'SP');

SPAdj = [];j=1;for j=1:3 Results = ols(SPRaw(:,j),SPRaw(:,4:end)); SPAdj(:,j)=Results.resid;end

OilRaw = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\alle.xls', 'Oil');

OilAdj = [];

for j=1:2 Results = ols(OilRaw(:,j),OilRaw(:,4:end)); OilAdj(:,j)=Results.resid;

end

All = [CopperAdj AlAdj ZincAdj SilverAdj GoldAdj OilAdj SPAdj];

variab = ['CRet';'CVol';'CLiq';'ARet';'AVol';'ALiq';'ZRet';'ZVol';'ZLiq';'SRet';'SVol';'SLiq';'GRet';'GVol';'GLiq';'ORet';'OVol';'ERet';'EVol';'ELiq'];

answer = vare(All,2);prt_var(answer,variab)

Implementation: IHclear allclose allclc

C = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\all1.xls', 'Copper');Regimes = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\all1.xls', 'Regimes');

S = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\all1.xls', 'SP');%Int = xlsread('C:\Documents and Settings\Dalia\Desktop\Master Thesis\all1.xls', 'Interest');

C = adjust(C);S = adjust(S);

C = C(:,2);S = S(:,2);

C1 = divid(C,Regimes);S1 = divid(S,Regimes);

C1 = divide(C,Regimes);S1 = divide(S,Regimes);

CIV = instrumental(C, Regimes);SIV = instrumental(S, Regimes);

%ahatC = inv(SIV'*S1)*(SIV'*C1)%ahatS = inv(CIV'*S1)*(CIV'*C1)

answ = ols(S1,SIV);

Shat = answ.yhat;

answ2 = ols(C1,Shat);

%fprintf('Beta = %9.4f \n',answ2.beta);%fprintf('Beta st.e. = %9.4f \n',answ2.bstd);fprintf('Beta tstat = %9.4f \n',answ2.tstat);fprintf('R-squared = %9.4f \n',answ2.rsqr);

answ1 = ols(S1,CIV);

%Shat1 = answ1.yhat;

answ3 = ols(C1,Shat1);

fprintf('Beta = %9.4f \n',answ3.beta);fprintf('Beta st.e. = %9.4f \n',answ3.bstd);fprintf('Beta tstat = %9.4f \n',answ3.tstat);fprintf('R-squared = %9.4f \n',answ3.rsqr);

Support: Adjustfunction Adj = adjust(x)

Adj = [];j=1;for j=1:3 Results = ols(x(:,j),x(:,4:end)); Adj(:,j)=Results.resid;endreturnSupport: instrumentalfunction ann = instrumental(x, regime)

len = length(x);n = [];z = 1;a = 1;b = 1;for z=1:len if regime(z,1)>0; ann(a,:)=x(z,:); a = a+1; elseif regime(z,1)<0 ann(a,:)=-x(z,:); a = a+1; endz = z+1;end