Distance Pairs on Tokyo Large Caps

Distance pairs, as in Gatev, Goetzmann, and Rouwenhorst (2006), match stocks whose normalized price paths stayed close and then bet that the gap mean-reverts. No cointegrating vector is estimated. The match is the sum of squared differences of two price paths that both start at one.

The universe is the same Tokyo large-cap panel as the overnight study, so the two Japan pages share one Yahoo download. The question here is different: after a one-year match and a six-month trade, does a book of at most eight disjoint pairs have a positive mean once both legs pay 5 bps to open or close?

Windows step forward by six months. Inside the formation year each price is divided by its first observation. The distance between names $i$ and $j$ is

$$d_{ij}=\sum _{t\in \mathrm{formation}}({\tilde{P}}_{i,t}-{\tilde{P}}_{j,t}{)}^2$$

Pairs are taken from the smallest distances, greedy, with no name used twice, until eight pairs are open or the list runs out. The formation spread ${\tilde{P}}_i-{\tilde{P}}_j$ supplies the mean and standard deviation for the z-score.

In the next six months the same normalization is extended. A flat pair goes long the first name and short the second when $z<-2$, and the other way when $z>2$. It flattens when $|z|<0.5$, when $|z|>4$, or after 40 trading days. Each leg is half the pair's capital, so the pair is dollar-neutral before costs. Opening or closing charges 5 bps on each leg.

Days with no open pair earn zero. The monthly series compounds those daily pair returns, averaging across the pairs that are live. The test is Newey–West on that monthly mean.

The wealth chart is the cost-adjusted book against the Nikkei 225. The pairs table lists the matches the rule actually opened, their formation distance, the number of days the position was on, and the compounded return inside that trading window. Only the first forty rows are shown.

Distance is not cointegration. Two names can track each other for a year because they share a sector factor, and the z-score will still fire. A Johansen screen would reject many of these matches.

Japanese short-sale flags, locate, and the tick size at the open are not in the cost. Five basis points per leg is a research haircut.

Yahoo Finance adjusted closes are not a point-in-time index membership file. The constituent lists are a liquid large-cap panel, fixed in the repository, not the official index as it stood on each rebalance date.

The risk-free rate is set to zero in every Sharpe ratio. A local bill rate would lower the ratios and would not, by itself, change a long-short spread.

Costs are a flat one-way haircut on weight turnover. They do not include borrow fees, lot-size rules, auction imbalance, stamp duty, or the Shanghai and Hong Kong short-sale bans that bind a live short book.

This is a research record. It is not a recommendation to trade the sleeve.