We provide evidence on how corporate bond investors react to a change in yields, and how this behaviour differs in times of market‐wide stress. We also investigate ‘reaching for yield’ across investor types, as well as providing insights into the structure of the corporate bond market. Using proprietary sterling corporate bond transaction data, we show that insurance companies, hedge funds and asset managers are typically net buyers when corporate bond yields rise. Dealer banks clear the market by being net sellers. However, we find evidence for this behaviour reversing in times of stress for some investors. During the 2013 ‘taper tantrum’, asset managers were net sellers of corporate bonds in response to a sharp rise in yields, potentially amplifying price changes. At the same time, dealer banks were net buyers. Finally, we provide evidence that insurers, hedge funds and asset managers tilt their portfolios towards higher risk bonds, consistent with ‘reaching for yield’ behaviour.