Blog - Investing Notes

March 2, 2007 - A New Era of Financial Markets Forecasting Confusion?

Suppose you think there is a relationship between a past trend in commodity prices and a future trend in stock prices. So you backtest a relationship between commodity prices for one month and stock prices the next month. But wait a minute. Instead of a month of commodity price history, how about three trading days, or 11 trading days, or 17 trading days? You would find the same general relationship, wouldn't you? In the February 2007 draft of their paper entitled "The Interval of Observation", Ben Jacobsen, Ben Marshall and Nuttawat Visaltanachoti show how the reliability and even the direction of stock market return forecasts fluctuate wildly even for slight differences in the historical interval of indicator observation. Using monthly data for three broad stock indexes and daily data for 20 individual commodities from initial availability through June 2006, they find that:

• Even after adjusting for data snooping bias, varying the historical interval of indicator (commodity price) observation sometimes generates: (1) significant results where results were insignificant before; (2) no significance where the conventional (monthly) interval of history indicates significance; and, (3) large changes in significance levels, even for very similar intervals of observation. For example, commodity returns over the last six trading days of the previous month are not predictive of stock returns the next month, but commodity returns over the last eight trading days of the previous month are strongly predictive.
• Most often, but not uniformly, longer intervals of historical observations offer stronger predictability.
• Specific results indicate that increases (decreases) in the prices of crude oil, copper, aluminum, heating oil, nickel, unleaded gas and and hogs predict movements in the S&P 500 index, perhaps because of their links to inflation.
• When applied to trading of stock indexes, the conventional (monthly) historical interval of commodity prices does not produce Sharpe ratios that consistently beat a buy-and-hold benchmark. In contrast, applying the optimal historical intervals to stock index trading produces Sharpe ratios that beat a buy-and-hold benchmark for 15 of the 20 commodity series, dramatically for some (copper, silver and soybeans). It seems that information may flow across financial markets in less than a month.
• In general, results suggest that stock market returns are slightly more predictable than indicated by conventional monthly intervals of historical observation.

The following table, extracted from the paper, shows the optimal number of preceding trading days of each of 20 commodities for the purpose of predicting the behavior of the S&P 500 index over then next month. For example, the behavior of copper over the last three trading days of a month is more predictive of S&P 500 index behavior over the next month than any other historical observation interval for copper in the range 1-22 trading days. The table also compares for each commodity the R-squared measure of explanatory power for the last month of commodity price movement and the R-squared for the optimal number of historical trading days. For example, the change in copper price over the past month explains 1.60% of the change in the S&P 500 index next month, but the change in copper price over just the last three days of the past month explains 5.86% of the change in the S&P 500 index next month. The shorter observation interval is far more predictive.

The authors note that a similar variability in predictive power may arise in many other empirical regressions in finance and economics.

In summary, the power of empirical regressions to predict stock market behavior may vary sensitively and drastically with the interval of historical observation for the selected indicator.

The authors did not experiment with different stock market return intervals, sticking with the next month. Perhaps the change in the price of copper the last three days of one month best predicts returns on the S&P 500 index over the first seven or 11 trading days of the next month. The possibilities are endless.

For related research, see Blog Synthesis: Big Ideas for Investing/Trading.