Kenneth Vetzal, Peter Forsyth, and Heath Windcliff
Abstract —Segregated funds have become a very popular investment instrument in Canada. Segregated funds are essentially mutual funds which have been augmented with additional insurance features which provide a guarantee on the initial principal invested after a specified time horizon. They are similar in many respects to variable annuities in the United States. However, segregated funds often have complex embedded optionality. For instance, many contracts provide a reset provision. This allows investors to increase their guarantee level as the value of the underlying mutual fund goes up. These contracts typically also offer features such as mortality benefits, where the guarantee is paid off immediately upon death of the investor. Furthermore, because the payment for the guarantee is usually amortized over the life of the contract, there are additional complications due to investor lapsing. In this work we describe hedging strategies which allow underwriting companies to reduce their risk exposure to these contracts. The hedging techniques incorporate the strengths of both actuarial and financial approaches. In particular, we look at some of the difficulties which arise due to the fact that in many cases the underwriting company is not able to take short positions in the underlying mutual fund. An alternative is to hedge using other actively traded securities, such as index participation units, stock index options, or stock index futures contracts. However, due to the mismatch between the hedging instrument and the segregated fund contract being hedged, there is additional basis risk. We investigate the performance of these types of hedging strategies using stochastic simulation techniques.