We are naturally wired to think linearly. It’s simple, intuitive, and works perfectly for basic math. Unfortunately, equity investing operates in a non-linear, exponential world. When compounding is at play, our quick instinctive decisions often lead us straight into traps.
Let’s break down few interesting mathematical fallacies that trick investors every day, and prime ourselves to avoid falling in such traps.
Asymmetrical Losses
This is perhaps the most brutal lesson in the market – “losing money is a lot easier than making it back”, but unfortunately is not obvious to the majority.
When an investment drops, it takes an exponentially larger recovery just to break even. The mathematical relationship between a loss and the required gain (expressed in decimals) to recover looks like this:
Because of this asymmetry, a 50% drop requires a 100% gain just to break even on your investment .
This math is the ultimate argument for strict stop-loss discipline. Letting a “dead stock” free-fall means you are digging a hole that requires a huge, low-probability rally to climb out of.
Mean Math of Volatility
Imagine your investment shoots up by 20% in Year 1, but dips by 10% in Year 2. Quick intuition says your average return is 5% per year i.e. (20% – 10%) / 2
But the reality of your portfolio is much different. Your actual total return over those two years is 8%, which translates to a Compounded Annual Growth Rate (CAGR) of approximately 3.9%.
This gap is also known as “volatility drag” which erodes the compounding engine even when the “average” numbers look decent.
Backloading Nature of Compounding
Investors seek for instant gratification. They want their investments to start showing profits immediately. The psychology behind this is to start feeling wealthy, and the satisfaction of “being right” in their decisions.
Instead, the math of compounding is painfully back-loaded. The real magic happens towards the latter half of your planned investment duration. Here is an illustration of the wealth multiplier for a INR 10,000 investment with 10% CAGR.
Patience isn’t just a virtue; it is a mathematical prerequisite!
Sequencing of Returns matter
When checking historical mutual fund performance, investors usually look at point-to-point CAGR (say, “Fund X gave 12% returns over the last 5 years). However, for Systematic Investment Plan (SIP) route, the order in which those returns happen matters more than the average return itself.
Consider two scenarios over 3 years for an investor putting in INR 10,000 every year:
Scenario A: Year 1: +30%, Year 2: +10%, Year 3: -20% - Final: ~ INR 28,000
Scenario B: Year 1: -20%, Year 2: +10%, Year 3: +30% - Final: ~ INR 35,000
In both cases, the point-to-point return of the market is exactly the same. But in Scenario A (bull market first), you bought fewer shares early on when prices were high; the late crash hit a large pile of money. While in Scenario B (bear market first), you accumulated a massive number of shares cheaply during the early crash; the late rally multiplied a huge base.
Mathematically, a bear market at the beginning of your investment journey maximizes your long term yield, which unfortunately goes against your psychological feeling of winning. Investors start to panic initially on seeing their portfolio in red.
The Dividend Yield Trap
When a company drops a high X% dividend yield, your intuition sees it as a “X% cash return, plus whatever the stock price does”. But what investors mathematically ignore is that a dividend is not a bonus payment; it is a truncation. When a company pays a dividend, its cash balance drops by that exact amount. Consequently, the share price is adjusted downward by the dividend amount on the ex-dividend date. Consider this (assume you are in 30% tax bracket) –
- The company pays you INR 1000 in dividends.
- The company’s intrinsic value drops by INR 1000, and accordingly the stock price.
- You pay INR 300 in taxes, leaving you with INR 700 to reinvest.
This dividend disbursement has essentially shrunk your compounding base. If they had retained that INR 1000 and compounded it internally at a high Return on Equity (ROE), your money would compound tax-deferred.
High dividends mathematically disrupt compounding efficiency for growth-oriented investors.
“Averaging Down” on Winners vs. Losers
When an investor owns a stock that has gone up 50% (say), they are often hesitant to buy more because it appears expensive and raises their average purchase price. Conversely, if a stock drops 25%, they eagerly buy more to lower their average cost. Mathematically, such bias works directly against portfolio quality.
- When a company’s stock is rising because its fundamental earnings are compounding rapidly, buying more at a higher price still yields a high geometric return because the underlying compounding engine is accelerating (your initial purchases, plus new ones)
- When you average down on a deteriorating business, you are allocating more capital to a shrinking or low-ROE business.
Lowering your cost basis from say INR 100 to INR 70 on a dead stock (stagnant company compounding single-digit at best) will mathematically underperform a winning stock bought at an “expensive” All-Time High that is still at double-digit compounding earnings. For more insights, check out my earlier post on Upward Averaging.
Be brave enough to incrementally bet on growth stocks, and let the compounding take over.
Pareto Principle – Power of portfolio concentration
The math of compounding in equities follows a Pareto Principle, wherein a tiny minority of stocks in your portfolio is likely to generate the vast majority of your total returns. (I wrote an article on this a while back which you can read here)
If you have a 100-stock portfolio, and one of your holdings turns out to be a multi-bagger (exaggerated growth of say 10,000% over 15 years), look at how concentration changes your life:
- Conviction Weight (5% min allocation per stock): Your 5% position grows to 500% of your initial total portfolio value. A massive, possibly life-changing win.
- Diluted Weight (1% allocation because you “diversified” too much): Your 1% position only grows to 100% of your initial portfolio value.
Under-allocating to a good stock is pratically the same as being wrong about it! Diversification protects wealth, but building deep conviction in your winners is what allows compounding to unlock its true, unchecked power.
Our brains love linear paths and comforting illusions like the safety of averaging down or the immediate satisfaction of a high dividend yield. But the mathematical reality of equity compounding operates on an entirely different set of rules.
By recognizing these non-linear fallacies, you can start using it to your advantage. Allow your winners to run, welcome early volatility, and give compounding the time it needs.
