The common follow-up to this phrase is “master of none,” which imparts a negative connotation on what could have been a reasonable compliment. As it applies to you and me, having a shallow understanding about a breadth of topics is often perceived as inferior to possessing specialized knowledge. However, perhaps even this full phrase is not entirely unfavorable when we apply it to quantitative models.
Suppose you are analyzing a simple momentum model across asset classes. You believe that momentum manifests itself somewhere over the range of 3 to 12 months, and you would like to investigate which time period has performed the best historically on each asset. At the same time, you are wary about picking different lookback periods for individual asset classes simply based on historical performance. Thus, in addition to 3, 6, 9, and 12 month periods, you decide to investigate a dynamic lookback window with the following properties:
1. When the volatility is 35%, the window should be about 3 months.
2. When the volatility is 10%, the window should be about 12 months.
3. The window should expand and contract as the volatility decreases and increases, respectively.
4. The window should be no longer than 12 months or shorter than 3 months.
A simple way to meet these criteria is to use linearly interpolation, where W is the window length in trading days:
W is then clamped to the range of [63, 252].
For the momentum measure, our model will generate an “on” signal when the closing price is above the SMA over the lookback period. To mitigate the effects of rebalance timing, we will turnover 1/21 of the portfolio each day depending on what the signal is, i.e. when the signal is on (off), we will increase (decrease) our holdings by ~4.75%. When the signal is off, we simply hold the uninvested fraction in cash at no interest.
We will look at the following asset classes using ETFs as proxies:
The charts below shows the fraction invested over time for US equities, gold, and long-term treasuries.
Momentum Holdings for US Equities
Momentum Holdings for Gold
Momentum Holdings for Long-term Treasuries
When the volatility increases, the dynamic window signal behaves more like the short-term momentum signal. Conversely, in periods of low volatility, the dynamic window signal acts more like the long-term signal.
The following tables show how the models performed on each of the ETFs. The results of each model were ranked based on Sharpe ratio, return to max drawdown, and average number of annual trades.
Sharpe Ratio Ranks
Return to Max Drawdown Ranks
Average Annual Trades Ranks
Shorter windows have historically performed better for long-term treasuries and commodities while longer windows have worked better for US equities and gold, based on these metrics. The dynamic window model consistently ranks in the middle of the pack and was even the master of a few asset classes.
While this investigation by no means proves that this form of dynamic momentum window is ideal, it does demonstrate the effectiveness of the method across asset classes. Some further areas of investigation might include looking at short portfolios using 1 minus the fraction invested, designating a neutral momentum signal, specifying different rules for the lookback window, and analyzing whether realized volatility is the best metric to use for window calculation.
Why do we care about having a model that works across asset classes? It is not merely a desire for a one-size-fits-all approach, but it’s more so a matter of robustness. We do not know whether each asset class will continue to behave as it has in the past, which means that a 12-month window that worked previously may fail in the future. Adapting to the fluctuating market environment is the primary concern, and by developing a model that is robust across asset classes, we can have some degree of understanding as to how the model would perform if one of those assets ever began behaving like another.
While this simplistic model may not be practical, its primary goal is to shed some quantitative insight into how a rules-based approach paired with a bit of intuition can improve upon more naive methods. Simple models can shed light upon complicated systems and help us to identify areas for further improvement (see this previous post for another example). Some particular problems with this simple model are:
1. Parameters or targets (e.g. volatility limits) chosen with the benefit of hindsight.
2. A constrained dynamic window with a constant range for all asset classes.
3. Fixed parameters rather than adaptive ones.
4. No account for whipsaw during periods of high volatility.
Newfound’s models and methods attempt to address these issues in ways that are both rules-based and designed to withstand the tests of dynamic markets by being adaptive and robust.
NOTE: All analysis in this post is hypothetical and backtested.