an empirical study on influence of inflation on
TRANSCRIPT
www.theinternationaljournal.org > RJSSM: Volume: 05, Number: 4, August 2015 Page 41
An Empirical Study on Influence of Inflation on performance of Sensex in India
Dr. Aparna Mishra
Asst. Professor
BanarsidasChandiwala Institute of Professional Studies,
Sector 11, Plot no. 9, Dwarka, New Delhi 110075
Dr Ajay Kumar Chauhan
Asst. professor
Institute of Management Technology, Gaziabaad
Raj Nagar, Hapur Road, Block 15, Sector 2, Raj Nagar, Ghaziabad, Uttar Pradesh 201002
Abstract
Stock Market plays a vital role in any countries economic growth and development. They have always
been an area of serious concern for policy makers, economists and researchers. They are often defined
as the barometer of any economy because they reflect the change and direction of pressure on the
economy.The available literature suggests thatsince the inception of stock markets researchers are
making attempts to establish relationship between change in macroeconomic factors and stock market
returns. The main domestic macroeconomic factors affecting the stock market in long run are
industrial production;inflation(wholesale price index) and interest rate. The present research study
makes an attempt to study the lag-lead relationship between Inflation and stock returns after analyzing
the inflation into expected and unexpected components. The stock returns-inflation relationship was
examined during the period 1998 to 2008 using indexes of BSE Sensex with WPI(Wholesale Price
Index). The period is characterized by different reforms in Indian economy and the global meltdown.
Therefore, boom and recessionary phases were observed during this period. The results obtained
through all standard econometric tests showed that there is no relation between stock returns and
inflation during the studied period. The unit root tests, Granger causality test and regressions were
performed for the purpose. The unitroot tests indicated that both the series, i.e., Inflation and Sensex
returns are stationary.The Granger causality test results suggested no significant relation between stock
returns and inflation.
Thus, the results of the study suggest that there exists no significant relation between inflation and
stock returns in the post-reform period in India. It implies that stock returns do not provide a hedge
against inflation. It can be said that investors aim at better returns and do not invest in stocks to hedge
against inflation.
Key Words: Inflation, WPI, Sensex Return, Macro Economic Variables, Stationary, Volatility
Introduction:
Stock market plays a vital role in any country‟s economic growth and development. A healthyand
flourishing stock market has been considered relevant for national economic growth by channelizing
capital toward investors and entrepreneurs. An economy is said to be efficientif it has a good banking
system and a good stock market exhibiting upward trend. Earliera country was considered strong and
efficient if it exhibited a sustained growth of GrossDomestic Product (GDP) and per capita income.
But, of late it has been recognized thatstock market exerts greater influence on national economy.
Market capitalization, savings,investment, consumption and sound banking and insurance system are
considered to be afew important indicators of economic growth. Several researchers have investigated
the relation between stock returns and inflation over many years. Equities have always traditionally
been regarded as a good hedgeagainst inflation because equities are claim against physical assets
whose real returns shouldremain unaffected by inflation. The Fisher (1930) hypothesis, in its most
familiar version,states that “the expected nominal rate of return on stock is equal to expected inflation
plusthe real rate of return”, where the expected real rate of return is independent of expectedinflation.
In other words, Fisher hypothesis implies that stocksoffer a hedge against inflation.Although a number
of papers have investigated the Fisher hypothesis, the emphasis hasbeen on the developed countries.
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Recently, the focus of research has been shifted towarddeveloping countries, partly due to rapid
growth and increasing liberalization in thesecountries. For instance, Spyrou (2001) and Floros (2004)
examined stock returns-inflationrelation in Greece, using the Johansen cointegration test. They found
that there is nosignificant long-run relationship between inflation and stock returns in Greece. Davis
andKutan (2003) investigated the Fisher effect in 13 developed and developing countries andfound
evidence that Fisher effect is not supported in international stock returns. Al-Khazaliand Pyun (2004)
investigated the statistical relationship between stock prices and inflationin nine countries in the
Pacific Basin. Using the Johansen cointegration test, they concludedthat stock prices in Asia reflect a
time-varying memory associated with inflation shocks thatmake stock portfolios a reasonably good
hedge against inflation in the long run. Fama (1981) argued that the negative relationship between
stock returns andinflation has its basis in the money demand theory and the quantity theory. Fama‟s
hypothesisstates that rising inflation rates reduce real economic activity and demand for money.
Wheneconomic activity dips, it negatively affects the future corporate profits and, hence stockprices.
The negative relationship between inflation and the stock returns is on account ofthe „proxy effect‟ in
the sense that it reflects the detrimental consequence of inflation onreal economic activity. According
to Fama, the statistical relationship between inflation andstock returns should disappear once the effect
of real output growth is controlled for. Geske and Roll (1983) studied the relationship forthe US for the
period from 1953:1 to 1980:12.The major empirical findings of the study were that, there is a
negativerelationship between stock returns and beginning of the period short-term interest
rate,contemporaneous change in short-term interest rates, and unanticipated inflation. Ahmadand
Mustafa (2005) studied the relationship for Pakistan, for the period from 1972-2002using monthly and
annual data. Results revealed that relationship between real returns and unexpectedgrowth and
unexpected inflation are negative and significant. Kim (2003) employed quarterly data for Germany
for the period from 1971 to 1994. Symmetric and asymmetric Granger causality test was
performed.Results demonstrated the negative correlation between stock returns and inflation and
theindicative role of stock returns in the real activity in an asymmetric manner of causality.Nelson
(1976) using the monthly data, studied the relationship for the US for the postwarperiod, 1953-1972.
Box and Jenkins‟ ARIMA method was used. The studydemonstrated a negative relationship between
stock returns and both expected andunexpected inflation.Samarokoon (1996) studied the relationship
between stock returns and inflation forSri Lanka, using the monthly and quarterly data for the period
1985 to 1996.The Box and Jenkins‟ ARIMA model was used. Empirical findings showed stock
returnsdo not provide hedge to Sri Lankan inflation. Jaffe and Mandelker (1976) utilized themonthly
data from 1953 to 1971 to study the relationship for the US. Results of thestudy revealed no relation
between stock returns and inflation. Kaul (1987) using dataseries in annual form for the post-war
period analyzed the relationship for the US(1953-1983), Canada (1951-1983), the UK (1957-1983),
and Germany (1957-1983).Findings of the study indicated that negative inflation-real activity relations
reinforcedby counter-cyclical monetary responses, explain the negative relation between stockreturns
and inflation witnessed in the post-war period.
Adam and Frimpong (2010) studied the relationship for Ghana for the sample period1991-2007.
Cointegration analysis was employed and the findings showed strongsupport for hedge hypothesis.
The evidence confirms that Ghana market is efficient ininflationary environment as investors are
compensated with high stock returns. Chopen andZhong (2001) studied the post-war period from 1968
to 1996. Vector Error CorrectionModel (VECM) of Johansen and Juselius (1992 and 1994) was
employed. The results revealedthe presence of economically meaningful long-run
relationships.Balduzzi (1994) studied the proxy hypothesis for the period from 1977 to
1990,employing the Vector Autoregressive (VAR) and Vector Moving Average (VMA)
models.Results revealed that inflation itself is responsible for most of the dynamic interactions
withstock returns. Lee(2008) analyzed the causal relationship in the UK. The sample period ranged
from 1830to 2000. The sample period was further divided into two subperiods, 1830-1969 and 1970-
2000.Unit root test, cointegration test, Bivariate Vector Autoregressive (BVAR) and GARCHmodels
were employed. The empirical findings of the study reported that there is a significantnegative
correlation between unpredictable stock returns and inflation for the subperiod 1970-2000. However,
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unpredictable stock returns were hardly correlated to unpredictable inflationduring the same
subperiod.Adrangi and Chatrath (1997) investigated possible negative relationship between thereal
stock returns and unexpected inflation for Brazil. Bhattacharya and Mukharjee (2003) studied the BSE
Sensex for the period ranging from1992-93 to 2000-01. They employed different techniques, such as
unit root tests,cointegration test, long-run Engel and Granger causality test, and the recently
developedToda and Yamamoto (1995) test. Results revealed existence of a bidirectional
causalityrelationship between stock returns and rate of inflation.Shanmugam and Misra (2008) studied
an emerging economy like India during thepre- and post-reform periods, 1980 to 2004, covering 288
months. The studycontributed to the stock returns-inflation relation in India. It tested whether the
Indianstock market provided an effective hedge against inflation. Ordinary Least Square
(OLS)regression method was employed. As the single equation treatment can lead to aninconsistent
estimate, therefore a two-step OLS procedure was employed to study therelationship between real
returns and inflation. The results demonstrated that the stockreturns and inflation are negatively related
when the whole sample period of 24 yearsis considered. With the lead of about six months, real
activity and inflation are negativelyrelated, while real activity positively influences the real returns.
The results provideda strong support to Fama‟s proxy effect. In addition, the analysis of sub periods
indicated that Fama hypothesis was valid only in the pre-reform period and not in the post-
reformperiod. The real stock returns were found to be independent of inflation during the post
reformperiod.
In this backdrop, the present study seeks to examine the stock returns-inflation relationshipin India
using the sample of BSE Sensex 1998:1 to 2008:12.The period is characterized by different reforms in
Indian economy and the global meltdown.Therefore, boom and recessionary phases of the economy
are observed during this period. During this period, the data series is analyzed with Wholesale Price
Index (WPI). The study attempts to understand the relationship between stock returns and inflation to
empirically assess and understandthe relationship between them in the post-reform period in India. The
empirical results of unit root, Granger causality,VAR model and Impulse Response Function (IRF) are
presented and discussed. Finally, theconclusion is offered.
Data and Methodology
Data
The study uses weekly values of BSE Sensex. The BSE Sensex indexes are considered as barometer of
Indian equitymarket and account for a major part of market capitalization and turnover. WeeklyWPI
are used as measures of inflation. WPI is a representative of the prevailing price situation because of
itswider coverage. It is available with a smaller lag ofone week, which is used extensively as a
measure of rising pricesin India, and important monetary and fiscal policy changes are often linked to
it.. The sample size chosen for the study gives asufficient number of observations to apply time series
methods. The index values of BSESensex are obtained from www.bseindia.com, while WPI data are
obtained from Central Statistical Organization(CSO) and Reserve Bank of India (RBI) respectively.
Methodology
In order to examine the relationship between stock returns and inflation time serieseconometrics tools,
such as unit root tests, Granger causality test and regression analysisare employed. The unit root tests,
Augmented Dickey-Fuller (ADF) andKwiatkowski, Phillips, Schmidtand Shin (KPSS) (Kwaitkowski
et al., 1992), are employed to test if the data series is stationaryor not. Further, to examine the causal
links between stock returns and inflation during entiresample period and for the subperiods, Granger
(1969) causality test is employed. Multiplelinear regression equation is also estimated to examine the
relationship between stock returnsand inflation. Vector Auto Regression is performed along with
IRF(Impulse Response Function) to test for robustness ofthe results.
Stock Market and Inflation in India
The relationship between stock market prices and inflation is of great importance from the policy point
of view. High inflation in the economy is considered harmful for the growth of the economy. Increase
in inflation is considered as a negative signal by the Central banks, especially in the developing
economies such as Indian economy. The monetary policy of a developing economy in most of the
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cases is focused to control the increase in inflation in the country. In high inflationary period the banks
increases the lending rates as well as deposit rates. This will increase the cost of capital for the industry
and attract investors to invest theirsavings in debt securities. In such a scenario the stock market have
more bearish sentiments, showing the downside movements. However, in real world the relationship
between stock price and inflation is more complex. The stock market prices may be related to the
domestic inflation and even if domestic inflation may not affect the quantity produced directly there
can be substantial impact of stock market prices on quantity produced.
In the developed world the stock market controls the real sector immensely whereas in the Indian
context the stock market used to be quite superfluous in this respect. That is because only a few
players control the stock market. However, over time the government intervention has tried to rule out
such “bull effect” and has made stock market more competitive which in return is expected to have
made both the stock market and other macro variables sensitive to each other. This motivation
prompted for theinvestigation into the questions such as“What is the relationship between inflation and
stock returns?” Holdingstocks is often thought to provide a good hedge against inflation, since the
payments to equity holders are not fixed in nominal terms and represent a claim on real assets.
The majority of empirical studies that have investigated the signof this relationship have found it to be
negative. Various explanationsof this puzzling empirical phenomenon have been proposed, including
alink through real activity. So, that real activity is negatively related to inflationbut positively related
to stock returns and therefore stock returnsand inflation is positively related. Clearly, inflation and
stock returns oughtto be simultaneously related given that the rate of inflation will affect the discount
rate applied to cash flows and therefore the value of equities,but the performance of the stock market
may also affect consumerdemand and therefore inflation through its impact on householder
wealth(perceived or actual).
In stock market in general which represent claims against the real assets of a business, may serve as a
hedge against inflation. Consequently, investors would sell financial assets in exchange for real assets
when expected inflation is pronounced. Thus, stock prices in nominal terms should fully reflect
expected inflation and relationship between stock prices and expected inflation should be found
positively correlated. Equities are assumed to be a hedge against inflation due to the fact that they
represent a claim to real assets and, hence the real change on the price of the equities should not be
affected. If we consider that firms are in a position to predict their profit margins and since equities are
claims on current and future earnings, it also follows that the stock market operates as a hedge against
inflation, at least in the long run.The earnings should be consistent with the inflation rate, and hence
the real value of the stock market should remain unaltered in the long run. The argument that stock
market serves as a hedge against inflation, implies that investors are fully compensated for increases in
the general price level through corresponding increases in nominal stock market returns and thus the
real returns remain unaffected. In other words, the argument is that the real value of the stock market is
immune to inflation pressures. This has been tested in the literature numerous times.
Changes in expected inflation are negatively related to stock returns. The present research study makes
an attempt to study the lag-lead relationship between stock returns and inflation after analyzing the
inflation into expected and unexpected components. It will examine whether expected and unexpected
components of inflation influence stock prices in positive direction or in negative direction, and
whether stock market responds to these components of inflation proactively or reactively. In the
research study, an effort is made to analyse the relationship between the level of inflation and stock
return behaviour. The effort is made to understand the nature of the time series data, the long-term
equilibrium relationship between the WPI and SENSEX, the contemporaneous and causal relationship
between the WPI and SENSEX. This paper is contributingto the emerging line ofresearch linking stock
return predictability to economic real activities (WPI).
The graphical representations of the behaviour of SENSEX and WPI during the sample period are
shown in fig 1.1 and fig 1.2. The figure indicates the presence of increasing trend in both the
variables.
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0
4,000
8,000
12,000
16,000
20,000
24,000
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/99
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7
6/18/0
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07
3/24/0
8
8/11/0
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12/29
/08
BSE
Fig 1.1: SENSEX behaviour during the sample study.
120
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260
4/6/98
8/24/9
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1/29/0
7
6/18/0
7
11/5/
07
3/24/0
8
8/11/0
8
12/29
/08
WPI
Fig 1.2: Wholesale Price Index during the sample study
0
2
4
6
8
10
12
14
4/6/98
8/24/9
8
1/11/9
9
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7
3/24/0
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12/29/
08
Change (%)
Fig 1.3: Wholesale Price Index (Calculated in percentage change) during the sample study
The table 1.1 and 1.2 indicates the descriptive along with the distribution of SENSEX and WPI series
during the sample study. The results indicate that the mean value of SENSEX during the sample period
is 7086 with the standard deviation of 4905. The high Standard Deviation value indicates the high
level of deviations in SENSEX during the sample period. The results also indicate the presence of
positive skewness and leptokurtic behaviour of SENSEX prices because of which, the distribution is
also not normal as indicated by probability value (0.000) of Jarque- Bera test statistic (260.1895).The
highest value of SENSEX is found to be 20812 during the period. The minimum SENSEX value
during the sample period is found to be 2651.
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Table 1.1: Descriptive Statistics of BSE SENSEX
0
20
40
60
80
100
120
4000 6000 8000 10000 12000 14000 16000 18000 20000
Series: BSE
Sample 4/06/1998 12/29/2008
Observations 561
Mean 7086.166
Median 4905.890
Maximum 20812.65
Minimum 2651.780
Std. Dev. 4631.286
Skewness 1.144197
Kurtosis 3.101120
Jarque-Bera 122.6481
Probability 0.000000
The results as indicated in table 1.2 and table 1.3 represents the descriptive statistics of the WPI series
and the growth rate in inflation in India during the sample period (1998 to 2008). The results indicate
that the average value of WPI index and its growth rate is 179and 5.27 percent respectively with the
standard deviation of 28 and 2.16. In India it is observed that the level of inflation is having too much
variations and it poses a serious problem in front of RBI to effectively control it. The high level of
variance in WPI series and its growth rate indicates the volatile nature of level of inflation in the
country. The presence of low level of positive skewness and leptokurtic behaviour in the distribution
of the series is observed in the results.
The probability distribution of the WPI series is also not normal as indicated by probability value
(0.000) of Jarque- Bera test statistic (31.616). The highest value of WPI index is observed as 241
during the period. The highest growth rate in inflation is found to be 12.82 percent. The minimum IIP
Index and its growth rate during the sample period are found to be 136 and 1.06 respectively.
Table 1.2: Descriptive Statistics of WPI Index
0
10
20
30
40
50
60
70
140 150 160 170 180 190 200 210 220 230 240
Series: WPI
Sample 4/06/1998 12/29/2008
Observations 561
Mean 179.2658
Median 173.8000
Maximum 241.7000
Minimum 136.3000
Std. Dev. 28.25341
Skewness 0.395817
Kurtosis 2.148003
Jarque-Bera 31.61665
Probability 0.000000
Table 1.3: Descriptive Statistics of growth in WPI Index
0
10
20
30
40
50
60
70
80
1 2 3 4 5 6 7 8 9 10 11 12 13
Series: WPI_CHANGE
Sample 4/06/1998 12/29/2008
Observations 561
Mean 5.275767
Median 5.201238
Maximum 12.82171
Minimum 1.062500
Std. Dev. 2.163216
Skewness 0.946173
Kurtosis 4.864633
Jarque-Bera 164.9768
Probability 0.000000
1.2Testing for Stationary/Non Stationary series
A time series is said to be strictly stationary if all the moments of its probability distribution (such as
mean, variance, skewness, kurtosis etc.) are invariant over time and weakly stationary process (also
called covariance stationary or 2nd-order stationary)if its mean, variance and auto-covariance remain
the same no matter at what point of time they will be measured.The stationary nature of the time series
(SENSEX and WPI) is analysed using Correlogram and unit root test.
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1.2.1 Correlogram
The Correlogram is the graphical representations of the set of autocorrelation coefficients (ACF) and
Partial autocorrelation coefficients (PACFs) at various lags. It is observed that anon-stationary series
will show very high autocorrelation close to 1.The Correlogram of the WPI and SENSEX data is
shown in fig 1.4 and fig 1.5 shown below:
Fig 1.4: Correlogram of SENSEX values
As shown, the Correlogram the autocorrelation function (ACF) is not exponentially dying and the
partial auto correlation function (PACF) at lag 1 is close to one. This indicates that the SENSEX
values are non-stationary in nature. But this is yet to be confirmed with the results of ADF unit root
test. If the series is found to be non-stationary, then some transformation is required to make the series
stationary.
Fig 1.5: Correlogram of WPI Series
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As shown in the Correlogram of the wholesale price index values, the autocorrelation function (ACF)
is not exponentially dying and the partial auto correlation function (PACF) at lag 1 is close to one.
This indicates that the WPI values may be non-stationary in nature, which will be reconfirmed with the
results of ADF unit root test.
The fig 1.6 and fig 1.7 represents the Correlogram of the growth rate of WPI and SENSEX returns. In
both of the cases the partial auto correlation function (PACF) at lag 1 is significantly less than one,
which indicates the stationary nature of the series.
Fig 1.6: Correlogram of growth rate of WPI
Fig 1.7: Correlogram of SENSEX returns
1.2.2. ADF Unit Root Test
Since many financial time series (BSE SENSEX and WPI in this study) are random walk or non-
stationary time series and contains unit root. Test of the presence of the unit root in the BSE SENSEX
and WPItime series is necessary as its presence may give invalid inferences in the analysis. Table 1.4
shown below indicates the results of unit root test applied on the BSE SENSEX and WPI using ADF
test.
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Table 1.4: Augmented Dicky Fuller Test of BSE SENSEX and WPI data
Series
ADF Unit Root Test Statistic
None With Intercept With Trend and
Intercept
Monthly data of BSE
SENSEX
At Level 0.133
(0.637)
1.098
(0.718)
1.841
(0.683)
At First
Difference
11.098
(0.000)
11.504
(0.000)
11.494
(0.000)
Monthly Data of IIP
At Level 6.201
1.000)
0.335
(0.916)
2.741
(0.220)
At First
Difference
7.636
(0.000)
19.139
(0.000)
19.122
(0.000)
The result indicates that both the time series BSE SENSEX and WPI are a random walk and non
stationary al their level (prices) but becomes stationary at their first difference. Hence for further
analysis the return series of SENSEX and growth rate of WPI is used. The returns of the SENSEX data
can be calculated using the following formula:
SENSEX Return = Ln (P1/p0) 1.1
Where P1 represents the SENSEX value of a particular month and Po represents the SENSEX value of
previous month.
Similarly the growth rate of the WPI data can be calculated using the following formula:
Growth Rate of Inflation =Ln (I1/I0) 1.2
Where I1 represents the WPI Index value of a particular week and Io represents the WPI value of
previous week.
1.3 The long term relationship between Inflation and SENSEX: A Cointegration Approach
The increase in the inflation rate in the economy motivates the central bank to increase the interest
rates in the economy in order to control the inflation. As a result the investors in the market also shift
their savings to debt securities due to increase in rates. The stock market in this scenario as an
indicator of the economy comes in bearish mode. Hence there may a long term equilibrium
relationship is existing but inverse in nature between inflation and the stock market. The existence of
this long term equilibrium relationship between the inflation ratemeasured by WPI and stock market
represented by BSE SENSEX can be tested using Johansan‟scointegration test. The cointegration test
originally was introduced by Granger (1981, 1983) and Engle and Granger (1987) to explain stationary
equilibrium relationship among the non-stationary variables. The cointegration test is useful in
analyzing the presence of a stationary linear combination among the non-stationary variables of the
same order. If such combination is found, an equilibrium relationship maybe existing between the
variables. The Johansen cointegration test is applied in the research study between the inflation rate
(WPI) and SENSEX weekly values. The result of the Johansen‟s Co-Integration Test is shown in table
1.5.
The result indicates that the probability value of both Trace test and Max Eigen value ofJohansen‟s
Co-Integration Test is more than five percent level of significance; hence at 95 percent level of
confidence the null hypothesis of “no Co-integrating relationship between inflation and stock market”
can be accepted. Hence as per the results obtained from the data it can be concluded that the inflation
rate in India and stock market is not having long-term equilibrium relationship between them. In fact
the stock market is affected by a large number of factors in which inflation may be one of them. Hence
due to the absence of any error correction mechanism between the stock market and inflation rate, no
long term or co integrated relation exists between them.
Table 1.5: Johansen’s Co-Integration Test on WPI and SENSEX values
Cointegration
Between
Lag
length
selected
Cointegration
test using
No. of
Cointegrating
Equations
(CEs)
Eigen
Value
Statistic Critical
value
at 5%
Probability
**
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Index of
Industrial
Production
(IIP) and
SENSEX
1 to 4 ( in
first
difference
of 2
series)
Trace test
H0: r=0
(None)
H1: r ≤ 1 (At
most 1)
0.012
4.37E-
05
7.261
0.024
15.494
3.841
0.547
0.876
Max-Eigen
Value test
H0: r=0
(None)
H1: r ≤ 1 (At
most 1)
0.012
4.37E-
05
7.236
0.024
14.26
3.841
0.461
0.876
Trace test indicates 1 Cointegrating equation at 5% level of significance
Max-Eigen test indicates 1 Cointegrating equation at 5% level of significance
Denotes rejection of null hypothesis at 5% level of significance
**Mackinnon et.al.(1999) estimated p values
1.4 Relationship between WPI and SENSEX
In the research study the weekly data of WPI and SENSEX is considered for the period between Jan
1998 up to Dec 2008. In the research study the effort has been put to analyse the relationship between
inflation rate and stock market behaviour. The analysis has been done with the help of correlation.The
results of the correlation analysis are shown in the table 1.6.
Table 1.6: Correlation Analysis between WPI and SENSEX
Correlation Between Pearson Correlation Sig. (2-tailed)
WPI and SENSEX -.118 0.005
1.4.1 Impact of Unexpected Component on stock market
There are two components of inflation rate in India: expected and unexpected. In order to analyse the
impact of expected and unexpected component of inflation rate on stock market, the forecasting model
is developed using ARIMA forecasting method. The forecasted values are saved and subtracted from
the observed values of WPI. The difference between the actual WPI values and estimated values are
considered as the proxy of unexpected component of inflation rate. The following ARIMA model is
applied in order to find out the expected values of WPI values:
(Growth rate in WPI)t = α + β1 GWPIt-1 + β2 GWPIt-2 + β3 GWPIt-4 1.3
Where, GWPIt-1 =Growth rate in WPI at lag 1
GWPIt-2 =Growth rate in WPI at lag 2
GWPIt-4 =Growth rate in WPI at lag 4
ARIMA"Auto-Regressive Integrated Moving Average." (p,d,q)models are the most general class of
models for forecasting a time series which can be stationery by transformations such as differencing
and logging. In fact, the easiest way to think of ARIMA models is as fine-tuned versions of random-
walk and random-trend models: the fine-tuning consists of adding lags of the differenced series and/or
lags of the forecast errors to the prediction equation, as needed to remove any last traces of
autocorrelation from the forecast errors.
In ARIMA, lags of the differenced series appearing in the forecasting equation are called "auto-
regressive" terms, lags of the forecast errors are called "moving average" terms, and a time series
which needs to be made stationary is said to be an "integrated" version of a stationary series. A non-
seasonal ARIMA model is classified as an "ARIMA(p,d,q)" model, where:
p is the number of autoregressive terms,
d is the number of non-seasonal differences, and
qis the number of lagged forecast errors in the prediction equation.
To identify the appropriate ARIMA model for a time series, the process begins by identifying the
order(s) of differencefor making the series stationary and to remove the gross features of seasonality,
perhaps in conjunction with a variance-stabilizing transformation such as logging or deflating. The
results of ARIMA forecasting model applied on WPI is shown below in table 1.7:
www.theinternationaljournal.org > RJSSM: Volume: 05, Number: 4, August 2015 Page 51
Table 1.7 ARIMA Model
Dependent Variable: Growth Rate in WPI
Method: Least Squares
Variable Coefficient Std. Error t-Statistic Prob.
C 0.000899 0.000177 5.084772 0.0000
AR(1) 0.184216 0.042236 4.361609 0.0000
AR(2) 0.097293 0.042426 2.293216 0.0222
AR(4) 0.092815 0.042212 2.198795 0.0283
R-squared 0.065998 Mean dependent var 0.000914
Adjusted R-squared 0.060922 S.D. dependent var 0.002689
S.E. of regression 0.002606 Akaike info criterion -9.054831
Sum squared resid 0.003749 Schwarz criterion -9.023747
Log likelihood 2521.243 Hannan-Quinn criter. -9.042690
F-statistic 13.00174 Durbin-Watson stat 2.018413
Prob(F-statistic) 0.000000
The residuals of the above mentioned ARIMA model and its Correlogram are shown in fig 1.8. The fig
indicates that that the residuals are stationary and the model is assumed to be fit.
Fig:1.8: Correlogram of the residuals saved of the ARIMA model
The diagram of forecasted Inflation (WPI) series is shown in fig 1.9.
120
140
160
180
200
220
240
260
5/12/9
8
9/28/9
8
2/15/9
9
7/5/99
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99
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0
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06
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7/23/0
7
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07
4/28/0
8
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8
Forecasted WPI Series ± 2 S.E. Fig1.9: Forecasted WPI series
www.theinternationaljournal.org > RJSSM: Volume: 05, Number: 4, August 2015 Page 52
The statistics associated with the forecasted model are shown below in table1.8:
Table 1.8: Forecasting Error Statistics
Statistic Value
Root Mean Squared Error 0.4952
Mean Absolute Error 0.3201
Mean absolute Percent Error 0.1762
The difference between the forecasted values of WPI and the actual values of WPI are considered as
unexpected values of inflation. In the research study the effort is made to analyse the impact of
unexpected inflation on the stock market. The regression equation can be expressed as:
SENSEX =α + β .Unexpected Component of inflation 1.4
Where α and β are regression coefficients.
The results of the regression are shown in table 1.9:
Table 1.9: Regression Results
Dependent Variable: SENSEX Returns
Variable Coefficient Std. Error t-Statistic Prob.
Unexpected component of inflation 0.01018 0.00361 2.81935 0.005
C 0.00149 0.00178 0.83796 0.402
R-squared 0.014145 Mean dependent var 0.001502
Adjusted R-squared 0.012366 S.D. dependent var 0.042429
S.E. of regression 0.042166 Akaike info criterion -3.490812
Sum squared resid 0.984999 Schwarz criterion -3.475269
Log likelihood 972.4457 Hannan-Quinn criter. -3.484741
F-statistic 7.948784 Durbin-Watson stat 2.109635
Prob(F-statistic) 0.004984
The results of the regression model indicate that the stock market is significantly influenced by the
unexpected component of the inflation rate in the Indian economy. However the impact is very low in
magnitude as represented by low value of R- square of 0.149 percent.
1.4.2 The Causal relation between the inflation rate and the stock market in India
The lead lag relation between the inflation and the stock market can be analysed with the help of
Vector Auto Regression model. Thevector auto regression(VAR)modelis one of the most
successful,flexible, and easy to use models for the analysis of multivariate time series. It isa natural
extension of the Univariate autoregressive model to dynamic multivariate time series. The VAR model
has proven to be especially useful fordescribing the dynamic behaviour of economic andfinancial time
series andfor forecasting. It often provides superior forecasts to those from univariate time series
models and elaborate theory-based simultaneous equationsmodels. Forecasts from VAR models are
quiteflexible because they can bemade conditional on the potential future paths of specified variables
in themodel.
In addition to data description and forecasting, the VAR model is alsoused for structural inference and
policy analysis. In structural analysis, certain assumptions about the causal structure of the data under
investigation are imposed, and the resulting causal impacts of unexpected shocks orinnovations to
specified variables on the variables in the model are summarized. These causal impacts are usually
summarized with impulse response functions and forecast error variance decompositions.
Before analysing the VAR model the optimum lag is to be identified. The optimum lag length can be
identified with the help of lag length criteria such as Akaike information criterion, Schwartz
information criterion etc. The results of lag length criterion are shown below:
www.theinternationaljournal.org > RJSSM: Volume: 05, Number: 4, August 2015 Page 53
Table1.10: Lag length Criterion
VAR Lag Order Selection Criteria
Endogenous variables: SENSEX Returns
Lag LogL LR FPE AIC SC HQ
0 567.0708 NA* 0.000436* -2.062302* -2.046586* -2.056160*
1 568.6816 3.203822 0.000440 -2.053582 -2.006433 -2.035154
2 569.0001 0.631226 0.000446 -2.040146 -1.961565 -2.009433
3 571.6277 5.188094 0.000448 -2.035138 -1.925123 -1.992139
4 572.2114 1.148199 0.000454 -2.022669 -1.881222 -1.967385
5 575.4484 6.344024 0.000455 -2.019885 -1.847005 -1.952315
6 576.6271 2.301442 0.000460 -2.009588 -1.805275 -1.929733
7 581.4159 9.315493 0.000458 -2.012467 -1.776722 -1.920327
8 585.6392 8.184668 0.000458 -2.013282 -1.746104 -1.908857
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
The results of lag length criterion indicate that the optimum length is one. This may be due to the fact
the stock market reacts immediately to the unexpected component of the inflation rate. Before
analysing the VAR model the optimum lag is to be identified. The optimum lag length can be
identified with the help of lag length criteria such as Akaike Information Criterion, Schwartz
information criterion etc.
In order to analyse the lead-lag relation between the inflation rate and stock market of India, the Block
Exogeneity Wald test is applied. The results of the Block Exogeneity Wald test are shown below in
table1.11. The results indicate no causal relation between the WPI rate and stock market of India.
Table: 1.11: Block Exogeneity Wald Tests
VAR Granger Causality/Block Exogeneity Wald Tests
Dependent variable: SENSEX Returns
Excluded Chi-sq Df Prob.
Unexpected Inflation Rate 0.296695 2 0.8621
All 0.296695 2 0.8621
Dependent variable: Unexpected component of inflation rate in India
Excluded Chi-sq df Prob.
SENSEX returns 0.274226 2 0.8719
All 0.274226 2 0.8719
The impulse response traces the responsiveness of the dependent variable in the VAR to shocks to
each of the endogenous variables. So, for each variable from each equation of the VAR separately, a
unit shock is applied to the error, and the effects upon the VAR system over time are noted. The
ordering of the endogenous variables may affect the results of impulse response; hence the generalized
impulses are considered for the analysis in order to neutralize the ordering effect. Figure 1.10
represents the pair wise impulse response relations between unexpected component of WPI and
SENSEX returns.
www.theinternationaljournal.org > RJSSM: Volume: 05, Number: 4, August 2015 Page 54
-.01
.00
.01
.02
.03
.04
.05
1 2 3 4
Accumulated Response of DLOG_SENSEX to DIFF
-.1
.0
.1
.2
.3
.4
.5
.6
1 2 3 4
Accumulated Response of DIFF to DLOG_SENSEX
Accumulated Response to Generalized One S.D. Innovations ± 2 S.E.
Fig 1.10: Impulse Response Function
As shown in the Impulse response diagrams no significant impact of unexpected component of WPI is
found on the stock market.
The Variance decompositions offer a slightly different method for examining VAR system dynamics.
They give the proportion of the movements in the dependent variables that are due to their „own‟
shocks, versus shocks to the other variables. The results of the variance decomposition analysis for the
period of ten days are given in Table 1.12. The results indicate that 98.51 per cent of variations in the
error terms of SENSEX returns can be explained with the help of its own lagged values however 1.48
percent of its variations can be explained with the help of lagged values of unexpected WPI. Similarly
99.95 per cent of variations in the error terms of unexpected WPI can be explained with the help of its
own lagged values however 0.049 percent of its variations can be explained with the help of lagged
values of SENSEX returns.
Table1.12: Variance Decomposition
Variance Decomposition of Unexpected component of Inflation
Period
S.E.
Unexpected component
of WPI
SENSEX Returns
1 0.498012 100.0000 0.000000
2 0.498118 99.99466 0.005340
3 0.498244 99.95088 0.049120
4 0.498245 99.95069 0.049309
5 0.498245 99.95064 0.049365
6 0.498245 99.95063 0.049366
7 0.498245 99.95063 0.049366
8 0.498245 99.95063 0.049366
9 0.498245 99.95063 0.049366
10 0.498245 99.95063 0.049366
Variance Decomposition of SENSEX Returns:
Period S.E. DIFF DLOG_SENSEX
1 0.042519 1.465957 98.53404
2 0.042595 1.487420 98.51258
3 0.042607 1.487786 98.51221
4 0.042607 1.487780 98.51222
5 0.042607 1.487779 98.51222
6 0.042607 1.487779 98.51222
7 0.042607 1.487779 98.51222
8 0.042607 1.487779 98.51222
9 0.042607 1.487779 98.51222
10 0.042607 1.487779 98.51222
Cholesky Ordering: Inflation rate,_SENSEX Returns
www.theinternationaljournal.org > RJSSM: Volume: 05, Number: 4, August 2015 Page 55
Conclusion:
The stock valuation model asserts that stock price is equal to the sum of the discounted present value
of all future dividend payments. In other words, the stock price reflects investors‟ expectations of
future corporate earnings. Hence, stock prices commonly react to economic news The present research
study makes an attempt to study the lag-lead relationship between stock returns and inflation after
analyzing the inflation into expected and unexpected components. The high Standard Deviation value
indicates the high level of deviations in SENSEX as well as WPI series during the sample period
which indicates the volatile nature of level of inflation and market in the country. the Correlogram the
autocorrelation function (ACF) indicates that the SENSEX values and WPI values both are non
stationary in nature. In both of the cases of the Correlogram of the growth rate of WPI and SENSEX
returns the partial auto correlation function (PACF) at lag 1 indicates the stationary nature of the
seriesHence for further analysis the return series of SENSEX and growth rate of WPI is used. By using
Johansan‟scointegration test it can be concluded that the inflation rate in India and stock market are not
having long term equilibrium relationship between them. Due to the absence of any error correction
mechanism between the stock market and inflation rate, no long term or co integrated relation exists
between them. There are two components of inflation rate in India: expected and unexpected. In order
to analyse the impact of expected and unexpected component of inflation rate on stock market, the
forecasting model is developed using ARIMA forecasting method. The difference between the
forecasted values of WPI and the actual values of WPI are considered as unexpected values of
inflation.The residuals of the above mentioned ARIMA model and its Correlogram indicate that the
residuals are stationary and the model is assumed to be fit.The results of the regression model indicate
that the stock market is significantly influenced by the unexpected component of the inflation rate in
the Indian economy. However the impact is very low in magnitude. In order to analyse the lead-lag
relation between the inflation rate and stock market of India, the Block Exogeneity Wald test is
appliedThe results indicate no causal relation between the WPI rate and stock market of India. The
Impulse response diagrams no significant impact of unexpected component of WPI is found on the
stock market. The results of the variance decomposition analysis for the period of ten days have been
calculated. The results indicated that majority in the error terms of SENSEX returns and WPI values
can be explained with the help of its own lagged values however very negligible percent of its
variations can be explained with the help of lagged values of unexpected component of the opposite
variable.
Thus, the results of the study suggest that there exists no significant relation between inflation and
stock returns in the post-reform period in India. It implies that stock returns do not provide a hedge
against inflation. It can be said that investors aim at better returns and do not invest in stocks to hedge
against inflation.
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