Mean-variance optimisation is the foundation of professional portfolio construction. But every practitioner who has worked with it knows it has serious weaknesses. The portfolios it recommends can look bizarre. A tiny tweak to one input can completely change the recommended allocation. Asset classes can vanish from the optimal portfolio without any obvious reason. This article explains the six main criticisms, shows why they matter, and explains the practical fixes practitioners use.
Criticism 1: Small Input Changes Cause Big Output Changes
Why this is dangerous: MVO is mathematically aggressive. It looks for every edge it can find and exploits it to the maximum. If two similar assets have slightly different expected returns, the optimiser may put everything into the higher-returning one and nothing in the other. Change the estimate by half a percentage point and the whole picture can flip.
A concrete demonstration: in a 12-asset optimisation, changing just two expected returns by 0.5% each caused UK large-cap equities, European equities, and emerging market equities to disappear from the optimal mix entirely. These three asset classes had not changed at all in their own return estimates. Their disappearance was purely a mathematical side effect of changes elsewhere.
The main fix is reverse optimisation, which grounds return estimates in market-capitalisation weights and removes the inconsistencies that cause instability. When returns are derived from market weights, they are consistent with each other in a way that arbitrary analyst forecasts are not. The optimiser then finds a well-diversified frontier rather than a concentrated one.
Criticism 2: Portfolios Concentrate in Too Few Assets
Left unconstrained, MVO tends to put most of the money into a small number of asset classes and ignore the rest. Real investors want diversification. The fix involves three tools used separately or together.
The first is the Black-Litterman model. This starts with reverse-optimised returns (which produce well-diversified allocations) and then allows the investor to tilt those returns based on their own views in a controlled, mathematically disciplined way.
Black-Litterman model: A model that blends reverse-optimised expected returns with an investor's own views on specific assets. The blend is controlled: strong views have more impact, uncertain views have less. The result is a stable, diversified set of expected returns
Ms C's wealth manager believes Asia Pacific equities will outperform European equities by 1% per year. Using the Black-Litterman model, this single view is blended with the reverse-optimised returns. Asia Pacific equities rise slightly in expected return; European equities fall slightly. Crucially, the impact spreads gracefully across correlated assets. Only the relevant corner of the portfolio changes. Without Black-Litterman, directly adjusting these two returns would have caused extreme and counterintuitive shifts across the whole portfolio.
The second tool is constraints. Specifying minimum and maximum allocations for each asset class prevents the optimiser from loading up on one asset class and zeroing out others. Good constraints reflect genuine real-world requirements such as investment policy limits, eligibility rules, or liquidity needs. Constraints used purely to force a more comfortable-looking output should be used carefully: if the unconstrained output looks wrong, the better answer is usually to revisit the inputs.
The third tool is resampled MVO. This combines Monte Carlo simulation with standard MVO. The optimiser runs thousands of times using slightly varied inputs and averages the resulting weights. The final allocation is smoother and more diversified because it reflects a range of plausible futures rather than one single set of estimates. The limitation is that resampling inherits the errors in the original inputs and lacks a strong theoretical foundation.
Criticism 3: Investors Care About More Than Mean and Variance
Skewness: The asymmetry of a return distribution. Negative skewness means the portfolio has a higher chance of suffering a very large loss than the normal bell curve would predict
Kurtosis: How fat the tails of the return distribution are. High kurtosis means extreme events occur much more often than normal
MVO treats all variance as equally bad whether it comes from occasional large losses or from ordinary fluctuations around the mean. In reality, most investors feel the pain of losses about twice as strongly as the pleasure of equivalent gains. This is prospect theory: losses loom larger than gains.
Historical data confirms the problem. Asset class returns are not normally distributed. Extreme outcomes occur roughly 10 times more often than the normal distribution predicts. For a portfolio that includes alternative strategies or options, this matters enormously. More advanced optimisers replace variance with measures like Conditional Value-at-Risk (CVaR), which directly penalises the severity of extreme losses.
Criticism 4: The Portfolio Looks Diversified But the Risk Is Concentrated
Risk budgeting: Analysing what percentage of total portfolio risk comes from each asset, not just what percentage of the money is in each asset
A portfolio with 54% equities and 46% bonds might look balanced. But equities are far more volatile than bonds. In practice, that same portfolio might derive 74% of its total volatility from equities and only 26% from bonds. The money allocation and the risk allocation tell very different stories. Risk budgeting makes the risk allocation visible.
Every asset has a marginal contribution to total risk (MCTR): how much portfolio volatility would increase if that asset's weight rose slightly. Multiplying MCTR by the asset's actual weight gives the absolute contribution to total risk (ACTR). A portfolio is optimally risk-budgeted when the ratio of excess return to MCTR is equal for every asset in the portfolio. If one asset has a much higher ratio than others, more weight should be shifted toward it.
In an optimised UK portfolio with total volatility of 10.88%, US equities hold 34.4% of the money but contribute 45.9% of total risk. Global ex-UK bonds hold 31.8% of the money but contribute only 12.3% of total risk. Cash holds 0.2% and contributes zero risk. The ratio of excess return to MCTR is 0.368 for every single asset class, confirming this is an optimal risk budget. If any one ratio were different from the others, the portfolio could be improved by shifting weight toward the asset with the higher ratio.
Criticism 5: MVO Ignores Liabilities
Most investors, whether a pension fund or a private individual, are not simply trying to grow money in isolation. They are trying to grow enough money to pay for something specific: retirement, education, a bequest, a pension obligation. Standard asset-only MVO does not connect the portfolio to what the money must eventually fund.
Sections 10 to 14 of the curriculum address this through liability-relative approaches. A brief preview: the surplus (assets minus the present value of liabilities) is what really matters. A portfolio that grows assets while liabilities grow faster is not serving the investor's true goal. Surplus optimisation replaces asset return with surplus return as the quantity being optimised.
Criticism 6: MVO Is Single-Period and Ignores Rebalancing Costs and Taxes
MVO produces one optimal portfolio for one period. It does not model what happens over time when the portfolio drifts from its target, when rebalancing triggers capital gains taxes, or when transaction costs accumulate across years of trading. For a taxable investor with a 20-year horizon, these real-world frictions can materially change which allocation is actually best.
Monte Carlo simulation addresses this. By running thousands of multi-period scenarios, each incorporating a specific rebalancing rule, a tax rate, and transaction cost assumptions, simulation reveals how different allocations actually perform after all costs over a realistic time horizon. The portfolio that looks optimal in a single-period MVO may not be the best choice once the full multi-period picture is considered.
Mr D holds two portfolios with identical single-period MVO-optimal weights. Portfolio 1 rebalances quarterly regardless of drift. Portfolio 2 rebalances only when an asset drifts more than 5% from target. Running 10,000 Monte Carlo scenarios over 20 years shows that Portfolio 2 ends up with meaningfully higher after-tax wealth. It triggers far fewer capital gains realisations. The single-period MVO cannot see this difference. Only the simulation reveals it.