Category: Investing Insight

Investing insight to make you a better investor.

Factor Momentum Performance Update

Factor performance tends to be sticky. If Value, Momentum, Quality, etc. out-performed in the recent past, they continue to out-perform in the near-future.

AQR wrote a paper on it back in January 2019: Factor Momentum Everywhere. More recently, the folks at Research Affiliates extended the research in their Factor Momentum paper. Based on AQR’s research, we setup a portfolio that mimics this for both US and Indian stocks in December 2019. We called it Factor Momentum III and Model Momentum Theme.

The performance of the US portfolio has been gangbusters. It sidestepped the Corona Crash of 2020 and has been on a tear since then. The Indian experience, however, has been disappointing.

US Factor Momentum

The Indian portfolio suffered from its inability to go into cash/bonds during crashes. Being fully invested took a bite out of its overall performance.

India Factor Momentum

The Indian version comes up short even if you compare its stats with its component factor portfolios.

India Factor Momentum Statistics

The intuition behind the Radar Plot above is that the larger the area under the points, better the strategy. Model Momentum is in pink and it pales in comparison to most of its constituents. Surprisingly, the Financial Strength Value Theme (light green,) that is rebalanced annually, beat out everything else.

What explains the underperformance?

  • Not being able to go into cash/bonds meant a larger hill to climb during recoveries. However, cash is a double-edged sword. If you get the timing wrong, you might end up going into cash after the bottom and watch the market recover helplessly. Unless the trend formation period is really short, cash is not a viable option.
  • High transaction costs can also be playing a role here. The difference between Gross and Net returns is ~15%. Not as high as a pure momentum strategy but not trivial either. Also, US portfolios do not incur STT and brokerages are essentially zero.
  • Maybe 20-months is too short a window to judge such a slow-moving strategy. The research looks solid and maybe all we need is to give it some time?

Getting Started

We are often asked by our readers to help them chart out a path for their investment journey. While we strongly believe that each investor’s risk appetite, hopes and goals are unique, we also understand that there are a lot of choices in front of the investor and sometimes, it could get overwhelming.

Here’s the path of least resistance:

  1. Go through Zerodha Varsity
  2. Understand the need for diversification and that there are not easy answers. No risk, no return.
  3. The best way to get started managing your own portfolio is to just dive into it. Onboard yourself onto our broker and get started on one of our momentum strategies. Great for portfolios between Rs. 15-30 lakhs.
  4. As a broker, we do not charge any additional fees for access to our strategies (over 50+, at last count.) And, you don’t have to worry about execution – we’ll take care of that.
  5. For larger accounts, where portfolio sizes are more than Rs. 25 lakhs, we offer customized solutions that typically involve risk-barbells. Get in touch with us!

We will keep this page updated as we go along – check back often!

Ranking and Visualizing Model Performance Metrics

On StockViz, we have over 50 quantitative models that are available for investing. They all have different risk and return profiles. It is fairly simple to pull up, say, the Sharpe Ratio of a particular model by navigating to its home page. However, it doesn’t say how it compares to all the other models we have going.

Let’s say you are looking to invest in one of our “Rapid-fire” Momo strategies. Our oldest ones are Relative, Velocity and Acceleration. Their (gross) performance metrics are displayed in a table.


If you add net performance metrics into the mix, you’ll end up with a combinatorial explosion. How do you pick the “best” one of them to invest in?

Enter Radar Charts.

These charts show you the relative rank of each of these models against all the other 50+ models we have going. Intuitively, larger the area under the yellow (net) lines, better the model.

The only caveat with these Radars is that you should compare them against models of similar vintage. For example, we went live with our All Star momentum model in May 2020. Since then, the market regime has been extremely favorable to momentum strategies. It should come as no surprise that its Radar looks like the Queen’s Crown.

With that caveat out of the way, Radars are a great way to visualize how models square up against each other.

Zero Knowledge

And you thought magic was not real

“Zero Knowledge”, contrary to what it sounds like, is actually quite interesting and fun. It might even be a solution to our long standing problem of validating the world’s transactions without a trusted third party or government or central bank. If you Google for the terms Zero Knowledge and Blockchains, you will be flooded with whitepapers, articles, explainers, investment advice, and everything in between.

What does Zero Knowledge (ZK) even mean? Let me start with a toy example, and then we can work our way up to world peace.

Say we both get the same newspaper and it has a Sudoku puzzle in the games page. I claim to you that I know the solution to this puzzle, but will not tell you what the solution is. Being the frenemy that you are, you won’t believe me, obviously. Can I prove it to you, beyond reasonable doubt, that I do know the solution to this Sudoku puzzle, without telling you what the solution is? More formally,

  • If I know a solution, I should be able to convince you of that. Without leaking any knowledge about the solution.

  • If I lie about knowing the solution, I should be caught – with overwhelming probability.

If both the above are possible, that would be a Zero Knowledge Proof of Knowledge of a Sudoku puzzle. There are some ingenious ways of doing this, which rely heavily on cryptographic primitives and protocol design. In fact, it’s possible to convince an audience that you know the solution for almost any puzzle without giving them any hint of the solution itself. Sudoku was just one example. You could prove that you know the solution to a crossword puzzle, or the Rubick’s cube, or that you know a cycling route from New York to Seattle that’s exactly 5000km, or that you have paid your rent, or that your bank balance is more than $10,000 or any such statement really – without actually revealing the actual solution to the statement.

Imagine the power of such a system, where you could convince others that something is true, without revealing how it is true. In most real world systems, including financial systems, to prove something to someone, you have to reveal the actual facts of the matter – and thereby reveal more than you have to.

For example, getting a visa to any country requires you to provide your bank statement – just to prove that you can afford the trip. It should be possible to prove that you can afford the trip, without revealing any financial information. Also, the proof should be real – as in, if you cannot afford the trip, you shouldn’t be able to prove such a thing and fool the visa-issuing agency. We want both sides, the prover and the verifier, to win. Just with no leak of extra information. The best kind of privacy, if you will.

Where is Waldo?

First, I will give an example of how such a Zero Knowledge protocol looks like, to make you believe that it’s possible. Below is Waldo: Say Hi to him.

Waldo is somewhere in the amusement park image below. Can you find him? Don’t try too hard, it’s not worth it.

This “Where is Waldo” puzzle lends itself very well to a Zero Knowledge protocol. I can prove it to you that I know where Waldo is without revealing his actual location on the image. How do I do that? We run the following protocol between the two of us.

  1. You blindfold yourself. I keep a large white sheet of paper on top of the amusement park image, and ask you to remove your blindfold. You can give me one of two challenges. You should choose these challenges randomly.

    1. Remove the sheet of paper and show you the amusement park image underneath.

    2. Cut out a small hole in the white paper right above where Waldo is on the image. If I do this, I must know where Waldo is.

  2. Repeat step #1 till you are satisfied.

Why does this protocol work?

  1. If I know where Waldo is, I can easily answer challenge #2. That part is easy. It’s not so easy to figure out why challenge #1 is required.

  2. I could cheat by keeping some other image under the paper which has just many images of Waldo on it. How do you know that it’s actually the amusement park image and not some other image that I made up? Challenge #1 to the rescue. If you had asked me challenge #1, I had to remove the entire paper and show you that this was the amusement park image in question.

  3. Note that you cannot give me both the challenges at the same time, as that would tell you where Waldo is. Only one challenge per protocol round.

If we do this entire exercise just once, you could have asked me to answer challenge #2 and I could still cheat with a probability of 50%. If we do it twice successfully, I can still cheat with a probability of 25%. If we do it three times, it reduces to 12.5%. If we do it 10 times, and you picked your challenge randomly each time, I can cheat only with a probability of 0.1%. If we repeat this 20 times, the cheating probability drops to 0.0001%. And so forth, exponentially. Again, this only works if you pick your challenge randomly. If I know in advance that you will ask me the challenge sequence, of say, 122212121222111 – I can pass all challenges easily. The protocol works only if I am unable to guess your challenge sequence.

Cryptographic researchers have proven that almost any statement can be proven in zero knowledge. Imagine that! Any statement! It’s one of the most celebrated results in theoretical computer science, all the way back from 1986. The concept of Zero Knowledge Proof itself was introduced in 1985, after the original paper was rejected in major scientific conferences in the prior years because of how absurd the idea sounded. It still sounds counter-intuitive, if you ask me.

One popularly used ZK-proof system, solving a very specific problem, is that of Digital Signatures. When you digitally sign a document, you are proving to the verifier that you know a secret key to your public key (which the verifier already knows, or is tied to your identity, or some such). For the longest time, general purpose ZK-systems, which could prove any statement, were just theoretical results – the actual proofs themselves can be quite unwieldy and inefficient. Theoretical work continued, but there were still no practical applications that needed these proofs to get smaller, or easier to understand, or even remotely workable. 25 years went by, and people were mostly happy with either revealing everything about something to prove it, or having a trusted third party (like a Bank Officer or Notary) signing a statement saying that something is true, without revealing the underlying details. Ho-hum.

Enter Bitcoin!

Bitcoin removed the trusted third party from financial transactions. Or at least, introduced the idea that it could be done with clever cryptography and protocol design. Researchers who were toiling away in obscure labs and universities were suddenly like: “Hey, there are these amazing theoretical cryptography results from decades ago, let’s use them”. These ideas suddenly seemed ripe for more R&D to make them practical. And boy did the researchers and engineers deliver! Here’s a short list of how Zero Knowledge pervades the cryptocurrency space.

  1. New cryptocurrencies: Zcash, Monero, Grin, Beam, Mina, etc.

    • Everything about a transaction is hidden. Who is paying. Who is the recipient. What is the amount. Everything is hidden. Crucially though, verifiers can verify that the transaction is valid, and no one is cheating anyone. Zero knowledge magic. Details differ, but this is the general idea.

    • Additionally, Zero Knowledge proofs can verify large numbers of transactions without needing to store all those transactions. So, these ZK-blockchains can be as small as a few KB. For comparison the Bitcoin blockchain is 350GB and growing. Ethereum’s blockchain is 1TB or 5TB (depending on whom you ask) and growing.

  2. Layer-2: ZK-Sync, StarkNet, etc. bring the benefits of ZK-proofs to legacy blockchains like Ethereum and increase throughput quite dramatically.

  3. Other Proofs: Exchanges can use ZK-proofs to convince their users that they are not doing fractional reserve or rehypothecation shenanigans, and in fact, do custody all their customer assets.

What next?

Some of these general purpose ZK-systems have quite advanced cryptography, and their security guarantees are proven sometimes under ideal settings. When I say security guarantees, what I mean is:

  • Can the prover cheat?

  • Can the verifier learn something by violating the zero knowledge principle?

  • Can we do the entire thing without relying on cryptographic assumptions?

  • Some systems rely on an initial ceremony where some trusted party has to do one-off computation. Can we remove such requirements?

Practical minded people say that this stuff is too advanced, or “moon-math” as they call it. These primitives will not make it to Bitcoin for a LONG LONG time, if at all. Bitcoin’s cryptography is from an even older generation, and has been vetted in traditional settings like e-commerce, national defense, etc. No moon-math for Bitcoin!

That doesn’t mean that Bitcoin won’t benefit from these new developments. Bitcoin has evolved to a place now where the core protocol itself won’t change that easily, but additional features have to be built on top, in other layers. ZK-proofs will reside on a secondary layer somewhere on top.

Ethereum, on the other hand, is more open to these ideas. ZK-proofs are making their way into Ethereum’s core-system slowly, but will definitely pervade Ethereum’s Layer-2 ecosystem quite thoroughly in the near future. Much faster than in Bitcoin, from what I can see. Newer blockchains will go all-in, and will be built around ZK-ideas, or will offer them as native operators or subroutines.

You have the entire spectrum of blockchain platforms – some boringly conservative, and just trying to be sound money. Some others on the bleeding edge of maths, offering true privacy through ZK-proofs and the like. I expect these to become more mainstream as privacy becomes non-negotiable. Currencies, smart contract platforms, exchanges, and every other financial intermediary will go maths-first!

Our crypto series in reverse-chronological order:

Gross vs. Net Returns

The Government always has first dibs

First time investors often get bedazzled by tall claims of “20%” returns in direct equities. All they need to do is subscribe to an “exclusive” telegram channel or advisory service and mint their way to millions. Even if these claims were true, gross returns – the number often marketed – has little to do with the net returns that the investor finally realizes at the end of the year.

Very few know that a high-churn portfolio that delivers 20% gross returns is equivalent to a mutual fund that delivers 14% net. So, who ate your cheese?

Layers of Transaction Taxes

Securities Transaction Tax (STT)

The STT is an automatic tax collected by the government on all transactions irrespective of whether you made money on it or not. On equities, it is currently set at 0.1% – if you bought & sold 1 stock worth Rs. 100, then the government collects 20p on it. This is one of the biggest drags on high-churn strategies.

Last year, the government collected ₹16,927 crore in STT.1

Exchange Transaction Charges

The trading venue, typically the NSE (National Stock Exchange) or the BSE (Bombay Stock Exchange,) levies a transaction charge for allowing you to trade through them. This varies by exchange and they are know to give rebates to high volume brokers to keep them loyal. The last time I checked, it was around 0.00345% on the NSE.2

Stamp Duty

When the Central Government is skimming off through STT, why should State Governments be far behind? The states too have their hands in the till through “stamp duty.”

Stamp duty is a state levy paid to register a document, typically an agreement or transaction paper between two or more parties, with the registrar. In an era where all transactions are electronic and registering transactions is just flipping some bits in a database, this is basically free money to the states.

Before 2020, every state had its own rate but thankfully, the Modi Government rationalized it to a common rate of 0.015% on the buy-side of equities.3

SEBI Turnover fees

If you though that SEBI was an arm of the government and should be entirely funded by the general budget, the joke is on you. If you have a look at your contract note that the brokers sends you on the days that you trade, you’ll find a “SEBI Turnover Fee.” This is 0.00015% on both buys & sells. While its one of the smaller taxes/fees on transactions, it is still a percentage of total volume, so it adds up over time.4

During 2019-20, the total amount of fees and other charges collected by SEBI was Rs. 608.26 crore.5

Short-term and Long-term Capital Gains Tax

The rationale behind STT, introduced in 2014, was to replace the long-term capital gains tax. It was said that there was a lot of “leakage” in collecting LTCG and that a tax on transactions collected directly by the exchanges would plug it. However, the 2018 budget saw the re-imposition of LTCG.6

However, if your strategy demands churn, then you need to be worried more about STCG (15% on profits) than on LTCG (10% on profits.)

A High Bar of Direct-Equity

After all these taxes, levies and charges, when the numbers are tallied up at the end of the year, most direct-equity investors would be better off with a mutual fund.

The napkin math (sheet) above doesn’t consider brokerage – since those are mostly zero – and DMAT charges – those charged by CDSL – since those are flat fees charged only on sales.

Direct-equity investing strategies need to walk a fine line between optimizing for lower transaction costs, risk management and taxes. This is where we find advisory disclosures lacking. Most advisors do not disclose portfolio churn rates and nor do they indicate what the net, after-tax, returns would look like.

Also, a mutual fund’s NAV includes all of these charges and your portfolio compounds tax-free until you redeem. So, if you have a 5+ year time horizon, then compounding the 15% STCG adds significant tailwinds to your portfolio.


While comparing different strategies, investors should also consider portfolio churn and try and back into what the net, after-tax, returns would look like at the end of the year. Know that mutual fund NAVs are net of transaction costs and can compound tax-free.

Direct-equity strategies should clear a high-bar.

Looking for a sensible way to invest? Here’s how to get started.