Aggregating Conditional Variance for Windowed Return Signals

Summary

The document describes a research problem involving a return series, a conditional mean, and a conditional variance estimated from factor returns. A first trading approach compares each day's realized return with its conditional expectation and trades when the deviation exceeds a threshold tied to conditional variance. The author reports that this produces excessive turnover and that transaction costs eliminate the profits.

A proposed second approach sums deviations over a fixed window, with the aim of reducing turnover. The question is how to set a threshold for that cumulative signal when each observation has its own conditional variance, including whether averaging the variances and scaling by the square root of the window length is appropriate. The document provides no answer, derivation, or empirical evidence for a threshold rule. It therefore frames a statistical aggregation question rather than establishing a trading method, and leaves dependence between returns and the treatment of trading costs unresolved.

Key ideas

• The initial signal trades daily deviations from a factor-based conditional mean when they exceed a variance-related threshold.
• The author reports that the daily approach has excessive turnover and costs that erase profits.
• A proposed alternative sums deviations over a preset window.
• The document asks how to combine the window's conditional variances to set a threshold, but does not resolve the question.
• The dependence structure of returns and the final strategy's performance remain unexamined.

Tags

# Rolling sum of conditional variance


# Rolling sum of conditional variance












I have a model to compute the conditional expectation and variance for a return series, given various factor returns. Initially attempted to trade the deviations of actual return for the day from the calculated conditional expectation if the deviations are greater than a threshold multiple of conditional variance. However quickly realized that turnover is too high and the costs kill all profits.

My second attempt was, to sum up, the deviations (actual return - conditional expectation) for a predefined window length. But I don't know how to calculate the thresholds given that I now have a series of conditional variances for the window length? Should I average them and multiply by square root of window length? Any suggestions?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.