Risk, uncertainty and stock returns predictability – a case of emerging equity markets

Rakesh Kumar (Department of Management Studies, Deen Dayal Upadhyaya College, University of Delhi, New Delhi, India)

Journal of Financial Economic Policy

ISSN: 1757-6385

Publication date: 5 November 2018

Abstract

Purpose

This paper aims to investigate the predictability of stock returns under risk and uncertainty of a set of 11 emerging equity markets (EEMs) during the pre- and post-crash periods.

Design/methodology/approach

Listed indices are considered to serve the proxy of stock markets with a structural break in data for the period: 2000-2014. As preliminary results highlight the significant autocorrelations in stock returns, Threshold-GARCH (1,1) model is used to estimate the conditional volatility, which is further decomposed into expected and unexpected volatility.

Findings

Results highlight that the volatility has symmetric impact on stock returns during the pre-crash period and asymmetric impact during the post-crash period. While testing the relationship of stock returns, a significant positive (negative) relationship is found with expected volatility during the pre-crash (post-crash) periods. The stock returns are found positively related to unexpected volatility.

Research limitations/implications

Business, political and other market conditions of sample stock markets are fundamentally different. These economies were liberalized in different years, which may affect the degree of integration with international equity markets.

Practical implications

The findings highlight that investors consider the impact of expected volatility in forecasting of stock returns during the growth period. They realize returns in commensurate to risk of their portfolios. However, they significantly reduce their investments in response to expected volatility during the recession period. The positive relationship between stock returns and unexpected volatility highlights the fact that investors realize extra returns for exposing their portfolios to unexpected volatility.

Originality/value

Pioneer efforts are made by using T-GARCH (1,1) procedure to analyse the problem. Given the emergence of emerging equity markets, new insight in dynamics of stock returns provide interesting findings for portfolio diversification under risk and uncertainty.

Keywords

Citation

Kumar, R. (2018), "Risk, uncertainty and stock returns predictability – a case of emerging equity markets", Journal of Financial Economic Policy, Vol. 10 No. 4, pp. 438-455. https://doi.org/10.1108/JFEP-08-2017-0075

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Publisher

:

Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited


1. Introduction

The recent US subprime crisis caused the crashing of stock markets worldwide. This crash led the policymakers in general and the investors in particular to pay considerable attention to fundamental issues such as:

  • impact of economic and non-economic events on stock returns under different economic conditions;

  • diversification of funds across the markets; and

  • investment allocations under risk and uncertainty.

The answers are important from the policy perspective because of the growing importance of emerging equity markets (EEMs) in past decades. These markets have reported considerable growth, especially after the deregulation of the financial system (Dhal, 2009; Kumar, 2016; Singh and Ahmed, 2016; and Kumar and Dhankar, 2017). The recent studies on EEMs have given considerable focus to dynamics of stock returns under the risk and uncertainty (Chen and Epstein, 2002; Hansen et al., 2006; Anderson et al., 2009; Chua et al., 2010).

The economic literature fundamentally differentiates risk and uncertainty (Knight, 1921). While dealing with the predictability of stock returns under risk and uncertainty, recent studies have the limitations of:

  • do not differentiate between developed and emerging stock markets;

  • are limited to developed stock markets;

  • are rather inconclusive; and

  • are limited to estimate the relationship between stock returns and expected volatility.

The present study bridges this gap by analysing the dynamics of stock returns under risk (expected volatility) and uncertainty (unexpected volatility) in a data set of emerging equity markets. We hypothesize that the investors tend to adjust return estimates vis-a-vis to expected volatility, while they tend to realize risk-weighted returns for exposing their portfolios to unexpected volatility in stock returns. We examine this hypothesis by tracking the relationship of stock returns with expected and unexpected volatility during the growth and recession periods. Researchers report significant relations between the stock returns and international economic and non-economic variables which cause volatility in stock markets (Rahman Md. and Uddin, 2009). The modelling of these variables serves the interest of investors in estimating the risk in EEMs.

1.1 Review of literature

The stock returns’ relationship with expected and unexpected volatility is widely researched in case of developed markets with lesser focus on emerging equity markets. Some studies have reported positive relationship between stock returns and expected volatility (French et al., 1987; Ghysels et al., 2005; Shin, 2005; Chua et al., 2010). For example, Al-Rjoub and Azzam (2012) uses T-GARCH model to examine the impact of financial crisis on Jordan stock market for the period: 1992-2009. They find negative impact of crisis on the stock returns of all sectors. Singhania and Prakash (2014) analyse the daily closing stock prices of SAARC countries (India, Pakistan, Sri Lanka and Bangladesh) for the period 2000-2011 by using GARCH class models. Their study reports no correlation between stock returns and conditional volatility, however, the relationship between stock returns and standardized residuals (unexpected volatility) is found significantly positive.

Further, Sehgal and Garg (2016) estimate the systematic volatility (SV) and unsystematic volatility (UV) of the stock markets of BRIICKS (Brazil, Russia, India, Indonesia, China, South Korea and South Africa) countries. The study finds that high SV portfolio exhibit low returns in the case of Brazil, South Korea and Russia. The risk premium is found significantly negative for these countries. It is further observed that high UV portfolios exhibit high returns in all the sample countries except China. Kumar (2016) examines the integration of nine emerging equity markets by using GARCH (1,1) in mean procedure. The results report significant integration between the expected and unexpected volatilities of sample stock markets. These results highlight the important element of investment strategy that investors across the markets tend to respond in the same line with the occurrence of global expected and unexpected shocks.

Further, Kumar and Dhankar (2017) use the GARCH class models to analyse the impact of world financial instability on the stock returns of emerging South Asian stock markets (India, Pakistan, Bangladesh and Sri Lanka). The results report that financial liberalization has integrated the South Asian stock markets to the world equity markets. The stock prices are directly affected by global expected and unexpected economic shocks. Adjei and Adjei (2017) apply GARCH in mean with exogenous variable while testing the impact of economic uncertainty on the forecasting of stock returns. The results report that economic uncertainty has negative impact on the stock returns during recession period. Another important study of Abaidoo (2017) finds that inflation and recession expectations tend to have significant impact on risk premium estimates in the short run while using the error correction model.

A good number of studies report a negative relationship between stock returns and volatility (Nelson, 1991; Brandt and Kang, 2004). For example, Glosten et al. (1993) examine the time series relationship between conditional mean returns and conditional volatility of a sample period from 1951 to 1989. They use T–GARCH to take into account the seasonal asymmetric effects of unexpected positive and negative shocks on stock returns. The results report a negative relationship between conditional mean return and conditional variance. Chiang and Doong (2001) investigate the time series behaviour of stock returns of seven Asian stock markets. Their study reports a significant negative relationship between stock returns and unexpected volatility for four stock markets and non-significant positive relationship with expected volatility. Dimitrios and Theodore (2011) investigate the risk-return relationship in seventeen international stock markets by using semi-parametric approach. They find a significant negative relationship for all the sample markets except Austria, Belgium and Luxemburg.

While testing the relationship between stock returns and volatility, some studies have documented the mix or inconclusive results. For example, Balaban et al. (2001) finds that the conditional volatility has a significant positive impact on stock returns in three out of nineteen countries and a non-significant positive impact for rest of the sample. Further, Balaban and Bayer (2005) study reports a mixed set of relationship between stock returns and volatility which is derived from the symmetric and asymmetric conditional heteroskedasticity models while using the data of 14 countries.

2. Research methods

2.1 Data source and description

We consider the sample of eleven emerging markets from the IMF list of emerging stock markets (www.imf.org) on the basis of availability of data for the time period: 2000-2014. The monthly closing prices of widely used listed indices are considered as the proxy for the stock markets: MERV of Argentina (AR), IBOVESPA of Brazil (BR), SSE COMPOSITE of China (CH), SENSEX of India (IN), FTSE–KLCE of Malaysia (MA), KSE 100 of Pakistan (PAK), RTSI of Russia (RU), BUX of Hungary (HU), TSEC of Taiwan (TA), IPCMAXX of Mexico (MEX) and JAKARTA COMPOSITE of Indonesia (IND). The sample period is divided into pre- and post-stock markets crash periods caused by the US subprime crisis highlighting the growth and recession periods respectively by applying structural break procedure.

The initial data set involves the absolute values of mentioned indices. A systematic research requires relative values wherein spike variations need to be neutralized with constant mean and variance. Using the monthly closing prices, the natural logarithmic returns are computed by equation (1):

(1) Rit=[ln(Pt)ln(Pt1)]×100
where, ln is natural log, Pt is the price of index in time period t, Pt–1 is the price in preceding time period t−1, and Rit is the rate of return of index “I” in time period “t”.

Figure 1 displays the index values of the sample stock markets. The study period highlights a mix set of two distinct phases in the evolution of the contemporary global economic environment worldwide. The first phase consists the time period from 2000 to 2007 is marked as growth phase with consistently rise in world equity markets. The second phase consisting the period from the early 2008 till 2009, witnessed the crash of stock markets worldwide caused by the USA subprime crisis, subsequently the recovery period wherein world equity markets started moving steadily upward.

Table I presents the fundamental financial and economic information of sample emerging economies for the three different years. It highlights:

  • annual GDP growth rates;

  • market capitalization of listed domestic companies as a percentage of GDP of the country; and

  • foreign portfolio equity net investments.

It is noted that India has reported highest GDP growth rate (7.29 per cent), followed by China (7.27 per cent) and Malaysia (5.99 per cent) in the year of 2014. Malaysia has the largest market capitalisation base of listed companies as a percentage of GDP followed by India. China is found the highest foreign portfolio investments followed by India.

2.2 Threshold-GARCH (1,1) model

The significant autocorrelations in stock returns highlight the non-normality of the error term commonly called heteroskedasticity. To model this type of time series data, researchers commonly use Auto Regressive Conditional Heteroskedasticity (ARCH) framework. The ARCH model uses conditional variance as a function of error term of past time periods. Bollerslev et al. (1992) further extend the ARCH process to the GARCH where the time varying conditional variance ( hit2) is postulated to be the function of lagged values of past error term ( εit12) and conditional variance ( hit12) as depicted in equation (2):

(2) hit2=α0+α1εit12+β1hit12

Further, empirical studies have reported that good/bad news account asymmetric impact of volatility of stock returns. Many empirical studies have found T-GARCH as developed by Glosten et al. (1993) suitable to capture the asymmetric nature of financial time series (Al-Rjoub and Azzam, 2012; Yeh and Lee, 2000; Chiang and Doong, 2001; Balaban et al., 2001; Singhania and Prakash, 2014; Kumar and Dhankar, 2017). Equation (3) shows the standard T-GARCH model:

(3)  hit2=α0+α1εit12+γεit12dt1+β1hit12
where, dt1={1ifεt<00otherwise

where, εit > 0, α1 ≥ 0, β1 ≥ 0, hit2 is conditional variance in time period “t” of index “I”, εit12 is lagged value of the error term, hit12 is lagged value of conditional variance. The asymmetric impact on volatility of index return is estimated by “γ” coefficient. Good news (εt > 0) and bad news (εt < 0) have differential impact on the conditional variance. A positive “εt–1” contributes “ α1εit12 ” to hit2, whereas a negative εt–1 has a larger impact (α+γ)εt12. If γ > 0, the leverage effect of bad/good news exists on stock returns.

T-GARCH model postulates that the volume and persistence of volatility in the current time period directly depend upon the sizes of “α1” and “β1” coefficients. A high “β” suggests that if volatility was high yesterday, it will still be very high today. It will take long time to die out. Similarly, the high value of “α” suggests that unexpected volatility react quite intensely to stock returns which causes spike unexpected volatility in the stock market. Following the studies (Engle and Ng, 1993; Al-Rjoub and Azzam, 2012; Yeh and Lee, 2000; Chiang and Doong, 2001; Singhania and Prakash, 2014; Kumar and Dhankar, 2017), we also use T-GARCH (1,1) to estimate the volatility with asymmetric impact of news information on stock returns in the given data set.

In the present study, the conditional volatility of sample stock markets as estimated by equation (3), are further decomposed into expected volatility caused by predictable economic and non-economic fundamentals and unexpected volatility caused by unexpected events (French et al., 1987; Singhania and Prakash, 2014; Kumar and Dhankar, 2017). This suggests that the expected volatility termed as risk is measured by the lagged value of conditional variance ( hit12). The unexpected volatility marked as uncertainty is measured by lagged value of error term ( εit12). In the present study, we build up the model that the volatility of stock returns is the function of unexpected volatility (UV) and expected volatility (EV).

3. Empirical findings

3.1 Preliminary results

The stochastic properties of stock returns of sample emerging markets are shown in Table II. The positive average returns of all the markets except the Hungarian highlight that stock indices have shown the upward rising tendency over the period. The mean percentage returns range from −0.04 per cent (Hungary) to 1.65 per cent (Pakistan). The aggregate volatility measured by standard deviation ranges from 4.39 per cent (Malaysia) to 10.71 per cent (Argentina). The Pakistan stock market has offered the highest return next to Argentina, subject to lower risk (8.06) compared to Argentina (10.71). The negative skewness of all markets suggests that these markets have a higher probability of providing negative return. The skewness of Pakistan and Indonesia stock returns has heavier tail than the normal distribution, implying concentration of returns at one level. We have used Jarque–Bera (J–B) test to analyse the normal distribution properties of stock returns. It is significant at 5 per cent level of significance, highlighting the non-normal distribution of returns.

The Ljung–Box Q statistics is applied to detect the autocorrelations in the stock returns with different lag lengths. The null hypothesis of no autocorrelations is tested against the alternative hypothesis of significant autocorrelations. The autocorrelations highlight the fact that the stock markets in question are deemed informationally efficient and investors primarily give weight to current information in the selection of stocks (Faff and Mckenzie, 2007; Kumar and Dhankar, 2017). As indicated by Table II, Ljung–Box Q statistics with lags length 1 through 10 are significant, outlines the significant autocorrelations in stock returns i.e. volatility clustering. The modelling this phenomenon in stock returns, researchers commonly use autoregressive conditional heteroskedasticity (ARCH) class of models.

The present study also attempts to analyse the degree of integration among the sample stock markets by estimating the correlations in stock returns (see Table III). The results highlight the significant positive correlations in the stock returns except between China and Pakistan, highlighting significant integration over the period. The findings are consistent with previous studies which highlight that flow of trade and investment resulting in the integration of stock markets (Darrat and Zhong, 2001; Kim et al.2005; Kumar and Dhankar, 2017).

3.2 Unit root test with structural break

The stationary is the most common property of the data requires to be tested by Unit root test with intercept and with intercept and slope. The nonacceptance of null hypothesis highlights the data series to be stationary. However, Perron (1989) highlights that the power to reject a unit root decreases when structural break caused by structural change is ignored in stationary series. The structural changes tend to occur in the economic system because of economic crises, policy changes or regime shifts.

Perron (1989) proposed three alternative models to allow the known structural breaks in the data. These are:

  • Model A (the crash model), allows structural break in the intercept;

  • Model B (the changing growth model), allows for a structural break in the slope; and

  • Model C (the crash-cum-growth model), allows the structural breaks in intercept and slope.

We have tested unit root by model A and model C in the given data set.

Model A has the following form:

(4) Δyt=μ+βt+θDUt+αyt1+i=1kciΔyti+εt

Model C takes the following form:

(5) Δyt=μ+βt+θDUt+αyt1+γDTt+i=1kciΔyti+εt
where, Δ is first difference operator, DUt is dummy variable for a mean shift occurring (break) at time TB, “T” is an index of time, DTt is the corresponding trend and shift variable, where:
DUt={1ift>TB0otherwise
and:
DTt={tTBift>TB0otherwise

The null hypothesis in the above models is α = 0, where the “yt” series contains a unit root with a drift that excludes any structural break, while the alternative hypothesis is that α < 0, where the “yt” series having a trend stationary process with a one-time break which occurs at a known point of time. We have taken worldwide stock market crash of 2007 because of the US subprime crisis as a structural break time. For the purpose, the successive month of the month with the highest value of the index of the sample stock markets around the December, 2007 is taken as possible structural break. For example, MERV was highest in October, 2007, reached to significantly lower level in November, 2007 highlighting structural break because of outburst of US subprime crisis. Similarly, IBOVESPA, SSECOM, SENSEX, FTSE-KLSE, RTSI and JAKARTA COMPOSITE were at highest level in the month of December, 2007 and reported structural breaks in the successive month. The results of Unit root test with structural break are reported in Table IV, highlighting the stationary properties of sample stock markets with significant structural break date.

3.3 Threshold-GARCH (1,1) results and diagnosis testing

Table V highlights the results of T-GARCH (1,1) model for pre-crash period in the given data set. It is noted that the GARCH coefficients are significant for eight stock markets except India, Pakistan and Brazil. It shows that the past volatility has significant symmetric impact on the volatility of stock returns in current time. The ARCH coefficients are found significant in case of four stock markets (Argentina, Malaysia, Mexico and Indonesia), highlight that unexpected volatility significantly contributes to volatility of stock returns in current time. However, the asymmetric coefficients of only four stock markets (Argentina, Russia, Mexico and Indonesia) are significant, highlights the asymmetric behaviour of investors towards market and non-markets events. The direct observations can be made here that reactions of the investors toward market and non-market events are symmetric in majority of sample stock markets during the growth period.

Table VI summarizes the results for post-crash period. The GARCH coefficients are significant for eight stock markets which allow the volatility of stock returns of current time period to be function of volatility of past time. The asymmetric coefficients γ are significant for all stock markets except the three stock markets (Brazil, Pakistan and Indonesia). One can directly infer that investment decisions are asymmetric in response to expected and unexpected fluctuations in stock prices because of exogenous factors in recession period. The T-GARCH (1,1) results of the current study are in the line of past study where T-GARCH class models are found better predictor of volatility (Corhay and Rad, 1994; Nelson, 1991; Brandt and Kang, 2004; Ghysels et al., 2005; Shin, 2005; Singhania and Prakash, 2014; Kumar, 2016; Singh and Ahmed, 2016; Kumar and Dhankar, 2017).

The ARCH-LM test is used further to test the best fit models in giving data set which can significantly explain the conditional volatility of sample emerging stock markets. The test statistic for Engle’s ARCH-LM test is the usual F statistic which conducts regressions on the squared residuals. A significant F value indicates rejection of the null hypothesis in favour of the alternative. It is clear from Tables V and VI that F value at different lags are not significant at five present levels of significance, indicating the normal distribution of the error term of fitted models.

3.4 Relationship of stock returns with expected and unexpected volatilities

Following the past studies (French et al., 1987; Poon and Taylor,1992; Chiang and Doong, 2001; Balaban and Bayer, 2005; Singhania and Prakash, 2014), we test the relationship of stock returns with expected volatility and unexpected volatility during the pre- and post-crash periods by estimating the equation (6).

(6) Rit=c0+c1Expectedvolatility+c2Unexpectedvolatility
where, Rit is the stock return of eleven stock markets in the time period “t”. The coefficients “c1” and “c2” require to be significant if expected volatility ( hit12) and unexpected volatility ( εit12) are significantly related with stock returns.

Table VII indicates the results for pre-crash period. It highlights that the regression coefficients “c1” of six stock markets (Argentina, Brazil, China, India, Pakistan and Indonesia) are significant highlighting the significant positive relationship between stock returns and expected volatility. It points out investment strategy that during growth period, investors take advantage of expected volatility by realizing higher returns. It may safely infer here that investors alter their investment decisions with respect to expected volatility, while the non-significant relationship between stock returns and expected volatility shows that investors absorb the impact of expected volatility in their investment strategy in advance. They remain invariable to the happening of expected volatility. The coefficient “c2” measuring the relationship between stock returns and unexpected volatility of stock returns are found positive for all sample stock markets. This suggests that investors take advantage of unexpected volatility during the growth periods.

Table VIII reports the results for the post-crash period. It is noted that the regression coefficient “c1” is significantly negative for five stock markets (China, Pakistan, Russia, Hungary and Mexico). The observations can be made here that investors dispose the stocks in anticipation of expected volatility during the recession period. The coefficient “c2” is significant for all the sample stock markets during the post-recession period. It highlights the fact that investors take advantage of unexpected volatility during the recession periods.

The overall results are in the line of the findings of earlier studies which support significant high correlation between expected stock returns and uncertainty and insignificant low correlations between stock returns and risk (French et al., 1987; Chiang and Doong, 2001; Ghysels et al., 2005; Shin, 2005; Anderson et al., 2009; Singhania and Prakash, 2014). These findings bring out the fact that investors raise the aspired risk-weighted returns in response to the uncertainty i.e. unexpected volatility in stock markets.

4. Conclusion and implications of the study

The dichotomous behavioural responses of investors under risk and uncertainty have several implications for the efficiency of the stock markets and portfolio diversification. The emerging equity markets have created enormous opportunities for investment and attracting the attention of foreign institutional investors in past decades. The significant autocorrelations question the random walk behaviour of stock returns and signifies the fact that the current stock prices have not absorbed the historical and publicly available information. These findings are consistent with that of the previous research, which finds non-linearity and seasonal variations in stock returns. The holding of such phenomena in stock returns necessitated the application of T-GARCH (1,1) model to explain the conditional volatility in stock returns under consideration.

The results bring out the important elements of investment strategy while testing the relationship of stock returns with expected and unexpected volatility. The results highlight that the volatility has symmetric impact on stock returns during the pre-crash period and asymmetric impact during the post-crash period. While testing the relationship, majority of the stock markets report a positive relationship between stock returns and expected volatility during the pre-crash period. This suggests the fact that investors tend to adjust risk premium estimates towards expected volatility. They realize returns in commensurate to risk. While the relationship is found to be negative for six stock markets during the post-crash period, these results bring out that investors tend to change their portfolios towards expected volatility during the growth and recession periods. They take into consideration the effect of expected occurrence of economic and non-economic events in making their investment decisions in advance and accordingly formulate their investment strategy. Further, the positive significant regression coefficients between stock returns and unexpected volatility indicate the fact that investors realize extra returns for making investments under uncertainty in the markets.

The empirical results show that investors tend to absorb the impact of expected volatility in estimates of stock returns. However, they would like to be better compensated for the unexpected volatility. These findings highlight that investors collectively react in the same fashion towards unexpected volatility. To conclude, the study reports that investors react in the same line towards exogenous events which have considerable impact upon the investment decisions in emerging stock markets.

Figures

Index values of sample stock markets

Figure 1.

Index values of sample stock markets

Financial indicators of sample stock markets

Annual GDP growth rate (%) Market capitalization of listed companies (% of GDP) Portfolio equity, net inflows (BoP, current US$, in million)
(1)
Country
(2)
1998
(3)
2006
(4)
2014
(5)
1998
(6)
2006
(7)
2014
(8)
1998
(9)
2006
(10)
2014
AR 3.85 8.40 0.45 15.16 19.51 11.19 −209.64 706.66 217.90
BR 0.34 3.96 0.10 NA 64.12 34.92 −1768.00 7715.81 11492.92
CH 7.85 12.69 7.27 NA 41.96 57.99 765.00 42861.20 51915.79
IN 6.18 9.26 7.29 NA 86.28 76.07 −601.15 9509.11 12369.28
MA −7.36 5.58 5.99 132.42 144.80 135.76 NA 2355.15 NA
PAK 2.55 6.18 4.74 8.71 32.72 NA −22.00 1152.00 762.00
RU −5.30 8.15 0.64 NA NA 20.74 713.99 7234.45 −12966.28
HU 4.21 3.81 3.67 NA 36.54 10.50 555.45 911.77 −324.87
MEX 4.70 4.94 2.23 18.28 36.09 37.09 −665.60 2805.15 4833.54
IND −13.13 5.50 5.02 23.13 38.10 47.51 −4371.00 1897.58 3259.25
TA NA NA NA NA NA NA NA NA NA

Source: World development indicators (2015)

Preliminary statistics (2000-2014)

Statistics AR BR CH IN MA PAK RU HU MEX IND TA
Mean 1.62 0.68 0.32 0.98 0.40 1.65 1.02 −0.04 1.11 1.13 0.33
Maximum 39.66 16.48 24.25 24.88 12.7 24.11 30.49 22.42 15.32 18.34 16.72
Minimum −45.81 −28.49 −28.27 −27.29 −16.51 −44.87 −44.91 −21.50 −19.66 −37.71 −33.44
SD 10.71 7.31 7.79 7.08 4.39 8.06 10.53 6.84 5.60 6.89 6.92
Skewness −0.16 −0.48 −0.54 −0.51 −0.52 −1.20 −0.65 −0.12 −0.52 −1.12 −0.76
Kurtosis 5.53 3.72 4.67 4.46 4.35 8.98 4.93 4.16 3.86 7.67 5.47
J–B
Statistic
48.86** (0.000) 11.08** (0.003) 29.97** (0.000) 24.08** (0.000) 22.17* (0.000) 312.59** (0.000) 40.86** (0.000) 10.51** (0.000) 13.66** (0.000) 22.34** (0.000) 63.13** (0.000)
Q test (5lags) 33.22** (0.000) 33.54** (0.000) 72.34** (0.000) 40.42* (0.000) 49.61** (0.000) 35.11** (0.000) 31.67** (0.000) 37.03** (0.000) 40.65** (0.000) 36.45** (0.000) 57.36** (0.000)
Q test (10 lags) 39.69** (0.000) 40.18** (0.000) 87.64** (0.000) 43.64** (0.000) 57.87** (0.000) 40.02** (0.000) 37.95** (0.000) 40.68** (0.000) 64.89** (0.000) 43.22** (0.000) 79.71** (0.000)
Notes:

Probability value in the bracket in case of Q test at 5 and 10 lags;

**

indicates significant at 5 % level of significance. All the variables are defined earlier

Source: Author’s own

Correlation matrix of returns of sample stock markets (2000-2014)

Country HU MA BR MEX IND PAK AR RU IN CH TA
HU 1.00
MA 0.48** (0.000) 1.00
BR 0.62** (0.000) 0.47** (0.000) 1.00
MEX 0.58** (0.000) 0.49** (0.000) 0.68** (0.000) 1.00
IND  0.50** (0.000) 0.52** (0.000) 0.45** (0.000) 0.56** (0.000) 1.00
PAK 0.37** (0.000) 0.13* (0.070) 0.27** (0.000) 0.26** (0.000) 0.15** (0.040) 1.00
AR 0.48** (0.000) 0.37** (0.000) 0.48** (0.000) 0.59** (0.000) 0.42** (0.000) 0.23** (0.002) 1.00
RU  0.62** (0.000) 0.39** (0.000) 0.57** (0.000) 0.60** (0.000) 0.48** (0.000) 0.28** (0.000) 0.49** (0.000) 1.00
IN  0.54** (0.000) 0.50** (0.000) 0.63** (0.000) 0.56** (0.000) 0.63** (0.000) 0.23** (0.002) 0.46** (0.000) 0.45** (0.000) 1.00
CH  0.29** (0.000) 0.34** (0.000) 0.36** (0.000) 0.26** (0.000) 0.25** (0.000) 0.07 (0.336) 0.28** (0.000) 0.30** (0.000) 0.34** (0.000) 1.00
TA  0.46** (0.000) 0.56** (0.000) 0.55** (0.000) 0.53** (0.000) 0.43** (0.000) 0.22** (0.002) 0.49** (0.000) 0.57** (0.000) 0.54** (0.000) 0.28** (0.000) 1.00
Notes:

Probability values in the bracket;

**

indicates significant at 5% level of significance;

*

indicates significant 10 % level of significance

Source: Authors’ own

Unit root test with structural break

Country Structural break date With intercept With intercept and slope
AR 11,2007 −11.422** −11.586**
BR 01,2008 −11.756** −11.851**
CH 01,2008 −12.518** −12.946**
IN 01,2008 −12.199** −12.783**
MA 01,2008 −11.617** −11.954**
PAK 04,2008 −12.289** −12.533**
RU 01,2008 −10.927** −10.900**
HU 08,2007 −11.721** −11.870**
MEX 11,2007 −12.235** −12.415**
IND 01,2008 −10.508** −10.792**
TA 12,2007 −11.612** −11.853**
Notes:

Critical value at 5% level of significance is −3.760;

**indicates significant at 5% level of significance

Source: Author’s own

Estimation of conditional volatility (pre-crash period)

Country Constant (α0) ARCH(1) (α1) Asymmetric (γ) GARCH(1) (β1) ARCH
LM test
AR −1.530* (0.070) −0.075** (0.012) 0.180** (0.005) 1.019** (0.000) 1.540 (0.217)
BR 27.654 (0.287) −0.021 (0.897) 0.366 (0.385) 0.422 (0.421) 0.002 (0.967)
CH 10.819 (0.305) 0.253 (0.151) −0.311 (0.162) 0.653** (0.011) 0.279 (0.598)
IN 26.328 (0.233) −0.010 (0.962) −0.175 (0.315) 0.529 (0.261) 0.152 (0.696)
MA 0.077 (0.825) −0.041* (0.092) 0.005 (0.854) 1.027** (0.000) 1.765 (0.187)
PAK 73.757** (0.003) −0.036 (0.710) 0.757 (0.141) −0.181 (0.482) 0.026 (0.871)
RU −1.988 (0.201) 0.023 (0.465) −0.134** (0.000) 1.027** (0.000) 0.143 (0.705)
HU 71.280** (0.000) −0.006 (0.930) 0.152 (0.157) −0.929** (0.000) 0.956 (0.331)
MEX 0.651** (0.000) −0.067** (0.000) −0.105** (0.000) 1.069** (0.000) 0.124 (0.431)
IND 4.552** (0.000) −0.201** (0.000) 0.116** (0.000) 1.062** (0.000) 0.121 (0.737)
TA 4.068 (0.265) −0.116 (0.262) 0.345 (0.140) 0.858** (0.000) 0.553 (0.458)
Notes:

Probability value in the bracket;

**indicates significant at 5% level of significance;

*indicates significant at 10% level of significance

Source: Author’s own

Estimation of conditional volatility (post-crash period)

Country Constant (α0) ARCH(1) (α1) Asymmetric (γ) GARCH(1) (β1) ARCH
LM test
AR 56.621** (0.045) 0.411 (0.156) 0.812* (0.063) 0.008 (0.981) 0.206 (0.651)
BR 27.155** (0.026) 0.222 (0.375) 0.643 (0.120) −0.033 (0.860) 0.327 (0.568)
CH −0.297 (0.529) 0.020** (0.000) −0.117** (0.000) 1.037** (0.000) 1.269 (0.263)
IN 1.265** (0.000) −0.151** (0.000) 0.168** (0.000) 1.022** (0.000) 2.303 (0.133)
MA 0.203 (0.243) −0.169** (0.000) 0.175** (0.000) 1.049** (0.000) 1.411 (0.238)
PAK 5.900 (0.283) 0.023 (0.626) 0.107 (0.146) 0.843** (0.000) 0.567 (0.452)
RU 10.021* (0.064) −0.064 (0.642) 0.397** (0.018) 0.734** (0.000) 0.299 (0.585)
HU 6.103 (0.180) 0.006 (0.946) 0.331** (0.003) 0.706** (0.000) 0.048 (0.826)
MEX 0.252 (0.426) −0.165) (0.112) 0.255** (0.000) 1.029** (0.000) 0.069 (0.793)
IND 18.349** (0.051) 0.347 (0.105) 0.731 (0.137) 0.042 (0.884) 0.002 (0.973)
TA −0.030 (0.893) −0.076) ** (0.029) 0.117** (0.000) 0.983** (0.000) 0.205 (0.651)
Note:

Probability value in the bracket;

**indicates significant at 5% level of significance;

*indicates significant at 10% level of significance

Source: Author’s own

Stocks returns linkages with expected and unexpected volatility (pre crash)

Country Constant (c0) Expected volatility (c1) Unexpected volatility (c2) R square (R2)
AR −1.332* (0.058) 0.014** (0.023) 9.661** (0.000) 0.90
BR −1.481** (0.000) 0.023** (0.000) 7.733** (0.000) 0.98
CH −0.663** (0.041) 0.021** (0.000) 6.919** (0.000) 0.94
IN −1.788** (0.000) 0.036** (0.001) 6.832** (0.000) 0.97
MA −0.016 (0.944) −0.009 (0.425) 4.455** (0.000) 0.96
PAK −0.928** (0.001) 0.013** (0.001) 8.223** (0.000) 0.96
RU −1.327** (0.025) 0.007 (0.152) 9.650** (0.000) 0.92
HU −0.425 (0.264) 0.007 (0.462) 6.167** (0.000) 0.97
MEX −0.971** (0.006) 0.012 (0.104) 6.051** (0.000) 0.91
IND −1.110** (0.006) 0.012** (0.032) 6.652** (0.000) 0.95
TA −1.327** (0.025) 0.007 (0.153) 9.651** (0.000) 0.92
Notes:

Probability value in the bracket;

**indicates significant at 5% level of significance;

*indicates significant at 10% level of significance

Source: Author’s own

Stocks returns linkages with expected and unexpected volatility (post crash)

Country Constant (c0) Expected volatility (c1) Unexpected volatility (c2) R square (R2)
AR −0.364 (0.306) 0.001 (0.953) 10.501** (0.000) 0.93
BR −0.186 (0.437) −0.004 (0.176) 6.427 (0.000) 0.92
CH 0.654 (0.177) −0.031** (0.000) 6.501** (0.000) 0.86
IN −0.556 (0.258) 0.002 (0.792) 6.363** (0.000) 0.81
MA −0.216 (0.445) 0.003 (0.826) 3.422** (0.000) 0.80
PAK 0.381 (0.463) −0.033** (0.001) 6.401** (0.000) 0.85
RU 0.898 (0.140) −0.007** (0.005) 10.159** (0.000) 0.85
HU 0.638** (0.043) −0.007** (0.036) 7.113** (0.000) 0.92
MEX −0.246 (0.418) 0.012* (0.090) 4.455** (0.000) 0.86
IND −0.271 (0.458) −0.003 (0.173) 6.395** (0.000) 0.81
TA −0.228 (0.588) 0.003 (0.800) 5.366** (0.000) 0.85
Notes:

Probability value in the bracket;

**indicates significant at 5% level of significance;

*indicates significant at 10% level of significance

Source: Author’s own

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Website

Supplementary materials

JFEP_10_4.pdf (7.7 MB)

Corresponding author

Rakesh Kumar can be contacted at: saini_rakeshindia@yahoo.co.in