Geometry of profits
If we are intellectually honest, as investors we will probably be wrong a few more times than we would like. And the longer the investment career, the higher the accumulation of errors. How can successful investors survive them and continue to build on their success?
In vacation mode, I was rereading some vintage Graham and Dodd, and what struck me was how minimal the damage from their mistakes would be, thanks to the safeguards built into their approach.
Benjamin Graham and David Dodd, through their groundbreaking work Security analysis (first published in 1934) and Graham’s later The intelligent investordeveloped a disciplined value investing framework explicitly designed to protect against judgment errors, unforeseen events and market volatility. While their approach famously shifted investing from speculation to rigorous business analysis, it was the built-in safeguards that limited the damage from inevitable mistakes.
The central element of the process was, of course, the margin of safety: buying securities at a significant discount to their conservatively estimated net asset value. If we ignore the material component of the intrinsic value calculation, the discount acts as a buffer because:
- It absorbs errors in valuation (for example, overestimating earnings and earnings growth), and
- It protects against setbacks in business, economic downturns or market downturns.
Graham and Dodd emphasized that the margin must be large enough so that even if conditions deteriorate or the analysis proves only partially correct, the investor can still avoid a permanent loss of capital. For stocks, this meant buying at two-thirds or less of intrinsic value; bonds required strong interest and principal coverage ratios.
Another aspect of the approach advocated broad diversification, suggesting positions were spread across at least thirty securities to ensure no mistake led to ruin.
Diversification supplements the margin of safety by limiting portfolio-wide damage from idiosyncratic risks or broader misjudgments, even if individual choices have a margin of safety.
A little arithmetic
When I think about it, the investors that hold out — the composite companies that have weathered multiple market cycles without imploding — all understand one fundamental truth.
The math of investing is not linear; it is asymmetrical, especially when it comes to losses.
You know the basics: Drop 20 percent on an investment and you need a 25 percent profit to break even. Loses 33 percent, and takes just over 50 percent to recover. If you dive 50 percent, you need a 100% rebound to break even.
But there is another element of portfolio calculation, and that is the difference between arithmetic and geometric returns. The arithmetic mean of returns ignores the compounding effect of successive returns. An average may seem acceptable – for example, a range of +50 percent and -50 percent equates to 0 percent – but geometrically speaking, after such a pattern of results, you would be 25 percent lower overall, because the loss is calculated based on a larger nominal number.
Knowing that can help you put into context a concept from the late Charlie Munger about thinking in reverse. He suggested that instead of fixating on ‘How can I win big?
Buffett and Munger prioritized avoiding catastrophe. That doesn’t mean that all risks should be avoided, but it does mean that we should embrace opportunities only after we have thoroughly understood and then mitigated the impact of potential downsides.
For example, the effect on a portfolio may be that your largest position or position is not necessarily the idea you are most optimistic about. It is the scenario where you have identified the worst-case scenario and the impact is the most acceptable.
Consider it an extra margin of safety, and it is necessary because ‘bullishness’ is emotional and does not guarantee accuracy.
You might also consider the Kelly Criterion developed by John Kelly in the 1950s to determine the optimal size of a range of investments. It is designed to maximize long-term prosperity by balancing high returns with the risk of ruin.
The Kelly Criterion calculates the optimal position size to maximize logarithmic capital growth while avoiding bankruptcies.
The formula, which yields the right fraction to invest based on the probability of winning, the probability of losing and the ratio of potential winnings to potential losses, shows that too many bets, even when you think you have an ‘edge’, will lead to ruin on repeated attempts.
You may have conviction, but you also need to have a calibrated position size.
The right idea is to combine Kelly’s agency and vulnerability with the sustainable competitive advantages and undervaluation of Buffett and Munger.
Application for 2026
So, what defines a desirable investment setup?
Consider the following four pillars:
- First, quantify your maximum loss. Is there a hard floor, for example supported by cash flows, cash itself or other liquid and tangible assets?
- Look for scenarios with a positive mathematical expectation. Expected value = (probability of gain * gain) – (probability of loss * loss).
- Filter for those wonderful companies where time is a friend, so compounding can work its magic. Remember that time is the enemy of a business with poor economic conditions: the longer you continue to invest in it, the worse the outcome.
- Size positions accordingly.
You cannot thrive unless you survive first. Buffett always talked about focusing on returns by capital before return on capital. Buffett and Minger made their fair share of mistakes, but their mistakes did not leave a lasting scar. And that has to do with ‘better estimates’, portfolio architecture and risk mitigation.
In my own diary of investing epiphanies, the greats seem to emphasize that their successes ultimately came from the deals they skipped, the fads they ignored, the temptations they resisted because the math wasn’t right.
So before you pull the trigger in 2026:
- Model the drawdown. Can your portfolio absorb this without forced selling?
- Vary your assumptions and see if the expected value (EV) remains positive.
- Question: Does holding longer lead to an increase in the odds via mean reversion or growth compound?
- Position size accordingly: Apply Kelly or a variant to properly determine exposure, even if you think the chance of success is 80 percent.
He is also the author of the best-selling investing guide to the stock market, Value.able – how to value and buy the best stocks for less than they are worth.
Roger regularly appears on television and radio, and in the press, including ABC radio and TV, The Australian and Ausbiz. View upcoming media appearances.
This post was contributed by a representative of Montgomery Investment Management Pty Limited (AFSL No. 354564). The main purpose of this message is to provide factual information and not advice about financial products. Furthermore, the information provided is not intended as a recommendation or opinion about any financial product. However, any comments and statements of opinion should contain general advice only, prepared without taking into account your personal objectives, financial circumstances or needs. Therefore, before acting on any information provided, you should always consider its suitability in the light of your personal objectives, financial circumstances and needs and, if necessary, seek independent advice from a financial advisor before making any decision. Personal advice is expressly excluded in this message.
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