Probability pertains to a relative frequency of occurrence.
Probability is a logical relationship between evidence and belief.
Probability measures a subjective degree of belief.
Probability is a measure of the propensity to occur.
- From Willful Ignorance
When we talk about probability, there is no simple definition. The above are four simple descriptions which provide insights on how to think about probability. It is work just sitting back and focusing on each one of the these.
Missing Billionaires: A Guide to Better Financial Decisions - This is a good book. It has been on several best books for the year in 2023. It is also an oddity. It is a book of investment advice for everyone, but it does not pull any punches with being simple and just wordy. It is grounded in modern finance with all the math that is necessary, yet it is still accessible and easy to read. Never has a set of authors done a better job of explaining the usefulness of expected utility and the use of core finance embodied by the work of Robert Merton.
There are two core theses with this book. One, make sure you get your bet sizes right. Two, understand your expected utility through knowing your level of risk aversion.
For the first point, understand the Merton share which like the Kelly Criterion states that the optimal bet size is related to your level of risk aversion time the expected return relative to volatility. There dictum is very clear. Do not take too much risk in any part of your portfolio. Temper your bets to ensure that you can maximize wealth through staying in the game.
The second point is critical for setting bet sizes, know and understand your risk aversion. You are not indifferent to risk and this aversion can be measured. When risk aversion is measured, it can help set bet sizes and portfolio risk.
The amazing part of this book is that seasoned investment professionals will get a lot from this work just the same as a novice. Even someone who has studied formal finance will find their framework thought provoking and useful.
Richard Nisbett, a leading psychologist, wrote a great book on the current research on how to think smarter in his book MIndware: Tools for Smart Thinking. This book provides more than an easy to read review of modern psychology research and thinking but an approach to viewing decision problems many will face. For an investor this is a great book for improving your thinking skills. While many of the chapters describe behavioral biases, the book provides a fresh take on how to implement this work to sharpen your decision skills. The take-aways from each chapter are helpful.
The schema and framing of problems matters. We often use the representative heuristic to find similarity, yet that framing creates the wrong assumptions. All perceptions and beliefs are just inferences which can be biases by incidences and irrelevant perceptions that affect our judgment.
Context matters and situational factors influence or behavior and as the environment changes so will we. Hence, it is critical to be formal in our thinking and generate a cost/benefit analysis to move beyond on unconscious thinking. Sunk costs are sunk and opportunity costs are real.
We are lazy, so we want to maintain the status quo and are susceptible to the endowment effect. Realize that observations are only samples, so you need to think about getting more data for any problem to reduce sample error. Of course, correlation is not causality and must always be placed in the front of the mind. When we think about correlation relationships, we must also consider reliability and validity. What we see and count is not immediately the true reality. We are susceptible to illusory correlations.
Even reasoning can be flawed; syllogisms from Western logic is a different perception of thinking from Eastern dialecticism. Others see the world differently which impacts decision-making.
Follow Nisbett's thiking and be a better decision-makers
Willful Ignorance: The Mismeasurement of Uncertainty by Herbert Weisberg is a great book on the history of probability and the measure of uncertainty. It is not so much a history but rather a discussion of how great thinkers have tried to develop probability to address problems of uncertainty.
Many of the great early thinkers about probability focused on gambling with set rules of the game. In real life, there are qualitative issues with uncertainty for which we must employ ignorance to make problems tractable. There is the need to think beyond the simple probability problem set-up and create a broader vision on problem context which addresses issues of uncertainty. Is this necessary? No, but thinking about uncertainty will lead to better problem descriptions and solutions.