Basis Risk in Variable Annuities

Abstract

This dissertation provides a comprehensive and practical analysis of basis risk in the U.S. variable annuity market and examines effective fund mapping strategies to mitigate the level of basis risk while controlling for the associated transaction costs. Variable annuities are personal savings and investment products with long-term guarantees that expose life insurers to extensive financial risks. Liabilities associated with VA guarantees are the largest liability component faced by U.S. life insurers and have raised concerns to VA providers and regulators. And the hedging performance of these guarantee liabilities is impeded by the existence of basis risk. I look into 1,892 registered VA-underlying mutual funds and two VA separate accounts to estimate the basis risk faced by U.S. VA providers at the individual fund level and the separate account level. To evaluate the degree to which basis risk can be mitigated, I consider various proxy instrument sets and assess different variable selection models. The LASSO regression is shown to be most effective at identifying the most suitable (combination of) mapping instruments that minimize basis risk, compared to other test-based and screening-based models. I supplement it with the Sure Independence Screening (SIS) procedure to further limit the number of instruments requested in the hedging strategies, and modify it by introducing the diff LASSO regression to restrict the changes in instrument allocations across rebalancing periods and, therefore, control for transaction costs. I show that VA providers can reduce their exposure to basis risk by applying data analytic techniques in their mapping process, by hedging with ETFs instead of futures contracts, and through diversification at the separate account level. Combining the traditional fund mapping method with the machine learning algorithm, the proposed portfolio mapping strategy is efficient at reducing basis risk in VA separate accounts while controlling for the tractability and transaction costs of the mapping and hedging procedure, and is practical to incorporate newly-developed VA funds, as well as the varying compositions of separate accounts. Overall, this study presents that U.S. VA providers have the ability to mitigate basis risk to a greater extent than the limited literature on this topic has suggested.