The first article in this series ("Momentum Vs. Rebalancing: Which Is Better?") considered momentum or rebalanced portfolios consisting of U.S. stocks, via the SPDR S&P 500 ETF (NYSEARCA:SPY), and U.S. long term treasury bonds, via the iShares 20 Year Treasury Bond ETF (NYSEARCA:TLT). I found that the momentum portfolio gave a higher CAGR than the rebalanced portfolio, but both beat buy and hold in terms of delivering superior risk-adjusted returns. Inspired by a comment from the first article, I then investigated the effect of lookback horizon on the performance of the momentum strategy on the SPY/TLT pair from 2003-2016 ("Momentum Vs. Rebalancing (Part 2): Effect Of Lookback Horizon"). It was found that a lookback period of 5 months gave the highest CAGR and Sharpe and Sortino ratios, and the second-highest MAR ratio.
In the comment stream of that article, astute reader IndyDoc1 noted:
If you use mutual fund proxies for SPY/TLT that is VFINX/VUSTX you can test all the way back to 1987. Using PV, since 1987, the monthly pair switch using 3 months look back had a better performance than 5 months look back period. The interesting thing is that equal weight is not bad either. Equal weight got slightly less CAGR than momentum one, with less draw down (using the 5 months look back period).
Another astute observed, drftr, commented:
The "best" lookback period actually depends on the test time frame, which means that for instance in the 1st decade of the test 7 months could be optimal while in a 2nd decade 1 month could be optimal. Of course if you always include at least the last / current decade in your backtest that will influence all results. Probably the best way to get around this problem is to use for instance rolling decades to calculate the best overall lookback period.
This article therefore aims to build on the previous study by extending the analysis in two ways. The first is to use the Vanguard 500 Index Fund (MUTF:VFINX) and the Vanguard Long-Term Treasury Fund (MUTF:VUSTX) pair in order to extend the analysis back to 1987. The second is to calculate the returns across rolling decades to study the time-dependence of the optimal lookback horizon.
The two portfolios
- Momentum strategy: Each month, buy either VFINX or VUSTX depending on which ETF has had the superior N-month trailing returns (i.e., at any time, you are 100% invested in only one of the two ETFs). In this study, N varied from 1 to 12.
- Rebalanced strategy: Each month, rebalance the portfolio so that it is equally weighted between VFINX and VUSTX (i.e., at the start of the month, you rebalance to 50% stocks and 50% bonds).
Portfolio Visualizer was used for this backtest study.*
(*As mentioned by astute reader Varan, Portfolio Visualizer has look-forward bias because trades are assumed to take place at the same instant (end of month) that trailing returns are calculated, which is not possible in reality. However it is my opinion that switching in the last 5 minutes of market close, when next month's choice of asset is nearly assured, should not lead to a big difference in results).
Effect of lookback horizon over longer periods
The CAGR and standard deviation of the VFINX/VUSTX pair from 1988 to 2016 to date for the various lookback periods is shown below. For comparison, VFINX had a CAGR of 9.91%, VUSTX 8.16%, and the rebalanced portfolio 9.67%.
We can see from the chart above that 3 months is now the best lookback period for the period of 1988-2016, consistent with IndyDoc1's finding above, rather than the 5 months that was optimal for the SPY/TLT pair from 2003-2016. Additionally, and surprisingly, there is a significant dip at 7 and 8 months, but this recovers when the period is extended to 9 months and beyond.
In terms of the volatility of returns, all lookback periods had standard deviations between 11 and 13%, with 7 months having the highest standard deviation of 12.62%, and 8 months having the lowest at 11.57%.
How does this compare with my previous shorter study, as well as a Gestalt U study on asset rotation with 10 asset classes from 1995-2013? These are compared on the chart below:
If you recall from my previous study, the CAGR of the SPY/TLT switching strategy from 2003-2016 deteriorated significantly when the lookback horizon was extended to 7 months or more. In contrast, with the VFINX/VUSTX study over the longer period of 1988-2016, this decay in performance is not as pronounced, and the shape of the trend more closely resembles that in the Gestalt U study (1995-2013).
Advanced metrics appear favor either 3 or 4 months as the optimal lookback period for the VFINX/VUSTX pair over 1988-2016. Surprisingly, 9 and 10 months also exhibit strong metrics - in fact, they ranked first and second for MAR ratio. Why is there this apparent discontinuity, where both shorter and longer lookback periods are favored, but not intermediate periods? I do not know the answer to this - if anyone has any explanation, please feel free to chime in in the comments section below!
The following chart shows the U.S. market correlation and maximum drawdown for the VFINX/VUSTX pair over 1988-2016 at different lookback periods.
Performance of rolling 10-year periods
To investigate the time dependence of the optimal lookback period, rolling 10-year performance numbers were calculated. As the data set for VFINX/VUSTX started from 1987, the first 10-year block has an end date of 1997, giving 20 rolling 10-year periods in this analysis. The following shows the CAGR of the 10-year rolling periods over end dates from 1997 to 2016 for different lookback periods. For clarity, lookback periods of 1-3 months are presented together, then 4-7 months, and finally 8-12 months.
We can see from the charts above that all of the lookback periods did fairly well in the rolling decades up to about 2000, which can be expected because all portfolios would have been nearly continually in stocks during that time.
For the shorter lookback periods (1-3 months), their CAGR during rolling 10-year periods declined sharply from 2000 to about 2008, then recovered afterwards. For the intermediate lookback periods (4-7 months), the dropoff to 2008 was less pronounced (with the exception of 7 months), and performance also rebounded afterwards. However, for the longer lookback periods (8-12 months), there was a steady decline in CAGR from 2000 all the way up to 2016, which is consistent with the inferior results that were observed for these longer lookback periods in the SPY/TLT study from 2003-2016.
In terms of consistency, 5 months appears to be the most consistent performer because its CAGR over 10-year rolling periods never dipped below 8%. 4- and 6-month lookback periods are also decent in this regard, as their CAGRs dropped below 8% only briefly.
This consistency can be seen from the below chart, which shows the average of the 10-year rolling periods for each lookback horizon, with error bars representing the standard deviation of the results. Of course, this method of averaging across all 10-year periods gives something that resembles the overall CAGR, which is also plotted for comparison. Note that the 5-month lookback period has the smallest error bars, which indicates that it was the most consistent lookback period.
Discussion and conclusion
For the SPY/TLT pair from 2003-2016, 5 months was the optimal lookback horizon as was found in a previous analysis. In this study, a longer backtest was conducted with the VFINX/VUSTX pair with data going back to 1988. For this longer period, we find that overall, 3 months was the optimal lookback period. Additionally, the decay in performance of the SPY/TLT pair for lookback periods of to 7 months or more was not observed for the VFINX/VUSTX system.
I surmise that the drastic drop off in the performance for the SPY/TLT pair from 2003-2016 is because there was only one major bear market that occurred during this time. Any lookback period greater than 6 months would have lingered in equities too long as the financial crisis hit, but then also overstayed in treasuries even after the recovery was well underway. In contrast, the longer time periods in the Gestalt U study and with the VFINX/VUSTX pair both span at least two major bear markets, and thus their performance at higher lookback periods were more similar to each other than with the SPY/TLT pair.
Computation of the rolling 10-year performance figures show that shorter lookback periods (1-3 months) faltered towards 2008, but then recovered afterwards, while for intermediate periods (4-7 months), the drop in 10-year CAGR near 2008 was less pronounced. However, longer lookback periods (8-12 months) became less effective as the time neared the present, which was consistent with the previous SPY/TLT study.
Was there a "best" lookback horizon for this 30-year period? While 3 months had the highest overall CAGR, the 5-month period was more consistent, as it 10-year CAGR never dropped below 8%. In contrast, for the 3-month lookback period, the 10-year CAGR dipped briefly even below 6% in about 2008. Whether 3 months or 5 months will remain the optimum period in the future is, of course, an unanswerable question. If history does not repeat itself exactly, will it at least rhyme?
Interested readers should peruse the comment section of my first two articles, which contain many insightful comments from experienced proponents and practitioners of the momentum/rotation strategy.
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