Estimating Value at Risk (VaR) and Expected Shortfall (ES) of market returns using ARMA and GARCH models. (A case study of Rwanda Forex Market.)

Abstract

There is tremendous turnover and liquidity that causes currency prices to fluctuate every second, so traders and investors are constantly looking for ways to protect themselves from these threats and unexpected fluctuations. This study consists of Estimating Value at Risk (VaR) and Expected Shortfall (ES) of market returns using ARMA and GARCH models in Rwanda forex market for each FX return time series for the sample size of 5 selected most traded currencies out of 62 present in Rwanda forex market with 2118 observations. The general objective of this study is to estimate the Value-at-Risk (VaR) and the Expected Shortfall (ES) of Rwanda forex market returns using ARMA and GARCH models. This study used unsupervised machine learning algorithms such as K-means clustering and hierarchical clustering methods. Using hierarchical clustering on this table 4.3, we observed that there are three groups which tend to have similar behavior such as group one: GBP and EUR, group two : USD and KES and group three : EGP. By using Kmeans clustering on this table 4.2, we observed that EGP is the riskiest currency. Fitting AR(1) + GARCH(1,1), we observed that the sum of alpha and beta are less than one, therefore we have stationary time series. Value at Risk (VaR) and Expected Shortfall (ES) are very important risk measures to consider when you invest in forex market in Rwanda. We observed that on this following table 4.10, USD, has small average loss (ES = 4626.5 FRW) compared to other currencies that traded in Rwanda market, thus we can invest in USD. We can invest in other currencies except EGP with high average loss 40725 FRW.