The Problem With "Expected Returns" — And Why A Physicist Spotted It Before Economists Did

 Let me start with a small question.

Think about the last time someone — a friend, a financial app, an advertisement — told you that a particular mutual fund or investment gives "12% average returns." Or maybe you read somewhere that "equity gives 15% CAGR over the long term."

Did you nod along? Most of us do.

But here is something nobody asks in that moment.

Average for whom, exactly?

That one word — whom — changes everything. And for most of financial history, nobody thought to ask it. Until a physicist did.

The Man Who Built a Different Kind of Model

His name is Ole Peters.

He is not a fund manager. He is not a financial planner. He does not manage anyone's money. Ole Peters is a physicist — the kind of person who studies how complex systems behave over time. Weather. Chaos. Stock markets. Things that evolve, shift, and surprise you.

Around 2009, Peters was looking at some standard ideas in economics — the kind that appear in textbooks, the kind that inform how mutual funds report returns, the kind that quietly shape how most of us think about investing. And something bothered him.

Not the math. The assumption behind the math.

He spent years on this. In 2011, he published his foundational argument in Quantitative Finance. In 2019, Peters and collaborators published a follow-up paper in Nature Physics — one of the most respected science journals in the world — that brought this idea to a much wider audience. The title was polite and academic. The argument inside was anything but.

He said, essentially: "Economics has been relying on the wrong kind of average — one that describes a crowd, not an individual living through time. And the implications of this error have been quietly ignored."

That is a remarkable thing to say about a field that has produced Nobel Prize winners, central bank governors, and the smartest financial minds of our time.

But let me show you why he had a point.

The Average That Isn't Really Yours

Let me tell you about Ramesh.

Ramesh is 38 years old, works in Pune, and has been doing a monthly SIP of ₹10,000 for the past seven years. He is a careful, sensible investor. He reads articles like this one.

One day, Ramesh reads in a financial magazine: "This fund has delivered 13% average annual returns over the last decade. Invest with confidence."

Ramesh nods. 13% sounds good. He stays invested.

Now here is the question. That 13% — whose experience does it represent?

It represents the average across all investors, across all ten years, blended together into one clean number. The person who started in 2014 when the market was recovering. The person who started in 2019 just before COVID. The person who redeemed in 2021 at the peak. All of them, averaged together, give you that 13%.

But Ramesh did not experience an average. Ramesh experienced a sequence. A specific order of good years and bad years, starting from the month he started his SIP, ending when he actually needs the money.

That sequence is his and his alone. No other investor had it.

And here is what Ole Peters made precise: the average of many different people's experiences is not the same as the experience of one person over time.

These are two genuinely different things. They can give you two genuinely different numbers. And for most of financial history, economics quietly assumed they were the same.

This assumption has a name. It is called ergodicity. And when something is non-ergodic — which your wealth is — the crowd's average does not predict your personal outcome.

How Did This Mistake Happen? A Small History

To understand why economics made this error, we need to go back about 300 years.

In the 18th century, a Swiss mathematician named Daniel Bernoulli was working on a famous puzzle called the St. Petersburg Paradox — a gambling problem that stumped mathematicians of his time. In solving it, he introduced the idea of expected utility — the notion that people do not just care about the average money outcome of a bet, but also about how much each outcome means to them personally. Gaining ₹10,000 feels different depending on whether you already have ₹1 lakh or ₹1 crore in the bank.

This was genuinely brilliant. It gave people a framework to think rationally about uncertain situations.

Later, economists took this framework and built almost everything on top of it. Expected returns. Risk-adjusted averages. The entire machinery of modern finance rests, at its base, on this idea: when you want to know if something is a good investment, calculate the expected average outcome across possible scenarios.

Here is the problem. This framework was designed for a very specific situation — where the average across a large group at one moment tells you what any one individual can expect over time.

In physics, a system where this holds is called an ergodic system.

A gas in a closed room is ergodic. The average pressure from measuring many molecules at once is the same as what one molecule experiences over a long time. The math works beautifully.

But your money? Your money is not a gas molecule.

Your wealth grows multiplicatively — each year's return multiplies on top of what you already have. One terrible year does not just subtract from the total. It shrinks the base on which future growth happens.

And most critically — if you run out of money, no amount of future good returns can bring you back. Zero is a wall, not a setback.

Ole Peters called this the ergodicity problem in economics. The real world of personal wealth is non-ergodic. But the models economists used relied on ensemble averages — what happens to a crowd — even when the question being asked was about an individual living through time.

Let Us Make This Very Concrete

Imagine 1,000 different investors. Each one starts with ₹1 lakh and invests in the same volatile asset.

After 20 years, you add up everyone's final wealth and divide by 1,000. The average looks impressive — maybe ₹5 lakhs or ₹6 lakhs.

But look more carefully inside those 1,000 outcomes.

In volatile, multiplicative systems like this, a small number of investors get spectacularly lucky early — their wealth grows to ₹30 lakhs, ₹50 lakhs, even ₹1 crore. These few people pull the reported average up enormously.

Meanwhile, hundreds of others experience major losses in their early years, never fully recover, and end up with ₹80,000 or ₹70,000 — less than what they started with.

The reported average is ₹5 lakhs. The majority's actual experience is far more modest — or worse.

Now here is the key question. Which of those 1,000 paths are you?

You do not know. You cannot know in advance. You will live exactly one of those 1,000 paths — not the average of all of them.

When economics says "the expected return is positive," it is describing the average across all 1,000 imaginary parallel universes. But you only get one universe. One life. One sequence of returns in the specific order they arrive.

This is what Peters meant. And this is what changes how you should think about investing.

What This Actually Means for You

I want to be careful here. This is not me saying "don't invest in equity" or "the financial system is lying to you." It is not that dramatic.

It is something quieter but more important.

First: Avoiding ruin is not a conservative attitude. It is the most rational attitude.

When your wealth falls to zero, there is no recovery. A 50% loss needs a 100% gain to break even. A 70% loss needs a 233% gain. This asymmetry is not just uncomfortable — it is mathematically permanent if you are forced to withdraw money at the wrong time.

This is why risk management is not the opposite of wealth building. It is wealth building.

Second: Why insurance makes more sense than it looks on paper.

If you only look at expected monetary returns, insurance appears to be a losing bet on average — you pay more in premiums over a lifetime than most people ever receive in claims. That is how insurers stay in business.

But that calculation misses the point entirely. You are not buying insurance to win on average. You are buying it to stay in the game — to avoid the kind of catastrophic loss that removes you from the compounding journey permanently. A medical emergency that wipes out your life savings does not just hurt you financially for one year. It can reset everything.

Insurance is how you protect your path. And your path is all you have.

Third: This is why sequence of returns matters so much — especially near retirement.

Two investors. Same fund. Same average return of 11% over 20 years. But one gets the bad years first and the good years later. The other gets the good years first and the bad years later.

Same average. Completely different final corpus. Because the order in which returns arrive is everything when you are withdrawing money during bad years.

This is not a new idea — you may have read about sequence-of-returns risk before. But ergodicity is where that concept comes from. It is the physics underneath the finance.

An Honest Word of Caution

Peters' argument was not universally welcomed. Some serious economists pushed back quite hard.

They argued that expected utility theory — the framework going back to Bernoulli — already accounts for individual risk preferences. Economists like Paul Samuelson and Robert Merton built frameworks that do not assume individuals are indifferent to variance. They said Peters was overstating a known limitation rather than revealing a hidden flaw.

The debate in academic circles continues even today.

I am not here to take sides in that debate. I do not have the standing to adjudicate between physicists and Nobel-winning economists.

But here is what I do believe: the practical wisdom that comes out of Peters' framing is sound and worth keeping.

The reminder that you are not a thousand investors. The reminder that your path matters more than any reported average. The reminder that ruin is permanent in a way that temporary loss is not. The reminder that the performance number on a brochure is a summary statistic — a compression of many different investor experiences into one clean percentage — and not a personal promise made to you.

That reminder — wherever it comes from — is worth a great deal.

The Money Vichara for Today

Every investment brochure you have ever read was built on summary statistics — averages of what happened across many investors, in many different situations, over many different time periods. Every reported performance number compresses a wide range of individual experiences into a single figure and hands it to you as if it were a forecast.

It is not a lie. It is just not your story.

Your story is one path. Starting from today. Moving through good years and bad years in a specific order you cannot know in advance. With a real life on the other side — retirement, a child's education, a parent's medical need — that cannot wait for the average to show up.

Ole Peters, the physicist, did not tell us to stop investing. He told us to stop confusing a crowd's summary with our own future.

And that is a distinction worth sitting with.

So here is today's vichara to carry with you:

When you look at the "expected returns" on your next investment — ask yourself honestly: am I thinking about what happens to a thousand imaginary investors on average? Or am I thinking about what happens to me, specifically, if the bad years come first?

Because the answer to that question quietly shapes every investment decision you will ever make.