Basis Risk

Pin Chung

In general, variable annuity (VA) writers can offer between 20 and 60 different funds to contract holders. The available range of funds typically covers a wide variety of investment styles, and consist of different types of assets, with most funds being actively managed – ie, their asset allocation is adjusted frequently to reflect the views of the fund’s manager. In most jurisdictions, it is not possible to short-sell these funds, which implies that they are not directly hedgeable – for example, to manage guarantees on these funds. To get round this problem, funds are related to more liquid indexes using a set of linear relationships called fund mapping. This procedure is used to determine a portfolio of hedgeable assets, usually equity indexes, which replicates the funds as close as possible. This portfolio is called a “surrogate portfolio” or a “replicating portfolio”. The surrogate portfolio can then be hedged rather than the funds.

Usually, but not always, fund mapping is performed by means of an ordinary least squared (OLS) regression using historical data of the fund and the indexes of its surrogate portfolio. As the returns of the funds can deviate from the returns of