An alternative strategy for balancing profit maximization and risk reduction

Abstract

Portfolio diversification is a central theme in modern investment theory. We revisit the classic return–risk trade-off and propose an alternative objective Q λ ( w ) = μ ⊤ w + λ ( w ⊤ Σ w ) − 1 / 2 that balances higher expected returns with a direct penalty on portfolio volatility via the inverse standard deviation. This objective belongs to the axiomatic class of mean–variance preferences (as formalised by [1] for additively separable forms) and admits tractable solutions, including a closed-form characterisation in the two-asset case. In rolling out-of-sample backtests on standard Fama–French equity portfolios with realistic trading costs and long-only constraints, Q λ delivers statistically significantly lower realised volatility (paired t-test p  < 0.01) and shallower maximum drawdowns than the Sharpe-maximising benchmark, while maintaining average performance comparable to Markowitz, equal-weight, and risk-parity strategies. These advantages persist across major stress episodes (GFC, COVID-19, 2022 rate shock) and are robust over a wide range of the trade-off parameter λ . The results position Q λ as a pragmatic alternative for investors who value smoother wealth paths and robust downside protection.