Analyzing Strategy Returns with Many Zero Observations
Summary
The document considers how to compare two return series when strategies often do not trade and therefore record zero returns. It asks whether zero observations should remain in a correlation calculation and how to compare strategies with different patterns of nonzero returns. The answer emphasizes that the right treatment depends on why returns are zero and on the analysis being performed. When inactivity is part of the strategy’s behavior, the zeros are endogenous and belong in the series; excluding them would discard meaningful information.
The response cautions against aggregating observations simply to remove zeros, since doing so can artificially raise a Sharpe ratio. It also suggests comparing strategy returns with a third series, such as the traded asset’s returns, and using rolling windows to examine behavior through time. These are possible analytical approaches, not a complete statistical protocol. The discussion does not resolve how to compare the example return patterns or address correlation’s limitations for time series, so interpretation must account for the strategies’ trading behavior and the chosen window.
Key ideas
- Whether to include zero returns depends on why the observations are zero and on the research question.
- When a strategy’s inactivity is part of its behavior, its zero returns belong in the analysis.
- Aggregating returns merely to eliminate zeros can distort risk-adjusted performance measures.
- A traded asset’s return series can provide a reference for comparing strategy return correlations.
- Rolling windows can help examine changing relationships, while correlation still has time-series limitations.
Tags
Full text
# How to deal with zeroes in returns? # How to deal with zeroes in returns? Suppose there are two time series that I want to analyze and compare. However, many, or most, of the data are zeroes for some reason. For example, consider a pair of intraday trading returns time series. In most days, the trading strategies don't trade at all, so most of the returns are zeroes. How can I understand their correlation? I suppose I can just keep all the zeroes, and use the raw data to calculate the correlation. Any other thoughts? If I want to identify the time period when the returns are different substantially, I must think about the zeroes carefully. For example, time period A gives 0.2% in each of 20 days out of 100 days, but time period B gives 0.1% in 40 days out of 100 days. How do I compare and determine them? ## Answer by madilyn (score 2) https://quant.stackexchange.com/a/8427 This depends on the nature of the zero returns. As Quartz has pointed out, if the zero returns are endogenous, then you should take the zeros into consideration as they are part of the strategy behavior - there is nothing wrong with regressing the two series in that case. Finally, it is always a very bad idea to aggregate the time series simply to avoid the problem as you're artificially inflating your Sharpe ratio. ## Answer by Alexey Kalmykov (score 1) https://quant.stackexchange.com/a/8428 The answer largely depends on what are the timeseries and what kind of analysis you are going to do. Also you should clearly understand the limitations of correlation for time series. In your 2 trading strategies returns example, I would try to: - Use a third time series to compare correlations of trades returns against it. For example, if both strategy are trading the same asset, you can take this asset's return time series. - Use rolling window and aggregate trading strategies return values inside that window.
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