What These Models Miss
The assumptions behind portfolio theory, set against what the data show: inputs that shift from one generation to the next, extremes the bell curve rules out, diversification that weakens when it's needed, and an investor who doesn't behave like the model.
The short version
Portfolio theory assumes that returns, risks, and correlations are known and stable, that returns follow a bell curve, that risk means volatility, and that the investor holds the portfolio the model chose. None of those holds reliably. The average return on shares was 7.5% a year in one 20-year stretch and 15.8% in the next. Bond volatility quadrupled between two others. Shares and bonds have fallen together in five years out of 98, and small companies fell in 22 of the 26 years that large ones did. Investors in funds have earned about a point a year less than the funds themselves. The tools remain useful for structure and comparison. What they can't do is turn an uncertain future into a number.
By the end of this lesson, you'll be able to
- Identify the main assumptions of portfolio theory and the evidence against each
- Explain why diversification is weakest in the conditions where it's most wanted
- Describe what remains useful from the models, and the practical habits that allow for what they miss
Why this matters
Each lesson in this track taught a tool and attached a warning to it. Read one at a time, the warnings can look like fine print. Put together, they describe where a carefully built portfolio is exposed. This lesson collects them. It isn't an argument against the tools. A map with known errors is far better than no map, as long as you know where the errors are.
Assumption one: the inputs are known and stable
Every formula in this track takes expected returns, standard deviations, and correlations as given. Expected Return and Standard Deviation showed that a century of data leaves the expected return on shares uncertain by several points. The table below shows the other half of the problem. Even the figures that were realized changed a great deal from one generation of investors to the next.
| Period | Shares: average | Shares: standard deviation | Bonds: average | Bonds: standard deviation | Correlation |
|---|---|---|---|---|---|
| 1928 to 1947 | 7.5% | 27.4% | 3.2% | 2.8% | 0.14 |
| 1948 to 1967 | 15.8% | 17.2% | 2.1% | 3.5% | −0.48 |
| 1968 to 1987 | 10.5% | 16.5% | 7.7% | 10.6% | 0.31 |
| 1988 to 2007 | 12.9% | 16.5% | 8.1% | 8.3% | 0.13 |
| 2008 to 2025 | 12.6% | 18.0% | 2.9% | 9.6% | −0.22 |
From Aswath Damodaran's yearly returns for the S&P 500 and 10-year Treasury bonds, before costs and inflation.1
An investor in 1948, using the previous 20 years, would have expected 7.5% a year from shares and got 15.8%. One in 1968 would have assumed bonds barely moved, with a standard deviation of 3.5%, and then lived through one of 10.6%. The correlation between the two changed sign three times. A model built on any one row gave poor guidance for the next, and an investing lifetime is only two or three rows long.
Assumption two: returns follow a bell curve
Standard deviation is a full description of risk only if returns are normally distributed. Distributions, Standard Deviation, and Fat Tails tested that on 14,037 daily changes in the Nasdaq Composite. A bell curve predicted fewer than one day in a million with a move beyond five standard deviations. There were 43.2
The consequence is that every measure built on standard deviation, including the Sharpe ratio, beta, and the efficient frontier, describes ordinary conditions well and the worst conditions badly. And a portfolio's survival is decided in the worst conditions.
Assumption three: diversification works when you need it
A correlation is an average over all kinds of years. What an investor needs to know is how the holdings behave in the bad ones.
| Average return in those years | Years it also fell | |
|---|---|---|
| S&P 500 | −13.5% | 26 of 26 |
| Smallest US companies | −15.5% | 22 of 26 |
| 10-year Treasury bonds | +4.3% | 5 of 26 |
Calculated from the same data.1 Two things stand out. Spreading money across different kinds of shares gave almost no protection: small companies fell in 22 of the 26 years, and by more on average. Shares share the risk that matters most. Bonds did much better, rising in 21 of the 26 years. But the five exceptions include 2022, when both lost about 18%, and a portfolio built on the assumption that bonds always cushion shares had no cushion that year.
Holdings that look different in calm markets can turn out to depend on the same thing: the same economy, the same interest rates, the same investors needing to sell. Diversification lowers risk. It doesn't remove the risk that everything you own falls together.
The rest of this lesson is for members
Still to come in this lesson: Assumption four: risk is volatility, Assumption five: the investor holds the portfolio, What the models leave out altogether, What survives, Habits that allow for the gaps, the key takeaways, and 2 quiz questions with explanations.
Membership opens every lesson in the curriculum, the capstone projects, the interactive tools, and the members-only channels in the Hyperion Entities Discord. The first lesson of every module stays free.
Go deeper
- Distributions, Standard Deviation, and Fat TailsMath and Statistics for Investors (depth track)
- Managing Risk Without Predicting EverythingPart 5: Building a Portfolio
- Why Smart People Make Bad Investment DecisionsPart 6: Strategy, Behavior, Accounts, and Taxes
- The Limits of DCF ModelsPart 4: Research and Valuation
Notes and sources
- Aswath Damodaran, NYU Stern School of Business. Historical Returns on Stocks, Bonds and Bills, with annual data through 2025 (updated January 2026). Checked 2026-10-12. Back to text
- Federal Reserve Bank of St. Louis (FRED), from Nasdaq OMX Group. NASDAQ Composite Index (NASDAQCOM), daily close. Checked 2026-10-12. Back to text
- Morningstar, Portfolio and Planning Research. Mind the Gap 2025 (August 13, 2025). Checked 2026-10-06.