Tag: momentum

Fractional Momentum

Investors love the returns of momentum strategies but hate its crashes. And there have been numerous attempts at making momentum investing smoother. After all, where there is demand, supply will be created. But, what if, momentum and crashes are two sides of the same coin? Is Momentum without crashes even possible? What if Volatility is Nature, not Nurture?

Last year, we had a look at the The High-To-Price (HTP) Momentum Strategy (backtest, live model). It lived up to its promise of low-drawdowns by staying in cash during the most recent market downturn. However, if it ends up being slow to react to market recoveries, then it will underperform at the beginnings of new bull-markets. It is yet to go through a full cycle (bull-bear-bull) for us to be 100% confident about it.

More recently, we back-tested trend overlays on momentum strategies (Part I, II, III). It is still early days.

Broadly, the biggest problem with the momentum strategies is that they are path agnostic – they all look only at asset returns. The raw signal treats a stock making a parabolic move and a stock making a gradual climb the same. The filters come in later. What if there was a way to incorporate the path as well?

We took a shot at this problem with our Dynamic Linear Model strategy that simply regressed prices to a 45* line and ranked them based on goodness of fit. The performance has been good but not great.

So, it was with great expectations that we teared through Momentum Without Crashes (SSRN). The authors take a fractional differencing approach to overcome the loss of path information. The fractionally differenced log price series is i.i.d. so the next period prediction of the differenced series is simply the mean of the series. This “predicted value” is then inverted to arrive at a prediction for the next-period log return. These predicted log returns are ranked and a portfolio is constructed. The differencing parameter d is computed empirically. Intuitively, d=1 will result in a traditional momentum portfolio and d=0 yields a reversal portfolio. The authors find that d=0.9 is optimal.


We did a full-sample back-test on monthly returns for the top 200 stocks by free-float market-cap between 2014 and now for d=0.9.

The Fractional Momentum strategy, as the authors call it, out-performs the NIFTY 50 index and the NIFTY 200 Momentum 30 index. However, it does have its periods of under-performance and it doesn’t quite live up its promise of avoiding crashes.

The approach is pretty interesting and they have tested it across multiple markets so we created monthly-rebalanced and momo versions of this strategy to see how it tracks in the real world.

You can find the charts for d in [0, 1] on github.

Trending Momo Models

Previously, we discussed how applying a trend filter to a midcap momentum index could make sense. Then, we extended that to our homegrown momentum models. In both cases, there are certain situations where trended momentum side-steps deep drawdowns. However, if you are only looking at “raw” returns, you would be better off with monthly rebalanced momentum versions.

In this post, we run a similar test on the Momo versions of our homegrown momentum models.

Momentum (momo)
Velocity (momo)
Acceleration (momo)

The problem with high turnover strategies, beyond transaction costs, is the higher operational risk it entails. You could probably get away with postponing trades by a day or two in the monthly rebalance strategies but with these, you need automated trading systems.

You can track these strategies here: Tactical Momo (Momentum), Tactical Momo (Velocity) and Tactical Momo (Acceleration).

Code and charts: github

Trending Momentum Models

Momentum is known to trend. Our previous post explored trend overlays on momentum indices. The question now is, does it make sense to do the same to our own homegrown momentum models?

Our Momentum, Velocity and Acceleration models created between 2013 and 2015 have a monthly rebalance schedule. As a risk management measure, trailing stop-losses were introduced to them in 2016 and their momo versions – Momo (Relative) v1.1, Momo (Velocity) v1.0 and Momo (Acceleration) v1.0 – were born.

While these momo strategies do well with sudden market crashes, the problem has always been markets that grind down. Does a trend overlay on the original strategies perform better than momos after transaction costs?


The trend-overlay strategies seem to avoid drawdowns and perform better than their momo counterparts. The post-2020 Corona Crash market rally was one for the record books. So, a strategy that sidesteps the crash may not necessarily perform better during the rally but the full dataset will show superior performance. What if we took the crash data out of the picture?


It looks like Momentum and Acceleration strategies saw big pickups in performance. A trend overlay on Velocity resulted in lower drawdowns but that came with a big performance penalty.

You can track these strategies here: Tactical Momentum, Tactical Velocity and Tactical Acceleration.

Code and charts: github

Trending Momentum

Can a simple moving-average be used to time momentum indices? Returns from 2010 through 2015 of NIFTY MIDCAP150 MOMENTUM 50 TR and NIFTY200 MOMENTUM 30 TR under different SMA strategies look like this:

It appears the moving averages with short lookbacks can at least help reduce drawdowns, if not boost returns. If you pick the “best” config from the dataset and apply it across data from 2016 through 2022, it looks promising.

Should expect trend returns to be much lower after incorporating taxes and transaction costs but the lower drawdowns merit a closer look.

Given how our trend-midcap strategy has performed, we expect trend effects to be stronger in midcap-momentum than in the largecap version.

Code and charts: github

Volatility and Returns of Momentum Indices

The standard deviation over 200-days and future 20-day returns from 2010 through 2015 of NIFTY MIDCAP150 MOMENTUM 50 TR and NIFTY200 MOMENTUM 30 TR looks like this:

Can historical volatility, as measured by standard deviation, be used to enter and exit momentum strategies?

On a rolling basis, there doesn’t seem to be a strong correlation between historical volatility and future returns. Back-tests over this period might give you a config that might look like it works but it is probably a fluke.

Given that liquid ETFs for these indices are not available and we are stuck with index funds for the foreseeable future, we setup a back-test to calculate the 200-day std. dev. at the end of each month to decide whether to hold it for the next month. Needless to say, the results were pretty lackluster.

We chose the 2010-2015 period because it avoids the 2008 crash and the subsequent recovery. The back-tests look phenomenal when you include that data but we wanted to see how such a strategy would perform in “normal” markets before stress-testing it. We don’t want to be the generals always fighting the last war.

Code & charts: github