Momentum is the speed with which a particular object moves. In the financial world, momentum refers to the speed with which the price of the stock or any other asset moves. A stronger momentum indicates a faster movement in the price of the assets in one particular direction. Momentum is generally measured as the ‘rate of change’ (ROC) of the price over ‘X’ periods of time. In this article, we discuss ‘Rolling Quantitative Momentum’, a quantitative approach to investment & portfolio management using momentum in the stock price and re-balance (rolling) the portfolio at regular frequencies.
The book ‘Quantitative Momentum’ by Wesley Gray & Jack Vogel is the basis of many of the ideas & analysis presented here. While the book analysis has used US stock market data, I’ve adapted some of these ideas to Indian stock market data – Nifty 500 stocks.
In our Rolling Quantitative Momentum strategy, we design our investment portfolio using stocks with strong momentum and then further refine it using quality of the momentum of stocks, holding period and portfolio size & investment size.
For the purpose of our study, we will use NSE’s Nifty 500 stock universe as they represent 97% of the turnover of the market.
How can we measure the momentum of stocks?. Momentum is generally measured as the rate of change (ROC) of the stock price over ‘X’ periods. In many cases, traders use MACD, moving averages, stochastics, RSI etc. In our study, we will use ROC for measuring the momentum. Now, momentum is usually measured over short periods of few days, intermediate periods of few months or long-term periods of few years.
Wesley Gray & Jack Vogel found that an intermediate period of 6-12 months is ideal for measuring the momentum which gives the stock enough room for further upside price action and has a better signal to noise ratio. Shorter periods of momentum measurement tend to have too much noise to signal ratio while long-term periods of momentum measurement doesn’t project further momentum in the future as it tends to taper off after a long period. Therefore, we will use 12 months of historical data to measure the momentum.
Monthly momentum values are calculated as cumulative returns over the past 12 months.
The monthly momentum is calculated in 3 steps
1) We calculate gross monthly returns by adding one to the percent monthly return. For example, from a monthly return of 5% (0.05), we get the gross monthly return value of 1.05 (0.05 + 1) while from a monthly return of -5% (-0.05) we get a gross monthly return of 0.95 (0.05 + 1.0).
2) We multiply all the gross monthly returns of past 12 months.
3) We subtract one from the resultant value from step 2 to get the net 12-month momentum score.
To illustrate this calculation, let’s say AUROPHARMA (Aurobindo Pharma) stock has moved by 2%, -5%, 4.3%, 0.5%, 10.1%, -2.2%, 6%, 3.6%, 0.1%, 0.4%, 1.4%, -2.6% over the past 12 months. Then, we add 1 to monthly return, multiply all of them & subtract one from it to get the momentum score.
Momentum Score = (1.02)*(0.95)*(1.043)*(1.05)*(1.101)*(0.978)*(0.94)*(1.036)*(1.001)*(1.004)*(1.014)*(0.974) - 1
This will give a momentum score of 10.45% (0.1045) to the Aurobindo Pharma Stock. We will now use the momentum score to build the portfolio.
Construction of the Quantitative Momentum Portfolio
We construct the portfolio with stocks showing strong positive momentum. For this study, we use NSE Nifty 500 stock historical data from the year 2000 to 2017 June.
First, we calculate monthly momentum scores for all the nifty 500 stocks and sort them by score & pick the top 10 stocks.
Here is a snapshot of Top 10 momentum stocks as of January 2017
We will construct the investment portfolio with 3 different variations
- Holding period – 1 month, 3 months, 6 months and 12 months
- Portfolio Size – 10 stocks, 20 stocks & 30 stocks
- Position Size – fixed investment vs cumulative investment.
Overlapping & Rolling Quantitative Momentum Portfolios
In this strategy, we invest in the momentum portfolios in an overlapping fashion and then rebalance (or rollover) the portfolio after the holding period is over. The overlapping investment in portfolios is best illustrated in Figure 1.
We divide our investment into 3 tranches & invest in the portfolios one at a time with a time gap. For example, in a 3 month holding period strategy, the first tranche is invested in January, second trance in February & the third tranche in March.
By the time we reach April, the holding period of first tranche investment is over and freed up for investing in April. And so on & so forth. As a result, we are able to capture the momentum of various stocks at various times and always stay invested.
Our overall portfolio investment is Rs. 7,50,000 & divided into 3 tranches of Rs. 250,000 in the case of where the holding period of the investment portfolio is greater than 1 month.
Momentum portfolio with various holding periods
In this particular study,
- We use historical data from the years 2002 to 2017 – 15 years.
- Portfolio investment size is Rs 7,50,000. Profits are not reinvested.
- For 1 month holding period, there is no overlapping of portfolios and therefore the whole 750,000 is invested in one portfolio and is rebalanced every month.
- The portfolio is rebalanced at the end of the period with top 10 new momentum stocks.
- We use equal-weight portfolio.
Here is the performance of momentum portfolios for 1 month, 3 months, 6 months & 12 months holding period from 2002-2017.
As one can see from results in Fig 2., the longer holding periods of momentum portfolio results in much better returns, better win-loss ratio, and lower maximum drawdowns and is also able to capture the momentum better than the shorter periods.
Furthermore, there are other advantages of holding the portfolio for longer periods. For example, one can use a 12 month holding period to get the long-term capital gains tax exemption. Since there are fewer rollovers (or rebalancing) of portfolios during longer holding periods, there are fewer transactions leading to lower brokerage charges. There is also higher possibility of receiving more dividends and bonus shares.
Overall, these results are in contrast to the results obtained by Gray and Vogel, where their analysis shows that frequent rebalancing of portfolio yields better returns than holding for long periods. This may be due to three factors – while they use value-weighted portfolio investing, I use equal-weighted portfolio investing and while their study comprises of almost 90 years of data, mine comprises of just 15 years of data and finally, the 15-year data from Indian markets mostly corresponds to a structurally bullish market barring the 2008 bearish market phase.
Momentum portfolio with Different Portfolio Size
In this particular study,
- We compare two portfolios containing 10,20 and 30 stocks each.
- We study portfolios with 3-month (short-term) and 12-month (long-term) holding periods.
- Investment size is 7,50,000 and profits are not reinvested.
- We use equal-weight portfolio.
Here are the results for portfolios with size of 10, 20 and 30 stocks
It’s clear from the results that increase in the number of stocks in the portfolio yields lower returns, though they show marginally lower drawdowns. The lower returns are mainly due to dilution of momentum as a result of picking stocks with relatively lower momentum. The inclusion of more stocks in the portfolio may increase the diversity but it comes at the cost of returns. Therefore, we can conclude that a concentrated portfolio with fewer high momentum stocks shows better performance than a larger but more diverse portfolio.
Momentum portfolio with Fixed vs Cumulative Investment
In this study,
- The performance of portfolios with fixed investment, where profits are not reinvested is compared with variable cumulative investment, where profits are reinvested. Profits reinvested are exclusive of dividends.
- The same number of stocks (i.e 10) is same in both portfolios.
- We chose Portfolios with 3-month (short-term) and 12-month (long-term) holding periods.
- We use equal-weighted portfolio.
- The 3 investment tranche become independent of each other.
Here are the results of fixed investment & cumulative investment portfolios
Momentum portfolio with fixed investment of 750,000 held for 3 month periods shows a profit of Rs 69 lakh with a CAGR of 17.25. And a cumulative investment, in which the profits are plowed back into the portfolio, shows a profit of Rs 50 crores with a CAGR of 54.36. The same portfolio strategy held for 12 month periods with fixed investment shows a profit of Rs 91 lakh with a CAGR of 19.52, while with the cumulative investment it shows a profit of Rs 45 crores with a CAGR of 53.37.
It is clear that when we reinvest the profits back into the portfolio, the returns are much higher. But the cumulative investment strategies suffer from huge maximum drawdowns because the capital & profits are totally invested and this can be devastating in a bear market.
We can draw three main conclusions from this study
- Quantitative momentum portfolios held for longer periods show better returns and lower drawdowns, at least in the Indian market context.
- Concentrated portfolios with fewer stocks do better than diverse portfolios with a large number of stocks. This is because of dilution of the momentum in the larger basket size portfolios.
- If profits are reinvested back into the portfolio, it shows almost exponential returns. But we should be aware of the pitfalls of larger draw-downs in these kinds of portfolios. In the case of portfolios with fixed investment, the returns are relatively languid but drawdowns are much lower.
Two main takeaways from this study are – hold momentum portfolios for longer periods (6-12 months) and keep the portfolio concentrated. On the point of reinvesting profits back into the portfolio, an investor should take the call depending on their risk appetite. If the investor wants lower risk strategy, stick to fixed investment. And if an investor wants huge returns even with large drawdowns, then he should reinvest the profits.
In the next article, I will present data & results on the importance of stocks with quality momentum in the portfolio and whether avoiding stocks with bad momentum is a good thing or not for the portfolio returns.
I wanted to see the performance of these quantitative momentum portfolios post this study and therefor I began creating 3 momentum portfolios of 10, 20 & 30 stocks at the end of every month & live tracking their performance by bench-marking it against the performance of Nifty50 & Nifty500 indices.
The aim is to see how they perform over one-year from now & whether their performance will reflect the past performance as shown in this study.
Many people who have read this article asked me if I have done Index balancing as part of the study because many stocks exited & entered the Nifty 500 index through the course of last 15 years.
To answer the question, no, I haven’t done the index re-balancing. I have used the same Nifty 500 index that was available during this study through out the back-test. So the question arises that if the returns presented are inflated due to the survivor-ship bias. Honestly, I don’t know. Though I can surmise that if there was any effect of survivor-ship bias on these portfolios it would have been marginal as the best performing portfolio size was of 10 stocks. So, please take these returns from the study with caution.