Commodity style integration is appealing because by forming a unique long-short portfolio with exposure to K mildly correlated factors, a larger and more stable risk premium can be extracted than with any of the standalone styles. A key decision that a commodity style-integration investor faces at each rebalancing time is the relative weighting of the factors. We propose a Bayesian optimized style-integration (BOI) strategy with excellent out-of-sample performance. Focusing on the problem of a commodity investor that seeks exposure to the carry, hedging pressure, momentum, skewness, and basis-momentum factors, the evidence suggests that the BOI portfolio achieves better Sharpe ratios and certainty equivalent returns, among other performance metrics, than the $1/K$ style-weighted integrated portfolio, and a battery of sophisticated optimized integrations. The findings survive the consideration of longer estimation windows, various commodity score schemes, and alternative Bayesian priors.

商品风格整合很有吸引力，因为通过形成一个独特的多空投资组合，接触 K 轻度相关因素，可以提取比任何独立风格更大、更稳定的风险溢价。商品风格整合投资者在每次重新平衡时面临的一个关键决定是因素的相对权重。我们提出了一种具有出色样本外性能的贝叶斯优化风格整合 (BOI) 策略。着眼于寻求利差、对冲压力、动量、偏度和基础动量因素敞口的商品投资者的问题，证据表明，除其他绩效指标外，BOI 投资组合实现了更好的夏普比率和确定性等价回报这$\mathrm{1个}/钾$风格加权的集成产品组合，以及一系列复杂的优化集成。考虑到更长的估计窗口、各种商品评分方案和替代贝叶斯先验，这些发现仍然存在。