Do asset price series in general reliably exhibit trends and reversals? In his May 2016 paper entitled “Trend, Mean-Reversion or Random Walk? A Statistical Analysis of Price Behavior in Major Markets”, Theo Athanasiadis tests a wide variety of financial market price series for existence of significant trends and reversals. He considers both spot and futures price series in U.S. dollars for 56 major markets: 16 developed equity market indexes; the S&P 500 implied volatility index (VIX); 25 liquid commodities covering all basic sectors; 5 liquid currency exchange rates versus the U.S. dollar; and, 9 liquid government bonds of varying durations. For futures contract returns, he uses the most liquid contracts (typically nearest or next-nearest) and rolls accordingly. He employs three statistical tests of time-series behavior: autocorrelation, variance ratio and positive/negative runs relative to median. He considers weekly, monthly, quarterly and semiannual returns in both univariate and multivariate tests. Using spot and futures price returns at the specified frequencies for all 56 markets as available during January 1999 through March 2016, he finds that:
- There are few exceptions to a random walk among markets over the sample period.
- Exceptions are split between trending and reversal and vary with time frame, price type (spot or futures) and market.
- Given the number of tests run, exceptions are suspect due to data snooping bias.
- Significant differences at longer measurement intervals between futures and spot prices (with the latter appearing more random) demonstrate the importance of carry in asset prices, especially for commodities, currencies and bonds.
- By asset class:
- Stock indexes reverse weekly and trend semiannually. There are few exceptions to randomness in monthly and quarterly returns
- VIX spot levels exhibit reversal, especially at weekly and monthly intervals. However, VIX futures exhibit only slight reversal in weekly returns.
- Commodity price behaviors vary considerably:
- Precious metals and some industrial metals walk randomly. Aluminum, tin and zinc trend quarterly.
- Grains walk randomly. Sugar and cotton futures (but not spots) trend weekly. Coffee and lean hogs (spot only) reverse and trend weekly, respectively. Cocoa, soybean meal (spot only) and lean hogs (spot only) reverse monthly. Coffee and lean hogs (spot only) trend and reverse semniannually, respectively.
- Energy commodities mostly walk randomly. WTI and Brent crude trend monthly (futures only), and gasoline reverses quarterly and semi-annually.
- Currencies mostly walk randomly. There is weak evidence for weekly reversal and monthly trending of the Yen, and quarterly trending of the Canadian Dollar.
- Long-term and medium-term bonds mostly walk randomly. There is weak evidence of weekly reversal for all bonds. Short-term bonds trend at all frequencies except weekly.
- Multivariate analyses that examine markets in aggregate generally support dominance of randomness over predictability in market prices.
In summary, evidence suggests that reliable detection of time series trends and reversals in asset prices is, at best, inherently very difficult.
Cautions regarding findings include:
- As noted, data snooping bias undermines sporadic findings of trending and reversal across assets and measurement frequencies. Also as discussed in the paper, findings sometimes conflict with prior research, suggesting that results are not stable over time due to snooping bias and/or market adaptation.
- As noted, findings do not address predictability other than time series.
