The current state will be the whole history, so I have to read potentially a lot of records to reproduce the status. I guess this could be done by a so called snapshot, but who's responsible for creating it?
In CQRS and event sourcing, queries are served by projections which are generated from events emitted by aggregates. You don't use the aggregate instance as reconstituted from the event store to display information.
The term snapshot refers specifically to an optimization of the event store which allows rebuilding the aggregate without replaying all of the events.
Projections are essentially event handlers which maintain a denormalized view of aggregates. Events emitted from aggregates are published, possibly out of band, and the projection subscribes to and handles those events. A projection can combine multiple aggregates if a requirement exists to display summary information, for instance. In case of a trading application, each view will typically contain data from various aggregates. Projections are designed in a consumer-driven way - application requirements determine the different views of the underlying data that are needed.
With this type of workflow you have to embrace eventual consistency throughout your application. For instance, if an end user is viewing their portfolio and initiating new trades, the UI has to subscribe to updates to reflect updated projections in an asynchronous manner.
Take a look at here for an overview of CQRS and event sourcing.