Interaction Between Forex and Stock Markets in India: An Entropy Approach

Abstract

Interactions between the foreign exchange market and the stock market of a country are considered to be an important internal force of the markets in a financially liberalized environment. If causal relationship from a market to the other is not detected, then informational efficiency exists in the other whereas existence of causality implies that hedging of exposure to one market by taking position in the other market will be effective. The temporal relationship between the forex market and the stock market of developing and developed countries has been studied, especially after the East Asian financial crisis of 1997–98, using various methods like cross-correlation, cross-spectrum, and error correction model, but these methods identify only linear relations. A statistically rigorous approach to the detection of interdependence, including non-linear dynamic relationships, between time series is provided by tools defined using the information theoretic concept of entropy. Entropy is the amount of disorder in the system and also is the amount of information needed to predict the next measurement with a certain precision. The mutual information between two random variables X and Y with a joint probability mass function p(x,y) and marginal mass functions p(x) and p(y), is defined as the relative entropy between the joint distribution p(x,y) and the product distribution p(x)*p(y). Mutual information is the reduction in the uncertainty of X due to the knowledge of Y and vice versa. Since mutual information measures the deviation from independence of the variables, it has been proposed as a tool to measure the relationship between financial market segments. However, mutual information is a symmetric measure and does not contain either dynamic information or directional sense. Even time delayed mutual information does not distinguish information actually exchanged from shared information due to a common input signal or history and therefore does not quantify the actual overlap of the information content of two variables. Another information theoretic measure called transfer entropy has been introduced by Thomas Schreiber (2000) to study the relationship between dynamic systems; the concept has also been applied by some authors to study the causal structure between financial time series. In this paper, an attempt has been made to study the interaction between the stock and the forex markets in India by computing transfer entropy between daily data series of the 50 stock index of the National Stock Exchange of India Limited, viz., Nifty and the exchange rate of Indian Rupee vis- à- vis US Dollar, viz., Reserve Bank of India reference rate. The entire period–November 1995 to March 2007–selected for the study, has been divided into three sub-periods for the purpose of analysis, considering the developments that took place during these sub-periods. The results obtained reveal that: there exist only low level interactions between the stock and the forex markets of India at a time scale of a day or less, although theory suggests interactive relationship between the two markets the flow from the stock market to the forex market is more pronounced than the flow in the reverse direction.

Dependency Relations among International Stock Market Indices

“…Transfer Entropy is also model-independent and is sensitive to non-linear underlying dynamics, unlike, for example, Granger causality [7], to which Transfer Entropy is reduced for auto-regressive processes [8]. Transfer Entropy has been applied to the theory of cellular automata, to the study of the human brain, to the social media, to statistics, and to financial markets [9][10][11][12][13][14][15][16][17][18][19][20] and [2].…”

Macroeconomic Variables and Security Prices in India during the Liberalized Period

“…They have concluded that FII and Stock Index are positive correlation, but fail to predict the future value. Reddy and Sebastin (2008) make an attempt to study the interaction between the stock price and the foreign exchange markets in India by using daily data on Nifty and the exchange rate of Indian Rupee vis-a-vis US dollar during the period from November 1995 to March 2007. Using various methods like cross-correlation and error correction model, they identify a linear relationship among the variables.…”

Technology Diffusion through Production Process and the Innovative Capacity of Local Suppliers

“…The major findings of their study include that there is no Granger causality between the exchange rate fluctuation and stock return. Reddy and Sebastin (2008) make an attempt to study the interaction between the stock price and the foreign exchange markets in India by using daily data on Nifty and the exchange rate from November 1995 to March 2007. The result reveals that there exist a low level of interaction between the stock prices and the forex markets of India.…”