Aligning International Stock Returns for Covariance Estimation
Summary
The document explains a timing problem in estimating covariances from daily returns on international stocks: markets close at different times, so their recorded closing prices do not represent the same point in the global trading day. It proposes first mapping exchange opening and closing hours onto a UTC time circle, accounting for daylight-saving changes and markets with both day and night sessions.
To align prices at a chosen common time, use intraday quotes for markets that are open. For markets that are closed, estimate prices from related instruments, such as that market’s futures when available, or from futures and stocks in other open markets. Returns measured from these aligned prices can then be used to estimate covariances for a minimum-variance portfolio. The response describes a practical framework rather than a tested estimator, and it gives no empirical comparison or model specification. Its results depend on the quality of intraday data and the estimates used for closed markets, so careful implementation is required.
Key ideas
- International market closes occur at different times, which can distort covariance estimates from unaligned daily prices.
- Map exchange sessions in UTC, allowing for daylight-saving shifts and separate trading sessions.
- Use intraday prices to value open markets at a shared timestamp.
- Estimate closed-market prices from futures or other markets that remain open.
- Build daily returns and covariances from the resulting consistently timed prices.
Tags
Full text
# Covariance matrix using world stocks # Covariance matrix using world stocks What is the best way to compute a covariance matrix of daily stock returns made up of international stocks. Knowing that the world markets are not trading simultaneously. This matrix could then be used to make a minimum variance portfolio. ## Answer by nbbo2 (score 2, accepted) https://quant.stackexchange.com/a/58275 As a first step it is helpful to draw a 'time circle' from 0000 to 2359 GMT/UTC and plot on this circle the opening and closing times of the major markets/exchanges. This gives an overview of the situation and makes it easy to answer questions like "at xxxx GMT what markets are open and what markets are closed". (Actually you may need to have several such circles because GMT trading hours shift when countries enter/exit Summer Time and this happens on different days in different countries). (And Market Open/Market Closed is an oversimplification, some markets have a day session when major trading is done as well as a night session with a more limited amount of trading). When a market closes (for example the close of DAX at 17:30 CET), the closing prices for that market can be used for your study, but what about the prices for other markets: (1) If the other market is open, the prices at that moment in time can be gotten from intraday data for that market. (2) If the other market is closed, the prices will have to be estimated by a model. If there is a futures market open for that market, you can simply mark up/down the closing prices for that market by the movement in futures since the stock market closed. If there is no futures market the model may have to be based on futures or stocks in other markets which are open. In this way you may obtain estimates of world stock prices at a consistent time each day, like 15:30 UTC (equivalent to 17:30 CET) and find the daily returns and their covariances. As you can see it is a fairly challenging project, with many details needing careful attention if it is to be done right.
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