I would like to start the process of thinking about equity factors. The goal is to understand how they're being used and also to come up with my own way of using them. First of all I am going to invent a historical narrative as a way of understanding how factors fit in to the world of investing, and what's likely to happen to them in the future.

First, there are two communities of analyst whose work is being replaced here. Equity analysts and econometricians. For over a hundred years, there have been approaches to the question: what investment should I make? And the first and, to my mind, most important kind of answer here is an economics based one - in which asset classes, with which distribution of capital and with which strategies. To answer, it would be great to have a predictive model of how the business cycle works . That way, you can drive your asset allocation and your sector rotation etc.

That's currently clearly not an easy path to take. Some macro based hedge funds do indeed excel at this, and even over long periods of time.

I am very drawn to this approach.

But bond futures, yield curves, international fx markets, derivatives, interest rate swaps, volatility regimes are all rather hard to get your head around.

Equities are in many ways simpler to understand by the masses, and the equity markets are also quite well developed. So there has sprung up a dedicated equity market in the West, which can sometimes make contact with economic models, but which also equally is happy puttering along in its own world.

In that world, then, there are some people who give advice on which equities to buy - in reality this too is a capital allocation question - implicitly you can assume that you own the market to start with, and all you're deciding is to which degree are you idiosyncratically deviating from this perspective.

The corresponding static (seemingly static) starting point for the economic model is some generalisation of the portfolio theory of Markowitz. Originally that theory asked what ratio of capital should be allocated between competing assets. Generalise that up and throw in all possible investable asset types and you can reach, in theory, a static level which maximises your expected returns over multiple business cycles. And this ratio ought to be the kind of mix we all have in our pensions.

Of course, the investment industry doesn't work like this and insofar as we each manage our own pension contribution ratios, we are all likely to be sub-par on this ideal static perspective.

Next you'd like the model to move. Not so much a singular static set of allocation parameters but a set of time-based ones which can then become sensitive, in theory to the vagaries of the business cycle, of the credit cycle, of the monetary cycle, of sector rotations.

When this is all sorted out, you'd then like to optimise your participation in the various markets - the bond and stock markets both have thousands of single names in there. Can I do better than owning the market? On this premise, most investment management is based. In general, the answer is NO. But marketing budgets, general ignorance and suspicion that knowledgeable insiders might know better than you leads one one to evacuate a large fraction of our potential lifetime investment profits down the gold plated toilets of the yachts of hedge fund managers the world over.

But equity markets take a special place in the hierarchy of potential investments. Because they correspond to entities and behaviours we ourselves feel comfortable with, this particular asset has become well developed and is indeed the heart of the capitalist system - perhaps one chamber anyway.

In other words there are people whose lives are dedicated to encouraging you, for a fee, to purchase a different mix of stocks than the market mix.

The investment professionals who do this come in all shapes and sizes but on average, after fees, they are not worth it. Individually, however, they can be worth it. Those individuals themselves have a method. That method can be parameterised and to some extent, replicated in an algorithm. Those algorithms constitute the centre of gravity of equity factor modelling. They determine what gets measured, what training data-sets are out there, what perspectives people look at. Part of the unspoken impossibility of equity factor modelling is in understanding which of these has any juice left, and how best to interpret them.

Equity factor modelling can be seen, in a way, as an attempt to do two things. First, to take a successful investment manager's success, analyse it, parameterise it, commodify it, turn it into an algorithm and apply that algorithm on an industrial scale (covering significantly more names than any one group of investment professionals can).

Second, there is a realisation that even among the better investment professionals, there will be behavioural biases, constraints, limits, and that in the market itself, there will also be mispricings based on these same behavioural biases - persistent discrepancies which can theoretically be exploited to make your returns on equity investment better than the market average.

This immediately begs the question: how long can any one wrinkle be exploited for? In the last 3 or so years, there have been literally hundreds of multi-factor ETFs created. If these prove popular, then they ought to iron away any advantage they spot. So the long term success of equity factor modelling it always going to be self-limiting.

Having said that, certainly for the next 30 years, there appears to be potentially enough juice in equity factor modelling to make it a viable and attractive business.

There's a bit of a catch 22 situation here. By the time there exists products which help equity factor modellers get their hands on the right kind of historical factor data, that implies you're already down the road a bit in the journey which leads to the factor being arbitraged away. Second if you're too early to the party with a new factor nobody has examined yet, then there's a chance the market won't see it yet as a mispricing and no convergence will happen, meaning that you observe no edge in your post hoc pnl.

I will call this the

**entropic fate of specific factors**. Too young, they appear to be noise to the market, too old, they are arbitraged away.
Even during their observable life, there is the problem of the optimal selection of factors for the current moment in time. Factors come in and out of fashion. Factors stop working for a while. Factor mix perhaps changes in ways which are poorly understood, This I will call the

**circadian rhythm of factor sets**.
And at any point in the life of an active factor model, there will come a moment when a new factor is born and you want to know how best to integrate it to your factor model. This I will call the

**ecological adaptation**of your factor model.
This last point is related to how you decide to add factors to your model, even at the outset.

Either you can get an edge with a factor model or you can't. Assuming a position of humility, the default factor model ought to be treated as a hurdle you only jump over when you are sure you can. When in doubt, the best is to revert to a model which just buys the market. This ought to be a general principle which takes you all the way back up to a static asset allocation which works in all weathers and economic climates. Only bother to deviate from the single market owning allocations when your confidence threshold is reached.

So the first principle of equity factor modelling is: this just may be self-deluded costly baloney, so move cautiously.

A decent leverage starting point is to see who's in the multi factor game and in particular who is offering those as product offerings. Which factors keep coming up and why. Perhaps it will turn out best to just buy these ETFs , perhaps with a degree of timing driven by an economic model.

However, separate from any investment consequence, I would like to pursue a more under the hood academic interest in the subject. I would like to build my own in principle.