# How Much of Momentum Is Caused By Randomness?

This is an example of a broad question we should always ask ourselves: "what would the random version of some process look like?"

*Randomness In Momentum Everywhere* (Link)

This post from Breakingthemarket.com contends that *randomness and rebalancing undoubtedly explain SOME of the findings* in favor of a momentum effect.

**Key Takeaways**

**Rebalancing increases a portfolio’s returns**

*The more often you rebalance the greater the benefit. With the 30 components of the Dow, increasing the rebalancing frequency increases both the portfolio’s arithmetic and geometric returns.*

Since most momentum studies examine portfolios which filter and rebalance momentum candidates, we would expect to see improvement over a passive benchmark due to rebalancing alone.

- Consider one of the original momentum studies by Jegadeesh and Titman:

*Their methodology is actually an equal-weight rebalancing scheme, with the 3 month “holding period”, serving as a 3 month rebalancing period, and a 6 month rebalancing period, a 9 month rebalancing period, and finally a 12 month rebalancing period. The finding that “momentum” is strongest over the shorter period and fades as the holding period grows is not a finding about momentum. It’s exactly what you would expect from random behavior when adjusting portfolio rebalancing frequency. Yes the slope of the momentum curve is much higher, but momentum stocks are also much, much more volatile than dow components.*

*This turns out to be a hint as why momentum is “found everywhere”. The act of rebalancing which is common to all the studies.*

- Note that finance blogger Jesse Livermore
*got close: momentum failed to work in individual securities but worked in indexes.*Recall from Fernholz discussion of EGRs, that portfolios have better logreturns than the weighted average of their components because the cross-correlations reduce the variance of the basket. Arithmetic return and geometric return differ by the the amount of variance.

**Momentum is really a volatility screen**

*Imagine two groups of 50 stocks. The first has an average return of 5% but volatility of 25%. The second has an average return of 10%, but a volatility of 15%. If you let the stocks randomly produce returns for a short period, and then select the 10 best stocks, is your sample more likely to come from the first group or the second?**Because the first group is more volatile, it is more likely to have extreme losers and winners. Momentum is a gigantic volatility screen, more so than a “momentum” screen. The momentum screen will lean toward picking stocks with higher expected returns. But importantly it will also be filled with high volatility stocks even if they have average or poor returns.*

**Fading momentum is explainable by geometric return math**

*Momentum is said to “fade over time” but this is exactly what happens with random returns as “All random compounded returns start out producing returns equivalent to the asset’s arithmetic returns. But with every repetition, the returns will converge toward a geometric return. A portfolio of stocks slows down this degradation of returns toward the geometric return, but it still happens.”*

*Note how a portfolio slows down the process of degradation vs single stocks**We already know momentum screens select high volatility stocks. High volatility stocks will inherently have a large spread between their arithmetic and geometric returns. Therefore,***the shape of the momentum return stream over time isn’t really an anomaly at all, but is expected…You don’t need stock “momentum” to explain the results of the study. The rules of the strategy alone create the illusion of momentum, even with random coin flips.**

**Randomness as the benchmark**

He concludes:

*Technically, I’m not saying that randomness explains ALL of the momentum effect. It may. I’m saying randomness and rebalancing undoubtedly explain SOME of the findings of these papers. The process of selecting high volatility stocks and rebalancing them frequently produces most of “momentum’s” performance. If researchers compared their results to a random data set, they would see this.*