Category: Investing Insight

Investing insight to make you a better investor.

Does Momentum Trend or Mean-Revert?


We consider long-only momentum returns to be composed of market returns plus excess returns.

If excess returns over a specified period, n-days, (say, 5- or 10-days) either trends or mean-reverts, then that can be used to trade the momentum portfolio.

One way to check if a time-series is trending is to calculate the Hurst exponent (H) over a rolling window (say, 5-years) of n-day excess returns . If H < 0.5, then the time-series is mean-reverting; if H > 0.5, then it is trending, else it is random.

A simple strategy would be, for H < 0.5 (mean-reverting), if excess returns is greater than its median, then exit or if excess returns is less than its median, then enter.

The problem boils down to specifying the excess-return calculation periods (n-days) and the Hurst exponent rolling windows so that it makes sense (avoid data-mining.)


We use the Barclays Euro-zone, UK, Japan and US momentum index data-sets to run our experiment. Since they provide both an excess-return index and a total-return index, we can use the former to time entries and exits in the latter.

We ran for two n-day configurations: 5 and 10. We set the Hurst (and median) rolling window at 5-years.

We expected to find H to be either consistently above or below 0.5. My personal expectation was that H would be above 0.5 (trend.)


Using the Hurst exponent did not improve momentum returns. In both 5-day and 10-day configurations, a strategy that went long if n-day returns were less than their median out-performed those that incorporated H.

The back-test using 5-day returns mostly worked on Euro-zone and US momentum indices. So we are skeptical that this approach can be generalized and it will likely fall prey to data-mining.

The back-test using 10-day returns saw buy-and-hold emerge a consistent winner.

The 5-day H toggled between trending and mean-reverting but spent most of its time trending. The 10-day H was consistently trending. For the specifications that we tested, momentum excess returns trends.

Code and Charts

The R code is here: 5-day and 10-day config. You can login to pluto and play around with the lookback and statWindow variables to see how H, median and back-test results change.

Questions? Ask them over at our slack workspace.

The Buy and Hold Bet

The biggest bet that buy and hold investors of a given country are making is that their government stays committed to increase, preserve and protect their citizen’s wealth. It is a combination of regulation, property rights, human capital, investor sentiment and global capital flows.

Buy and hold worked out great for US investors in the last 30-years. Inflation was mostly under control and they enjoyed a dollarized world with the rest of the world sending their surpluses to the US. But It wasn’t always like this.

The year 1980 was a turning point for US bonds and equities. Not that there weren’t hiccups along the way – Black Friday, tech bust, GFC, etc – but it was the beginning of a huge tail-wind that continues to blow even today. Compare the simulation results of pre-1980 equity returns vs. what came next:

Pre-1980: 5% possibility of loss in a buy-and-hold portfolio
Post-1980: 0% possibility of loss in a buy-and-hold portfolio

The post 1980 data-set is so skewed that when you use the entire data-set – 1964 through 2019 – for running the simulation, you end up with a 0% loss as well.

1964-2019: 0% possibility of loss in a buy-and-hold portfolio

With this data-set, it is easy to conclude that a buy-the-market “passive” buy-and-hold strategy is superior to everything else. But that would be a very aggressive conclusion to draw.

There are quite a few countries with equity returns (since 1993) in the low single digits: GREECE, CHINA, JORDAN, JAPAN, IRELAND, AUSTRIA, PAKISTAN.

CHINA, a country that grew its GDP in double digits, was a very poor equity investment. And JAPAN was the world’s second largest economy in 1995 but their equities are a joke on twitter.

Only DENMARK, USA and SWITZERLAND had an extremely small chance of posting negative buy-and-hold returns.

Out of the 43 Country specific MSCI indices we analyzed, half had more than a 10% chance of giving negative returns to buy-and-hold investors. India had a 6% chance.

6% possibility of loss in a buy-and-hold portfolio

Any analysis done on US stocks should be taken with a pinch of salt. The rest of the world does not work that way.

This post expands on an earlier one on the same topic.

Buy and Hold probably works only for US stocks

Social science research is said to have a WAGS problem. Most of their research is based on White American Graduate Students and fail to replicate in the real world.

Finance has a similar problem where, thanks to the depth of the data available on the US markets, most investment research is based on American data.

And US data clearly demonstrates the superiority of Buy and Hold. Over a 25+ year period, the probability of ending up with a loss is less than 0.1%


If future returns are in the same vein as their past returns, US investors would be fools not to buy and hold forever.

However, this does not mean that the rest of the world should do the same thing. Every market is different. The Japanese experience is a study in contrast.


The probability of a negative outcome is a whopping 21% for them. i.e., there is a one-in-five chance that investors will not make any money investing in Japanese equities. If past is indeed prelude.

Indian investors have been better off than their Japanese counterparts. There is only a 6% chance of not making any money investing in Indian equities.


All this goes to show that the US is a statistical outlier. “Buy and Hold” working in the US is an outlier. In every other market, there is a non-trivial chance that you will not make any money buying-and-holding equities.

When you look at research based on US markets, keep in mind that the probability distribution of returns that it is based on are an outlier. Anything that is long US equities will “look good.”

All investing is forecasting. And these probabilities will change – we are talking about equity markets after all. But know this before you adopt the “buy and hold” mantra.

Portfolio Churn

There is a famous scene in the “Wolf of Wall Street” where Matthew McConaughey (Mark Hanna) is explaining to Leonardo DiCaprio (Jordan Belfort) the concept of fugazi:

Mark Hanna: Number one rule of Wall Street. Nobody… and I don’t care if you’re Warren Buffet or if you’re Jimmy Buffet. Nobody knows if a stock is gonna go up, down, sideways or in f***ing circles. Least of all, stockbrokers, right? You know what a fugazi is?”

Jordan Belfort: *Fugayzi*, it’s a fake.

Mark Hanna: *Fugayzi*, fugazi. It’s a whazy. It’s a woozie. It’s fairy dust. it doesn’t exist. It’s never landed. It is no matter. It’s not on the elemental chart. It’s not f***ing real.


Gross returns of a high turnover portfolio is just that – fugazi.

Assume that there is an investment strategy that produces 12% in gross returns every year. Notionally, $1 should grow to $3.11 in 10 years. However, even if you assume brokerage charges are zero, demat charges don’t exist and there are no other taxes whatsoever, STT – Securities Transaction Tax – will take a slice of the portfolio at every churn.

A x600 churn, where 25% of the portfolio is replaced every month, will leave you only $2.94 in 10 years. A x1200 churn, where 50% of the portfolio is replaced every month – not uncommon with most momentum strategies – will leave you with only $2.79.

12% notional returns

And STT is not the only tax that is paid on a direct-equity portfolio. Capital gains tax of 10-15% also apply. These taxes have a non-linear impact on a portfolio’s compounded returns.

Investors should keep these in mind while comparing direct-equity portfolio returns.

Also, mutual fund NAVs are net returns. It is highly inappropriate to compare gross direct-equity returns with mutual fund NAVs.

Code for this analysis can be found on github. You can play around with it on pluto.

Mid-caps vs. Large-caps – A false choice?

It is generally believed that mid-caps give better returns than large-caps. But if you compare their historical returns, the difference is minuscule.

Is the pain worth the gain?

But mid-caps have often inflicted a lot of pain on their investors – spending most of their time in drawdowns. There is no diversification benefit because both of them play in the same circus. If you are a buy-and-holder, why bother with mid-caps at all?

Check out the notebook on pluto. You can play around with it once you login with your github account.