How Momentum Can Coexist With Weak Return Autocorrelation
Summary
The document addresses an apparent conflict: returns may show little short-lag autocorrelation even when price charts appear to trend and momentum strategies are used. One explanation is that return dependence can differ by horizon. Adjacent returns may be negatively correlated, consistent with short-term mean reversion, while returns separated by a longer interval or aggregated across multiple days can exhibit positive correlation. Thus a momentum signal based on multi-day returns need not be captured by testing only consecutive daily returns.
A second response notes that random fluctuations in returns accumulate into visible price paths, and cites research showing that unbiased random walks can produce apparent trends. This cautions against treating visually persuasive runs as proof of a predictive effect. The discussion gives no empirical test of the Bitcoin example and does not establish that a profitable momentum strategy follows from these observations. It also flags that price levels are nonstationary, which complicates formal correlation analysis.
Key ideas
- Return correlations can differ across short and longer horizons.
- Negative correlation between adjacent returns can coexist with positive correlation in returns separated or aggregated across multiple days.
- A momentum signal should be measured at the horizon relevant to the strategy.
- Random walks can generate visually convincing price trends without predictable returns.
- Visual trend patterns alone do not establish a profitable trading effect.
Tags
Full text
# How can momentum trading strategies work if returns are not serially correlated?
# How can momentum trading strategies work if returns are not serially correlated?
Returns are demonstrably not serially correlated in most financial time series (Day 1 returns are uncorrelated to Day 2 returns etc.) . Since this is the case, how can momentum trading strategies work? What is the mathematical basis that can explain why momentum trading strategies work if there is not, in fact, a correlation between today's price movement and tomorrow's?
EDIT: As an example, take Bitcoin (it's what I'm looking at). I think it is intuitively/visually/conceptually obvious that there are strong momentum patterns. However, I have looked at autocorrelation in returns on timeframes ranging from 1 day to 30 days, and there is no autocorrelation. Perhaps my question should be the following: How can this "subjectively obvious" momentum be expressed, if not in autocorrelation of returns (which is absent)?
## Answer by Michael Isichenko (score 1)
https://quant.stackexchange.com/a/67881
Let $R_d$ be the return for day $d$. Mean reversion means that $cor(R_d,R_{d+1})$, $cor(R_{d+1},R_{d+2})$, etc. are all negative--which is actually close to truth. Under conditions not too hard to come up with, you can have $cor(R_d,R_{d+2})>0$ and $cor(R_d+R_{d+1},R_{d+2}+R_{d+3})>0$ simultaneously with mean reversion. The last inequality is a two-day momentum. As correctly stated in the comments, momentum is usually observed over longer horizons (and occasionally also intraday).
Correlation inequalities are useful and demonstrated by a quant interview question (among others in this book): If the correlation between A and B is 90% and the correlation between B and C is 90%, what is the correlation between A and C?
## Answer by demully (score 1)
https://quant.stackexchange.com/a/67883
The crux of the answer is that a non-significant serial correlation will produce significant price action. Granger and Newbold (1973) showed that completely unbiased random walks of returns generated statistically significant "trends" in price more often than not :-)
[The rising variance over time violates the stationarity of price, if you want to get formal]
That is the essence of the problem here ;-) DEMShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.