Optimal portfolio selection with volatility information for a high frequency rebalancing algorithm

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 specifc 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 proftability 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 proftability 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 proftability, the profts of portfolios of varied sizes do not signifcantly difer. 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 proftable than the PR and TR strategies. This achievement of the HFRA is also validated statistically using the Fisher-Pitman permutation test.