# 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?