Synchronise your data or you get out of step with your risksBy Bernd Scherer, Professor of Finance, EDHEC Business School, Member, EDHEC-Risk Institute and Board Member, London Quant Group
After the credit crisis, practitioners are rushing for better, more frequently updating risk models. Daily stock market data are used in multifactor risk models by commercial software vendors or in trading desk risk models. The use of daily data is motivated by the fact that risk (unlike return) estimates are becoming more and more precise as we increase the observation frequency. This allows us to estimate risk models with the required degrees of freedom on shorter time intervals. We simply do not have to include a lot of economically irrelevant history to satisfy our need for data. Equally, it allows us to include more explanatory variables for the same time interval, without having to worry about arriving at noisy estimates. However, this advantage comes at a cost that is worryingly overlooked. Daily data exhibit autocorrelations as well as spuriously low correlations due to little common trading time over the course of a day.
What is the problem? Suppose we manage the risks of a global equity portfolio of Japanese, German and US stocks. When the market in Japan closes, the German market has not even opened yet and when the German market closes, the US stock market is still open. When the US market finally closes, what will be the value of our portfolio? It is incredibly naive to use each market close (as is currently done by many practitioners). If major negative economic news forces the US market to sell off 5%, this information must impact German and Japanese stocks. We donít see this effect in todayís prices as both markets are already closed i.e. their accounting values remain stale, while their economic value will move. This move is reflected (at the earliest) when the Japanese and German markets open. In the specific example, both markets are likely to sell off the next day (in the absence of further positive information releases). The described process will lead to spuriously low correlations between stock markets because not all day t information is reflected in all day t returns practitioners download from databanks. If unadjusted for, risk models will arrive at excessively low (high) Value at Risk forecasts for long-only (long/short) portfolios; risk managers will arrive at excessively small hedge ratios and asset allocation advice assumes excessively optimistic diversification benefits as reviewed in Scherer (2010).
What needs to be done? The answer is that we need data synchronisation models. Synchronisation adjusts accounting returns by subtracting returns due to market information released before the asset started trading (which caused the asset to jump at the opening to reflect this information) and adding returns that an asset would have generated from information released after its close (which left the asset stale due to its market being closed). In statistical terms, we need to model the multivariate data generation process for accounting returns. Once we have modelled this process (this usually involves vector autoregressive or vector moving average models) we can model the abovementioned conditional expectations to arrive at a new set of synchronised returns. They can be seen as an estimate for the return of an asset if it had been traded throughout the day (from the opening of markets in Japan to the close of markets in the US), i.e. contain all day t information releases. The in-built predictability is fake, as in reality it cannot be traded on. It simply tells us where we for example can expect the Japanese market to open after we observed all market closes on the previous day (and no further market relevant information is released between the US close and Japanís opening).
How important is this? I calculate differences in Value at Risk estimates for a VMA (1) model versus a naive model using daily accounting returns for a 30-day time horizon at the 99% confidence interval. The universe is the same as in Burns/Engle/Mezrich (1998), but I use a much longer history and an unconstrained synchronisation model. The result is shown in Exhibit 1.
The use of daily accounting data would have underestimated the Value at Risk of an equal-weighted portfolio of G7 equity stock markets almost all the time. The use of unadjusted daily data becomes most troubling in periods of market crisis where underestimated correlations suggest a diversification benefit that is not real. Correlations between US and Japanese stocks increase from 0.3 for accounting data to 0.8 for synchronised data. Daily risk models without data synchronisation are hazardous.
- Burns/Engle/Mezrich (1998), Correlations and Volatilities of Asynchronous Data, Journal of Derivatives, pages 8-18.
- Scherer (2010), Risk Budgeting and Portfolio Construction, 4th edition