How can investors confidently assess risk of strategy crashes (tail events) when there are so few crashes even in long samples? In their March 2019 paper entitled “Time-Series Momentum: A Monte-Carlo Approach”, Clemens Struck and Enoch Cheng present a Monte-Carlo simulation procedure for strategy backtesting that both preserves time series and cross-sectional return characteristics while diversifying time series simulation inputs. They use this procedure to test intrinsic (absolute or time series) momentum on S&P 500 Index futures and on an equal-weighted multi-class portfolio of 27 futures series. They consider long-short and long-only (long-cash) versions of time series momentum (TSM), with or without volatility adjustment. For testing actual histories, they consider lookback intervals of 1, 3, 6, 9 and 12 months to measure momentum. For simulations, they focus on optimal lookbacks from actual histories and consider multiple time series models. Their in-sample subperiods are 1985-2009 for the S&P 500 Index and February 1989-2009 for the multi-class portfolio. Their out-of-sample subperiod is 2010-2018. They roll each futures series at the end of each month into the next front contract, using spot indexes prior to the availability of some futures. They use buy-and-hold portfolios (with rolling) as benchmarks. Using monthly prices for nine equity indexes, four government bonds, eight commodities and six currencies futures/spot series in U.S. dollars over the specified sample period, they find that:
- For actual S&P 500 Index historical data:
- In-sample, based on gross Sharpe ratio, long-short (long-cash) TSM beats buy-and-hold for lookback intervals 9 or 12 (6, 9 or 12) months, with 9 months optimal. Winning TSM variations also have shallower maximum drawdowns. Long-cash TSM generally beats long-short TSM. Volatility adjustment has little effect.
- However, out-of-sample, the best in-sample strategy variations almost uniformly underperform buy-and-hold based on both gross Sharpe ratio and maximum drawdown. Long-cash TSM again generally beats long-short TSM. Volatility adjustment improves TSM performance.
- For actual multi-class portfolio historical data:
- In-sample, TSM strategies generally beat buy-and-hold based on gross Sharpe ratio and maximum drawdown, with the 12-month lookback optimal. Long-cash TSM generally beats long-short TSM. Volatility adjustment generally improves TSM performance.
- Out-of-sample, all gross Sharpe ratios are much lower, with some TSM variations better and some worse than buy-and-hold. All TSM variations beat buy-and-hold based on maximum drawdown. No TSM variations are clearly superior.
- For S&P 500 Index simulations with optimal historical 9-month lookback:
- In-sample, based on gross Sharpe ratio, probabilities of long-short (long-cash) TSM beating buy-and-hold range across models from 3% to 8% (13% to 25%).
- Based on maximum drawdown, probabilities of long-short (long-cash) TSM beating buy-and-hold range across models from 78% to 88% (33% to 49%).
- For multi-class portfolio simulations with optimal historical 12-month lookback:
- Out-of-sample, based on gross Sharpe ratio, probabilities of long-short (long-cash) TSM outperforming buy-and-hold range across models from 9% to 53% (36% to 90%).
- Based on maximum drawdown, probabilities of long-short (long-cash) TSM outperforming buy-and-hold range across models from 14% to 50% (1% to 7%).
In summary, sophisticated simulation offers little support for belief that intrinsic (time series) momentum strategies are attractive out-of-sample for either S&P 500 Index futures or equally weighted multi-class portfolios of futures.
Cautions regarding findings include:
- The short out-of-sample subperiod, with no market crashes, is a difficult one for momentum and trend following strategies.
- Returns are gross, not net. Accounting for trading frictions would reduce all returns, more for momentum strategy variations than for buy-and-hold. Volatility adjustments may elevate momentum strategy turnover.
- Testing 20 momentum strategy variations on actual data and eight time series models for simulations introduces data snooping bias, such that the best-performing variations overstate expectations.
- All simulation modeling involves assumptions about asset returns that simplify observed behaviors.
For summaries of other research on intrinsic/time series momentum, see results of this search.
