We propose a high-frequency rebalancing algorithm (HFRA) and compare its performance with periodic rebalancing (PR) and threshold rebalancing (TR) strategies. PR refers to the process of adjusting the relative weight of assets within portfolios at regular time intervals, whereas TR is a process of setting allocation limits for portfolios and rebalancing when portfolios exceed a specific percentage of deviation from the target allocation. The HFRA is constructed as an integration of pairs trading and a threshold-based rebalancing strategy, and the profitability of the HFRA is examined to determine the optimal portfolio size. The HFRA is applied to a dataset of real price series from cryptocurrency exchange markets across various trends and volatility regimes. Using cointegrated price data, it is shown that increasing the number of assets in a portfolio supports the profitability of the HFRA in an up-trend and reduces the potential loss of the HFRA in a down-trend in a high-volatility environment. For low-volatility regimes, although increasing portfolio size marginally enhances the HFRA’s profitability, the profits of portfolios of varied sizes do not significantly differ. It is demonstrated that when volatility is relatively high and the trend is upward, the HFRA can yield a substantial return via portfolios of large sizes. Moreover, the profitability of the HFRA is compared with that of the PR and TR strategies for long-term application. The HFRA is more profitable than the PR and TR strategies. This achievement of the HFRA is also validated statistically using the Fisher–Pitman permutation test.

中文翻译：

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高频再平衡算法的具有波动性信息的最佳投资组合选择

我们提出了一种高频再平衡算法（HFRA），并将其性能与周期性再平衡（PR）和阈值再平衡（TR）策略进行了比较。 PR是指定期调整投资组合内资产相对权重的过程，而TR是为投资组合设定配置限额，并在投资组合偏离目标配置超过特定百分比时进行重新平衡的过程。 HFRA 被构建为配对交易和基于阈值的再平衡策略的集成，并检查 HFRA 的盈利能力以确定最佳投资组合规模。 HFRA 适用于来自加密货币交易市场的各种趋势和波动机制的实际价格序列数据集。使用协整价格数据表明，在高波动性环境中，增加投资组合中的资产数量可以支持 HFRA 在上升趋势中的盈利能力，并减少 HFRA 在下降趋势中的潜在损失。对于低波动性制度，虽然增加投资组合规模会略微提高 HFRA 的盈利能力，但不同规模的投资组合的利润并没有显着差异。事实证明，当波动性相对较高且趋势向上时，HFRA 可以通过大规模的投资组合产生可观的回报。此外，将 HFRA 的盈利能力与长期应用的 PR 和 TR 策略的盈利能力进行了比较。 HFRA 比 PR 和 TR 策略更有利可图。 HFRA 的这一成就也通过 Fisher-Pitman 排列检验进行了统计验证。