Minimizing the Expected Lifetime Spent in Drawdown under Proportional Consumption

TL;DR

This paper derives the optimal investment strategy for an individual aiming to minimize the expected duration of wealth in drawdown, considering constant proportional consumption in a Black-Scholes market.

Contribution

It introduces a novel approach to minimize expected drawdown time, revealing the myopic nature of optimal investment strategies under proportional consumption.

Findings

Optimal strategy minimizes expected time in drawdown.

Individuals behave myopically in investment decisions.

Comparison with related problems highlights strategy differences.

Abstract

We determine the optimal amount to invest in a Black-Scholes financial market for an individual who consumes at a rate equal to a constant proportion of her wealth and who wishes to minimize the expected time that her wealth spends in drawdown during her lifetime. Drawdown occurs when wealth is less than some fixed proportion of maximum wealth. We compare the optimal investment strategy with those for three related goal-seeking problems and learn that the individual is myopic in her investing behavior, as expected from other goal-seeking research.