## Perfect, Putrid and Mediocre portfolios

I cam across an interesting blog article by Patrick O’Shaughnessy, “The Putrid

His argument is largely this: let us define the “Perfect Portfolio” as those stocks that perform the best. If you then apportion those stocks by starting valuation, you find that they appear most often (13%) in the cheapest decile. There’s a cavaet, though: the distribution of the star performers has a fair amount of uniformity to it. 12% percent lie in the 8th decile (i.e. towards the expensive end) and 11% lie in the 9th percentile.

Contrariwise, if we define the “Putrid Portfolio” as those stocks that perform the worst, then there is a definite skew in favour of the cheap end. Only 6% of the stocks that performed abysmally were in the cheapest decile, whilst over 25% of them were in the most expensive decile.

So, the ratio of Perfect to Putrid was around 13:6 (2.17) for the cheapest decile, they were 9:27 (0.33) for the most expensive decile.

The author concludes, therefore, that it is best to search in the cheap deciles, where your odds are better.

It’s an interesting article, and I’d like to add some thoughts of my own.

One problem is that he doesn’t give us the probability of a stock being in the perfect portfolio. He chooses 25 stocks out of the liquid large-caps. Well, how big is that? Is that 100 stocks, 500 stocks, 1000 stocks, 2000 stocks?

It would be useful to know this. For although we know the probability of being cheap given it has superior performance (13%), we don’t have enough information to determine the probability of a superior performance given that it’s cheap (which is the number we’re most interested in).

If I assume that the “liquid large cap” universe consists of 500 stocks, then I have around only a 6.5% chance of selecting one at random if I choose from the lowest decile ( there will be 50 stocks in the lowest decile of cheap, 13% of the 25 of the 500 will be stellar performers, i.e. 0.13*25/500). Those are not especially good odds, and they will only get worse if the universe is a lot larger.

Secondly, although the cheapest decile is the best, the odds look fairly comparable if one were to choose from the cheapest third of stocks.

Thirdly, one can’t necessarily make deductions about correct choices solely from percentages. One needs to know payoffs. For example, suppose I give you a choice of 2 boxes: red and blue. If you choose the red box, then there is a 25% that you will win £100, but a 75% chance that you will lose £10. If you choose the blue box, there is a 75% chance that you will win £10, but a 25% chance you will lose £10.

Which box will you take? Well, with if you choose the red box, you will more than likely lose if you just look at probabilities alone. But, the expected return for choosing the red box is £17.5, whilst for choosing the blue box it is £5.

Although my example is of course fictitious, and I can make up whatever numbers I want to prove my point, it is often the case that the markets tend to skew there returns.

It is, perhaps, a trifling consideration, especially as it might be a reasonable to hypothesis to assume that the payoffs are similarly distributed between the low and high deciles.

Fourthly, we need to consider what I might call Mediocre portfolios, i.e. portfolios that a not perfect or putrid, and basically don’t do much. As the universe of stocks gets bigger, so does the pool size of the Mediocre stocks. As the Mediocre pool gets larger,then it will increasingly dominate the returns you would expect. My previous point about expected payoffs looms even larger.

There’s an interesting repercussion to this. If you expect the pool of mediocre investments to be large relative to the perfect and putrid portfolios – which seems like a pretty good assumption to me – then one of your best strategies would be to look at cheap stocks (say the bottom third) and deliberately try to avoid mediocrity. If you manage to do that, then you are much more likely to outperform.

I haven’t, of course, defined mediocrity. The sort of thing I had in mind, though, are perhaps what I might call “reasonable probability, low upside” stocks … the ones that most sensible and sane value investors are likely to choose. If you have a system for ejecting the putrid ones too, then your system will work even better.

It also argues in favour of a well-diversified portfolio, in recognition of the fact that the process is a largely statistical one. It also seems an interesting area to apply Fuzzy Logic; but I am not familiar with the mathematics of it.

Just something for you to think about.