Aligning Global Equity Returns for Cross-Market Regression
Summary
The document asks how to align daily returns from markets with different holidays when regressing a Japanese stock on the S&P 500. The response says alignment should follow the prediction or relationship being studied, and notes that simply matching calendar dates may overlook the markets’ different closing times. When one market closes before the other, the earlier market’s return may lead the later market’s return, creating timing effects or information leakage in a same-date regression.
The response also flags currency exposure: a yen-denominated stock and a US index may require an exchange-rate variable, depending on the question. It suggests that, for a basic correlation estimate, omitting or assigning zero returns on unmatched holidays may have little effect if those periods are ordinary, while using weekly or monthly data can change the measured relationship more substantially. These are conditional suggestions, not a universal alignment rule; the intended prediction target and time zone matter.
Key ideas
- Choose return alignment based on the prediction or relationship the regression is meant to estimate.
- Different market closing times can make same-date returns asynchronous and introduce timing effects.
- Currency movements may need to be included when comparing a Japanese stock with a US index.
- Zero returns on unmatched holidays are suggested only when those periods are not abnormal.
- Weekly or monthly aggregation may materially change the estimated relationship.
Tags
Full text
# What date to pick for regression on global stocks # What date to pick for regression on global stocks Let's say I have a return of a stock in Japan that I wish to regress on the S&P 500 index using daily data for 1 year. Since the Japanese stock market has different holidays than the US, the dates might not correspond to each other. For example : ``` US trading dates -> 2008-01-02 2008-01-03 2008-01-04 2008-01-05 Japan trading dates -> 2008-01-01 2008-01-03 2008-01-05 ``` In this case, should the regression be done on the same dates for both markets, thus ignoring the dates that are not identical? Giving us two usable dates: 2008-01-03 2008-01-05. Or is there a better way to do the regression? ## Answer by alexprice (score 1, accepted) https://quant.stackexchange.com/a/55716 The way to setup the regression depends on what do you want to predict. Once you formulate exactly what do you want to predict, you should set up your regression in exactly same way. Daily regression of returns of JPYStock ~ SPX can be done in several ways, and you should consider these differences: - holidays as you mention - End of trading day time (i.e. one will be ahead of other, thus there is information leak) - currencies are different, i.e. you might want to include USDJPY spot FX in your regression Even if you disregard these differences, and just focus on daily regression (which is basically just estimating Pearson correlation and vols,ignoring FX moves, and accepting that there is information leak), then these holidays differences do not matter if during the holidays period the returns are not abnormal. Estimating correlation over few years, and adding some dozen of non-abnormal returns will not change this correlation significantly. (by adding i mean substituting the returns by 0 if not available on holiday date) as noob2 mention you might want to calculate this correlation over longer periods, such as weekly, monthly etc. This will change your correlation more than effect of including/excluding same holidays. ## Answer by Kphysics (score 0) https://quant.stackexchange.com/a/55713 It is not clear you want to regress changes or indexes themselves? If you regress the indexes, then the 12 hour time difference will not matter. If you regress changes, you better take as the "x" variable the series that leads and as "y" series that lags (by 12 hours). It means that if you want to take d(Nikkei) = a*d(S&P)+b then you want to take the Nikkei change for the next day.
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