Safety-first portfolio optimization: Fixed versus random target

Safety-first portfolio optimization is concerned with maximizing the expected portfolio return subject to a safety-first constraint, which is defined as the probability of failing to achieve a specified target. Commonly the target is assumed to be fixed, which, however, leads to significant conceptual disadvantages, e.g. when an actively managed portfolio seeks to track or outperform a random benchmark, such as a stock index. In this paper we consider both a fixed and a random target strategy and give an answer to the question which strategy is better off. In detail, we compare optimal expected returns of both strategies under the normal assumption and obtain following results: The random target strategy outperforms the fixed target strategy if the portfolio return and the random target are positively correlated and riskless investing is prohibited, whereas the fixed target strategy outperforms the random target strategy if the portfolio return and the random target are non-positively correlated. Furthermore, we show that these results also hold when relaxing the normal assumption.