What the theory gets wrong

Eleven chapters built a theory. This one says where it breaks, in order of how much it matters — and then says what is left, because the honest answer is "more than you would expect".

1. The inputs are estimates, and the means are hopeless

This is the failure that matters most, and it is not about the mathematics at all.

Chapter 4 counted: 1,325 estimates for a 50-asset problem. Chapter 5 described what an optimiser does with them — loads up on whatever the estimation errors flattered, producing concentrated portfolios that swing violently when the window moves.

And the worst-estimated input is the one the answer depends on most. Variances and covariances can be estimated tolerably from a few years of data. Expected returns cannot. The Nifty 50 returned 6.38% a year over five years and 12.12% since inception — same index, two defensible windows, a gap of nearly six percentage points. Feed the first to an optimiser and it barely holds equities; feed the second and it holds little else.

Markowitz is clear-eyed about this from the start:

Of course, none of us know probability distributions of security returns.

His answer was that an investor should act on "probability beliefs" where objective probabilities are unknown. That is philosophically coherent and practically brutal: the theory tells you what to do with your beliefs and has nothing to say about whether your beliefs are any good.

What follows from this, and it is the chapter's main practical conclusion: the less a method depends on estimated expected returns, the more robust it is. Equal weighting, market-cap weighting and minimum-variance portfolios all avoid the means entirely, which is most of why they survive out of sample better than optimised portfolios do.

2. Correlations move, and move worst when it matters

Chapter 3's formula is exactly right. Its input is not reliable.

Correlations are measured in ordinary markets and tend towards 1 in disorderly ones. The Risk subject's chapter on correlation is specifically about this, and it is not a quibble — it means the diversification benefit is largest in the states where you do not need it and smallest in the states you bought it for.

Even in ordinary data the estimate is unstable. The Nifty200 Quality 30's correlation with the Nifty 50 is 0.84 over five years and 0.91 since inception. Nothing happened to either index; the window changed.

And chapter 3 showed how much rests on it. Thirty stocks at an average correlation of 0.2 carry 14.3% risk; the same thirty at 0.4 carry 19.4%. An input that moves by 0.2 moves the answer by a third.

3. Variance is the wrong measure, and nothing better aggregates

Sharpe concedes the point in his own paper on the ratio built from it:

comparisons based on the first two moments of a distribution do not take into account possible differences among portfolios in other moments or in distributions of outcomes across states of nature that may be associated with different levels of investor utility

In plain terms: two portfolios can have identical means and variances and be very different things. The Measuring your return subject lists the specific defects — variance punishes upside, assumes thinner tails than markets have, can be flattered by illiquidity, and is silent about the worst case.

But chapter 2 gave the reason variance is used anyway, and it is not laziness. Variance of a sum decomposes into terms over every pair. Downside deviation does not decompose that way, so a theory built on it does not produce a frontier, a tangency portfolio, a beta or a capital market line. The elegance of chapters 2 to 7 is purchased with this specific assumption, and no one has found a cheaper price.

4. Nobody borrows at the riskless rate

Chapter 6 found that the capital market line beats the efficient frontier by up to 1.44 percentage points at 14% risk — and that reaching those points requires borrowing 185% of capital at the policy rate.

At a realistic personal borrowing cost the advantage reverses, as chapter 6 computed: at 9% borrowing the levered position returns 5.98% for the same risk, against 11.00% from simply holding equities.

So the upper half of the central result is unavailable to individuals. That is a genuine limitation on a genuine result, and the right response is to use the half that works — cash plus a diversified risky portfolio — rather than to discard the chapter.

5. One period, and no human in it

The whole framework is single-period. It asks what to hold over "the" horizon. Real investors have decades, contribute monthly, withdraw irregularly, and change their minds.

Three things the framework cannot see:

Sequence. The Measuring your return subject's distinction between time-weighted and money-weighted returns exists because when a loss happens matters when there are cash flows. Mean and variance contain no information about order.

Capacity against tolerance. The Risk subject separates how much risk you can afford from how much you can stand. The frontier offers a menu and has nothing to say about which point suits a person — and chapter 5 showed that an emergency fund is mean-variance inefficient and should still be held exactly as it is.

Behaviour. The Behavioural finance subject's measured gap is the difference between a portfolio's return and its holders' returns. A theoretically efficient portfolio that its owner abandons in year three has delivered none of its efficiency, and nothing in chapters 1 to 11 represents that.

6. The equilibrium story requires everyone to be doing this

Chapter 7's derivation needs every investor to optimise the same way on the same inputs. They plainly do not — the Behavioural finance subject documents how far actual behaviour sits from it, and chapter 10 reports that the resulting prediction fails: size and value were priced when CAPM says nothing but beta should be.

And the market portfolio is not observable. CAPM's market is every risky asset in existence, including property, private businesses and human capital. Every test uses a proxy, so a rejection might be the proxy's fault — a criticism that has been made since the 1970s and has never been fully answered.

What survives

Now the other side, because "the theory is wrong" is a conclusion people reach too cheaply.

Diversification works, and the mechanism is arithmetic. Chapter 3's decomposition does not depend on CAPM, on equilibrium, on normality or on anybody optimising. It is algebra: the own-variance term is divided by $N$ and the covariance term is not. The only input is that correlations are below 1, which is observable and robust.

Risk is a property of combinations, not of holdings. Chapter 4's demonstration — that adding a riskier asset can lower portfolio risk — is secure. "This is a risky asset" is an incomplete sentence, and knowing that changes how you read every recommendation you will ever be given.

Only undiversifiable risk can be paid for. Chapter 7's robust layer. If a risk can be removed for free by anyone willing to hold more things, nobody can charge for bearing it. You can reject CAPM's claim that the undiversifiable part is one-dimensional and keep this entirely.

Dominance is real. Chapter 5's argument requires almost nothing about the investor. If one portfolio offers more return at less risk, the other should not be held, whatever your preferences.

Scaling with cash beats changing the contents. Chapter 6's lower half. To take less risk, hold the same diversified portfolio and more cash — no borrowing, no leverage, no assumption that fails.

And the ratio is the right question. Chapter 9's X-versus-Y example: judge a holding by excess return per unit of risk, not by return alone, as long as you remember it ignores correlation.

Notice what all six have in common. None requires an estimate of an expected return. The parts of the theory that survive are precisely the parts that do not depend on the input the theory cannot supply — which is a tidy summary of where to trust it.

Working the problem

The claim: CAPM fails empirically, correlations collapse in crises, optimisers produce unusable portfolios — so you may as well pick stocks you like.

Premise 1: CAPM fails empirically. True. Chapter 10 showed size and value were priced over a century when CAPM says nothing but beta should be, and chapter 8 showed a low-beta Indian index earning the market's return. Conceded without reservation.

Premise 2: correlations collapse in crises. True. Point 2 above. Conceded.

Premise 3: optimisers produce unusable portfolios. True. Point 1. Conceded, and it is the strongest of the three.

So all three premises stand. And the conclusion does not follow from any of them.

Here is the gap. Every premise is an objection to a specific, advanced part of the theory — the equilibrium pricing model, the stability of an input, the output of an optimisation procedure. None of them touches the elementary results, which require no equilibrium, no stable correlations and no optimiser:

What is attacked	What is untouched
CAPM's beta pricing	that specific risk averages away
correlation stability	that correlations below 1 reduce variance at all
optimiser output	that dominated portfolios should not be held

And the conclusion proposes something strictly worse than what it rejects. "Pick stocks you like" is an undiversified portfolio chosen on expected returns — which means it relies entirely on the one input the theory's critics correctly identify as unreliable, while giving up the one benefit everyone agrees is real.

It is the opposite move to the one the criticism supports. If estimating expected returns is hopeless, that is an argument for a method that does not need them — a broad, cheap, diversified holding — and against a method that is nothing but an expected-return estimate.

The Behavioural finance and Technical analysis subjects supply what happens next. Barber and Odean's most-active quintile earned 11.4% a year against 18.5% for the least active, and SEBI's derivatives data has roughly nine in ten individual traders losing money each year from FY22 to FY26. The alternative being proposed has been measured, and it is not a close call.

What I would say instead. Keep the elementary results, which are arithmetic and survive every objection raised. Treat the advanced results as a vocabulary for thinking rather than as a machine for producing weights. Be deeply suspicious of anything that requires you to estimate an expected return precisely, including your own stock-picking. And accept that the remaining decision — how much risk, given your obligations and your temperament — is a judgement the theory was never going to make for you.

Sharpe's own framing of this is the right note to end on: any measure that summarises performance in a single number "requires a substantial set of assumptions for justification", and in practice such assumptions "are, at best, likely to hold only approximately." That is the correct attitude to the entire subject — useful, not true.

The point

The theory's worst failure is that its inputs are estimates and expected returns cannot be estimated, which is why optimisers produce unstable concentrated portfolios and why the same index gives 6.38% or 12.12% depending on the window. Correlations move and move worst in crises; variance is the wrong risk measure and nothing better aggregates into a frontier; nobody borrows at the riskless rate; the framework is single-period and contains no human; and the equilibrium story needs everyone to optimise and an unobservable market portfolio. What survives is everything that does not need an expected return: diversification's arithmetic, risk as a property of combinations, the impossibility of being paid for diversifiable risk, dominance, scaling with cash rather than changing contents, and judging by excess return per unit of risk. The criticisms are sound and they argue for a cheap diversified default — not for picking stocks you like, which depends entirely on the input the criticisms destroy.