Blockchain or, more generally, distributed ledger technology allows to create a decentralized digital ledger of transactions and to share it among a network of computers. In this paper, we argue that the implementation of this technology in financial markets offers investors new options for managing the degree of transparency of their holdings and their trading intentions. We first identify two intrinsic features of a distributed ledger that impact the availability of these new options, namely the mapping between identifiers and end-investors and the degree of transparency of the ledger, and we then examine how the implementation design of these critical features affects investor trading behavior, trading costs, and investor welfare, in a theoretical model of intermediated and peer-to-peer trading. The most transparent setting yields the highest investor welfare, despite the risk of front-running. In the absence of full transparency, welfare is weakly higher if investors are allowed to split their holdings among many identifiers.