This study examines the information flow between convertible bonds (CBs) and other investment assets, such as stocks and bonds. In particular, we employ transfer entropy (TE) as a proxy for the causal effect between the two assets considering that one of the most widely used methods, Granger causality, requires strict assumptions. When adopting TE, we find that asymmetric information flow arising between assets depends on macroeconomic phases. The stock and bond markets affected the CB market prior to and during the global financial crisis, respectively. In the post-crisis period, we find no meaningful information exchange between CBs and other investment assets concerning their return series. However, we observe a significant cause–effect relationship between CBs and stocks in the rise–fall patterns of their price series. The findings suggest that the appearance of one-directional information flow depends on macroeconomic conditions and the level of data, for example, return series or price fluctuations. Accordingly, investors could exploit this pattern predictability in their portfolio management. In addition, policymakers must closely monitor the information flow among the three markets. When any two markets exchange information in a state of strong market integration, unbalanced regulation between them could lead to market distortions and regulatory arbitrage.