The investment management for a downside-protected equity-linked annuity under interest rate risk

Abstract

In this paper, we investigate the optimal asset allocation in the distribution phase for an equity-linked annuity scheme of a DC pension plan. We extend previous research to consider the interest rate risk. To prevent a shortfall on the annuity payment in case of poor investment performances, a minimum guarantee on the annuity payment is included in our model. We show that the optimal asset allocation could be represented by a weighted average of two portfolios. The first portfolio is the so-called growth optimal portfolio, which maximizes the expected growth of annuity payment over the planning horizon. The second portfolio is the replicating portfolio, which replicates the returns on a level life annuity. The optimal portfolio weights on these two parts are decided by the coverage ratio of the fund size to the present value of guaranteed annuity payments. Numerical examples show that a high level of guarantee effectively reduces the uncertainty of future annuity payments but loses the opportunities for fund growth. The demand for stocks decreases with the level of guarantee, while the demand for bonds is insensitive to the level of guarantee.