## Introduction

We, as well as many other contributors of the seeking alpha community, have shown that a very simple and well-diversified portfolio may be made up of two instruments, one representing the total stock market and the other the total bond market. These portfolios are quite robust and achieve decent returns using simple strategies such as rebalancing and momentum based asset allocation.

The momentum factor has been the subject of numerous academic studies. The simplest momentum strategy ranks the assets of the portfolio by their total return over a fixed lookback period. From the academic studies, it was concluded that a lookback period of 12 months performed on average the best.

In our experience, the 12-month lookback period performed very poorly in recent years. Instead, we found that, most often, a 3-month lookback period works much better. For this reason, we decided to explore the drift of the optimal value of this parameter.

Our portfolio contains two funds:

Data for these assets was available since 1987. Since our longest lookback period is 12 months, we can cover in our simulation the period starting with January 1988. The simulations are done using the free application on the Portfolio Visualizer (PV) site.

**Results**

In order to study the effect of the lookback period, we simulated the momentum strategy for periods from 1 month to 12 months. After a first analysis of the results, we decided to compare in detail only two periods, 12 and 3 months. We also divided the whole time period in two successive periods; the first one from 1988 to 2008, and the second from 2009 to 2019.

**Results over the 1988-2008 period**

Here is a link to the PV simulation.

First, we show the performance of the 12-month lookback over the 1988-2008 time interval.

Figure 1. Portfolio performance for model timing with 12-month lookback from 1988 to 2008.

Source: All figures and data results were generated by the PV application.

Figure 2. Annual returns for model timing with 12-month lookback from 1988 to 2008.

Figure 3. Drawdowns for model timing with 12-month lookback from 1988 to 2008.

Figure 4. 3- and 5-year rolling returns for model timing with 12-month lookback from 1988 to 2008.

By looking at Figures 1, 2, 3 and 4, we see that the timing model with 12-month lookback period performed the best overall, over the period from 1988 to 2008. It produced the highest return, with the lowest drawdowns. The equal weight portfolio lagged the buy-and-hold strategy from 1988 to 2007, but because of its good performance in 2008, it ended up with a total return above the benchmark.

The timing model had only two small losing years, 1994 and 2005. The equal weight portfolio had four years with small losses, 1994, 2001, 2002 and 2008. The benchmark, VFINX, had suffered losses in five years, 1990, 2001, 2002, 2003 and 2008. The losses in 2008 and 2002 were quite large.

From Figure 3, we see that the timing model did not have any 3- and 5-year negative rolling returns. That is in contrast with the benchmark, which had four negative 3-year rolling returns and two negative 5-year ones.

In the following four figures, we show the simulation results over the period from 1988 to 2008 with a 3-month lookback period.

Figure 5. Portfolio performance for model timing with 3-month lookback from 1988 to 2008.

Figure 6. Annual returns for model timing with 3-month lookback from 1988 to 2008.

Figure 7. Drawdowns for model timing with 3-month lookback from 1988 to 2008.

Figure 8. 3-year and 5-year rolling returns for model timing with 3-month lookback from 1988 to 2008.

In Table 1, we give the numerical values of some selected performance indicators for the timing models, the equal weight and the benchmark portfolio.

CAGR % | maxDD % | Sharpe ratio | |

Momentum 12-month | 13.07 | -15.38 | 0.75 |

Momentum 3-month | 11.16 | -16.45 | 0.65 |

Equal Weight | 9.66 | -16.72 | 0.63 |

Benchmark | 8.67 | -44.82 | 0.36 |

Table 1. Portfolios performance over the period from 1988 to 2008.

It is clear that the 12-month lookback performed the best over all three indicators. Nevertheless, the 3-month lookback performed quite well, still better than the equal weight and the market benchmark.

**Results over the 2009-2019 period**

In the following eight figures, we show the simulation results over the period from 2009 to 2019, first for the 12-month, and next for the 3-month lookback periods.

Figure 9. Portfolio performance for model timing with 12-month lookback from 2009 to 2019.

Figure 10. Annual returns for model timing with 12-month lookback from 2009 to 2019.

Figure 11. Drawdowns for model timing with 12-month lookback from 2009 to 2019.

Figure 12. 3-year and 5-year rolling returns for model timing with 12-month lookback from 2009 to 2019.

By looking at Figures 9, 10, 11 and 12, we see that the timing model with 12-month lookback period performed the worst overall. It produced a much lower return than the other portfolios with the largest drawdowns.

Figure 13. Portfolio performance for model timing with 3-month lookback from 2009 to 2019.

Figure 14. Annual returns for model timing with 3-month lookback from 2009 to 2019.

Figure 15. Drawdowns for model timing with 3-month lookback from 2009 to 2019.

Figure 16. 3 and 5-year rolling returns for model timing with 3-month lookback from 2009 to 2019.

In Table 2, we give the numerical values of some selected performance indicators for the timing models, the equal weight and the benchmark portfolio.

CAGR % | maxDD % | Sharpe ratio | |

Momentum 12-month | 3.11 | -23.12 | 0.29 |

Momentum 3-month | 13.88 | -4.97 | 1.13 |

Equal Weight | 8.96 | -3.21 | 1.16 |

Benchmark | 12.97 | -4.52 | 0.94 |

Table 2. Portfolios performance over the period from 2009 to 2019.

The main observation from the Figures 9 to 16, as well as from Table 2, is that the 12-month lookback performed the worst over all the performance indicators. The momentum strategy with a 3-month lookback period performed the best. Still, one can argue that for this long bull market, the best strategy was the buy-and-hold. The difference in performance between the 3-month momentum and the market benchmark is relatively small. Both strategies produced excellent results, much better than the historical average.

**Takeaway for Investors**

The performance of momentum asset allocation is quite sensitive to different values of the lookback period used for comparing the relative strength of the assets. We have shown that the optimal value of the lookback parameter is not stable and may vary in a very wide range. While the 12-month period was the best in the 21 years from 1988 to 2008, the optimal value of the period switched to a very different value of 3-month during the next time interval from 2009 to 2019.

While many academic studies determined that a 12-month lookback period for evaluating the momentum factor had the highest average returns over most of the last century, we suggest that it is not advisable to blindly apply that result. Markets are evolving and the optimal value of the lookback period is drifting. Therefore, investing strategies should be flexible and should allow for variability in their parameters. The search for strategies with constant optimal parameters over long historical intervals may be counterproductive.

**Disclosure:** I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.