Short-term correlation modelling for gold and equities

Abstract

The only deterministic aspect of stock market is uncertainty. Historically, many academicians have tried to mathematically model the uncertainty using statistics and stochastic processes. The factors used in the process were volatility of historical movements (variance) and risk associated with the price movements (standard deviation). This resulted in forceful fitting of the price movements into normal distribution with average return and standard deviation to factor in volatility. Recent research has proved that the asset returns are not exactly normal but close to Tdistribution with fatter tails and higher kurtosis. The fatter tails of the t-distribution signify that there will be high volatile movements on either side more often than one has estimated through modelling the asset class using normal distribution. Thus, the predictions of the indices generally are not that accurate as normal distribution fail to factor in the higher volatility. One solution to this is to find out a single or combination alternative asset classes (including exogenous variables) having significant shortterm correlation in the price movement to model the market indices.

In this research, we are proposing a method to model the short-term correlation between Nifty50 and Nifty100 with Gold to factor-in the changes in correlation due to the volatility. To have robust and exhaustive analysis, we propose to see the effect of various exogenous variables like bond rates, interest rates, VIX index, fear in the market and few other psychological and environmental variables. The GARCH (1,1) method is used to predict the volatility using the historical time series data captured for different time frames and different frequencies (weekly, monthly). Based on the significance of the variables on the correlation we come up with a dynamic model, which would be most accurate in predicting the correlation between market index and asset class. We modelled the correlation between the Gold and Nifty to predict the future correlation using DCC-GARCH which was then regressed with other exogeneous variables to see their significance. The research has direct influence on determining the movement of the index, which can be used to take investing decisions, portfolio allocation and rebalancing and formulating hedging strategies.