Optimal Dynamic Asset Allocation for DC Plan Accumulation/Decumulation: Ambition-CVAR

Abstract

We consider the late accumulation stage, followed by the full decumulation stage, of an investor in a defined contribution (DC) pension plan. The investor's portfolio consists of a stock index and a bond index. As a measure of risk, we use conditional value at risk (CVAR) at the end of the decumulation stage. This is a measure of the risk of depleting the DC plan, which is primarily driven by sequence of return risk and asset allocation during the decumulation stage. As a measure of reward, we use Ambition, which we define to be the probability that the terminal wealth exceeds a specified level. We develop a method for computing the optimal dynamic asset allocation strategy which generates points on the efficient Ambition-CVAR frontier. By examining the Ambition-CVAR efficient frontier, we can determine points that are Median-CVAR optimal. We carry out numerical tests comparing the Median-CVAR optimal strategy to a benchmark constant proportion strategy. For a fixed median value (from the benchmark strategy) we find that the optimal Median-CVAR control significantly improves the CVAR. In addition, the median allocation to stocks at retirement is considerably smaller than the benchmark allocation to stocks.

Keywords: optimal control, ambition-CVAR, asset allocation, DC plan, resampled backtests

JEL Classification: G11, G22