Estimating Profit and Loss for Cross-Instrument Combined Trading Rules: A Method Based on SR Vector Distance and Backtesting Results
This article is the eighth installment in the Portfolio Optimization Series. The author proposes using the Euclidean distance of SR vectors across multiple trading rules for each instrument to determine whether to combine cross-instrument returns, calibrates 95% critical values for different historical lengths using random data, and then obtains pseudo-instruments through hierarchical merging. The author compares three approaches—full merging, algorithmic merging, and no merging—using in-sample backtests across 214 futures instruments. The results show inconsistent out-of-sample performance, with longer sample data favoring no merging. The author ultimately concludes that the algorithm is highly complex and the grouping results lack intuitive logic, so it will not be adopted for now, and future research will explore simpler merging rules.
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