How long is the half-life, and how long to learn the edge?

The formation-window residual of the HDFC Bank/ICICI Bank spread has AR(1) coefficient $\hat\phi = 0.9778$ with standard error 0.0102 (504 daily observations). (a) Compute the half-life $h = \ln 2/(-\ln\hat\phi)$ in trading days, and a 95% interval by mapping the endpoints $\hat\phi \pm 1.96\,\mathrm{s.e.}$ through $h(\phi)$. (b) Compute the delta-method standard error of $\hat h$ and the symmetric 95% interval $\hat h \pm 1.96\,\mathrm{s.e.}(\hat h)$. Explain why it differs so much from (a), and which you would report. (c) The playbook's time stop is three half-lives, rounded up. How many trading days is it? What does the interval in (a) imply about a time stop chosen this way? (d) The backtest of the rule over all 23 pairs gives mean net R $E = 0.101$ and standard deviation $s = 1.173$. Using M03 (3.2a) and (3.2b), how many independent trades are needed for $t = 2$ in expectation, and for 80% power? (e) At 55 trades a year, how many years is each? Why is even this an understatement of the time needed?