Momentum and Volatility factors

In a previous post on Fama-French factors we have discussed Market, HML (returns of High B/M stocks over low B/M stocks) and SMB (returns of small market cap stocks over large market cap stocks) factors. In this post we will discuss two factors which are very popular among the Quant traders. These factors have been religiously studied by academicians as well.

Momentum factor (MOM):

This factor represents returns continuation over medium term horizon. In simplest terms, stocks which have outperformed over the last year are going to continue outperforming in recent future. This factor was first discussed by Jegadeesh and Titman in 1993. Since then a lot of research has been done on this factor. Numerous studies have claimed that over long horizon, this factor tends to generate considerable alpha.

Volatility factor (VOL):

This factors talks about future performance of stocks based on their historical volatility. Stocks with high level of volatility under perform stocks with low level of volatility. This factors goes against the traditional wisdom that high returns is compensation for high risk (volatility). In my view this is a very useful factor for stock selection strategies.

Methodology for factor calculation:

1. Everyday top 200 stocks( in terms of market capitalization) are chosen. This is done to avoid survivorship bias.
2. These chosen stocks are sorted based on their past 252 trading day returns. Top and bottom quartile of stocks are selected from this list.
3. The equal weighted out performance of the top stocks (highest returns) over bottom stocks (lowest returns) for the next day is the return of MOM factor for the next day.
4.  Above three steps are repeated for all the days to get a time series of MOM daily returns.
5. The cumulative sum of  these daily returns is the MOM index.

Similarly to calculate VOL factor sorting is done based on past 252 days volatility. Daily returns are then the out performance of low volatility stocks (bottom 25%) over the high volatility stocks (top 25%).

Factor perfomance in Indian stock market:

Following is the behavior of these factors since 2006. First 253 days show zero returns due to the look back needed to compute these factors.

MOM has not generated any significant alpha over the last 6 years. There is a big draw down in the in 2009 when the market was recovering from the 2008 crash. This post crisis failure of momentum strategies is a well known phenomena known as Momentum Crashes.
VOL has been consistently generating alpha over the last 6 years. Similar to MOM factor, VOL factor tends to suffer whenever there is a spike in the market.

Randomness tests:

Following are the result of some randomness tests on these factors:

Test	Parameter	Random Walk	MOM factor	VOL factor
ACF	Lag 1	0	0.25	0.15
Runs test	Number of runs	913	794	803
Variance ratio test	Variance ratio(period=2)	1	1.25	1.15
Variance ratio test	Variance ratio(period=5)	1	1.55	1.28

These factors show significant positive auto-correlation. The number of runs is also very less, indicating trending behavior. The variance ratio is much higher than 1 indicating mean averting properties. Looking at the results of the above tests we can safely assume that the MOM and VOL factors are trending in nature. This is a very important conclusion as it can be used to predict future market regime.

Why bother with these factors?

The most important use of these factors is in alpha generation. With proper modifications these factors can be used to generate considerable returns in a capital neutral fashion.

These factors can be used for market regime identification. They can be also be used to affirm bullish or bearish trends in market(due to negative cross correlations with market). In a true bull market, these factors are going to show a drawdown. 

Returns of various trading strategies can be regressed against the returns of these factors to understand if the strategies are betting on a specific type of risk to generate alpha.

These factors show significant positive autocorrelation. So money allocation to the strategies which use these factors can be dynamically altered based on their recent performance. So a VOL factor long strategy should be allocated less money when VOL factor is falling as the trend is likely to continue.