I recently received a post on my previous update noting that strong performance records, based on a change of investment decisions, can be a good indicator against a ‘random walk’ hypothesis within financial markets. I replied to the comment noting that, usually, it’s just not that simple.

Having worked with fairly large financial datasets throughout the past three years and, unfortunately, also throughout the painful recent crisis, I’ve noticed one reliable and certain trend out there: it’s easy to find information that you want out of a particular data set. This hindsight and confirmation bias is a basic fundamental (did I mention I liked fundamentals?) that we all have to look out for. Unfortunately, data does spring to our eyes but we are also extremely skilled at choosing to see that which supports us and rapidly ignoring that which inconveniences us.

So Does This Mean The 4!-Moments Algo was Just a Waste Of Time?

Possibly… I am, and will clarify a bit further down, of the opinion that there is something in it at the moment but before I can get to that step I need to check some basic assumptions.

Let’s imagine, for a moment, that the algo is not based on historical prices at all but instead is based on the roll of a six sided dice. If I get a roll above three, I buy, if I get a roll below or equal to three, I sell. I can then complicate the results a little bit by saying that I will weight my orders out based on the latest roll’s value. Now what would I get?

Well I would get something resembling a binomial normal distribution with half buys and half sell. Now, what if I go further and ‘ran’ this algo during the 1000 day windows that I have been reviewing so far? Well, then I would start getting returns from my trades over time. Now imagine that these returns then match up, or even outperform the benchmark over say 55% of the windows tested, then what does that mean?

At first sight, it might look as though I am getting highly correlated returns with the benchmark with a slight amplification factor, but wait a second, all I’ve done is roll a random six-sided dice multiple times… So in fact, all that I’ve proven is that I’ve produced a ‘random-walk’ of returns and that’s about it. No super model to predicting the market, no magic free returns, just rolls of the dice…

But Wait… That Didn’t Answer the Question, is the 4!-Moments Algo a waste of time?

Okay, now there are other factors out there in the model but perhaps, again, this is just the result of confirmation bias: I am looking therefore I see but that’s only because I’m blind to begin with.

So what are the factors that might be interesting and that need to be verified? Well, there’s the correlation issue that is observed and needs to be explained. Perhaps it is purely a random occurrence that just builds up during particular periods randomly. So I would need to check how random those correlation patterns actually are (in fact, they’re quite temporal and within particular performance bands, but again that’s not enough in and of itself to mean anything).

Well then there’s the hedging factor and the fact that it seems to position itself quite well during harsh times usually providing at a minimum up to 100 to 200 basis points ahead of the benchmark. Hmmm…. Not quite good enough either. The benchmark is one running index, the algo runs on cash and the index, so it might just be randomly entering late but getting the early return from risk-free cash which can be enough to skew the performance up, but nothing either predictable or valuable. Instead what we would then have are the differences between two investment models: one mixed cash/equities, the other straight equities, but both are still random yet slightly correlated.

Well, is there anything out there?

Okay, you might have noticed one aspect of the model that I’ve highlighted across the different run tests: the momentum sensitivity factor. Now let’s say that I can change this factor through-out and, as a result, create different standard deviations of returns and control the benchmark correlations as well. That I can define this within particular narrow bands and also relate this across trading windows. That the 4!-Algo could maintain a consistent lower standard deviation than the benchmark and also set itself to skew itself away from the benchmark as it’s own volatility increased. Perhaps here we might, and might is used loosely here, have something… Perhaps…

One thing you might have noticed though is that the algo offers more ‘normal’ returns than the BM when run over particular timeframes, the 90s to today being one particular example, which again might look interesting. But remember, you could probably still get this from just rolling the dice as mentioned above… The question then becomes: is it more efficient/profitable to roll the dice or to run the algo once you are net of fees and transaction costs? (FYI all returns presented so far were net of fees and completely unleveraged…)

I hope this little interlude gives a bit more depth into some of the research so far which is still at very early stages. As I mentioned before, this was a stylised model: let’s run a momentum algo through loads of data and see what we get. And, as I said before, I could have left it just there, but then the whole thing took a momentum of its own…

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