Author: shyam

Low Volatility: Stock vs. Portfolio

shyam January 7, 2020January 7, 2020

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.

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:

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.

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)

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.

Categories Investing Insight Tags quant, volatility

Book Review: The Man Who Solved the Market

shyam January 4, 2020January 4, 2020

In The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution (Amazon,) Gregory Zuckerman chronicles the rise of Renaissance Technologies (RenTec) and its founder, Jim Simons.

It is a fascinating book. You should absolutely, without a doubt, read it.

The basic question that Jim Simons asked was: Is it possible to develop a mathematical model of the market and use it to trade profitably?

Turns out that it is a qualified “yes.” There are a handful of people who can do it successfully over a long enough period of time to become billionaires without blowing up. And they are extremely secretive of the methods they use.

Reading through the book, I realized that some of the machine learning models they seemed to be using in early 2000’s is what Google has commercialized now. It looks like they have a 10-15 year head-start in some areas over everybody else in things like sentiment analysis and language translation.

Also, Simons, worried about the capacity of his algorithms, capped the size of his fund a long time ago and kicked out outside investors. Today, the fund is run for and by its employees.

The gains Simons and his colleagues have achieved might suggest there are more inefficiencies in the market than most assume. In truth, there likely are fewer inefficiencies and opportunities for investors than generally presumed. For all the unique data, computer firepower, special talent, and trading and risk-management expertise Renaissance has gathered, the firm only profits on barely more than 50 percent of its trades, a sign of how challenging it is to try to beat the market—and how foolish it is for most investors to try.
The Man Who Solved the Market

Recommendation: Must Read!

Categories Books Tags book, review

Book Review: Narrative Economics

shyam December 16, 2019December 16, 2019

In Narrative Economics: How Stories Go Viral and Drive Major Economic Events (Amazon,) Robert Shiller, Nobel laureate, pitches the importance of incorporating popular narratives in economic and financial models.

The biggest problem I have with the way most research is done in quantitative finance is that whatever data is available gets analyzed to death while data that is hard to get, unorganized or tedious to collate is ignored. And given the adaptive complex dynamic nature of the markets, signals derived from the former attenuate at a much faster rate as time goes on.

When markets break quant models, it is often because the underlying narrative has changed. The word “narrative” is just a fancy word to describe the stories we tell each other. And stories are virus. The spread of a narrative can be modeled like how epidemiologists model the spread of contagions. And the main thrust of the book is that it is high time economists and policy-makers began to incorporate narratives into their models and playbooks.

By 1932, the bottom of the stock market decline, the US stock market had lost over 80% of its 1929 value in less than three years. We have to ask: Why did people value the market at such a low level? A big part of the answer was a narrative that went viral: modern industry could now produce more goods than people would ever want to buy, leading to an inevitable and persistent surplus.
Narrative Economics, Shiller 2019

Investors would do well to take Shiller’s ideas and start to systematically track narratives that could impact their portfolios. Maybe, instead of Risk-Parity, try Narrative-Parity portfolios!

Recommendation: Must Read!

Categories Books Tags book, review

Factor Momentum Everywhere

shyam December 12, 2019December 16, 2019

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

Results

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.

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

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.

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!

Questions? Slack me!

Categories Investing Insight Tags momentum, quant

Reducing Crash Risk in the Nifty Alpha Indices

shyam November 21, 2019October 27, 2020

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

NIFTY ALPHA 50 TR vs NIFTY100 ALPHA 30 TR

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.

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:

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.

Conclusion

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!

Categories Investing Insight Tags momentum, NIFTY, volatility