RIYADH—Saudi Arabia’s state-owned Public Investment Fund is poised to become one of the world’s biggest investors. But the fund is troubled by disappointing investments, including in Uber Technologies Inc., and has struggled to calculate its own value.

This week, investing luminaries including chief executives of BlackRock Inc. and Blackstone Group LP and leaders from Goldman Sachs Group Inc. and J.P. Morgan Chase & Co. are descending on a Riyadh palace for a conference where the fund is expected to discuss its strategy,...