@Pravin, any trading strategy has for payoff matrix: Σ(H∙ΔP). Therefore an ongoing portfolio's assets can be expressed as: A(t) = A(0) + Σ(H∙ΔP) – ΣExp. The section of interest is: Σ(H∙ΔP) which characterize the trading strategy. And, it does reduce the portfolio management problem to some inventory management methods under uncertainty.
In a market-neutral strategy is requested a 50/50 long/short scenario:
A(t) = A(0) + 0.50∙(Σ(H∙ΔP) – ΣExp) + 0.50∙(Σ(-H∙-ΔP) – ΣExp)
where, -H is the short inventory where profits come from declining prices -ΔP. Evidently, if ΔP is positive on your short trades, you are losing money, just as if ΔP is negative on long.
Such a portfolio should end up with: A(t) = A(0) + Σ(H∙ΔP) – ΣExp.
This is great. It does say that you can have your lunch and eat it too. But, that is on the premise that you make as much on your longs as you do on your shorts.
You could be market-neutral, have low beta, low volatility and low drawdowns, and still maintain your expected long-term average market CAGR. There would be, evidently, trading expenses, but then nothing is perfect. There is always a price to pay.
However, it is not what I see in all those market-neutral strategies. They usually barely beat the risk-free rate, and that is if they do. Usually, performance is less than the average market return which could have been had simply by buying indexed funds.
Since the outcome of a trading strategy depends on the trading methods used, one would have to conclude that the methods themselves are at fault.
For instance, if the trading methods used are not that good at shorting, then we should not expect the short side to do its part. And if the strategy is not that good on the long side either, then we should not expect much from such a market-neutral portfolio.
As for the slide presentation you cited, their methods limit the size of the square matrix used since they need a matrix inverse. Also, they need really sparse matrices where anomalies would be really really sparse, and where background noise would be minimal. None of which the market can provide. And, even from where they are, they are trying to ascertain the size of the forest with their nose on a single tree.
It is like the imaging system. You might not need much math to differentiate photos. You take a snapshot with no people, and one with people. Then isolate the people with a simple subtraction... But, still, it won't tell me where they are going for lunch.
As a footnote. Where were those factors today? What did they predict?
BTW, I found the other mentioned paper on statistical arbitrage by Avellanda more interesting and quite well written. There is more that can be extracted from there.