Portfolio Sizing

For a long time, I kept thinking what is the best strategy for deciding how to decide on the optimal size of allocation to a given stock.

Valuation and default allocation choices

I agree with Aswath Damodoran that valuation is part science and part art, which makes it a craft. I see how people can reasonably disagree over valuation of the same company and because we cannot know the future, it will never be an exact science. There will always be a necessity to use a judgement call (which is also why AI will not replace humans in high-level capital allocation, but might be a useful input if not too blackboxy). It is worth noting that I am a fan of concentrated portfolios - I usually have less then 20 stocks, excluding times when I "index" into some market.

The most straightforward choices I see are:

1. Equal-weight
2. Market-cap based

On one hand, equal weight sounds promising - if I feel good about owning a small set of companies on risk/reward basis, why not like them equally? But that makes it hard to make two kinds of bets - a rock-solid, well undervalued company where I feel good to "bet the farm" on it. Think Berkshire until recent run-up in price or Buffet's 40% bet on American Express. On the other hand, if I find high-risk, high-reward stock, I might prefer to limit the maximum loss in a concentrated portfolio.

But as a value investor, I have some valuation (or distribution of them) and perhaps some 'confidence' attached to it, right? It seems natural to use these to make decisions on buying/selling a certain number of shares at certain prices. This should be an easy task to do this in optimal way and it should enhance the returns, while reducing risks.

Alternative stock allocation and pricing buys and sells

To my surprise, I could not find much on the topic with casual Google search. Asset allocation is of course big, but irrelevant topic. Kelly criterion is often mentioned, but rarely in the context of multiple simultaneous allocations, let alone stock market. And I could not find anything based on assessment of intrinsic value. Perhaps this is a result of inherently individual way in which value investors assess intrinsic value and their confidence in it.

One more problem that I found little discussion of is how to price entering and exiting a stock. How to go beyond "buy once - sell once"? One could consider such decisions independently for each stock purchase/sale, but that's problematic given that these concern the same stock and therefore expected returns are highly connected, even with different buy/sale prices. I read some value managers buy half of a position initially, to allow buying more if it goes down. Or keep 30% of the stock even if it exceeds assessed intrinsic value, to make use of the momentum. These are all interesting ideas, but there is no 'science' to them.

Today, I mostly rely on my gut feeling and scale the investment with my confidence the value assessment. I also try to average down. The challenge with the latter is that when my recent Valeant purchase went down 15%, I have bought additional shares with too narrow steps and in total more than what I would normally consider a reasonable allocation for such a risky stock. In even more cases I undersized my position because market went away from my limit orders (recently: Fairfax, Gilead, Markel, Pershing Square Holdings, Alleghany, Valero). My top investment is roughly 50x the  bottom one. All of this seems to be a very suboptimal approach.

Long time ago, I read about progressive asset-allocation system called SIP (in Polish). It was quite novel and interesting, and while I outgrown many of the assumptions that this system makes (using futures to go long, expecting 20%+ yearly returns, stock-markets-always-rise, etc.). I think this is an interesting twist on dollar-cost-averaging and the idea of "expected price" can be easily swapped with intrinsic value.

Backtesting

I am not a big fan of backtesting complex algorithms on financial data. Markets and businesses change. There are various one-time events such as abandoning gold standard, PC/Internet revolutions, HFT, surge in index funds or stock-based compensation accounting changes that make various periods hardly comparable. And one cannot simply do an objective intrinsic valuation of a company from long time ago, as "future" will inevitably spill into their thinking.

But backtesting a stock allocation system might make sense, even with a few years worth of data and intrinsic valuations. Perhaps even analysts' price targets might be used in lieu of own intrinsic valuation, as I am only concerned about alpha provided by asset allocation, not the quality of price targets themselves.

I will try to come up with such a system, see how it would perform for my recent investments and maybe also do some backtesting.