  We carry out a large-scale empirical data analysis to examine the efficiency
of the so-called pairs trading. On the basis of relevant three thresholds,
namely, starting, profit-taking, and stop-loss for the `first-passage process'
of the spread (gap) between two highly-correlated stocks, we construct an
effective strategy to make a trade via `active' stock-pairs automatically. The
algorithm is applied to $1,784$ stocks listed on the first section of the Tokyo
Stock Exchange leading up to totally $1,590,436$ pairs. We are numerically
confirmed that the asset management by means of the pairs trading works
effectively at least for the past three years (2010-2012) data sets in the
sense that the profit rate becomes positive (totally positive arbitrage) in
most cases of the possible combinations of thresholds corresponding to
`absorbing boundaries' in the literature of first-passage processes.
