The manager of a large pension fund faces the following conundrum: The expected contribution period for fund members is 25 years. On average, upon their retirement members will receive an annuity expected to last 20 years. The plan is set up as a defined benefit plan - therefore, regardless as to the fund's investments perform over the investment period - a defined payout amount has been set. According to the latest review, the fund's investments have not performed well enough to meet their obligations. The fund's first annuity payout is expected to commence in 5 years' time. 

Explain how Arbitrage Portfolio Theory could be useful to this fund manager?