Using Smooth Transition Regressions to Model Risk Regimes

The smooth transition regression (STR) methodology was developed to model nonlinear relationships in the business cycle. We demonstrate the methodology can be used to analyse return series where exposure to financial market risk factors depends on market regime. The smooth transition between regimes inherent in STR is particularly appropriate for risk models as it allows for gradual transition of risk factor exposures. Variations in the methodology and tests its appropriateness are defined and discussed. We apply the STR methodology to model the risk of the return series of the convertible arbitrage (CA) hedge fund strategy. CA portfolios are comprised of instruments that have both equity and bond characteristics and alternate between the two depending on market level (state). The dual characteristics make the CA strategy a strong candidate for nonlinear risk models. Using the STR model, we confirm that the strategy’s risk factor exposure changes with market regime and, using this result, are able to account for the abnormal returns reported for the strategy in earlier studies.