Broadly worded arbitration agreements such as those that encompass claims ‘arising out of’, ‘with respect to’, or ‘in connection with’ the underlying contract may lead an arbitral tribunal to wrongly determine that it has jurisdiction over statutory claims. This article addresses the distinction to be made between statutory claims and contractual claims – irrespective of the legal label the parties assigned to the claims – and identifies the situations where such statutory claims fall out of the scope of the arbitration clause. While some national courts refer to a ‘sufficient connection test’, such test is particularly relevant to shareholder disputes, insofar as they are usually framed with both contractual and statutory causes of action based on the same set of facts.