The Obliquity Portfolios: weighting games

As part of the construction of the Obliquity portfolios, as previously introduced, I’ve had to come up with a way to weight selection criteria and the stocks themselves.

A binary choice

The selection criteria is composed of nine individual factors, which will be introduced in a later post, that are combined to make a pass or fail outcome for each company being considered for inclusion in the portfolio.

I’ve considered three possible scoring schemes:

  • Binary pass/fail
  • Ternary pass/fail/neutral
  • A “star” grading system from 1 to 5 (poor to good)

The star-like system seems to be popular in many contexts and appears to be a sweet spot in granularity to judge, and read about judgements, of qualitative criteria. It’s granular enough to express a variety of opinions, yet doesn’t fall into the excess precision of say a percentage scale. Most people could judge say a hotel on a scale of 1 to 5 but few could make a difference  between 52% and 53% good.

For the purpose of the Obliquity Portfolio, it though introduces the problem that for quite a few criteria, given the resources available to me, the judgement I make is really a vaguely, sometimes very vaguely, educated guess. There is often not enough information to make a 1-5 judgement, while there is often a sense whether the stock passes or not the criterion.

Ultimately, given the issue of trading costs and manageability, the portfolio cannot be the full universe of available stocks weighted according to an average score, so we may as well apply the fact that a stock is either in or out at the level of the individual criterion.

The ternary solution was mildly appealing, but in the end it seems simpler to opt for binary criteria. This wasn’t a strong decision and maybe I will change to a ternary version in the future. Having a middle option would help when the situation is not clear cut either way, or when no or not enough information is available. But then there’s the question that “middling” and “don’t know” are really different things. The finer grained the choices, the more the computation to aggregate the individual scores becomes complicated.

So, despite the imperfections, binary criteria it is. There is some scope for a small amount of cheating, or shall we say flexibility: when two criteria that are hard to decide overlap, it’s possible to consider them in aggregate which reintroduces a ternary choice (fail+fail, pass+fail, pass+pass) through the back door.

As for combining the criteria into the final choice, I use a threshold of seven: the stock must pass 7/9 of the selection criteria to be admitted. This is a practical choice: allowing only one fail would be too tight with too few stocks passing, and 5 passes definitely too weak, so it was 6 or 7, and in the end 7 seems, empirically, a better choice.

Weighting stocks and rebalancing

The weighting scheme for the portfolio is a hybrid of market cap and equal weights: the portfolio buys fixed size allocations, similar to equal weighted, but does not rebalance them so as to behave like a cap weighted portfolio as time passes. This minimises transactions and simplifies record keeping.

The rebalancing scheme is not an issue I need to fix in stone just yet — I don’t expect to have to sell anything any time soon — but the basic idea is that when a position becomes too big — perhaps when it doubles — damaging the diversification of the portfolio, it will be trimmed back to the corresponding lot size, as if it were a new position, if it still matches the selection criteria. The entire holding of a stock that convincingly stops matching the selection criteria will be sold.

In a similar vein, dividends and the proceeds of corporate action will be contributed to the free cash and and when there’s enough spare cash and the market is auspicious, used to buy new holdings that match the criteria. Total return performance contributions can be computed separately.

To account for the greater intrinsic diversification of large caps, I have settled for three sizes: 1 base unit for small cap or special situations with unusual risk, 2 base units for mid-caps and 3 base units for large caps. The allocation to each category is done qualitatively depending on how diversified and risky I think the company is, so say a large-ish but narrow company could end up in the mid-cap section. Although in general there are few surprises: size 2 is for companies that are usually classified as mid-caps and 3 large caps. I’ve not as yet selected any size 1 candidates.


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