Happy new year!

I have noticed that my quantitative posts get the most readership and discussion. So this year, I’ll be posting a lot more research and will start the year off by exploring momentum’s robustness.

There are two good ways to test the robustness of a rules-based trading strategy:

**The test of time**- how does the strategy behave in different market regimes?**Parameter sensitivity**– how stable is the performance if the strategy’s parameters are varied

__Test of Time__
The goal is to see how well a strategy performs over a very
long-term, under different market conditions. Gary Antonacci has some good
articles on the importance of having a long-backtest period (see

*Bring Data*and*Bring More Data*).In 1937, Cowles & Jones did the first paper showing that 12-month momentum works. In 1967, Robert Levy did the first computer backtest on momentum. In 1993, Jegadeesh & Titman wrote their seminal paper showing 3-12 month momentum works. Also in that year, Eugene Fama (father of the efficient market theory) called momentum the "premier anomaly."

In 2013, Geczy and Samonov published a paper showing a momentum backtest that went back over 200 years. The following year, Greyserman and Kaminski did an 800 year backtest. Both papers show that the momentum anomaly is persistent over the long-run.

The table below is how the

*Global Equities Momentum*(GEM) strategy has performed from 1971-2015.
While these results are nice, looking at cumulative outperformance
over a backtest period is not enough – we should also look at individual
periods within the data.

I did a post a while back showing what happens when we add
Gold to the GEM model (see

*Should we consider gold?*). GEM’s annual returns (since 1970) jumped from 18% to 21% by including gold. At first glance, this sounds exciting. But a closer look showed all this additional gain came from the 1970s when the US went off the gold standard. No longer being suppressed, the price of gold rapidly rose in just a few years. We need to be careful not to be misled by these types of one-time events.
The graph below shows that equities (red and green lines) had
a secular bear market during the 1970s and 2000s, and a bull market during the
80s and 90s. In both market types, GEM (blue line) did well.

Let’s dig further with a longer period of data. How does
momentum do on a decade-by-decade basis?

Meb Faber looked at this in his paper “

*Relative Strength Strategies*” (read here). The table below shows the outperformance each decade of a US sector momentum strategy (hold the top performing sector and rebalance monthly) compared to the entire US stock market.
While some decades were better than others, momentum had
positive alpha every decade since 1930. This is an indication that the momentum
anomaly has persistence.

OK, all this looks nice however…

While momentum (and all trend-following) strategies tend to
perform well in trending markets, they typically fail in very erratic, sideways
markets. An extreme market-regime test is to see how momentum would fare using
Japan’s Nikkei stock index, which has traded sideways for 30 years. This will
be the topic of my next post. Let’s continue on.

__Parameter Sensitivity__

Any quantitative strategy has one or more input variables. GEM
has two: the

*lookback period*(length of time over which past performance of assets is measured) and*rebalancing period*(how often you check for a new trading signal). GEM’s recommended parameter settings are 12 months for the lookback and monthly for the rebalance.
By varying these input parameters, we want to see how the
strategy’s performance changes. I want to be clear: this is NOT done to find
the optimal parameter settings. That would be data mining. Instead, this test
is done to determine the model’s sensitivity. A sign of a robust trading
strategy is one whose performance is not affected by small changes in its
settings.

*Note: The analysis that is presented below was done using daily data and MATLAB software. Source code and data is available upon request.*

We first look at how GEM’s performance (between
1988-2016) changes as we vary the rebalancing period from 1 to 100 trading days
while keeping the lookback period constant at 12-months.

We see from above that a rebalancing period between 15-25 trading days results in returns performance that is stable while providing high returns and low portfolio
turnover. This confirms the recommended setting of 20 trading days (1 calendar month).

It’s interesting to see that a rebalancing period less than 10 trading days results in very high portfolio turnover and with lower returns
(due to whipsaw losses).

__There is absolutely no reason to be doing weekly rebalancing with GEM__.
Next, we look at how GEM’s performance changes as
we vary the lookback period from 30 to 500 trading days, while keeping the rebalancing
period constant at one calendar month.

We see above that any lookback period less than 200 trading
days results in higher whipsaw losses and higher portfolio
turnover. A lookback between 250-350 trading days results in stable performance with fairly low
portfolio turnover. This confirms the recommended setting of 12 calendar months (250 trading days).

The 12 month look back period was first discovered by Cowles
and Jones in 1937. Various other research since then has shown momentum works
best with monthly rebalancing and a 12-month lookback period. The results above
confirm this, as well as demonstrate how the prior research has held up since
it was first published.

__Conclusion:__
Momentum has passed several checks for robustness. It has proven
itself over a long backtest period and in different market regimes. In
addition, the performance of a simple momentum strategy like GEM is not
sensitive to small changes in the strategy’s parameters.

I often get asked about using much shorter rebalancing and
lookback periods to be able to adapt faster to market changes. Up until now, I
have just verbally been telling people that this would create higher # of
trades and whipsaw losses. Now I can back up my recommendation with
quantitative evidence.

I leave you with Dilbert’s take on model sensitivity.

*Results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Additional information regarding the construction of these results is available upon request. Past performance is no assurance of future success. Please see our*

*disclaimer page*

*for more information.*