The Factor Zoo and the Animal that is MomentumThe Factor Zoo and the Animal that is Momentum

Capitalmind Financial Services Private Limited | SEBI Registered Portfolio Manager: INP000005847

Popularized by John Cochrane, the “factor zoo” describes an ever-growing pool of factors that claim to explain asset returns. A factor is any measurable characteristic or thematic attribute of a security (stock, bond, ETF) that helps explain additional returns over what is expected by the market. The term zoo is meant as a critique of academics and practitioners that churn out hundreds of factors, which make it nearly impossible to distinguish genuine market signals from statistical noise. This article is meant to make sense of this landscape by studying one such animal in the zoo, momentum, closely. 

We do it in a few parts. First, we'll define the factor. Next, we break down the definition and the complexity around how a single description can have various interpretations depending on the choices you make. We also talk about why these choices matter and how you should have the proper reasoning for it. Finally, we look at well known momentum indices and their interpretation of the definition.

Defining the Animal

To illustrate how absurdly vast the zoo is, let us walk through the process of identifying a factor. It will also showcase how trivial it is to do so. As advertised, we’ll talk about Momentum, the factor that has built Capitalmind Wealth’s quantitative identity over the past 7 years. The definition of momentum states that stocks that have done relatively well in the recent past will continue to do so in the near future. The italicized words are the knobs, what we practitioners call parameters, that you can turn to arrive at your own version of momentum. For example, the top 50 stocks that have delivered the highest returns over the last 3 months will carry on delivering the highest returns for the next 1 month. Now, imagine the permutations that statement can have. 

The Tyranny of Choice

While intuitive, the actual factor strategies produced by academics are more nuanced. Primarily, two things change. 

• First, instead of a fixed number of stocks, 50 in our case, the process usually consists of investing in a slice of the stock universe, say 10% or 25%. This results in the number of positions changing as the size of the universe changes. 
• Second, factor investing typically has a long and short leg. You not only buy the winners but sell the losers as well. The reason this is done is to strip the strategy of market exposure so that whatever returns remain can be solely attributed to being exposed to momentum.
  For example, if the whole market rallies, everything goes up alongside the winners. We can’t say the winners won because they had momentum or simply because they rode the wave. Shorting the losers cancels out the tide.

However, we digress. The focus is to address how extensive a single definition can get. 

Even the pioneers of momentum investing, Jegadeesh and Titman, came up with 16 different momentum factors by turning just the lookback (recent past) and holding (near future) period knobs. We ran all sixteen on NSE-listed stocks. The table below shows the compounded annual return of each combination over more than 15 years, going long the top decile of stocks by trailing return and short the bottom decile, with no gap between the lookback and holding windows. To keep the exercise realistic, we restricted the universe to the top half of the market by capitalization. Momentum in illiquid smaller caps looks great on paper but is difficult to trade. 

Rows are lookback periods and columns are holding periods. So the top left number is a strategy that ranks stocks based on their performance in the last 3 months and holds them for the next 3, returning 16.78% a year. 

The obvious takeaway from the table is to hold stocks for shorter periods, and to look back over shorter periods too. Momentum does better when you change the portfolio more frequently. That makes intuitive sense. Momentum decays. The stocks leading the market today aren't the ones that led it a year ago. A portfolio you leave untouched slowly fills up with yesterday's winners. 

This raises a question about the allure towards quarters. This grouping isn’t arbitrary and it also isn’t justified by the fact that these combinations earn attractive long-term returns. One economic explanation as to why momentum works is the “slow diffusion of information”, the idea is that news about a company travels more slowly than we assume. When new information about a company emerges, not everyone gets to know it at the same time. The price adjusts as more investors learn of the news and act on their convictions. Since companies report earnings every quarter, aligning the lookback and holding periods to the same frequency as that of information disclosure is one way to expose yourself to momentum, assuming the initial hypothesis holds true. 

However, having a 3-month lookback and holding periods are a choice. Nothing stops us from being more granular. Three months is roughly 63 trading days, so why not have a lookback period of 64 days and a holding period of 62 days? Play around with both those parameters together and the neat sixteen combinations we showed earlier balloon into hundreds. 

Now layer on the other knobs that we haven’t even touched. How do you define stocks having done well? Raw returns or risk adjusted returns? How much of the universe do you hold? The top 10% or the top 30%? Each combination creates another species, and the animal we started off with turns out to contain a zoo of its own. 

“If you torture the data long enough, it will confess to anything.” — Ronald H. Coase

The point here is not to get the best combination of knobs that would have delivered the best returns. Like we said, it takes negligible effort to come up with a factor. On the contrary, the point is to take a step back. At the core of all factor investing is a testable hypothesis. The uncomfortable part is the ease with which one can rig their test. Find the right window within the right universe and the right set of knobs, and you may find yourself to be the master of the markets. The data will support almost everything if you look enough. But you might end up building a factor that earns generational wealth in the backtest and wipes you out in the real world. All this boils down to having economic intuition, not just statistical evidence, as to why a factor is working. 

Relatively Speaking

That brings us to another knob, and a good example of why statistical evidence should validate economic intuition, not replace it. There's a word in the definition we've been taking for granted. Stocks that have done relatively well. The question is, relative to what. So far, the answer has been “to each other”. Assuming a long-only constraint, which is a realistic one in the Indian market, this means a falling stock can be top ranked as long as it falls less than other stocks. This is relative momentum, i.e., performance relative to other stocks. This is the version that academics like Jegadeesh and Titman, and indices such as Nifty 200 Momentum 30 and Nifty 500 Momentum 50 mean when they talk about momentum. 

Another way to interpret “relatively” would be comparing a stock against itself. Has the stock gone up in the past 12 months? Here we view each stock in isolation and ascertain whether it has delivered a net-positive return above a fixed deposit return. This is absolute momentum, i.e., absolute performance on its own, and it follows a different economic intuition than relative momentum. 

Absolute momentum bets that a trend, once established, tends to continue. Relative momentum on the other end bets that the ordering of winners and losers persists. 

The difference isn’t just semantic or academic. Picture a market where all the stocks in our universe are falling due to a market correction. Relative momentum would stay fully invested, still holding losers, albeit ones who have lost less than others, but lost regardless. Absolute momentum, however, would fully go to cash when no stock is delivering positive returns. 

None of this is meant to be an advertisement for absolute or relative momentum, or for any one specific setting of knobs. Momentum isn’t a specific strategy one uses or doesn’t. It has a plethora of choices that need to be made. However, the choices need to be informed by what you’re trying to do and what your core hypothesis is about why momentum works in the first place.

Animals in our Backyard

That’s enough theory. Let’s see how India’s two best known momentum indices construct their factor. Nifty 200 Momentum 30 and Nifty 500 Momentum 50, run on identical logic, just in different universes. 

A small note before we dive deep. Running a factor strategy has a lot of moving parts: selecting your stocks, choosing how much of each stock to own, and lastly deciding how often to make those choices. As you may have already noticed, this article deliberately focuses on how stocks can be selected based on a specific definition of momentum. How a stock is weighted and how frequently the portfolio is rebalanced warrants an article of their own. With that out of the way, let’s talk about the factor construction of the indices. 

What makes these indices interesting is how they set our two knobs. Starting with “stocks performing relatively well”, the indices don't rank stocks based on raw return. They rank stocks based on their performance adjusted by their risk, i.e., the stock's return divided by its own volatility. In other words, return per unit of turbulence. Two stocks that have gone up the same amount don’t get the same score; the one with a smoother ride wins. 

The lookback is where it gets fascinating. The indices don’t operate on a single lookback. They use the performance of stocks in the past 6 months and the past 12 months. Each is then divided by that same one-year volatility to get two risk-adjusted momentum ratios per stock. 

The indices follow relative momentum, so each stock is given a rank on both momentum ratios, higher the better. The indices combine the ranks over both the lookback periods into a single rank. The top 30 and the top 50 on the combined momentum rank are then chosen by the Nifty 200 Momentum 30 and Nifty 500 Momentum 50 respectively. 

Just a heads up, before you let the animal indoors. Our explanation belies the ease with which these indices select their stocks. There is a particular sequence of steps that these indices follow in constructing their factor and flipping any one of them changes things materially. These indices are also a unique example where weighting of the stocks in the portfolio is also dependent on their momentum-based ranking. Changing the rationale of the factor definition upstream has far reaching consequences downstream. 

Before You Start Turning Knobs

All of this to say that constructing your own factor means working in a world where data will have you wear rose-tinted glasses when looking at backtests. Guarding against that takes more than a solid hypothesis. Every step from hypothesizing to factor construction has to be a deliberate decision, each with its own economic rationale. The hypothesis that you come up with must be validated by data, not informed by it. 

This is particularly critical in times when the in-sample (backtest) that promised so much, failed out-of-sample (in the real world). Was it an unfavorable market regime? Were the stocks that were selected an accurate representation of the factor? Was the factor an accurate representation of the hypothesis? The answer to all these questions can only be found if you understand the economic intuition before tweaking the knobs to find your own species of the factor. 

The factor zoo isn't just large because there are many animals in it. It's large because every animal, when looked at closely, becomes a zoo in itself. Momentum was only one of the several we chose to walk through today. 

That leaves us with a question that we’ve not touched upon yet.

Why We Are Writing this Piece

Capitalmind Wealth (our PMS business) was one of the first in India to operate a momentum portfolio. We have written about factor-based investing (especially Momentum) for a long time as researchers and practitioners. Our Adaptive Momentum investment approach has been live since March of 2019. Over its history of more than 7 years, the strategy has delivered a CAGR of 17.4%, and at its peak, the strategy managed over ₹1000 crores in AUM. As we have managed this strategy for close to a decade, our understanding of how momentum works in Indian markets has also evolved. As the strategy went through more economic cycles and regimes, the more data we had to understand its performance or lack thereof. Therefore, the strategy of Adaptive Momentum, too, has evolved over time.

Now that we have discussed the two primary flavors of momentum, relative and absolute, your natural question would be “So how does Capitalmind Wealth construct its momentum factor for the Adaptive Momentum Investment Approach?”. In an upcoming article, we’ll walk you through our rationale, process, and the other moving parts of our quantitative model for running our Adaptive Momentum investment approach. Stay tuned for how we have a fresh and more-robust approach to running a momentum portfolio in India.

 

 

 

Capitalmind Financial Services Private Limited is a SEBI Registered Portfolio Manager (INP000005847). This post is for informational purposes only. Nothing here constitutes investment advice, a recommendation to buy or sell any security. Past performance of any strategy does not guarantee future returns. Please consult your financial advisor before investing.