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Former All Black captain David Kirk, now chair of Rugby New Zealand, joins Listener.co.nz as a columnist taking a conversational look at money, finances and living well. The cofounder and chairman of Bailador Technology Investments, Kirk sits on a number of other boards including investee companies of Bailador and charitable organisations.
This week, using calculations based on probabilities to decide which companies to invest in, under Donald Trump’s threat of tariffs.
When I was at primary school everyone had a favourite number. Mine was five, the same day of the month as my birthday. Most of the favourite numbers were single digits and as I remember them there were a greater number of odd than even numbers. Lots of threes and sevens and virtually no twos and fours. Not sure why.
Christian religious story-telling and simple theology was prevalent and may have had some influence. The Holy Trinity, the seven deadly sins, and the nine choirs of angels, are set against the 10 commandments, the four gospels and the twelve apostles … except … actually, there were 13 apostles. Matthias joined late after Judas self-selected out.
Soon enough, favourite numbers for no good reason fade away and our heads are filled with a vast array of numbers that mean something. First in the playground are the cardinal numbers: “There are five on our team and you’ve got six. We get a two-try head start.” Then the ordinal numbers: “We get first pick, you get second and we get third like that until everyone is picked.”
In the classroom, we move through the positive and negative integers, fractions, prime numbers, irrational numbers, perfect numbers and at high school, if we have stuck it out that long, imaginary and complex numbers. And then there are the three numbers that aren’t numbers at all but nevertheless have their place in the ranks. Zero, plonked right in the middle, and if we move either way along the number line we arrive at the two infinities at either end. Except, how can there be two infinities when, by definition, one infinity is everything? Two times everything is still the same everything. Hmmm.
What happens next as we learn about the different types of numbers is sometimes fun and often frustrating. We start to be taught how to apply “operations” to numbers. Operations are formulae and techniques that allow us to manipulate numbers for useful or simply interesting ends. Arithmetic is the first and by far the most enduringly useful operation.
After simple arithmetic, we head off into more complicated arithmetic – squares and cubes and square roots and cube roots and all that stuff. And after that to the connection of numbers to spaces, shapes, angles and curves in the form of geometry and trigonometry, and then on to algebra and calculus and whatever else resides on the top of a mathematical mountain I have never scaled. I do know some of what lives in the rarefied atmosphere of pure maths is definitely in the Hmmm department.
After school, most of us have very little to do with formal mathematics beyond arithmetic. Only those working in engineering, insurance, auditing, actuarial and other financial services wrestle with mathematical problems in their daily work.
Arithmetic however is ubiquitous in our daily lives in business and at home, as Mr Micawber points out in David Copperfield: “Annual income £20, annual expenditure 19 and 6; result happiness. Annual income £20, annual expenditure £20 ought and 6, result misery.”
Another branch of mathematics that oddly isn’t taught much at school and should be is probability theory. Probability theory is used casually all the time in our daily lives and should be used in a more disciplined way by most investors.
Probability theory is a many-headed beast, and I will doubtless wander my way back to it sometime in the future but a good place to start is with “probability-weighted outcomes”.
In investment terms, this means that instead of thinking generally about events that might be good or bad for an investment, we probability-weight various potential outcomes.
For example, let’s assume the share market-listed business you are thinking of investing in exports products to the United States. There is talk of tariffs being applied to these products and there are four possible outcomes: no tariffs, a 10% tariff, a 20% tariff and a 50% tariff. You estimate every 10% increase in tariffs reduces the profitability of the company by 5%.
You decide there is a 40% chance no tariff will be applied, a 35% chance a 10% tariff will be applied, a 20% probability of a 15% tariff, and only a 5% probability the tariff will be 50%. You can now ask and answer important questions about your potential investment, including: is there a more than 50% probability of a tariff having no impact on the company? (Answer yes because you assess there is only a 40% chance there will be any tariffs) and, what is the probability I will lose money?
This depends on how much you assess the possibility of tariffs being applied is already factored into the share price of the company. If you think most people are assuming 15% or higher tariffs will be applied and the current price reflects this, but, as above, you think there is only a 20% chance of this outcome, then you should buy the stock.
Postscript: The answer to the paradox of the two infinities is to recognise a misuse of language. We move along the number line in whatever direction through the infinity of numbers. There is not an infinity of numbers waiting for us at the end of our journey. We are already there.
