Geometry of gains
As investors, if we’re intellectually honest, we’re bound to be wrong a few times more than we would like. And the longer the investment career, the higher the accumulated mistakes pile up. So how do successful investors survive them and continue to build on their success?
In holiday mode, I was re-reading 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 seminal work Security Analysis (first published in 1934) and Graham’s later The Intelligent Investor, developed a disciplined value investing framework explicitly designed to protect against errors in judgment, unforeseen events, and market volatility. While their approach famously shifted investing from speculation to a rigorous, business-like analysis, it was the built-in safeguards that limited the damage from inevitable mistakes.
The central element of the process, of course, was the Margin of Safety – buying securities at a substantial discount to their conservatively estimated intrinsic value. Ignoring for a moment the tangible asset component of the intrinsic value calculation, the discount acts as a buffer because:
- It absorbs errors in valuation (e.g., overestimating earnings and earnings growth), and
- It protects against business setbacks, economic downturns, or market declines.
Graham and Dodd insisted that the margin must be large enough that, even if conditions worsen or analysis proves only partially correct, the investor still avoids a permanent capital loss. For stocks, it meant buying at two-thirds or less of intrinsic value; for bonds, it required strong coverage ratios for interest and principal.
Another aspect of the approach advocated broad diversification, suggesting spreading holdings across at least 30 securities to ensure no single mistake caused ruin.
Diversification complements the margin of safety by limiting portfolio-wide damage from idiosyncratic risks or broader misjudgments, even when individual picks have a margin of safety.
A little arithmetic
Thinking about it, the investors who endure – the compounders who’ve navigated multiple market cycles without imploding – all grasp a fundamental truth.
The math of investing isn’t linear; it’s asymmetric, especially when it comes to losses.
You know the basics: Drop 20 per cent on an investment, and you need a 25 per cent gain to break even. Lose 33 per cent, and it takes just over 50 per cent to recover. Plunge 50 per cent, and you require a 100% rebound, to break even.
But there’s another element from portfolio arithmetic, and it’s the difference between arithmetic and geometric returns. The arithmetic average of returns ignores the compounding effect of sequential returns. An average might look acceptable – for example, a sequence of +50 per cent and -50 per cent averages to 0 per cent – but geometrically, after such a pattern of results, you’d be down 25 per cent overall because the loss is calculated on a larger nominal number.
Knowing that helps put a concept from the late Charlie Munger, about thinking in reverse, into context. He suggested that instead of fixating on “How can I win big?”, we should ask, “What paths lead to disaster, and how do I avoid that?”
Buffett and Munger prioritised ‘catastrophe avoidance’. That doesn’t mean avoiding all risks, but it does mean embrace opportunity only after rigorously understanding and then limiting the impact of potential downsides.
The effect on a portfolio, for example, might be that your largest position or holding isn’t necessarily the idea you’re most bullish about. It’s the one where you’ve mapped out the worst-case scenario and the impact is most acceptable.
Think of it as another margin of safety, and it’s required because ‘bullishness’ is emotional and doesn’t guarantee accuracy.
You might also consider the Kelly Criterion developed in the 1950s by John Kelly to determine the optimal size of a series of investments. It was designed to maximise long-term wealth, by balancing high returns with the risk of ruin.
The Kelly Criterion calculates optimal position size to maximise logarithmic wealth growth while avoiding bankruptcy.
The formula, which produces the appropriate fraction to invest based on the probability of winning, the probability of losing, and the ratio of potential wins to potential losses, reveals betting too much, even when you believe you have an ‘edge’, leads to ruin over repeated trials.
You might have conviction, but you must also have a calibrated position size.
The right idea is to combine the optionality and fragility avoidance of Kelly with the durable competitive advantages and undervaluation of Buffett and Munger.
Application for 2026
So, what defines a desirable investment setup?
Consider the following four pillars:
- Quantify your max loss first. Is there a hard floor, backed, for example, by cash flows, cash itself or other liquid and tangible assets?
- Look for scenarios with a positive mathematical expectancy. Expected Value = (probability of win * gain) – (probability of loss * loss).
- Filter for those wonderful businesses where time is a friend so that compounding can work its magic. Remember, time is the enemy of a business with poor economics – the longer you remain invested, the worse the outcome.
- Size positions accordingly.
You can’t thrive unless you first survive. Buffett used to speak of focusing on the return of capital before the return on capital. Buffett and minger made their fair share of mistakes but their errors didn’t leave a permanent scar. And that’s down to ‘better guesses’, portfolio architecture, and risk mitigation.
In my own journal of investing epiphanies, the greats seem to highlight their successes came ultimately from the deals they skipped, the fads they ignored, the temptations resisted because the math didn’t stack up.
So, before pulling the trigger in 2026:
- Model the drawdown. Can your portfolio absorb it without forced sales?
- Vary your assumptions and see if expected value (EV) stays positive.
- Ask: Does holding for longer boost odds via either mean reversion or growth compounding?
- Position size accordingly: Apply Kelly or a variant to appropriately establish exposure, even if you believe there’s an 80 per cent likelihood of success.
Roger Montgomery is the Founder and Chairman of Montgomery Investment Management. Roger has over three decades of experience in funds management and related activities, including equities analysis, equity and derivatives strategy, trading and stockbroking. Prior to establishing Montgomery, Roger held positions at Ord Minnett Jardine Fleming, BT (Australia) Limited and Merrill Lynch.
He is also author of best-selling investment guide-book for the stock market, Value.able – how to value the best stocks and buy them for less than they are worth.
Roger appears regularly 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 principal purpose of this post is to provide factual information and not provide financial product advice. Additionally, the information provided is not intended to provide any recommendation or opinion about any financial product. Any commentary and statements of opinion however may contain general advice only that is prepared without taking into account your personal objectives, financial circumstances or needs. Because of this, before acting on any of the information provided, you should always consider its appropriateness in light of your personal objectives, financial circumstances and needs and should consider seeking independent advice from a financial advisor if necessary before making any decisions. This post specifically excludes personal advice.
