We all know that over-diversifying our stock portfolios is bad for our wealth. Even if our main aim is simply to avoid the problems of correlated stocks all falling together it's well known that you can get most of the benefits of diversification from a portfolio of no more than fifteen companies. Anything else isn't diversification it's diworsification: it adds no benefit and costs us more. Only, like so many well-known truths about stocks, this is a myth. Owning as few as fifteen stocks opens you up to all of the terrible things that happen to investors that take on too much risk. In the worst case everyone loses money and you get a socialist government. How bad is that?
Defined by Outliers
Consider two portfolios each of fifteen stocks. Each stock holding costs us a thousand dollars. After ten years all fifteen stocks in the first portfolio have doubled and are now worth two thousand bucks each. In the second fourteen of the stocks haven't changed their price at all but the fifteenth holding has multiplied sixteen times and is now worth sixteen thousand dollars. Both portfolios have precisely doubled in price. To a first approximation these two portfolios, chosen at random, will probably correlate to their underlying market which will also have roughly doubled. But how lucky did you need to be to pick up that sixteen bagger? Well, actually, you had about a one in six chance in a fifteen stock portfolio. And, unfortunately, it's the second portfolio with a host of very average performers and the odd standout success that's more typical of the real markets. This, then, is the problem with fifteen stock portfolios: your chance of matching the market is a mathematical artefact of the modelling process. In reality five in six of us will be glumly looking for left-wing politicians under the bed.
Risk Revisted
The problem is that the fifteen stock portfolio is that bane of our imperfect lives, an outcome of a mathematical model, which aims to reduce the diversifiable risk in a portfolio by ensuring we select stocks which aren't correlated with each other, the idea being that if one stock falls dramatically the others shouldn't. This can't eliminate the risk of systemic risk when everything crashes, but it does reduce the pain of individual stock collapses. Trouble is that this is a world…
