Hedge fund replication based on factor models is encountering growing interest. In this paper, we investigate the implications of substituting standard rolling windows regressions, which appear ad-hoc, with more effcient methodologies like the Kalman flter. We show that the copycats constructed this way offer risk-return profles which share several characteristics with the ones posted by hedge funds indices: Sharpe ratios above buy-and-hold strategies on standard assets, moderate correlation with standard assets, and limited drawdowns during equity downward trends. An interesting result is that the shortfall risk seems less important than with hedge fund indices and regressions-based trackers. We fnally propose new breakdowns of hedge fund performance into alpha, traditional beta, and alternative beta.