Decile Dissection

We often talk about factor returns as a single percentage, similar to a broad index return. The measures are helpful to get a quick understanding, but do not reveal much about the underlying dynamics. A factor’s return (also called a spread) is derived by the difference in returns of the top-ranked stocks and the bottom-ranked. This is done by quantizing the stocks into equal groups of similar rankings, based on a certain metric. Deciles, quintiles, or quartiles are popular to use. A decile spread is the average return of stocks in the top decile (D1) subtracted by the average return of stocks in the bottom decile (D10).

Returns to the momentum factor were extreme in early September. A lot has already been said about those days, including our own previous post. There, we discussed the magnitude of momentum returns, as well as other factors, in early September. Here we investigate momentum a little further. Not to diagnose a cause, but to put the returns into a little more context.

Utilizing our medium-term momentum model within the Russell 1000 Index, we see how September 9th was a large negative outlier and the volatility of the return spread rose sharply in a short period. Also noticeable, is the period between October 2015 and July 2016 where daily spreads and the standard deviation were above normal. So, how were September 9th and 10th even more unique?


Source: S&P Global, 361 Capital Research.

Momentum returns for September 9th and 10th are notable not just because they were the largest negative returns for momentum over the last five years (1st and 3rd in absolute return), but also because deciles 1 and 10 each experienced significant above-average returns, with one positive and the other negative, while the index was flat. To help show why September 9th and 10th were so extreme, below is a table that ranks the top five days (by absolute return of D1 minus D10) in the five-year period ending October 23, 2019. Three days in the first quarter of 2016 also made the list.

Source: S&P Global, 361 Capital Research

What stands out is the muted return of the Russell 1000, but also the z-scores of both D1 and D10 (columns three and five) on September 9th and 10th. (Z-score is a measure of how far each data point is from the mean, scaled by its standard deviation). The individual decile z-scores do not appear extreme on those days. However, the D1 and D10 returns on the 9th and 10th are larger than normal at the same time and the market barely moved. To compare, the Russell 1000 declined 1.2% on March 8, 2016 so the large momentum return makes sense on that day (row 2). The large momentum spread on March 8, 2016 was mainly a function of the decline in decile 10, as decile 1’s return was not extreme. February 4th and March 23rd of 2016 were similar stories. Both saw relatively outsized returns from decile 10 with relatively mild returns from decile 1, with more pronounced index returns.

The graphic below plots the Z-scores for deciles 1 and 10. The coloration represents the absolute return percentile of the Russell 1000 Index. The very light dots are either very large positive or negative returns. The returns for the Russell 1000 are labeled for the dates in the above table.

Source: S&P Global, 361 Capital Research

The scatter plot shows how deciles 1 and 10 were simultaneously extreme, in opposite directions, on September 9th and 10th. The dark blue color of those data points also shows how minor the Russell 1000’s returns were on those days, compared to rest of the period. Points in the top right quadrant are days when both deciles are positive, and the lower left is when both are negative. Those days can be categorized as when most stocks are either rising or falling together on a given day. The top left and bottom right quadrants are when high and low momentum stocks diverge. The bottom right are days when high momentum outperforms lower momentum. The top left is when low momentum outperforms high momentum. The further away from center, the larger the performance of the decile, relative to its average. Again, we can see that neither September 9th or 10th is extreme in terms of individual D1 or D10 z-score. It is the combination of each decile’s above average and opposing moves.

A cursory analysis of the most extreme days in terms of D1-D10 returns over the last five years in the large cap universe, suggests strong momentum returns appear to be driven more so by outsized returns of decile 10 as opposed to a large move in decile 1 (table below). On days where the D1-D10 spread had a positive z-score of 2.5 or greater, the average decile 1 return was -0.59% and the average decile 10 return was -3.05%. On days where the D1-D10 spread had a negative Z-score of -2.5 or less, the average decile 1 return was +0.06% and the decile 10 average was +2.50%.


Source: S&P Global, 361 Capital Research.

Behaviorally, this makes sense. On days of heightened concern and market declines, investors are prone to sell losers, which are presumably riskier, and buy/hold outperformers with the belief that sticking to recent winners is a safer strategy. Interestingly, when the momentum spread is more positive than average (z-score > +2.5), the Russell 1000 is negative and on days when the momentum spread was largely negative, the Russell 1000 increased, on average.

This makes sense too. When investors are more optimistic, they feel confident owning riskier stocks, which tend to be those with recent poor performance. Increased optimism tends to translate to higher index returns as well.

Momentum returns are not just a single “thing”. The overall return is the interaction between high and low momentum stocks. Based on this simple exercise, the lowest-ranked momentum stocks had a greater influence on the factor’s spread on days when there were extreme returns (z-score +/- 2.5).

Read our recent blog post, Market Growth or Slowdown? A Portfolio Forecasting Tool >