By Peter Logan, University of Technology, Sydney

The last Space Shuttle recently returned to Earth. That reminded me that 45 years ago I was undertaking a PhD in physics at Australian National University, investigating the re-entry of the space shuttle. A fellow college student was doing his doctoral research in economics and was convinced that the easiest way to make money was gambling on horses. This provided us with a diversion from our doctoral research. We collected lots of data on horse racing. We found that it seemed possible to make money because other punters wanted a quick return on their investment. People would rather have twenty returns of $1 than one return of $20. So by betting on a certain class of horses quoted at long odds, it was possible to make a modest profit. We obtained our PhDs and moved on.

Recently I discovered that another researcher had apparently discovered the same phenomena and related phenomena that we had, gave it a name (Prospect Theory), won the Nobel Prize for Economics in 2002 and also became the author of an excellent bestselling book: Thinking, Fast and Slow.

As we considered that gambling on horses was not a noble (or Nobel) profession, we moved on to the stockmarket with our modest capital and our ways parted. This paper reflects on my findings about the stockmarket from an academic perspective and notes the role “rocket science” played in those observations. My interest and the perspective of this paper are in long-term investment, not day trading.

Forecasting

As one wise physicist said “prediction is very difficult, especially about the future”. I reasoned that the best judge of the future was the past. Hence, at the start, I looked for companies whose value had increased by 20% over both the last year and by twenty per cent per year over the last three years. This data was readily available in most investment magazines. This proved reasonably successful and required little effort except trawling through the data of the more than 2000 stocks listed on the Australian share market to find stock that met the criterion. Recently, spreadsheets have greatly assisted that task.

There is a related method that uses the past to predict the future which is called a “chartist” approach. With this approach one simply draws the graph of stock prices against time and extends it into the future (extrapolation). Of course the price will jump and to obtain a smoother curve, people take a moving average over an appropriate period. Suggested periods are 5 days (a week) and 21 days (a month).

I developed an approach, similar to graphing, with relatively new companies. It was suggested that in times of early growth, the growth of the company follows a graph like that shown in figure 1. The company grows slowly at first and then takes off and grows very quickly until finally reaching a saturation point. I came across this type of graph during my doctoral research. In the sixties, we used photographic emulsions to record the data. The graph that specifies the emulsion is called a Characteristic curve and is a graph of the density of the photographic emulsion against the light intensity falling on the emulsion (expressed as a logarithm). This graph had the same shape as the one displayed in Figure 1.

Figure 1. A graph of price against time for new companies.

Peter Logan

From my doctoral research I had the equation for this curve and so it was quite easy to match a stock growth curve and come up with the equation. This was done using a statistical package and 2 or 3 years of data. The statistical package also tells us if the equation is a good fit to the data and, if so, one can predict future behaviour and the apparent “saturation” value.

Fundamentalist approach

The other approach is called the fundamentalist approach. If the current fundamentals of the company are poor, the past performance is immaterial. Analysts using this approach have a number of favourite parameters to calculate and criteria that must be met. These include: return on equity, return on capital, earning yield, price to earning ratio, price to net tangible assets, earnings per share growth and earning stability. These definitions can be found on Wikipedia.

Analysts believe that, from past experience, it had been seen that the increase in share price had been related to a particular one of these parameters or a combination of parameters. Using the selected criteria, one can obtain a list of appropriate companies, but then one has to determine how to rate the companies on the list. It is straightforward if only one parameter is involved, but what happens if there is more than one relevant parameter? A statistical analysis can provide the most important parameters and their weightings.

A recent analysis I carried out on Australian shares showed that the important parameters were the ‘return on equity’, the ‘earning yield’ and to a lesser extent the ‘price per net tangible assets’.

A mixture of approaches

There is, of course, no reason to only use fundamental parameters in the statistical analysis in the previous section; one can use past performance as well. This results in an equation that combines both approaches and the statistics gives the relative weightings. When this analysis was done, the important three parameters for Australian shares were found to be the ‘return on equity’, the ‘earning yield’ and the ‘return over the last twelve months’.

Behaviour of the markets

The normal (or Gaussian) distribution was developed for measurements in physics, but can be applied to other situations. However one situation where it cannot be applied is the behaviour of the stockmarket The distribution of the daily variation of the stock index has a tail that is longer than that of the Normal distribution. For example the chance of a price movement of three standard deviations on a normal distribution is about one in 370 whereas it has occurred fourteen times in a recent 750 days period in the ASX. Unfortunately, Black and Scholes used the normal distribution in their famous equation and Scholes won the Nobel Prize in 1997. Scholes’ investment company “Long-Term Capital Management”, which used their equation, collapsed in 1998.

The phrase “black swan” was coined by scholar Nassim Taleb after hedge Long Term Capital Management collapsed after an unexpected Russian government debt default. Image from www.shutterstock.com

Zipf’s Law

Due to a chance meeting with an anthropologist in Papua New Guinea, I used my mathematical model for the behaviour of a shock front to explain the behaviour of different village populations in the rural areas of developing countries (Physics for Anthropologists). As a result, I came across Zipf’s Law, which says that one expects the second largest entity to be half the size of the first, and the third largest is one third the size of the first and so on. So the nth largest entity is an nth the size of the largest one.

A recent analysis of the top 200 Australian companies found that the Market Capitalisation (MC) can be expressed as a damped power law distribution, called the Zipf-Mandelbrot Law.

How big a portfolio?

It is universally agreed that you should invest in more than one company. A Bloomberg report noted a recent Finnish study that found a direct link between IQ and equity market participation. Tobin won his Nobel Prize in 1981 for his “don’t put your eggs in one basket” portfolio theory. Glossy business magazines tend to suggest ten to twelve companies, whereas Mandelbrot in his “The Mis-behaviour of Markets: A Fractal View of Financial Turbulence” commented that conventional wisdom holds that, if picked correctly, thirty different stock can provide an optimal portfolio, whereas he found you need three or four times that number for optimal performance.

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Peter Logan does not work for, consult to, own shares in or receive funding from any company or organisation that would benefit from this article, and has no relevant affiliations.

This article was originally published at The Conversation. Read the original article.