Category: Investing Insight

Investing insight to make you a better investor.

Low Volatility: Stock vs. Portfolio

Lower the Risk, Higher the Returns?

Typically, investors expect higher returns from high risk investments compared to low risk ones. However, realized returns are the opposite of what they expect.

High Beta vs. Low Vol

This anomaly, where lower risk systematically results in higher returns, has spawned a number of “betting against beta” strategies. A common approach is to rank a universe of stocks by volatility and create a portfolio off the top-N. However, this approach could lead to a highly volatile portfolio if relative correlations are not considered.

1+1 = 0

Here are two stocks with their volatility plotted against time:

correlated low-vol stocks

If you create a portfolio off these two stocks, what happens to portfolio volatility?

A portfolio made off low-vol stocks can be high vol

In the worst case scenario, where all the volatilities are correlated, portfolio volatility can end up being a sum of all component volatility.

If low-vol stocks can create a high-vol portfolio, can high-vol stocks create a low-vol portfolio? Yes! It all depends on how the volatilities are correlated.

inversely correlated high-vol stocks

In the best case scenario, portfolio volatility can be a very low constant value if the components are inversely correlated.

a low-vol portfolio created off volatile components

It doesn’t matter if individual volatilities are high or low. What matters is the correlation of volatilities.

Portfolio Optimization

A simple ranking of stocks will not help in creating a low-vol portfolio. What we need is a holistic approach that considers the correlation of volatilities and optimizes the entire portfolio.

One way to go about this is to use gradient descent. Start with a random portfolio and go in the direction that minimizes variance (min-var) or expected tail loss (min-ETL)

min-var and min-ETL backtest

With a monthly rebalance, the chances of the portfolio getting trapped in a local-minima are low. And the backtest looks promising.

Investing in Low-Volatility Portfolios

Equity investors can map our Minimum Variance and Minimum ETL Themes to their portfolios to gain exposure to these low-vol strategies.

Factor Momentum Everywhere

Earlier this year, AQR had published a paper that showed momentum behavior also exists in equity factors (like value, quality, etc.) and not just in vanilla equities.

In this article, the authors document robust momentum behavior in a large collection of 65 widely-studied, characteristic-based equity factors around the globe. They show that, in general, individual factors can be reliably timed based on their own recent performance. A time series “factor momentum” portfolio that combines timing strategies of all factors earns an annual Sharpe ratio of 0.84. Factor momentum adds significant incremental performance to investment strategies that employ traditional momentum, industry momentum, value, and other commonly studied factors. Their results demonstrate that the momentum phenomenon is driven in large part by persistence in common return factors and not solely by persistence in idiosyncratic stock performance.

Factor Momentum Everywhere – Tarun Gupta, Bryan T. Kelly (AQR)

We put this idea to the test by constructing a long-only portfolio with five of the strongest factors – Momentum, Quality, Low-volatility, Value and Small-cap. The strategy was to go long whatever factor had the best returns over the last 12-months. We also looked at going long the best factor from the previous month. In both cases, the portfolio was re-balanced every month.

The representative indices and ETFs used for this back-test can be perused from the code: factor-momentum-india.ipynb and factor-momentum-US.ipynb


The strategy using a 12-month formation period was a disappointment. There was no discernible improvement over a buy-and-hold of the large-cap index.

India (12-month Formation)
US (12-month Formation)

However, the one-month formation period widely out-performed the large-cap benchmark.

India (1-month Formation)
US (1-month Formation)

Needless to say, shorter the look-back period, larger the number of trades. So we added another back-test that averaged factor returns over 6-through-12 months to check if there was an acceptable middle-ground. Turns out, there is.

India (6..12-month Formation)
US (6..12-month Formation)

Forward Test

We setup US portfolios back in May this year when we first got to know about this paper. The 12-month and the 6…12-month formation period portfolios can be found here and here. They both seem to have out-performed SPY and MTUM so far.

We constructed the Factor Momentum 6-12 Theme for Indian equities that tracks the last strategy outlined above but given the lack of liquidity in factor ETFs, it trades the underlying stocks directly.

Investing in Factor Momentum

Indian investors can use brokers like TD Ameritrade or Interactive Brokers to invest in US stocks. The trades are posted on the slack channel mentioned on the pages linked above. You can execute the trades yourself by monitoring the messages on the channel.

If you are interested in executing this strategy on Indian equities, talk to us!

Factor Holding Periods for Excess Returns
Funding Your Dollar Dreams

Questions? Slack me!

Reducing Crash Risk in the Nifty Alpha Indices

The NSE has a couple of strategy indices – the NIFTY Alpha 50 Index and the NIFTY100 Alpha 30 Index – based on historical CAPM alphas. The former selects 50 stocks from the largest 300 stocks whereas the latter selects 30 stocks from the NIFTY 100 index.

First, a look at a simple buy-and-hold strategy.

Buy-and-Hold Curves


The alpha indices have out-performed the plain-vanilla NIFTY 50. However, what jumps out off the page is the sheer depth and length of the drawdows that these indices have made.

Even though they give vastly better returns than the NIFTY 50 index, the lived experience would be too painful for most investors. Is there a way to reduce these drawdowns while retaining most of the out-performance?

In a 2012 paper, Momentum has its moments, Barroso and Santa-Clara outline a way in which historical volatility could be used to reduce momentum crashes.

Strategy Outline

The basic idea is that momentum risk is time-varying and sticky. And, periods of high risk are followed by low returns.

rolling 100-day sd
rolling 200-day sd

To test this theory out on the Alpha indices, we first split the time series into halves. The first to “train” and the second to “test.” We need a training set because we are not sure what the appropriate look-back for calculating risk should be (we check 100- and 200-days). The test set is a check of out-of-sample behavior of the strategy.

The theory laid out in the paper, that periods of high risk is followed by periods of low returns, is true. Subsequent returns when std. dev. is in the bottom deciles show large negative bias. Also, perhaps indicating a bit of mean-reversion, returns after std. dev. is in the 7-9th decile, have fat right tails.

NIFTY ALPHA 50 200-day cumulative returns by 200-day sd decile
NIFTY100 ALPHA 30 200-day cumulative returns by 200-day sd decile

Train In-Sample

The next question is the appropriate lookback and deciles for calculating the std. dev. Running this on the training set, we find:

training set: NIFTY ALPHA 50 – 200
training set: NIFTY100 ALPHA 30 – 200
training results

A strategy that goes long Alpha when std. dev. is in the 1-5 deciles side-steps severe drawdowns in the training set. Note, however, that it under-performed buy-and-hold during the melt-up of 2007.

Test Out-of-Sample

Applying a 200-day lookback on both the indices over the test set, we find that the strategy continues to side-step drawdowns but no longer out-performs buy-and-hold by a large margin.

test set: NIFTY ALPHA 50 – 200
test set: NIFTY100 ALPHA 30 – 200
test results


Using historical volatility (std. dev.) reduces drawdown risk in Alpha indices. But it comes at the cost of reduced overall returns over buy-and-hold over certain holding periods. However, given the magnitude of the dodge in 2008 and 2016, it is well worth the effort (and cost) if it helps keep the discipline.

Check out the code for this analysis on pluto. Questions? Slack me!

Does the tail-end add value?

A wise man once said, the decision to go passive is a very active one.

At first, going passive meant buying and holding a broad-based index fund. But that was over 40 years ago. Since then, in the US, the market has evolved and the number of indices, index funds and ETFs have exploded. Think of a theme, strategy, asset class, market or geography, there is an ETF for that.

As of today, there are 2,319 ETFs in the US. And given the intense competition over the last decade, fees have been driven to single-digit basis-points in most cases. Given this fee pressure, US based issuers looked east and landed on Europe a couple of years ago. And there too, competition quickly reduced fees and expanded access.

The next big virgin market is India.

Given this back drop and the small but increasing interest in passive indexing, if a DIY investor wishes to just buy and hold a market-cap based index, which one should she buy?

The most practical choices boil down to NIFTY 50, NIFTY NEXT 50 (collectively forming the NIFTY 100) and the NIFTY 500 indices.

Given the fee differentials between the NIFTY 100 and NIFTY 500 based ETFs/funds, the big question to ask is: Is there any advantage of reaching below the 100 mark? Is 100 enough?

Market-caps follow a power-law. For NIFTY 100, 80% of the index is covered by the top 35 stocks and for NIFTY 500, the number is 82. So unless the rest of the stocks in the index deviate to an extreme degree in terms of total returns (change in price + dividends,) the top 35/80 stocks power most of the returns.

Cumulative Returns
Annual Returns

So, the answer is No. Unless NIFTY 500 based ETFs/funds achieve fee and liquidity parity with the NIFTY 100 based ones, investors are not missing out on anything by sticking with the mega-caps.

Check out the goodies on pluto. Questions? Slack me!

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!