Category: Investing Insight

Investing insight to make you a better investor.

Synthetic Indices

Popular indices, like NIFTY 50 & MIDCAP 150, are useful if you are benchmarking long-only portfolios. However, if you have a long-short portfolio, then you need a long-short benchmark.

When Are Contrarian Profits Due To Stock Market Overreaction? (Lo, MacKinlay, 1990) describes a naïve portfolio construction process that is fit for purpose.

For momentum, portfolio weights are in proportion of excess returns over an equal-weighted index and for mean-reversion, they are the inverse.

For example, if you subtract the returns of each of the components of the NIFTY 50 index with the returns of NIFTY 50 EQUAL-WEIGHT index and divide by 50, you end up with the portfolio weights for the next day. Each look-back period used to calculate returns will produce a different set of weights (and a different synthetic index.)

As impractical as constructing such a portfolio may seem, they are useful as a benchmark for long-short mean-reversion/momentum portfolios. Here are index returns since April 2020 with 20- and 50-day look-backs.

This is especially interesting if you are looking at market dislocations and subsequent recoveries. Here are indices since June 2019 with 5-, 20- and 50-day look-backs.

Counter-intuitively, naïve mean-reverting long-short seems to out-perform momentum.

ETFs for Asset Allocation

Building blocks for a diversified portfolio

Over the last few years, most brokers in the US have started offering no-frills accounts with zero-brokerage and fractional shares. However, new investors who are just getting started are either over-served by advisors or under-served by social media. In this post, we list out ETFs that every investor should be aware of if they are interesting in building a diversified portfolio.

We filtered for

  • Assets under management (AUM) – larger the better

  • Cost (expense ratio) – lower the better

  • Liquidity and popularity – higher the better

We cover equities, bonds, real-estate and commodities across the US, DM (Developed Markets) and EM (Emerging Markets.)


The Vanguard Total Stock Market Index Fund ETF is a $250 billion whale of a fund that is probably the only equity ETF a small-ticket first-time investor should consider.

Covering the entire US equity market, it is as passive as they come. With an expense ratio of 3bps (you pay $3 for every $10,000 investment,) it is the cheapest as well.

ETF, Vanguard


The iShares Core U.S. Aggregate Bond ETF is one of the largest bond ETFs on the planet with $90 billion in assets. It has everything from treasuries, agencies, CMBS and ABS to investment-grade corporates. You pay 4bps for the privilege.

Split your funds 60% into VTI and 40% into AGG and you basically have a portfolio that has traditionally outperformed 99% of the hedge funds out there.

ETF, iShares

With the Big Two out of the way, if you still have some risk appetite and time on your hands, you can reach out for more returns (potentially.)


The Schwab International Equity ETF tracks all Developed Markets other than the US. With an AUM of $27 billion and an expense ratio of 6bps, it is a decent equity fund if you feel that US stocks are over valued.

Its largest exposure is to Japanese stocks followed by British, France, Germany, Canada and Switzerland. Unlike some other funds in this space, it also includes South Korea.

One caveat though, the fund is not currency hedged. The topic of buying hedged vs. unhedged ETFs is a topic that we will not get into right now. Suffice to say that hedging is not free – it is a price you pay to insulate yourself from fluctuations and you should weigh the cost vs. its benefits over your investment time horizon.

ETF, Schwab


The Vanguard Total International Bond ETF provides exposure to Developed Market (ex-US) investment-grade government and corporate bonds. It is a monster of a fund with $136 billion in assets. An 8bps expense ratio is a wonderful bargain.

The fund is currency hedged.

ETF, Vanguard

We are not fans big fans of EM/FM (Emerging/Frontier Markets) investing from the US through ETFs. In the recent past, these markets have only been a source of risk and not returns. Gains in local currencies, when converted to US Dollars, haven’t compensated for the additional risk. However, for investors who believe that the future is going to be different, these ETFs are worth considering.


The iShares MSCI Emerging Markets ETF is perhaps the largest in this space. $32 billion in AUM and a 70bps expense ratio, it is the go-to ETF for EM investors.

However, the wrinkle is that Hong Kong and China form more than 37% of the portfolio. For investors worried about geopolitical risk, this may be a point of concern. This is where EMXC comes in.

The iShares MSCI Emerging Markets ex China ETF is a minnow by comparison (less than $1 billion in AUM) but it doesn’t include China and Hong Kong, making it palatable. However, there’s another wrinkle while investing in EM – some of those countries are ruled by despots. What if you want to invest in EMs that are democratic and respect personal freedom? Enter FRDM.

The Freedom 100 Emerging Markets ETF tracks the Life + Liberty Freedom 100 Emerging Markets Index. The Index is a freedom-weighted EM equity strategy that uses human and economic freedom metrics as primary factors in the investment selection process. And this means excluding China, Hong Kong and India – 3 of the largest markets in EM.

ETF, iShares


The iShares JP Morgan USD Emerging Markets Bond ETF an index of US-dollar-denominated sovereign debt issued by EM countries. It holds USD-denominated rather than local-currency debt. This eliminates direct currency risk for US investors. With $20 billion in AUM and an expense ratio of 39bps, its an attractive fund for investors looking to diversify into EM bonds.

ETF, iShares

Now that we have equities and bonds out the way, lets look at real estate. A REIT is a publicly traded security that invests in real estate through properties or mortgages. For the most part, in the past, their returns were correlated to interest rates. From investopedia: In a study done by the S&P, which analyzed six periods beginning in the 1970s where the yield of the 10-year Treasury grew significantly, of these six periods of interest rate increases, REIT returns increased during four of them.


VNQ, The Vanguard Real Estate ETF has about $75 billion in AUM and charges 12bps. It captures much of the US real estate market.

VNQI, Vanguard Global ex-U.S. Real Estate ETF has about $5 billion in assets and an order-of-magnitude larger than the closest alternative. It contains property companies from both developed and emerging countries, excluding the United States. Japan, China and Hong Kong are the top three geographies where it invests. Like with any other EM/FM investments, caveat emptor!

Some investors view gold as a tail-risk and inflation hedge and some prefer to add commodities to their portfolio to ride on emerging market demand. While it is debatable whether these assets live up to their expectations in the future, there have been lengthy stretches in the past where gold and commodities have outperformed other asset classes.


GLD tracks the gold spot price, less expenses and liabilities, using gold bars held in London vaults. With about $65 billion in management and 40bps in expense ratio, its probably the best way to add exposure to the yellow metal in your portfolio.

PDBC holds a diverse basket of futures contracts on 14 commodities across the energy, precious metals, industrial metals and agriculture sectors. Has about $6 billion in AUM and its 59bps expense ratio is a bargain compare to the effort involved in actively managing a futures portfolio in a tax-efficient manner.

There are over 2500 ETFs listed in various US stock exchanges. We hope that our short list of 12 ETFs above helps investors get started. Do watch the discussion below:

Already have a basic portfolio and looking for quantitative strategies on US stocks and ETFs? Head over to

Transfer Entropy

In investing, we are always trying to find the relationship between two entities. For example, to hedge a long portfolio, we typically calculate the “beta” with respect to an index and use that to go short the index. Here, the biggest assumption is that the relationship is linear (or at least, piecewise linear.)

However, relationships in finance are typically non-linear. Using the math behind calculating entropy is one way to overcome the “beta” problem.


From Wikipedia: Transfer entropy is a non-parametric statistic measuring the amount of directed (time-asymmetric) transfer of information between two random processes.

It tries to answer a simple question: what the effect of one entity over another, given a lag?

From StackExchange: TE(X↦Y)=0.624 means that the history of the X process has 0.624 bits of additional information for predicting the next value of Y. (i.e., it provides information about the future of Y, in addition to what we know from the history of Y). Since it is non-zero, you can conclude that X influences Y in some way.

Quick Look

Luckily, both R and python have libraries that help calculate transfer entropies between two variables.

Here’s the TE between Stock Futures and the NIFTY with a 500 day lookback and a single-day lag. FLOW_TO is a measure of information flow from the stock to the index and FLOW_FROM is the opposite direction.

Next Steps

This has interesting applications in portfolio risk management. Instead of calculating beta and hoping for the best, we could use TE to get a better understanding of how the individual constituents are affected by the index and hedge only those that have large values.

This post was inspired by Concepts of Entropy in Finance: Transfer entropy. Code and images for this post are on Github.

DeFi for the rest of us

How zoomers trade baseball cards for Furbies

DeFi stands for Decentralized Finance.

Decentralized: Ideally, any single entity should not be able to stop the process or program or system in question. It’s running on some unstoppable system where anyone can execute operations.

Finance: Savings, Loans, Exchanges, Margin Trading, Synthetic Assets (Equities, for example), Lotteries, Insurance, Collateralized Debt Obligations (why not?), and such.

Before the advent of Bitcoin/Ethereum, financial products were run on a computer that some entity controlled. This entity had a physical address, and could be visited by law enforcement or regulators or more generally, whom I call “men with guns”. Bitcoin/Ethereum run on so many computers that it’s not possible for men with guns to stop it. Smart contracts running on Ethereum are hard to take physical control of – and stop, or modify unilaterally by men with guns. This is the decentralization that we are interested in. Because of this, we have “unstoppable programs”, at least in theory.

First, a simple example of where these “unstoppable programs” come in. Let’s say you want to buy some Ether. You could submit your KYC details to a centralized exchange like Coinbase or Kraken and get an account. You then wire-transfer some dollars to their bank account, with some routing instructions so that the money goes to your account. You wait for the dollars to show up in your dashboard, and then buy some Ether with it. You could let the Ether stay there (like how you let your money stay in a real world bank) or you could self-custody by transferring the Ether out to your own hardware wallet. Like you withdraw cash from a bank and self-custody under a mattress, for example.

Decentralized Exchange

BUT! Coinbase and its ilk are still “centralized” and men with guns can make them block your account. What then?

Enter DEX’es, or decentralized exchanges. Uniswap is one such DEX. It’s a set of smart contracts that run on the Ethereum network. The specific Uniswap smart contract that accepts USD and gives back Ether is located at the address 0xb4e1…c9dc on the Ethereum blockchain’s “main-net”. Think of it as the unchanging IP address of the smart contract on the Internet. If you make a request to this smart contract with some USD, and it returns some Ether to your address. Think of it as making a web-search request to with a query and getting back 10 blue links as the result. But to start this process, you need to have USD in a form that the smart contract can accept. Enter Stablecoins.


Stablecoins are tokens that 1:1-track external fiat currencies like the US Dollar or Euro, external (to the system in question) cryptocurrencies like Bitcoin. This token system is implemented as an ERC-20 token (which I explained in my post on NFT’s).

Take USDC for example, which is a stablecoin that tracks the US Dollar. Every token minted by the USDC smart contract can be redeemed for $1. How do you mint a USDC token? You create an account on Coinbase, you transfer USD to it, and you buy 1 USDC for 1 USD. This 1 USDC is an ERC-20 token that can be transferred from your Coinbase account to your computer, or some other contract, or exchanged on Uniswap for something else. The 1 USD you owned earlier is now on the Ethereum blockchain in the form of 1 USDC. To redeem this 1 USDC back to 1 USD, you transfer this USDC back to your Coinbase account, and sell if for 1 USD. Note again, that there is no USD, ever, on the Ethereum blockchain. Ethereum does not know about USD at all. All it knows is USDC. Coinbase is your bridge from the real world to the ethereal world.

Coinbase is able to redeem USDC to USD because they have a traditional bank account somewhere that stores the USD that backs the USDC.

Coming back to our earlier use case: now that you have USDC on Ethereum, you can use the Uniswap contract to buy Ether with it, without going through Coinbase for the swap. But hey, we had to go to Coinbase to buy USDC in the first place. So, didn’t we just move the trusted third party from the exchange to the stablecoin issuer? We did. But it’s not that bad. You can get USDC without going to Coinbase as well – it’s just an ERC-20 token that anyone can transfer to you on the Ethereum blockchain without permission from anyone else. And you can use this to exchange to any other token on Uniswap without anyone’s permission as well. If more and more of the economy “moves on chain”, the on and off ramps to fiat currencies like USD will become less important. But for now, someone, somewhere has to store 1 USD in a bank account to be able to generate the equivalent stablecoin “on chain”.

Automated Market Makers

So, how does Uniswap know the exchange rates for every token pair that it allows us to trade with? Each token-pair is run as a smart contract, where you can make function calls to swap one token for another. The smart contract also has a liquidity pool under its control which stores both the tokens in some ratio, and this ratio is used to infer the market price. The assumption is that if this ratio goes out of sync with the external market price, arbitrageurs will trade in the other direction to take tiny profits and revert the pool ratio back to reflect external market price. Users with excess liquidity in any token can fund these liquidity pools and take a small cut of each trade that hits their liquidity pool. We now have a liquidity provider who can get some yield on their capital. Notice that this system of smart contracts is not relying on any external data to be ingested into the system. The exchange rate between token is entirely set by market dynamics.

Let’s say you wanted to provide liquidity to the token pair ABC-XYZ on Uniswap, but you have neither token with you. On the other hand, you have more than enough Bitcoin that you want to HODL and not want to sell. Can we use this Bitcoin as collateral to get a loan of some ABC tokens that you can then use to fund the ABC-XYZ Uniswap pool? Enter DeFi loans.


In the traditional world of finance, loans are given out to parties with good credit rating, and defaults are prevented/mitigated by a combination of social pressure of reputational damage, law enforcement, liquidation of other assets, or such. In the world of cryptocurrencies, the users have just one identity – a public key, which looks like this: 0x12cb…Tu3S. How do you cause reputational damage to this public key? Traditional default protection ideas fail here. So most crypto-loans are, for that reason, over-collateralized.

You want to borrow 100 tokens of ABC? You put up 150 ABC worth of Bitcoin as collateral, and then you take 100 ABC. As long as the smart contract can convince itself that the loan remains over-collateralized, you are good. If the value of Bitcoin goes down, you are expected to put up more collateral – or risk being liquidated.

Why would someone borrow an amount of X by pledging a collateral of 1.5X? Well, one obvious reason is that the borrowed token is more useful than the collateral token. It could be that the borrowed token is undervalued by the market vis-à-vis the collateral token. It could be that the borrower knows that the collateral token will tank in value the next day, and wants to willfully default on the loan. It’s all possible.

What next?

“TradFi” could get disrupted by “DeFi” because of how automated these smart contracts are, and how they can easily build on top of each other. Everything is an API, and API’s are open.

On the other hand, men with guns could mess with the trusted third parties that, say, back stablecoins – and take down the whole system.

Or, they could just run in this little corner of the general financial ecosystem, and everyone wins.

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

A Gentle Introduction to Hedging

What? Why? Who?

What is Hedging?

Here are a couple of popular definitions and explanations to get the conversation started:

Investopedia: A hedge is an investment that is made with the intention of reducing the risk of adverse price movements in an asset. Normally, a hedge consists of taking an offsetting or opposite position in a related security.

Varsity: Hedging makes sense as it virtually insulates the position in the market and is therefore indifferent to what really happens in the market. It is like taking vaccine shot against a virus. Hence when the trader hedges he can be rest assured the adverse movement in the market will not affect his position.

The way it is commonly described, hedging is the act of taking offsetting positions against a portfolio to even out the bumps in the market.

The CAPM β

According to EMH, a portfolio’s return could be fully explained by the market (source):

r = rfß(rm – rf) + α


  • = Expected rate of return

  • rf = Risk-free rate

  • ß= Beta

  • (rm – rf)= Market risk premium

If you set the risk-free rate (rf) to zero, you get r =  ß*rm + α

Now, subtract away the market from the asset returns and you’ll be left with α.

Basically, a perfectly hedged portfolio will be a completely market neutral portfolio who’s returns will be pure alpha.

The offsetting positions can be taken via futures or options. To keep it simple, we will use futures to illustrate an example.

An Example

It is 2005 and the master analyst that you are, you expect HDFCBANK and KOTAKBANK to be decades long compounders. So, you setup an equal weighted portfolio that has only those two stocks.

If you stayed with this portfolio, then you truly have 💎🤲

Even though the annualized returns during the ~15 year period is twice that of NIFTY 50’s, very few investors would have stuck through the 70% drawdown that the portfolio had in 2008 and the 40% drawdown it had in 2020. Not to mention the numerous 20% dips along the way.

The question that hedging tries to answer is as timeless as time itself: Can I have my cake and eat it too? Is there a way to get only the excess returns without the market’s ups and downs?

What is the “market?”

Given that your portfolio consists entirely of banks, what exactly is your “market?” The answer to this question is not trivial.

You could go with the NIFTY 50 index but it has companies from different sectors like oil, metals, IT, etc. How much of an offset do you expect it to provide?

Or, you could go with the NIFTY BANK index. Intuitively, you would expect it to be a better hedge because it is composed almost entirely of banks – just like your portfolio.

Rolling βs

Rolling βs of the portfolio to each index gives us an idea of the appropriate benchmark to use.

What this is telling us, with perfect hindsight, is that the NIFTY BANK index comes close.

Theoretically, Hedging works in Theory

The math checks out. Irrespective of whether you hedge against the NIFTY or the NIFTY BANK index, you end up with much lower drawdowns.

For example, if you hedge against the NIFTY BANK, assuming no frictions and slippage, drawdowns never exceeded 20% and returns came in at a respectable 12% annualized.

Reality Sucks

Hedged portfolios have high Sharpe ratios and look attractive in backtests. However, reality is quite different.

βs are not Stable

The chart of rolling betas of the portfolio over different indices highlight the biggest problem with hedging: the hedge ratio needs to be constantly adjusted because the relationships are unstable.

Adjust it too often, then you lose to transaction costs. Adjust it too slowly, then you are no longer perfectly hedged.

βs > 1

Sometimes, betas can exceed 1. This means that your portfolio is net short during those periods. If the original intent of setting up the portfolio + hedges was to just even out the market fluctuations in a long-only portfolio, then being net-short is something that you may not have bargained for.

Margin requirements Vary

The backtest presented above allocates 90% to the cash (long-only) part of the portfolio and 10% towards margin requirements. However, during periods of market stress, brokers are known to hike margins to protect themselves. This might end up putting you in a position where you will need to pare back some of your long-only exposure to raise funds to meet the increased margin requirements. Basically, selling the dip.

Markets have a Positive Drift

Over long time horizons, markets typically have a positive drift. With a hedged portfolio where you are short the market, you are betting that this drift is overshadowed by volatility and portfolio alpha. It may very well be true, but you are betting against the winds.

Who should Hedge?

Leveraged Investors

Hedging doesn’t make sense for long-only cash portfolios. If you are a CNC (Cash N’Carry) investor, then you are better off de-grossing (reducing overall exposure or positions) and focusing on diversification rather than trying to hedge your portfolio.

Investors who employ leverage, however, should hedge. For example, if you were to take levered positions in HDFCBANK and KOTAKBANK through futures, then it makes sense to try and hedge out the market risk. Futures have 5x leverage built in, so it has the potential to boost your CAGR, as long as you can meet the mark-to-market during the 20% drawdowns.

Tactical Positioning

Some investors may prefer to hedge only when they expect market volatility. In our introduction to Tactical Allocation, we touched upon how we can use moving averages to shift between stocks and bonds. Instead of trading in-and-out, investors might prefer to add a hedge instead.

Needless to say, we are not big fans of investors trying to time the market like this.


Hedging makes sense if you are a leveraged investor. Given the costs, complexity and performance drag involved, it doesn’t make much sense for cash investors to hedge.

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