Measuring Alpha Decay Across Signals of Different Strength

Summary

The document examines how to describe signal decay when comparing lagged information ratios. Its example uses two orthogonal signals with equal autocorrelation and the same absolute decline in information ratio, but very different starting strengths. Expressing the decline as a percentage makes the weaker signal appear to decay more sharply; in one case the later information ratio is negative, making a simple percentage interpretation undefined.

The question challenges whether percentage decay is a fair comparison and asks for a more consistent framework, especially for low-information-ratio strategies. It highlights the distinction between absolute changes in predictive performance and proportional changes relative to a signal’s initial strength. However, the document contains no answer, proposed alternative metric, empirical evidence, or guidance for estimating decay. The numerical illustration is hypothetical and should be read as motivation for methodological discussion, not as evidence that signal autocorrelation determines information-ratio decay or that one decay measure is universally preferable.

Key ideas

• Equal absolute information-ratio changes can imply very different percentage decay across signals.
• Percentage decay can be misleading when a signal starts weak or crosses below zero.
• The example holds signal autocorrelation equal while comparing different signal strengths.
• The document raises the measurement question but does not recommend a solution.

Tags

# Alpha decay for strong vs weak signals


# Alpha decay for strong vs weak signals












Assuming you are computing alpha decay similarly to shown here (e.g., exponential decay of the information ratio with lagged signals).

I'm wondering whether it is preferable to treat strong vs weak signals differently.

For example, assume you have two orthogonal signals $s_1$ and $s_2$, with the same autocorrelation $Corr(s_{1,i}, s_{1,i-1}) = Corr(s_{2,i}, s_{2,i-1}) = 0.9$. And the standard + lagged information ratios are:

$IR(s_{1,i}) = 1.0, IR(s_{1,i-1}) = 0.7$

$IR(s_{2,i}) = 0.1, IR(s_{2,i-1}) = -0.2$

In both cases, the absolute decay in information ratio is equal to $0.3$. However, percentage-wise, the decay in $s_1$ is $30\%$ and the decay in $s2$ is $100\%$ (though technically undefined, because the lagged information ratio is negative).

Does it make sense to treat decay in this way, especially given that the autocorrelation of both signals is relatively high at $0.9$?

It seems like if we define the decay as the percent degradation in information ratio, then lower strength signals will by definition decay at a faster rate than higher strength signals, even though the absolute amount of the decay might be the same. Wondering if there's a more consistent paradigm to describe alpha decay, especially for strategies with lower information ratio?

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