It is well documented that equity momentum has predictive power for corporate bond returns. We show that an equity momentum strategy applied to corporate bonds exhibits significant time-varying exposures to common equity and bond risk factors. The strategy thus bets on the persistence of these factor returns. We are able to improve upon a traditional momentum strategy, by focusing on the firm-specific component of stock returns. This residual momentum strategy not only lowers the exposures to the risk factors, but also reduces the volatility of the strategy with about 50%, resulting in a substantially higher Sharpe ratio. We find that our results are robust to changes in the formation and holding period of the strategy, the estimation window, the specification of the factor model, and the formation of subsamples based on liquidity and credit rating.