Return Autocorrelation, Momentum, and Portfolio Weighting
Summary
The document asks whether a stock with high return autocorrelation deserves a larger portfolio weight, including when its Sharpe ratio is poor. The response cautions that apparent predictability must persist and generate gains after transaction costs and slippage. It also warns that a short-lag AR(1) view may miss a slower momentum process, while modeling many lags can create multicollinearity and overfitting risk.
The response argues that serial dependence may indicate a broader momentum effect rather than a simple next-day forecasting signal. It says that if returns are not independent, conventional mean-variance allocation assumptions may no longer provide a sound basis for setting weights. It does not offer a replacement allocation method, empirical results, or a way to distinguish robust autocorrelation from noise. Thus, autocorrelation alone is not presented as sufficient grounds for overweighting an asset; costs, persistence, model fit, and allocation assumptions all matter.
Key ideas
- Return autocorrelation is not enough to justify a larger portfolio weight without evidence that it persists and survives trading costs.
- A daily AR(1) model may fail to capture slower momentum behavior or intervening corrections.
- Models with many lagged returns can become difficult to estimate because of multicollinearity and overfitting.
- Serial dependence challenges the random-return assumptions underlying traditional mean-variance allocation.
- The response identifies no alternative weighting rule or empirical test for deciding how much to allocate.
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# Should a stock with high return autocorrelation be weighted more heavily in a portfolio? # Should a stock with high return autocorrelation be weighted more heavily in a portfolio? Some say the presence of autocorrelation (aka serial correlation) in a stock's financial return time series helps with forecasting its next-day movements, unlike a stock that has low serial correlation between its return observations. Does this mean that a stock with high serial correlation should be weighted more heavily in a portfolio with other stocks that have lower serial correlation than it? Why? What if the stock with high serial correlation has a lousy Sharpe ratio? ## Answer by demully (score 3) https://quant.stackexchange.com/a/60937 Hmm... some notable implicit assumptions made en passant here ;-) How persistent are these autocorrelations (ACs)? Let's unpick a little. One obvious question is whether your AC process is strong enough to overcome transaction costs and slippage, if markets are almost-random. Then someone trying to trade that could easily just get their position sizes whipsawed for little or negative net gain. Then there's the question of what your autocorrelated AR(1) process looks like, if you look at it from an AR(2) perspective. How consistent is the correlation of T-1 and T-2 implied by the betas here with the correlation of T-2 and T-3? The latter being T-1 versus T-2 with one day's lag, does the autocorrelation process change to something different overnight? To which the answer I'd give, if I were asking your own question myself, would be that there could be a serial momentum effect. But that it was a broader issue than a daily AR(1) process. The underlying process was more like a 65-200d undercurrent. The problem trying to model trading this are obviously intra-period corrections. You are faced with a menu of momentums; and which are the more relevant? Put in its most horrible possible way, an AR(200) process that allows for a slow autocorrelation process creates 200x200/2 = 20,000 interactions between your lagged variables. You don't have a p>n regression problem, because you're only looking back 200 days and thus have 200 inputs. But it's a massive incentive for the model/fit to overfit through multicollinearity. I merely suggest that the investment-related industries are overweight econometricians; and if they hadn't tried to find some ARCH, GARCH, ARMA, ARIMA, etc. "secret sauce" to markets on their own time, they'd probably already have been fired. But yet momentum still seems to be a "thing". A thing that pisses these people off like no other, precisely because it defies modelling. It defies rational explanation theoretically; while being so tantalisingly beyond reach ;-) To your actual question, even if the momentum effect was real and measurable, then - THEORETICALLY - this should NOT cause you overweight such assets. The reason being that the invalidation of random residuals pretty much blows the traditional mean-variance framework for asset allocation out of the water from the get-go. Pragmatically - if it works, of course you should buy them and avoid the rest. But your answer to how much is predicated on a random process that is no longer random! Null that hypothesis; and you need to re-invent asset allocation... that's the real problem here. keep well, DEM
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