Variable annuities and the option to seek risk: Why should you diversify?

We analyze the impacts of an additional rider incorporated in recent retirement products. The payoff is linked to the performance of a multi asset investment strategy and includes a minimum interest rate guarantee. In addition, the buyer receives the option to decide on the investments dynamically. Prominent examples are so called variable annuities. Due to the embedded guarantee, these products are interesting for risk averse investors who benefit from diversification. However, the price setting of the provider takes into account the most risky strategy. This implies that the investor mitigates optimally between the diversification and the worst case strategy. We analyze the distortion and utility effects caused by the additional rider in the presence of background risk and borrowing constraints. A simulation analysis sheds light on the question if the additional rider is worth its costs.