Understanding the interplay between covariance forecasting factor models and risk‐based portfolio allocations in currency carry trades

With the exception of naive methods for portfolio selection, such as the equal weighted approaches, all other methods of portfolio allocation are more or less sensitive to the quality of the inputs considered in constructing the models and risk measures utilised in the allocation framework. The extensively used factor model proposed initially by Sharpe has provided a robust backdrop for development of relevant, micro, macro and context specific or asset specific explanatory variables to be incorporated in a statistical manner as inputs to forecasting models that can then be used to obtain risk measures upon which portfolio allocations are based. However, like all statistical models a set of statistical assumptions accompany this factor model regression framework, one of which has recently been highlighted as seemingly non-validated in financial data. This is of course the assumption such factor models make on homoskedasticity or weak sense covariance stationarity of the returns processes being modelled. Such factor models, therefore have typically failed to cope with an important and ubiquitous feature of financial assets data which often demonstrates heteroskedasticity of the returns variances and covariances.
We propose a novel generalised multi-factor forecasting structure utilizing a covariance regression model which allows us to incorporate the required heteroskedasticity effects whilst also admitting potential dependence in the idiosyncratic error terms. We argue that such a modelling approach allows for more explicit relationships to be interpreted between the driving factors and the conditional responses of the portfolio returns. We then compare the forecasting performances of our model with the multi-factor model and the time series DCC model through a currency portfolio application.