**JOURNAL OF RESEARCH IN NATIONAL DEVELOPMENT VOLUME 8 NO 2, DECEMBER, 2010**

**
SPECULATIVE BUBBLE AND THE NIGERIAN STOCK MARKET**

**
P.P.
Njiforti and Akaolisa Chidiogo
**

**
Department of Economics, Ahmadu Bello University,
Zaria**

**
E-mail**:
**njifortica@yahoo.com**

**
**

**
Abstract**

*
This
paper investigated the characteristic growth in
the NSE by considering the share prices of
selected banks and insurance companies. Time
series data on daily basis for price-dividend
ratio, share prices, dividend from 1 ^{st} quarter
of 2008 to 4^{th} quarter of 2009 were
used for analysis. The Augmented Diker Fuller
(ADF) test, Augmented Engel Granger (AEG)
cointegration test and the Autoregressive
Conditional Heteroskedascity (ARCH) are the
econometric techniques used to investigate the
characteristic bahaviour of the NSE. The ADF
result suspected speculative bubbles in most of
the banks and insurance companies (i.e. the
price-dividend ratio, share prices and dividend
were non stationary). The AEG result confirmed
that the ADF conducted on the
residuals for most of the banks and insurance
companies were non stationary The GARCH estimates suggested
volatility
clustering meaning that the shock in these
stocks were persistent. TARCH estimate indicated
that positive and negative shocks /news are
asymmetry and have asymmetric effect on
volatility.
Therefore, it is
concluded that bubble existed in the NSE in the
period under review. Information should be well
circulated about the stocks in the market and
Investors especially illiterate ones should be
tutored before they make their investment decision*

Key words: Speculative, bubble, stock market,
share price, dividend

**
**

**
Introduction**

Bubbles can be
defined as increase in share prices and volumes
that are far from intrinsic values. It is
described as a steep and persistent increase in
the price of an asset which is followed by a sharp
fall, whatever the causes of price movements
(Pratten 1993:29). It is also described as a
situation when the price for an asset exceeds its
fundamental price by a large margin (WEO.2003).
Prices rise or bubble when investors become greedy
and act as risk lovers.
The bubble is not completed until prices fall back
down to normalized levels; this usually involves a
period of steep decline in price during which most
investors panic and sell out of their
investments. While each speculative bubble has its
own driving factors and variables, most involve a
combination of fundamental and psychological
forces. In the beginning, attractive fundamentals
may drive prices higher, but over time behavioral
finance theories suggest that people invest so as
to not "miss the boat" on high returns gained by
others. When the artificially high prices
inevitably fall, most short-term investors are
shaken out of the market after which the market
can return to being driven by fundamental metrics
(Investopedia).
Moreover, a bubble is not indefinitely
sustainable. Prices cannot go up forever, and when
price increases end, then the increased demand
that the price increases generated ends too. Then,
a downward feedback can replace the upward
feedback.

Nigeria, from a market capitalization of
2.94billion in 1999, the Nigerian Capital Market
as at June 2007 had reached a stock value of 63
billion and by March 6, 2008 reached a peak of
12.6 trillion. We see that the percentage increase
is quite high and that from history a huge and
rapid growth in the stock market will most times
lead to a feedback correction mechanism owing to
the fact that the growth or increase may not have
been genuine, efficient or realistic in the case
of those nations.
However in the case of NSE we see that this growth
(sudden rise in prices of stock) was not sustained
for a long period of time such that by the month
of March 2008, the market started declining. It
was like a joke to the stock market brokers and
the NSE body as a whole because they were busy
telling people then that it was just a correction
that will quickly take place and not affect their
investments such that within a little time the
market will bounce back. This seems not to be true
because
as at March 2009 the market has lost over
50 % from that high peak of March 2008. It is
necessary to see if the growth that was in the
market between 2004 and March 2008 could be
explained by fundamentals or not, and its impact
on the economy. Also relating what is happening
globally in the economy it is seen that the melt
down or sudden decrease have been experienced
might be as a result of domestic factors or
foreign factors.Having
seen these
experiences by others, it becomes expedient
to look at this financial term “bubble” in the
case of Nigeria Stock Market knowing that
countries that had this experience never remained
the same in that despite the fact that their
income grew around that period the negative effect
was undesirable and disastrous. As believed by
most authors that a bubble will always be followed
up by a crash due to the imperfections in the
financial market it then becomes necessary to
consider the NSE and its behavior to observe the
following to verify if the NSE has experienced a
speculative bubble, and whether the bubbles had
impact on the economy.

**
**

**
Theoretical literature**

The
efficient market theory assumes rational
behaviour. It states that the price of a stock at
any given time is equal to the expected present
value of the stream of future dividends that will
accrue on the stock. This theory can be seen as
theory of competitive equilibrium applied to
assets market. EMH evolved in the 1960s from the
PhD dissertation of Eugene Fama in which he
defined an efficient market as a market where
there are large numbers of rational profit
maximizers, actively competing with each other
trying to predict future market values of
individual securities and where important current
information is almost freely available to all
participants. If a market is perfectly efficient,
price at all times will reflect consensus of value
determined by buyers and sellers acting upon their
assessment of all pertinent information (i.e.
unexpected news) will cause prices to change
quickly until a new consensus of value is reached
too quickly for traders to profit from the news
unexpected events randomly occur thereby making
the market either bullish or bearish (Herbst
1992).

**
**

**
Arch and garch**

The ordinary least square (OLS) lacks the ability
of estimating fat fail, clustered volatility and
large effect nature of financial data because of
its assumptions of constant variance and normal
Gaussian distribution, this therefore makes it
insufficient to handle financial data.

However, this led to the discovery of ARCH – type
modes by Engle with a new class of stochastic
processes that model time varying conditional
variances by relating them to variables known from
the previous periods.

The ARCH type-models fit in well with the
financial time series data for some reasons like.

I.
Probability distributions for asset returns
often exhibit fatter tails than the standard
normal or Gaussian distribution.

II. To
explain the volatility clustering that is usually
exhibited by financial time series. This
volatility clustering is when large changes tend
to follow large charges and small changes follow
small changes.

III. The ARCH
type-model helps to capture leverage effects that
are evident in financial data or assets. (in which
asset returns are often observed to be negatively
correlated with changes in volatility.

The ARCH model was first introduced by Engle
(1982) and as GARCH (Generalised ARCH) by
Bollerslev (1986). They have proven to be useful
in financial time series analysis. ARCH
which is the same as Autoregressive conditional
Hetro-schedasticity is specifically designed to
model and forecast conditional mean and
conditional variance. Conditional here implies a
dependence on the observations of the immediate
past while autoregressive emphasizes that there is
a feedback mechanism involved which incorporates
past observations into the present to explain
future variances.
Standard econometric tests applied to
simulated data confirm that the extent of ARCH
effects depends on agent aggressiveness and on the
variance of the potential extraneous element that
might enter the mystical forecast. If the latter
variance is small relative to the variance of the
fundamentals or if agents are not very aggressive,
then the asset price tends to follow fundamentals
nearly all the time. If the variance of the
extraneous element is larger and agents are more
aggressive, then asset prices show occasional
bubble behaviour and both Engle’s (1982) test for
ARCH and estimates of a GARCH(1,1) model support
the conclusion that the data can be described as
ARCH/GARCH for many of the simulations.

GARCH which is Generalized Autoregressive
conditional Hetro-schedasticity enables you to
take care of the declining effect of information
on volatility ie it allows the user to model the
serial dependence of volatility.

Two specification are required in the application
of ARCH model and are

y_{t}= a+X_{t}Y +є_{t
} ------------------------------
(1)

^{2}_{t}=
^{2}_{t-1 }+ β^{2}_{t-1}
------------------------ (2)

Where eq (1) is the conditional mean and eq (2) is
the conditional variance.

X_{t}Y__ exogenous variables

Ф__ mean

є^{2}_{t-1 __}News about
volatility from the previous period, measured as
the lag of the squared residual from the mean
equation, which is the ARCH component.

^{2}_{t-1}____ last periods
forecast variance which explains the GARCH term

& β___ _parameters to be estimated

While eqn. (1) is a function of exogenous
variables with an error term, eqn. (2) is a
function of mean, lag of the squared residual from
the mean equation and last periods forecast
variance.

Variables that have been shown to help predict
volatility are trading volume macroeconomic news
announcements, implied volatility from option
prices and realized volatility, overnight returns,
and after hours realized volatility. (Ziovt,
2008).

Volatility clustering and non-Gaussian behave
often financial returns is typically seen in
weekly, daily or intraday data.

We test for ARCH effects in daily returns using
modified Q-statistic or Ljung Box.

**
Asymmetric ARCH and GARCH models**

ARCH/GARCH models thus far has ignored information
on the direction of returns, only the magnitude
matters but it has been shown that for broad based
equity indices and bond market indices, it appears
that market declines forecast higher volatility
than comparable market increases do. A stylized
fact of financial volatility is that bad news
(negative shocks) tends to have a larger impact on
volatility than good news (positive shocks). That is
volatility tends to be higher in a falling market
than in a rising market, this has been attributed
to the fact that bad news tends to drive down the
stock price.
Thus increasing the leverage (i.e. the debt
equity ratio) of the stock and causing the stock
to be more volatile.

This asymmetric news impact on volatility is
commonly referred to as the leverage effect and
can be tested for using the GARCH, EGARCH, TGARCH
and PGARCH models are all capable of modeling
leverage effect. Zivot (2008)

E-GARCH model is an asymmetric ARCH model and was
proposed by Nelson (1991). It stands for
exponential Generalized Autoregressive Conditional
Hetroschedasticity. It allows for the asymmetry in
the responsiveness of returns to the sign of
shocks to policy change and is specified in
logarithms thereby not imposing the non negativity
constraints on parameters. Specified as:

Where h_{t}= log^{2}_{t}

An advantage of the E-GARCH model over the basic
GARCH model is that the conditional variance ^{2}_{t
}is guaranteed to be positive regardless of the
value of the coefficient in eqn. (3), because the
log of ^{2}_{t} instead of ^{2}_{t}
itself is modeled.

GARCH-M
model allows the conditional variance to affect
the mean. Engle, Lilien and Robins (1987) proposed
to extend the basic GARCH model so that the
conditional volatility can generate a risk premium
which is part of the expected returns. This
extended GARCH model is often referred to as GARCH
in the mean or GARCH-M model. The estimated
coefficient on the expected risk is a measure of
the risk return trade-off and is specified thus:

y_{t} = X_{t}Y + β^{2}_{t}
+ є_{t}

y_{t }____conditional mean return

^{2}_{t}____conditional variance
as previously defined

X_{t}Y____exogenous variable included in
the mean deviation

є_{t }_____error term

TGARCH model is the threshold GARCH model and was
proposed by Zakoian (1990) and Glosten, Jaganathan
& Runkle (1993). It is specified as follows:

Where S_{t-i }denote a dummy variable
equal to unity when
S_{t−i} = 1 if є_{t−i}
< 0

0 if є_{t−i} ≥ 0

This then means that depending on
whether є_{t−i }is above or below the
threshold value of zero
є^{2}_{t-I }has different effects
on the
conditional variance ^{2}_{t}
such that when
є_{t−i} is positive, the
total effects are given by
a_{i}є^{2}_{t-I} when є_{t-I}
is negative, the total effects are given by (a_{i
}+ γ_{i})є^{2}_{t-I}.
So, one would expect γ_{i} to be positive
for bad news to have larger impact.

**
Methodology and analytical techniques**

**
Unit root test**: This is a stationarity test that is
necessary in time series data. According to
Kasmir& Koskinen (2005) a characteristic property
of rational bubbles is that the price-dividend
ratio has a unit root. It is carried out using the
ADF test. In this case we will investigate
univariate time series of price-dividend ratio
using unit root tests of ADF test. The ADF test
constructs a parametric correction for higher
order correlation by assuming that the time series
of price-dividend ratio follow an AR (p) process
and adding ‘p’ lagged difference terms of the
dependent variable –price-dividend ratio to the
right hand side of the test regression. So that

Where
y_{t}
-time series of (price-dividend ratio)

y is a stationary series if -1<ρ<1 if
the absolute value of ρ is greater than 1, the
series becomes explosive and doesn’t make economic
sense and so the null hypothesis is tested against
the one sided alternative i.e.

Null hypothesis H_{0}:=0

Alternative hypothesis H_{1}:<0

Also if =0 then ρ =1which implies
non stationary

If <0 then ρ<1 which implies stationary

Running the above model in the
E-view, the evidence of a unit root in the
price-dividend ratio will be consistent with
rational bubbles, this then means that
non-stationary price-dividend ratio are consistent
with existence of rational speculative bubbles
while stationarity implies that deviations from
market fundamentals are short lived therefore
showing absence of bubbles.

**
Co-integration**

In the stock market if the prices
truly reflect the value of the expected future
flow of dividends, we should be expecting a
cointegration between dividends and stock prices
in the long run despite the fact that they both
follow random walks.
Shiller (2001) quoted Campbell and Shiller
(1987) to have argued that if dividend and stock
prices fail to co integrate, then there is
evidence of a bubble. If a
cointegration exists between the stock price and
dividends, it will be suggesting absence of
bubbles meaning that there was no serious
deviation from fundamentals. In a case where it
shows no co-integration it will then suggest that
speculative bubble is present and that there is
actually a serious deviation from price.
After we must have tested for random walks in the
both variables using the unit roots test and found
out if ∆dividends and ∆prices are stationary, we
can then test for their co-integration by running
the OLS regression i.e.

We then test whether the residuals,
єt from this regression are stationary. If
dividends and stock prices are not co-integrated,
any linear combination of them will be
non-stationary and hence the residuals єt will be
non-stationary. So we test the hypothesis that єt
is not stationary which is the hypothesis of no
co-integration. This test of the hypothesis єt is
non stationary will be done in two ways.

1.
Using the ADF unit root test on the
residuals estimated from the cointegrating
regression. Then we check the significant values
based on the Engle Granger (EG) and augmented
Engle Granger tests (AEG).

2. Using CRDW (Cointegrating
Regression Durbin Watson) test. This will be done
by using the Durbin Watson Obtained from the
cointegrating regression and testing it against
the null hypothesis that d=0 instead of the
standard d=2. Such that if the computed d-value is
smaller than the critical values then we reject
the null hypothesis of cointegration depending on
the level of significance we decide to use.

**
Arch & garch model**: The stock market (price) is one of
the financial time series that exhibit volatility
clustering. From Singh Ajit(1996),Yartey &
Adjasi(2007), Zivot (2008),Xavier (2006),
Gurkaynak (2005) It is therefore important for
investors in the stock market to know about
volatility because high volatility which is a
character of bubbles could mean huge losses or
gains & hence greater uncertainty, which suggests
why we are testing for it in this work. While the
ARCH model is a mechanism that includes past
variances in the explanation of future variances,
the GARCH model takes care of the declining
effects of information on volatility.

In constructing an ARCH model, two
specifications are needed i.e. one for the
conditional mean and the one for conditional
variance so that the standard GARCH (1, 1)
specification will be

**
Sources of data **

Data were sourced from the Daily Price Listings
from NSE, NSE fact book, Securities and Exchange
Commission quarterly magazine and Central Bank of
Nigeria (CBN) statistical bulletin. The banks
considered are Access bank, GTB, Intercontinental,
UBA and UBN and the Insurance companies are Aiico
insurance, Cornerstone insurance, Lasaco
insurance, Law union Rock and Niger insurance. The
variables considered are the price-dividend ratio,
share price
and dividend for the selected banks and
insurance companies.

**
Results and discussions**

**
Stationarity test of price-dividend ratio using
adf test**

The price-dividend ratio for all
the banks were integrated of order 1 I(1) when the
Mackinon critical values were considered at 1% and
5%. (appendix 1.1 and 1.2) The price-dividend
ratio for the insurance companies were equally
integrated of order one [I(1] except for Niger
insurance which showed stationarity at levels
(Appendix 2.1 and 2.2). Consequently, the result
attested that bubbles existed
according to Kasmir & Koskinen(2005).

The
ADF test for bank share price and dividend
(appendix 3.1 and 3.2) were stationary at first
difference [I(1)].

The
AEG cointegration test on the residuals of banks
share price and dividend indicated that bubbles
existed in three out of the 5 selected banks
(appendix 3.3 and 3.4).
Access, GTB, & Intercontinental banks
showed the existence of bubbles while UBA and UBN
showed the absence of bubbles.

For the
insurance companies,
the ADF result for the share price and
dividend were integrated of first order for test
for Cornerstone, Lassaco & Lawunion And The Aeg
Cointegrated Test
indicated the existed of bubbles for these
insurance companies. However
the result for
AIICO and Niger was
inclusive because one was integrated at level and
the other at first difference (appendix 4.1, 4.2,
4.3 and 4.4)

For the 5 companies under the
banking sector, ARCH and GARCH estimates, all but
PGTB reflected persistent volatility. For the
insurance companies, only PNIGERIN did not
indicate volatility clustering. The
rest suggests persistent volatility meaning that
the shock in these stocks were persistent
(appendix 5.1 and 5.2).

TARCH estimate (appendix 6.1
and 6.2) indicated that positive and negative
shocks /news are asymmetry and have asymmetric
effect on volatility. PINTER,
PUBA and PUBN are negative but significant, which
implies that volatility tends to fall when the
returns surprises are negative i.e. when they come
as bad news. In other words negative shocks in
these three banks cause less volatility than the
positive shocks which means that they contradict
the theoretical expectation that negative shocks
cause greater volatility than the positive shocks.
In essence the effects of bad news on these three
banks led to less volatility. However, the other
two banks show positive relationship meaning that
bad news brings about more volatility. This then
suggested that the market had both stabilizing
agents and destabilizing agents since most stock
markets in reality do not adjust too quickly nor
do they persist in their instability. The
destabilizing agents are those who follow a
behavior that will prolong the unexpected shock
and cause persistent volatility while stabilizing
agents are those that would see that when there
was an unexpected (rise) fall in prices they would
expect the prices to (fall) rise.
Therefore,
disturbance from previous mean and variance
varied and contributed to the volatility in the
stock market because of information asymmetry. TARCH
estimates for insurance companies (appendix 6.2)
was similar to that
of the banks i.e. two were negative and two
were positive while PNIGERIN had a near singular
matrix and so no result could be given for it.

Therefore, it is can
concluded that bubble existed in the NSE in the
period under review since both sectors exhibited
bubbles except two companies in the insurance
sector. In the banking sector the residuals of two
banks UBA and UBN were stationary. However
because the banking sector has been observed as
the main contributor to the market capitalization
of the NSE it can be said that the existence of
bubbles in 3 out of the 5 banks sampled influenced
the market and made others to also reflect the
presence of this bubbles. The ARCH and the GARCH
estimates equally manifested volatility clustering
and the TARCH confirmed information asymmetry.

**
**

**
Summary and recommendations**

The pd-ratio of the insurance
and banking sector showed the existence of
bubbles.
That the prices and dividends for most of
them did not co integrate i.e. they violated the
EMH that expected the price and dividends ratio to
co integrate at the long run therefore showing an
imperfect market that was run by things outside
fundamentals.
The fact that most of them violated the EMH
means that information is not complete i.e. there
is information asymmetry. Since
bubbles have been tested to be in existence it
means that the crash that was being experienced
might not be out of place since a feedback
correction mechanism was expected after bubbles to
bring the market back to fundamentals. 6)
Since banking & insurance sectors of the stock
market contribute more to the market
capitalization and it has been seen that bubbles
existed in a greater percentage of the ones
examined, therefore, bubbles existed in the NSE as
a whole.
It was equally found that iInformation
asymmetry and other factors contributed to the
market deviating from its fundamentals.

Therefore, information should
be well circulated about the stocks in the market
so that investors will have every necessary
information on what they want to invest into.
Investors’ especially illiterate ones should be
tutored before they make their investment
decision.
The NSE body should have a way of
moderating the market so that it is not falsified
by activities of greedy brokers and investors.
The SEC (Security Exchange Commission) and NSE
directors should be at alert when they see unusual
purchases or sales going on in the market and
should put a limit to the activities of the
brokers so that they don’t do whatever they feel
like doing thereby affecting the market adversely.
To improve efficiency they should carry out
measures that will develop systems that facilitate
smooth dissemination of important information to
potential investors and rules should be set out to
ensure that information is made known at the same
time to all and on time.

**
**

**
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