Tag: investing

Equal-Weighted vs. Cap-Weighted

There are a number of ways in which you can allocate funds (weigh) the stocks in your portfolio. The simplest of them are equal-weight and market-cap weight.

In an equal-weight portfolio, all stocks get the same allocation. If you have 20 stocks, then each stock would have a 5% weight in the portfolio. So the WAVG capitalization of these portfolios end up skewing towards mid/small caps within the portfolio.

In a cap-weight portfolio, each stock gets an allocation based on its market-capitalization. So large-cap stocks get a large weight and smaller-cap stocks get a smaller weight.

The advantage of a cap-weight portfolio is that unless you want to change the constituents, you don’t have to do anything. The individual weights will be always tracking their corresponding market-caps. But in an equal-weight portfolio, you need to rebalance once a month/quarter to bring back all the constituents to their original weights. You will be selling your winners to add to your losers.

Needless to say, the all-in cost of maintaining an equal-weight portfolio will be more than that of a cap-weigh portfolio. Is it worth it?

The American Experience

For the US markets, lucky for us, Wilshire Indices has index data covering both the market-cap and equal-weight versions of the same portfolio starting from 1970. And the over-all out-performance of the equal-weight portfolio looks spectacular.

Cap-weight vs. Equal-weight

Whenever you see out-performance like this, you have to keep in mind that it is usually a combination of investor behavior and investment risk.

The reason why an investment strategy out-performs could be because it is prone to long draw-downs followed by large, but short-lived, upswings. Investors flood into the strategy during the upswing, only to exit during the soul-crushing drawdown. Happens in value and momentum investing a lot.

The second reason why something works is because of higher volatility. Stocks are more volatile than bonds so over a long enough period of time, they out-perform them.

To visualize if investor behavior is driving out-performance, you can look for the swings in annual returns and periods for which the strategy under-performs its benchmark.

Large swings imply difficulty of staying invested
Long periods of under-performance imply difficulty of staying invested

The equal-weighted index also has a larger standard-deviation (a measure of volatility) ~6% compared to ~4.4% of the market-cap index.

In short, equal-weighted portfolios are more volatile and there are significant periods where they under-perform their cap-weighted cousins in the short-term. This results in a larger probability of adverse investor behavior, partly explaining the out-performance over a longer period of time.

However, we don’t live in the 70’s anymore. The market structure has evolved. Costs have come down drastically and more investors are aware of the equal-weight strategy. If you think liquidity is thin in small-cap stocks today, it was impossible to trade them 20 years ago unless your uncle ran a brokerage firm. So some of the earlier-period excess returns are only theoretical – you could not implement this strategy even if you knew about it.

So, is it still a free-lunch? One way to visualize this is to plot the Information Ratio of the equal-weight returns over that of market-cap returns.

No longer a free lunch!

Equal-weight, as a strategy, has been losing its mojo and maybe, its best days are behind it. Excess returns could be entirely explained by higher risk.

The Indian Experience

It maybe too early for a large commitment to equal-weight portfolios in India.

First, India has a Securities Transaction Tax of 0.1% on the total notional amount traded. So, a market-cap weight portfolio that is rebalanced twice a year will have a far lower cost than an equal-weight portfolio that is rebalanced every month.

Second, there is no liquidity beyond the top 70-100 names by market-cap. So one cannot create an equal-weight version of the NIFTY 500 index. An equal-weighted NIFTY 50 is probably the only version that makes sense if you want to reduce impact costs. NIFTY 100 is the second-best option.

If you go with NIFTY 50, an equal weight portfolio of 50 stocks means than each stock has a 2% weight. Since you are constantly selling winners and buying losers, low dispersion in returns between their returns will have a big impact on the relative performance of the equal-weighted portfolio over its cap-weighted cousin.

For example, YESBANK, at its peak, had a 1.74% weightage in the NIFTY 50. And its recent troubles have brought it down to about 0.18%. In the equal-weighted NIFTY 50, this would have been a constant 2% through-out. Not exactly participating fully in the up-side but doubling down on the down-side.

Price chart of YESBANK since it was added to NIFTY 50 in March 2015

YESBANK wouldn’t have been a big problem if we were equal-weighting the NIFTY 500. But it is a problem with NIFTY 50.

NIFTY 50: cap-weight out-performs
NIFTY 100: cap-weight out-performs

As expected, the gap between NIFTY 50 equal/cap is huge compared to that between NIFTY 100 equal/cap.


  • Equal-weighting may not be “free lunch.” Excess returns are could mostly be explained by higher risk.
  • Makes sense only on large portfolios. Maybe 500 stocks is the magic number.
  • We wary of costs.


  • Portfolio selection: the power of equal weight (arvix)
  • notebook with R code for the plots.

Questions? Slack me!

Systematic Buy-the-Dip


We often hear the term “buy-the-dip” whenever the markets are correcting. However, here are some questions that face an investor:

  1. What exactly is a “dip?”
  2. Where does the cash come from?
  3. How much should I buy?

The answers to these questions will determine how much alpha you will generate by employing this strategy.

What is a “dip?”

A dip is a percentage loss from a near-time peak (also called a drawdown.) For example, if the NIFTY posts a 50-day cumulative loss of 5%, then that is a 5% dip over where the NIFTY closed 50-days ago. To get a sense for how these 50-day dips/drawdowns are distributed, we do a density plot.

drawdown.density.NIFTY 50

drawdown.density.NIFTY MID100 FREE

As we can see, most of the NIFTY dips are at around 5%. A more than 10% dip is a “back the truck up” event where we deploy all our cash. For MIDCAPs, it is around 10% and 15%.

The back test

Every day, an investor has Rs. 1 that he needs needs to invest. He can either buy the NIFTY/MIDCAP or he can park it a short-term bond fund/savings account. Additionally, if it is a “back the truck up” dip, he can liquidate the bond fund and buy the NIFTY/MIDCAP. Let’s tag this as DIP.

In a DIP, the investor only buys NIFTY/MIDCAP if it is in a dip. Otherwise, he buys Rs. 1 worth of bonds.

The base case is that the investor buys Rs. 1 worth of NIFTY/MIDCAP every day. Let’s tag this as SIP.

Should you buy the dip?

Yes, buying the dip allows you to build a bigger corpus, if your transaction costs are zero. Here are the NIFTY and NIFTY MIDCAP buy the dip (DIP) vs. daily purchase (SIP) final corpus:


Given how small the alpha is, net of fees/commissions/slippage/taxes, this is a losing proposition. You are better off with a SIP.

Cliff Asness on Momentum Investing

In a wide ranging interview with Tyler Cowen, Cliff Asness discussed momentum and value investing strategies, disagreeing with Eugene Fama, the economics of Ayn Rand, bubble logic etc. The first half of the conversation was mostly about momentum investing and how it works.

Excepts on momentum:

A momentum investing strategy is the rather insane proposition that you can buy a portfolio of what’s been going up for the last 6 to 12 months, sell a portfolio of what’s been going down for the last 6 to 12 months, and you beat the market. Unfortunately for sanity, that seems to be true.

To some, it’s very intuitive. Just buy what’s going up.

It has horrible streaks within that of not working. If your car worked like this, you’d fire your mechanic, if it worked like I use that word. I think it is harder than you might guess, even if something works long term, to have it go away because a lot of investors can’t live through the bad periods. They decide why it’s never going to work again at the wrong time.

Why it works
Underreation: News comes out. Price moves but not all the way. People update their priors but not fully efficiently. Therefore, just observing the price move is not going to move the same amount again but there’s some statistical tendency to continue.

Overreaction: People in fact do chase prices.

How to make it work
If you’re going to be momentum, you’ve got to really do it. You’ve got to be disciplined. You’ve got to come in every day, and you’ve got to count on these under- and overreaction things.

Momentum strategies on StockViz

We have been offering the Momentum Theme for more than two years now. It implements a relative momentum strategy where you compare the strengths of a universe of stocks to each other. 2014 returns were +90% and +36% so far this year (Compare.)

This year, we have introduced Velocity – an absolute momentum strategy – and Acceleration – a strategy that tracks changes in momentum.

If you are interested in momentum investing, please get in touch with us!

Source: A Conversation with Cliff Asness
Related: Small Cap Momentum Style Fund

Will Your Strategy Outperform?

Came across an interesting paper: Will My Risk Parity Strategy Outperform? Robert M. Anderson, Stephen W. Bianchi, CFA, and Lisa R. Goldberg. Even though they discuss risk parity, they make some pretty interesting points that relate to all investment strategies.

Today’s alpha is tomorrow’s beta

… the introduction of new securities can have an indirect effect; a strategy that was seemingly profitable in the past might have been less profitable if the new securities had been available and thus made the strategy accessible to a broader class of investors.

Before index ETFs, there was no cost-effective way of replicating an index. For example, NIFTYBEES was listed in 2002 and came with an expense ratio of 0.80% while retail brokerage charges were in the 0.5-1.0% range. Replicating the NIFTY index before NIFTYBEES came around was expensive. So any backtest before 2002 that that tries to argue the benefits of buying-and-holding an index ETF is likely bogus. Similarly, today’s active management strategies available to a select few hedge-fund investors are tomorrow’s “smart beta” ETFs that will be available to anybody with a demat account.

Leverage is an external source of risk

The notion that levering a low-risk portfolio might be worthwhile dates back to Black, Jensen, and Scholes (1972), who provided empirical evidence that the risk-adjusted returns of low-beta equities are higher than the CAPM would predict.

There are periods when banks pull their lines of credit based on macro factors that has nothing to do with your strategy. For example, during the 2008 financial crisis, your bank/broker would have pulled your credit lines forcing you to sell near the bottom and preventing you from buying the bounce. Any strategy that uses leverage – risk-parity, for example – should factor this risk.

Performance depends materially on the backtesting period

Even if we were reasonably confident that one strategy achieved higher expected returns than another without incurring extra risk, it would be entirely possible for the weaker strategy to outperform over periods of several decades, certainly beyond the investment horizon of most individuals…

Besides, most strategies have a rebalancing frequency – once a month, once a year, and so on. The specific day you choose to rebalance can have a material impact on your strategy. For example, rebalancing during options expiry, corporate events, etc… can meaningfully skew your risk/returns.

Borrowing and trading costs can negate outperformance

Value-weighted strategies require rebalancing only in response to a limited set of events. The risk parity and 60/40 strategies require additional rebalancing in response to price changes and thus have higher turnover rates. Leverage exacerbates turnover.

There is huge execution risk involved in strategies that requires shorting of shares. Given the regulations surrounding SLBS – lending/borrowing allowed only on those securities that are listed in F&O and that too only in increments of lot-sizes – the friction involved in shorting stocks are prohibitive.

Execution drift

There is likely going to be a big difference between model execution prices and actual execution prices. For example, when we rebalance our Themes, we use the latest available price in our database. These prices themselves could be stale by over 10 minutes. These changes then have to percolate down to investors who execute them in the market. From start to finish, there could be a price gap of over 20 minutes – a significant source of drift between the ideal P&L and actual P&L.


Investors should have a deployment checklist for their strategies that addresses the issues raised above. What we have found is that most strategies that look good on a simple backtest don’t look that great when costs, variable periods, drift and half-lives are factored in.

Profiting from PE Ratio Obsession


We are not big fans of using the Price-to-Earnings ratio. We saw how funds that use the market PE to time the market are no better than a buy-and-hold strategy (sometimes B&H performs better,) and we followed that up with how every single “ratio” has a caveat. And PE is the dumbest of them all.

However, if a large group of market participants pay attention to single flawed metric, then there should be a profitable arbitrage strategy that exploits that anomaly?

Exploiting PE obsession

Researchers in the US figured out a way to do just that.

Active investors with limited attention and capital constraints use fundamental metrics to screen and sort potential investments. Price-earnings (P/E) ratios are extremely popular, and are typically calculated using four trailing quarters of net income. Changes in the rankings of published P/E ratios may influence investor attention and subsequent excess returns. From 1974-2013, decile long-short portfolios formed on characteristics of P/E rankings which are rebalanced monthly earn value-weighted monthly excess returns of 101 basis points with annual Sharpe ratios of 0.79. Decile long-short portfolios which are rebalanced daily earn value-weighted daily excess returns of 16.99 basis points with annual Sharpe ratios of 2.91. Excess returns are robust to size, value, profitability, investment, price momentum, earnings momentum, short-term reversals, and relative volume. Changes to a stock’s P/E ranking predicts excess returns even when the stock’s P/E ratio itself does not change. The return premium cannot be explained by fundamental risk, clustering of attention at round number P/E ratios, or autocorrelation in the regressors.

We haven’t tested this for the Indian market yet. But this is just too cool not to share!

Paper: Rankings of published price-earnings ratios and investor attention