6.3 Nonsynchronous Data
A time series {–αq, –α+1q, … , 0q} is said to be synchronous if components tqi for each term tq are realized simultaneously. Otherwise, it is said to be nonsynchronous. Nonsynchronous data complicates multivariate time series analyses.
6.3.1 Causes of nonsynchronous data
In finance, nonsynchronous data typically arrises for one of two reasons:
- Trading effects relate to instruments that trade infrequently or fail to trade for a period of time. It also encompasses certain effects such as brokers failing to provide timely indicative quotes during a period of heavy trading volumes.
- Timing effects relate to instruments trading in different time zones or according to different schedules. Some exchanges—such as the Singapore Exchange—have different closing times for different instruments trading in the same time zone. This causes settlement prices to be nonsynchronous.
We have already mentioned trading effects. They primarily affect opening or closing transaction price data. As we indicated, they may also affect firm or indicative quotes. High and low transaction prices are not expected to be synchronous since different assets will attain their high and low prices at different times each day. If instruments do not trade for a day or more, the resulting nonsynchronicity can be a serious issue. Trading effects generally do not affect settlement prices. Each exchange has its own methodology for determining settlement prices. Most are based upon some average of transaction prices occurring immediately prior to the market close. If trading is not active at the close, a common practice is to poll traders and base the settlement price on some average of the indicative quotes.
As an illustration of a timing effect, the Tokyo, London, and New York stock exchanges stop trading each day at 3:00 PM, 5:00 PM, and 4:00 PM, respectively, in their local times. Because of time zone differences, Tokyo actually closes 11 hours before London, and London closes 4 hours before New York.1 Closing prices collected from the respective exchanges are nonsynchronous.
6.3.2 Impact of nonsynchronous data
For value-at-risk analyses, nonsynchronous data complicates the task of assigning a current value 0p to a portfolio if the current value 0r of the key factors is collected nonsynchronously. Cross-hedged positions may appear to not be hedged. Arbitrage conditions that should hold may appear to not hold. The resulting value for 0p may be misleading or even nonsensical.
If time series models are not implemented specifically to address nonsynchronous data, inferred correlations will be lower, in absolute value, than they would be if the data were collected synchronously. Spurious auocorrelations between different risk factors will also arise.
Consider the stocks of two companies that trade on the same exchange and tend to move in tandem. The first trades actively; the second does not. News arriving late in the day will not be reflected in the inactive stock’s closing price if that stock fails to trade subsequent to the arrival of the news. This tendency will suppress the inferred return correlation between the two stocks and induce a positive autocorrelation between the stock’s returns lagged by one day. If the inactive stock sometimes fails to trade for a day or more, such autocorrelations may persist for several days.
Eurodollar futures are traded on both the CME in Chicago and the Singapore Exchange. The two contracts are essentially identical. For a given expiration date, we may treat closing prices in Chicago and Singapore as being for the same contract, but collected at different times.2 By comparing these closing prices to closing prices of some other contract, we may assess the impact of nonsynchronous data. For such an analysis, we collect daily settlement price data from May 3, 1999 to February 1, 2000 for the following contracts:
- CBOT June 2000 Treasury bond future,
- CME June 2000 Eurodollar future, and
- Singapore Exchange June 2000 Eurodollar future.
The CBOT and CME are both in Chicago, so settlement prices for the CBOT Treasury bond contract and CME Eurodollar contract are synchronous.3 The settlement price for the Singapore Eurodollar contract is set 8 hours earlier.4 Also, 16 hours after the Chicago settlement prices are set, the subsequent day’s Singapore Eurodollar settlement price is set (assuming this is also a trading day). This is illustrated in Exhibit 6.2:
We expect the Treasury bond contract to be positively correlated with both Eurodollar contracts, but because the Singapore Eurodollar contract is nonsynchronous, we expect its correlation with the Treasury bond contract to be lower. The Treasury bond contract should also exhibit a modest autocorrelation with the Singapore Eurodollar contract. To test these hypotheses, we calculate return correlations and return autocorrelations as indicated in Exhibit 6.3:5
Prices for Treasury bond and Eurodollar futures move in tandem, as indicated by the .808 correlation for the two contracts traded in Chicago. However, nonsynchronicity causes the Chicago Treasury bond future and Singapore Eurodollar future to have a correlation of just .142. If the Treasury bond future is lagged a day, the autocorrelation is .634.
The effect of nonsynchronicity on correlations tends to diminish if data is collected at longer intervals. If prices are collected monthly, the effect of nonsynchronous data will be modest, as long as the prices are not too mean-reverting.
The most effective way to address nonsynchronous data is to avoid it in the first place. If transaction prices are highly nonsynchronous because of nontrading, consider using firm, indicative, or settlement prices instead. To the extent possible, try to collect prices in a single time zone. If this is impossible, consider collecting most prices in a particular time zone, and obtain prices from other time zones as broker quotes, which offer some flexibility in the timing.