Trend-following systems typically use the past performance of a particular asset to trigger a buy or a sell on that asset. A research paper that came out in 2019 looked at whether the historical performance of multiple assets can be used to trade them.
Pitkäjärvi, Aleksi and Suominen, Matti and Vaittinen, Lauri Tapani, Cross-Asset Signals and Time Series Momentum (January 6, 2019). Available at SSRN: https://ssrn.com/abstract=2891434
From the abstract:
We document a new phenomenon in bond and equity markets that we call cross-asset time series momentum. Using data from 20 countries, we show that past bond market returns are positive predictors of future equity market returns, and past equity market returns are negative predictors of future bond market returns.
Unfortunately, the paper did not look at Indian markets to check if this worked. So, we rigged up a simple backtest to see for ourselves.
Rules
A simplified equity-bond cross-asset trading strategy at the beginning of month t can be constructed as follows: Compute the past 12-month equity return (E past) and the past 12-month bond return (B past). If:
a) E past is positive and B past is positive: Buy equity b) E past is negative and B past is negative: Sell equity c) E past is negative and B past is positive: Buy bonds d) E past is positive and B past is negative: Sell bonds e) Otherwise, invest in the risk-free rate. Hold the portfolio for one month and then repeat the same procedure in month t+1 (source.)
Backtest
We used the NIFTY 50 TR index to represent equities, NIFTY GS 10YR index for bonds and the CCIL Index 0-5 TRI for risk-free rate.
Since our risk-free index starts only from 2004, our backtest only goes back 16 years. However, the markets have been through a lot since then, so it is unlikely we are losing much by not being able to go back much earlier.
The 12-month look-back approach massively under-performs the NIFTY 50 TR buy-and-hold. We shortened the look-back to 3-months to see if we could make the strategy more responsive to trend reversals.
To our dismay, we saw only marginal improvements in overall returns but the draw-down profile of the long-only portfolio was much better.
Conclusion
While the approach outlined in the paper might be valid for the selected subset of markets, it fails a simple backtest on Indian market indices.
Profit by investing in stocks that have hit their all time highs
We launched the All Star Portfolio last week along with our discussion on momentum strategies. It is a great way for investors new to momentum (or equity investing, in general) to follow along a systematic momentum portfolio. We like this particular strategy because:
Lower risk compared to other momentum strategies.
Go-to cash if there aren’t viable candidates.
A wide trailing stop-loss to exit outliers.
Works with top-300 stocks by market cap – doesn’t depend on small caps to drive performance.
Lower churn compared to other momentum strategies.
Historical Performance
We start from 2010 and rebalance monthly. Observe the drawdowns and the relative out-performance of the All Star.
The reason for the lower drawdowns is the ability of the strategy to stay in cash when things are bad. While we can take up to 25 positions, the slots are not always filled. An equal weighted portfolio (4% per slot) with only 5 positions will have 80% in cash.
Moreover, the per-position max loss during the time frame has been less 10% in a given month.
By keeping a trailing stop-loss of 15%, we ensure that only the true outliers are caught by it and not the run-of-the-mill corrections that are bound to happen.
The Fama French 5-Factors came in two installments. The first 3 were published in 1992 and the rest in 2014. They capture “fundamental” factors, i.e., factors that can be derived from looking at balance-sheet and income statements. In 1993, Jegadeesh and Titman published their ground-breaking work on momentum: Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency (pdf)
Their paper singularly propelled momentum (or, trend-following) into the mainstream by giving it the academic vigor it lacked earlier. While its findings may not have been earth-shattering for most traders, most professional investors looked at momentum strategies as something that “traders” did and avoided them. But within a decade of the paper being published, momentum strategies were firmly established as a “legitimate” strategy that could be allocated to.
Basic Design
The J/T paper constructs a long-short portfolio by ranking stocks based on their prior 12 month returns (skipping the most recent month.) The top decile portfolio is called the “losers” decile and the bottom decile is called the “winners” decile. In each month, the strategy buys the winner portfolio and sells the loser portfolio. This is the classic 12_1 momentum, where 12 denotes the formation period and the 1 is the number of skip months.
The reason for the skip month is to account for the short-term reversal effect associated with momentum. Some researchers, like Fama and French, do 12_2 momentum, where the most recent 2 months are skipped. However, a more recent study by Medhat and Schmeling (2018) finds that once we discard the stocks with the lowest turnover, equity returns exhibit short-term momentum rather than short-term reversal. So, the short-term reversal effect may not be as prevalent as is usually thought and one could even go with a 12_0 momentum.
The French Momentum Library
Luckily for us, Ken French (of the Fama French fame) regularly updates factor statistics on his Tuck School of Business webpage.
While the momentum factor (MOM) has out-performed the market factor (MKT = rm – rf = Market risk premium), over the long term, it is not without its share of pain.
Long-only Momentum
As “retail” investors, we typically invest in long-only portfolios. This makes momentum investing an extremely gut-wrenching ride. One day, you might be thinking which Greek island you are going to buy and the next day you might be scrambling to pay rent.
Momentum strategies have been packaged as an ETF for retail investors in the US for a while now. PDP, the Invesco DWA Momentum ETF, and MTUM, the iShares MSCI USA Momentum Factor ETF, are the 800-pound gorillas in the room.
The differences in performance highlight the different ways momentum strategies can be implemented.
The Indian story is relatively new. A monthly-rebalance momentum strategy has delivered superior returns (although, with a massive dose of heartburn.)
Measures of Momentum
Once the J/T paper was out, academics got to work and systematically mapped out more than a dozen different ways to setup up momentum portfolios. The most common ones are:
12_2/12_1/12_0: These are the “original” momentum portfolios formed by only looking at absolute returns.
Relative: For each stock, create a distribution of relative returns over every other stock in the universe and use it to drive portfolio formation.
Acceleration: Rank stocks based on how well they have performed over the last 6-months vs. their preceding 6-month returns.
CAPM-α: Rank stocks based on their α over an index.
Sharpe ratio: Rank stocks based on their Sharpe ratios.
Idiosyncratic/Residual: Rank stocks based on what is left after fitting a Fama-French 5-factor model. i.e., whatever cannot be explained by the 5-factors.
52-week or All-time Highs: A portfolio of stocks who’s prices have hit either one-year of all-time highs.
These are further combined with some sort of risk management measure, like a stop-loss or a trend overlay. So, based on the universe of stocks, frequency of rebalancing, momentum measures and risk-management technique applied, there are hundreds of different “momentum” portfolios that can be created.
Conclusion
While momentum is now a well established investment strategy, it is not an easy one to be married to. Differences in portfolio construction: formation periods, skip months/weeks, stock universe, stop-losses, etc. have a big impact on overall performance.
While momentum definitively underlines the “no pain, no returns” maxim, in a twist of irony, academics discovered the “low-volatility” anomaly. What if, investors can take less pain for more returns? Stay tuned for our next Free Float!
Introducing the All Star Portfolio
Given the large number of choices in front of investors these days, we felt that there should be an on-ramp for those who want to just follow along a systematic strategy without committing their portfolios.
So, we built a momentum portfolio that is easy for first-time investors to follow along. We call this the All Star Portfolio and is based on stocks hitting their all-time-highs. Just subscribe to our substack and receive emails whenever there is a change in the portfolio.
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 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!
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 NIFTY 50 TRNIFTY100 ALPHA 30 TR vs NIFTY 50 TRNIFTY 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.
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
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!
