Volatility Modelling and Forecasting for NIFTY Stock Returns


In this paper, an attempt has been made to model the volatility of NIFTY index of National Stock Exchange (NSE) and forecast the NIFTY stock returns for short term by using daily data ranging from January-2000 to December-2014, which comprises 3,736 data points for the analysis by using Box-Jenkins or ARIMA model. The volatility in the Indian stock market exhibits characteristics similar to those found earlier in many of the major developed and emerging stock markets. It is shown that ARCH family models outperform the conventional OLS models. ADF test and unit root testing is done to know the stationarity of the series; later, the AR(p) and MA(q) orders are identified with the help of minimum information criterion as suggested by Hannan- Rissanen. As per the analysis, ARIMA (1,0,1) model was found to be the best fit to forecast the volatility of NIFTY stock returns. The model can be used by the investors to forecast the short run NIFTY stock returns and for making more profitable and less risky investment decisions.


It is very important for any economy to achieve efficiency in the dynamics of the stock markets. For any stock market, volatility and returns are the two important factors around which the entire stock market revolves. The emergence of informationefficient financial markets is an important facet of any country’s economic modernization. Moreover, it is observed from the prior literature that stock prices are noisy which can’t convey all available information to market dynamics of stock prices and trading volume. Therefore, studying the joint dynamics of volatility and returns is essential to improve the understanding of the microstructure of stock markets.

Volatility is a measure of variability in the price of an asset. Volatility is associated with unpredictability and uncertainty about the price. It is often used as synonymous with risk which means higher the volatility, higher the risk in the market (Kumar & Gupta, 2009). In other words, we can say that in case of high volatility, the market does not function properly and it leads to disruption of market. As a concept, volatility is simple and intuitive. It measures variability or dispersion about a central tendency. To be more meaningful, it is a measure of how far the current price of an asset deviates from its average past prices. Greater the deviation, greater is the volatility. At a more fundamental level, volatility can indicate the strength or conviction behind a price move (Raju, 2004). It is difficult to estimate about the future trend of volatility in market because it is affected by a large number of factors including political stability, economic fundamentals, government budget, policies of the government, corporate performance, etc. However, by calculating historical volatility, a prediction can be assumed about the future trend in the volatility.

Modeling and forecasting volatility of a daily financial asset price return is an important and challenging financial problem that has received a lot of attention in recent days. It is widely agreed that although returns of daily and monthly financial asset prices are approximately unpredictable, volatility of returns is a highly predictable phenomenon with important implications for financial economics and risk management. The decision of the investors to sell or to buy depends directly on the volatility of securities’ prices that they expect to happen in the near future, since they build their predictions on the movements of the securities’ prices – whether up or down, to protect themselves from the losses that they may meet, or to reduce it as much as possible.

The relationship between the volatility and returns in the stock market are of common interest as they may result in forming a base for profitable trading strategies and this has implications for the market efficiency (Chen & Yu, 2004). Karpoff (1987) cited four reasons for discussing price-volume relation. First, it provides an insight into the structure of financial markets, such as the rate of information flow to the market, how the information is disseminated, the extent to which market prices convey the information, and the existence of short sales constraints. Second, the relationship between price and volume can be used to examine the usefulness of technical analysis. For example, Murphy (1985) and De Mark (1984) emphasized that both volume and price incorporate valuable information. A technical analyst gives less significance to a price increase with low trading volume than to a similar price increase with substantial volume.

Third, some researchers, such as Garcia et al., (1986) and Weiner (2002) have investigated the role of speculation to price volatility (stabilizing or destabilizing), where speculation is closely related to trading volume. Finally, as Cornell (1981) pointed out, the volume-price variability relationship may have important implications for fashioning new contracts. A positive volume-price variability relationship means that a new futures contract will be successful only to the extent that there is enough price uncertainty associated with the underlying asset.

Thus, to improve the understanding of the microstructure of the stock market, the relationship between volatility and returns has received substantial attention in the market microstructure for a number of years. In addition, the volatility and returns relationship sheds light on the efficiency of stock markets.

Univariate Box-Jenkins (UBJ) or Autoregressive Integrated Moving Average (ARIMA) models are especially suited to short-term forecasting. Pankratz (1983) considered short-term forecasting, because most ARIMA models place heavy emphasis on the recent past rather than the distant past. This emphasis on the recent past implies that long-term forecasts from ARIMA models are less reliable than short-term forecasts.

Financial literature has documented the various flavors of volatility and returns especially in US stock markets (see survey in Karpoff (1987). By contrast, relatively little attention has been devoted to this relationship in India. The present study attempts to measure the short term returns of NIFTY index stocks on NSE by applying ARIMA modeling.

The rest of this paper is organized in the following order –
Section 2 presents review of literature;
Section 3 presents data, methodology and results;
Section 4 concludes the study.

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