Time-Series Momentum on Shanghai Indices and ETFs

The cross-sectional momentum pages on this site rank stocks against each other. Time-series momentum does not. Each series is long or short from its own past return, which is the rule behind managed-futures books and the Moskowitz, Ooi, and Pedersen (2012) evidence across asset classes.

Shanghai is a useful place to rerun that rule because the listed menu is not only equities. Yahoo Finance returns a full history for the Shanghai Composite and for the SSE-listed ETFs, and only a stub for the SSE 50, SSE 180, CSI 300, and CSI 500 index levels themselves. The sleeve therefore uses the Composite plus the ETFs that track those benchmarks (510050.SS, 510300.SS, 510500.SS), the SSE dividend ETF, a Treasury-bond ETF (511010.SS), and a gold ETF (518880.SS). A sign that only works when every series is the same equity factor is easier to see once bonds and gold are in the same weight vector.

Monthly returns are month-end to month-end on adjusted closes. At month $t$ the signal for series $i$ is the sign of the return from $t-12$ through $t-2$, the same 12-1 skip used in the US momentum studies so the position is not a one-month reversal bet.

$$w_{i,t}=\frac{\mathrm{sign}(R_{i,t-12,t-2})/{\sigma }_{i,t}}{{\sum }_j|\mathrm{sign}(R_{j,t-12,t-2})/{\sigma }_{j,t}|}$$

${\sigma }_{i,t}$ is the trailing 36-month standard deviation. Absolute weights sum to one, so a month in which every signal is positive is a fully invested long book with larger weights on the quieter series. A month in which signals disagree is long some indices and short others.

The net return subtracts 5 bps times L1 turnover. The benchmark is the equal-weight of the same live series, rebalanced monthly, without a signal. The reported test is the Newey–West t-statistic on the difference.

Wealth of 1 is compounded from the net monthly returns. Series with fewer than about two years of daily history are dropped before the signal starts, so a late-listed ETF does not enter on a handful of months.

CSI 300 and CSI 500 include Shenzhen names. Their SSE-listed ETFs are in the sleeve because those are the benchmarks a Shanghai cash book is judged against, and because Yahoo does not return a usable history for the index levels. They are not a pure SSE 50 portfolio.

Index series and the ETF that tracks the same index move together. The volatility scaling down-weights duplicates; it does not delete them. Overlapping equity indices still dominate the risk if bonds and gold are quiet.

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.