| Abstract: |
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
$(\theta,\varepsilon,\Omega)$, namely, starting ($\theta$), profit-taking
($\varepsilon$) and stop-loss ($\Omega$), 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 about $1,784$ stocks listed on the first section of
the Tokyo Stock Exchange leading up to totally ${}_{1,784}C_{2}=1,590,436$
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
$(\theta,\varepsilon,\Omega)$ (`absorbing boundaries' in the literature of
first-passage processes). |