Causal Modeling with Applications to the Foreign Exchange Market

A combination of time series models and causal search algorithms is applied to the foreign exchange markets to find causal linkages between the six most widely traded currencies (Australian dollar, Canadian dollar, euro, Great Britain pound sterling, Japanese yen, and United States dollar). This information is used in portfolio management to improve risk management, to visualize the causal connections between currencies, and enhance the forecasting ability of time series models.

In the first section, a method is presented that decomposes portfolio risk so that risk contributions sum to the total portfolio?s risk. This decomposition is based upon a market?s underlying independent risk factors, which are found empirically using a causal search algorithm based on independent component analysis. In an application, independent risk contributions are constrained during portfolio optimizations, and the internal risk characteristics of the resulting portfolios are shown to be superior to those constructed using more traditional constraints.

In the second section, three causal search algorithms are used to identify causal relationships amongst the six most widely traded currencies in the years 2009-2011. The intent is to discover causal relationships within each year and to observe how these causal relationships change over time. The causal relationships are presented as directed acyclic graphs, and these are relatively stable over time. There might be, however, latent variables that affect the six most widely traded currencies.

In the third section, probability forecasts of the Swiss franc/euro (CHF/EUR) exchange rate from three different time series models are generated before, surrounding, and after the placement of a floor on the CHF/EUR exchange rate by the Swiss National Bank. The goal is to determine whether the exchange rate floor has a positive, negative, or insignificant affect on the calibration of the probability forecasts. Forecasts from the models are ranked with score metrics, and a graphical d-separation criterion is used in an attempt to identify the preferred model based on forecast performance. The study finds evidence that the floor on the CHF/EUR has a negative impact on the forecasting performance of the three time series models.