Geometric vs. Arithmetic Returns: Why Your Mate’s 47% Average Return Means Absolutely Nothing

Listen, I’m going to tell you something that will either save your account or make you hate me. Possibly both.

Back in 2011, I knew this trader—absolute charlatan, honestly—who would ring me up every Friday spouting on about his “47% average monthly returns.” Beautiful lad, terrible trader. Two years later, he was living in his mum’s spare room. The irony? His arithmetic was technically correct. His geometric returns? Catastrophically negative.

That’s the disconnect nobody wants to talk about at the pub.

The Fantasy: Arithmetic Returns

Arithmetic returns are what every YouTube guru, every TikTok “trader,” and every pension fund brochure uses to make themselves sound impressive. They’re simple, they’re elegant, and they’re dangerously misleading.

Here’s how it works: Add up all your monthly returns, divide by the number of months, and boom—you’ve got your average. Dead easy.

Month 1: +10% Month 2: +15% Month 3: -20%

Average? 1.67%. Lovely. Print it on your business card.

Except here’s the bit that keeps me awake at night: that’s not what actually happened to your money.

If you started with £10,000:

• After Month 1: £11,000
• After Month 2: £12,650
• After Month 3: £10,120

Your actual return wasn’t 1.67%. It was 1.2%. That’s arithmetic versus reality, mate. And that’s the small gap. Wait until you’ve got real leverage and real volatility involved.

The Reality: Geometric Returns

Geometric returns—also called the Compound Annual Growth Rate (CAGR) when you’re discussing annual figures—is what actually matters to your bank account. It’s the only return that matters.

Why? Because money compounds. It’s the eighth wonder of the world, except when you’re losing it, and then it’s the eighth circle of Hell.

Geometric returns answer one question: “If I had £X at the start and £Y at the end, what was my actual annual growth rate?”

The formula’s a bit gnarly (and honestly, you should use our calculator for this, that’s why you’re here), but the concept is simple: it’s the return that, if you earned it every single period, would leave you with exactly the same amount of money you actually have.

With our example:

• Starting capital: £10,000
• Ending capital: £10,120
• Geometric return: ~1.2%

Mundane? Yes. But true.

Why Arithmetic Lies and Geometry Tells the Truth

The difference gets properly spicy when volatility enters the room. And in Forex, volatility is always lurking in the corner like an angry bouncer.

Here’s the dirty truth: High volatility destroys geometric returns, even when arithmetic returns look decent.

Imagine two traders over a year:

Trader A (Steady Eddie):

• Returns every month: +1%, +1%, +1%, +1%, +1%, +1%, +1%, +1%, +1%, +1%, +1%, +1%
• Arithmetic average: 1%
• Geometric return: 1% (they’re identical here, which is the only time they are)

Trader B (Volatile Vic):

• Returns: +50%, -30%, +50%, -30%, +50%, -30%, +50%, -30%, +50%, -30%, +50%, -30%
• Arithmetic average: 10%
• Geometric return: -6.2%

Same average return. One trader’s up, one trader’s flat-out losing money. Volatile Vic looks brilliant on paper and absolutely tanks in reality.

This is what I call “return illusion,” and it’s how people convince themselves they’re not terrible traders.

The Position Sizing Apocalypse

Here’s where it gets properly dark. Most retail traders don’t understand this concept at all, which is why they blow accounts while claiming they had a “winning strategy.”

Let’s say you’re trading with 20:1 leverage (rookie numbers, but bear with me). You’ve got a strategy that wins 55% of the time with a 1:2 risk-reward ratio. On paper, arithmetic returns look solid—maybe 3-4% per month average.

But leverage amplifies volatility, and volatility is the enemy of geometric returns.

Suddenly, a string of losses hits harder. Your drawdowns compound in reverse. Your geometric return collapses while your arithmetic return still looks tidy. By the time you realize what’s happened, your account’s down 40% and you’re wondering why the maths didn’t match reality.

They never do. Not with arithmetic.

The Calculator’s Purpose

This is why we built the geometric returns calculator. Not to make you feel better—though you might—but to give you the truth.

When you plug in your actual trading results, it spits out your real return. The geometric one. The one that actually matters.

If there’s a gap between your arithmetic and geometric returns, you’ve found the problem: volatility is eating your lunch.

Fix that by:

• Better position sizing (kill the leverage, you muppet)
• Tighter stop losses (reduces drawdown severity)
• More consistent trading (boring works)

The Philosophical Bit

I’ve been doing this for nearly two decades. I’ve seen strategies with 70% win rates blow accounts. I’ve seen boring 55% win-rate strategies turn £5,000 into £500,000. The difference? Understanding that geometric returns are what your actual money experiences, and arithmetic returns are just a number for the brochure.

The best traders I know talk in geometric terms. They know their Calmar ratio. They obsess over max drawdown. They understand that one massive loss can wipe out months of steady gains.

The worst traders? They’re still calculating arithmetic averages on notepads, convinced they’re geniuses because they can cherry-pick a metric that makes them look clever.

Final Word

Use our calculator. Compare your arithmetic returns to your geometric returns. If they’re similar, you’ve got a consistent strategy. If there’s a massive gap, you’ve got a ticking time bomb masquerading as a trading system.

Because the brutal truth is this: Your account doesn’t care about your average. It only cares about what you actually have left.

Everything else is just noise.

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Need to calculate your actual returns? Stop lying to yourself. Use the calculator.