Analyzing the effectiveness of mean-Gini framework for estimation of currency hedge ratio

Abstract

Several approaches to finding the optimal spot currency hedge ratios have been explored. The most simplistic and widely used approach is the minimum variance model under portfolio approach which attempts to minimize the variance of the portfolio assuming some distributional characteristic of the spot and futures rates. The mean-Gini framework has been proposed by Shaffer and Demaskey (2005) as an alternative to the portfolio approach where they have demonstrated the effectiveness of this approach. Mean-Gini framework requires estimation of the underlying price distribution which is also called the cumulative distribution function (CDF) of spot and future and spot changes. CDF has been estimated by Kemal estimation and Empirical distribution method. CDF and hence hedge ratios have been estimated by Kernel Distribution Function (KDF) or Empirical distribution Function (EDF) method by Shaffer and Demaskey (2005) for few developed and developing market currencies. The historical spot and forward rates show very high deviations from distributional properties assumed for effective application of portfolio approach. Hence, we have extended the above study to study hedge ratio behaviors for Indian currency. The study shows a similar behavior of KDF and EDF hedge ratios for Indian rupee as was demonstrated for other developing market currencies such as Peso or Real. The study further attempts to predict the interest term structure by interpolation and hence future spot and forward rates. It then estimates the hedge ratios for the predicted spot and forward rates. The result shows that the interpolation methods have a significant influence on the optimal hedge ratios. The historical data for spot and forward rates for Indian Rupee show very high kurtosis and skewness. We attempted to model this distribution and tried to develop a wiener like a process for such skewed distributions. SGSH distribution as described by Fischer (2002) has been used to simulate the price paths for the spot rates with a very high kurtosis and high skewness. The existing analyzing the effectiveness of Mean-Gini framework for estimation of currency hedge ratio work can be extended to develop the Weiner like the process to study issues such as pricing of derivatives for such distributional properties of the underlying.