This study explores the risk and return characteristics of convertible arbitrage, a dynamic trading strategy employed by hedge funds. To circumvent biases in reported hedge fund data, a simulated convertible bond arbitrage portfolio is constructed. The returns from this portfolio are highly correlated with convertible arbitrage hedge fund indices and the portfolio serves as a benchmark o f fund performance. Default and term structure risk factors are defined and estimated which are highly significant in explaining the returns of the hedge fund indices and the returns of the simulated portfolio, and when specified with a convertible bond arbitrage risk factor in a linear factor model, these factors explain a large proportion of the risk in convertible arbitrage hedge fund indices. The residuals of the hedge fund indices estimated from this model are serially correlated, and a lag of the hedge fund index return is specified correcting fo r the serial correlation and the coefficient o f this term is also interpretable as a measure o f illiq u id ity risk. A linear multi-factor model, incorporating several lags o f the risk factors is specified to estimate individual fund performance. Estimates o f abnormal performance from this model provide evidence that convertible arbitrageurs generate abnormal returns between 2.4% and 4.2% per annum. The convertible arbitrage hedge fund indices and individual hedge fund returns used to evaluate performance generally exhibit negative skewness and excess kurtosis. Residual Augmented Least Squares (RALS), an estimation technique which explicitly incorporates higher moments is used to robustly estimate multi-factor models o f convertible arbitrage hedge fund index returns. Functions o f the hedge fund index residuals are specified as common skewness and kurtosis risk factors in a multifactor analysis of individual fund performance. Results from this analysis provide evidence that failing to specify third and fourth moment risk factors w ill bias upward estimates o f convertible arbitrage individual hedge fund performance by 0.60% per annum. Theoretical non-linearity in the relationship between convertible arbitrage hedge fund index returns and default and term structure risk factor is then modelled using Logistic Smooth Transition Autoregressive (LSTAR) models.