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