In analysing financial asset risk, it must be noted that the existence of these features makes conditional variance models more suitable.
Models put forward to represent the evolution of volatility in financial returns are expected to exhibit the above properties usually observed in financial returns. Given that stock returns are non-normally distributed and often exhibit the above stated stylised features, ARMA models may not appropriately capture stock volatility. A number of models have been developed that are especially suited to estimate the conditional volatility of financial returns, and the most well-known and frequently applied models for this volatility are the conditional heteroscedastic models.
Such models have been constructed to represent dynamics of stock return volatility in an attempt to forecast it. Coffie in concordance with Nelson and Glosten, Jagannathan and Runkle concluded that the standard symmetrical ARCH or GARCH models can model three important characteristics of financial time series, namely leptokurtosis, skewness and volatility clustering, but is unable to capture the dynamics of a fourth important feature of financial time series, the leverage effect.
In order to capture the asymmetric effect in modelling the stock returns volatility, the threshold generalised autoregressive conditional heteroscedasticity TGARCH propounded by Zakoian , the exponential generalised autoregressive conditional heteroscedasticity EGARCH by Nelson can be used as noted by Islam The advantage of using the logarithmic construction on the EGARCH model is that the conditional variance will be positive always, so there will be no need to impose a restriction of non-negative coefficients.
Following the above methodology utilising E-views 7 statistical package, the results obtained are discussed hereunder.
In order to lay bare the nature and distributional features of the selected SADC stock markets, the researchers computed the mean return, standard deviation, 3rd and 4th moments of distribution and Jarque-Bera using individual samples as presented in Table 2. The Jarque-Bera statistic measures whether the variable is normally distributed or not.
Looking at the p -value for the Jarque-Bera statistic which is zero for all variables , we can safely reject the null hypothesis. This indicates that the variables are not normally distributed. Portfolio managers and investors are therefore encouraged to be careful when applying concepts and tests that assume normality.
Such concepts include the modern portfolio theory, efficient market hypothesis and traditional finance framework. Excess kurtosis above 3 evidenced in all the markets under consideration suggests that big shocks of either sign are more likely to be noted. Positive skewness noted in Zimbabwe and Namibia implies that the return distribution has a long right tail implying that large positive movements in stock prices are not usually matched by equally large negative movements.
The reverse can be said for Malawi, Zambia and South Africa returns which are negatively skewed. Honouring the Jarque-Bera test statistic and the corresponding p -values, it can be safely concluded that all the markets under study do not follow a normal distribution.
The variation in the returns observed in these markets can be attributed to differences in economic and financial development which is of notable difference among the markets under study. Such variations in return can also be a function of nation specific or individual attributes such as foreign direct inflows and brown field investments which are significant in all other nations save Zimbabwe.
On a positive note, small standard deviations which is an absolute measure of risk noted in all the markets under study indicates that risk is generally low. This can be attributed to the fact that the SADC region is generally stable politically and financial sector wise.
Capital inflows into the region were promoted by the global financial crisis which negatively affected developed nations who in turn courted the SADC economies in an attempt to diversify risks. A stationary variable gives us the green light to use stochastic models in analysing the dynamic behaviour of returns volatility over time. A unit root test examines whether a time series variable is stationary or non-stationary using an autoregressive model approach. To verify the order of integration and avoid spurious regression in the conditional mean equation , the study adopted the common Augmented Dickey Fuller ADF test.
The results of the ADF unit root test are presented in Table 3. As clearly presented, all the stock markets returns were stationary in levels integrated of order zero implying no need for any transformation before the variables are used for model estimation. What legitimises the use of ARCH family models is the presence of autocorrelation of variance or heteroscedasticity, excess kurtosis and skewness, which are prevalent in developing nations as argued by Kim and Ng and also in developed nations as concluded by Kim and Kon The results from the heteroscedasticity test are shown in Table 4.
This gives us the green light to estimate a GARCH model which is appropriate only if such effects exist. Leverage effects negative shocks or variance having larger impact on future returns volatility than positive news of the same effect were noted in the stock markets of Namibia, Zambia and South Africa. The stock markets of Zimbabwe and Malawi evidenced the presence of reverse asymmetry in which case positive shocks on stock returns have larger impact on future volatility than negative shocks of the same size. Similar findings were obtained by Kalu and Friday looking at Nigeria market and Wan et al.
Looking at volatility persistence in the stock markets, all the markets indicated long memory significant persistence except for Malawi indicating that shocks quickly die out short memory. Leverage effects were noted in Namibia and South Africa, whereas Zambia, Malawi and Zimbabwe indicated the absence of asymmetric volatility indicating that both positive and negative shocks on stock market returns have the same impact on future return volatility. Similar results of same effect were also noted by Cheng et al.
Such a result is contrary to the results obtained by Niyitegeka and Tewari who noted the existence of volatility persistence on South African stock markets and Emenike analysing volatility behaviour in Nigeria. The differences in volatility features among the markets under study are attributable to different approaches towards macro-economic stability in both monetary and fiscal policy , tax and foreign investment policies which are not fully harmonised, lack of depth and liquidity in the stock markets and disparities in trading, clearing and settlement procedures and infrastructure.
The lack of co-movement and integration among the stock markets and economies is evidenced by varied volatility behaviour. Consistent results were obtained on the presence of leverage effects in Namibia and South Africa indicating that negative shocks on the markets will result in greater impact on future return volatility than positive shocks of the same magnitude. Such results are acute opposite of the results obtained by Saleem and Aliyu who noted the existence of reverse asymmetry volatility. This implies that market participants overreact to negative news or shocks and under-react to positive news.
Investors interested in these stock markets are encouraged to take into account leverage effects in their estimation of VAR. Firms intending to raise capital in Namibia and South Africa should be prepared to pay a risk premium as the suppliers of capital are exposed to significant uncertainty or risk. Investors interested in these markets are recommended to go beyond portfolio optimisation and consider these stylised features skewness, excess kurtosis and leverage effects in their decision-making process.
All other stock markets indicated divergent results depending on the distribution type assumed. Findings from this study are in disharmony to such authors who noted the absence of asymmetric effects such as Oskooe and Shamsaravi examining Iran stock market and Niyitegeka and Tewari analysing South African stock markets. Volatility asymmetry evidenced in South Africa can be attributed to a wave of few large managed divestures of local listed companies by foreign parents, shaking an investor confidence already bruised from political fallout in late As already noted, South Africa and Namibia are members of the SACU which is likely to promote transmission of economic performance among member states.
Volatility asymmetry noted in the mentioned nations is also attributable to the trading activities of uninformed and informed agents in South Africa and Namibia Avramov et al. In the former case, uninformed traders sell when stock prices fall, leading to an increase in stock returns volatility, whereas informed investors sell after stock price rises, which leads to a decline in volatility. Advancement in information technology promotes the use and abuse of data among investors.
Information overload might promote overreaction especially to negative news which results in volatility asymmetry. Malawi is the only market where volatility shocks quickly die out absence of significant volatility persistence. This sweetener to investors promotes investor confidence, reduces the cost of capital and makes capital easily available, other things being equal. As a result of insignificant volatility persistence in Malawi, the cost of providing liquidity is likely to be small, thereby promoting the liquidity of the whole market. The remaining four markets indicated significant volatility persistence implying that shocks on the stock market take time to decay, thereby making volatility prediction possible.
Persisting volatility makes investors more averse to holding stocks because of uncertainty, which in turn demands a higher risk premium to insure against the increased uncertainty.
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A greater risk premium results in a higher cost of capital, which subsequently leads to less private investment Emenike Volatility persistence is attributable to market inefficiencies where investors take time to fully and correctly impound information into prices. A large body of investors in such markets means that their beliefs, forecasts and assets evaluation methods also vary greatly.
Firms in Zambia, Zimbabwe, Namibia and South Africa where volatility persistence is significant are likely unable to use their available capital efficiently because of the need to reserve a larger percentage of cash-equivalent investments in order to re-assure lenders and regulators of their stability and soundness as argued by Ndwiga and Muriu Educational workshops carried out by the stock exchange are likely to be bearing positive results as the participants are likely to be fully equipped when workshop comes to impounding information into prices.
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Therefore, shocks or effects of news quickly die out as the participants are fully geared up when it comes to analysing information. To add on, lack of liquidity which remains a challenge as investors maintain a hold strategy might be another reason why shocks quickly die out as the participants are incapacitated financially to implement their decisions. As such, investors in Namibia and South Africa are encouraged to include leverage effects in portfolio optimisation and value-at-risk computations. Firms raising funds in these nations should be prepared to incur a risk premium as compensation to creditors for assuming high uncertainty or risk.
Other nations reflected mixed results depending on the distribution assumed. As such, raising capital in such nations is expected to be expensive and difficult coupled by market illiquidity, other things being equal. We are very grateful to Dr F. Kwenda, now a research associate, at University of KwaZulu-Natal, who assisted us in obtaining data for the study from Bloomberg database. The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.
Abdalla, S. Aliyu, S.
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