Due to potentially extreme price volatility, the expansion of intermittent renewable generation has raised questions about the viability of wholesale electricity markets. To understand the role of commercially-provided electricity storage in attenuating the volatility of wholesale markets, we build a dynamic competitive equilibrium framework of investment in speculative storage and renewable generation capacity with stochastic demand and supply of electricity. We show that a recursive competitive equilibrium exists, is first best, and features well-behaved supply and demand relationships that are able to generate the rents required for investment in storage and generation capacity. Nonetheless, policymakers face a number of market design challenges. Our comparative static results show how, when there is low investment in storage capacity the market can feature many extreme price events, resulting in high levels of investment in generation capacity used as a form of insurance. In this case, storage and generation act as substitutes and crowd out each other's marginal returns. In markets with higher levels of storage capacity, storage and generation are complements. Our simulations suggest storage and generation are substitutes under current capital prices. Imposing electricity price caps to keep prices at current “politically feasible levels” does not affect investment in storage capacity and only slightly reduces returns to generation capacity, especially when combined with additional demand flexibility.