Beyond Markowitz
This article was co-authored by Pinaki Ghosh and Isaac Vergara.
This is a continuation of our previous article on Markowitz Optimization Theory. To view that article, click here: Portfolio Optimization Series — Part 1: The Markowitz Mean-Variance Framework Applied to S&P 500 Sectors | by Quantitative Finance & Analytics Club | Medium
I. What Markowitz Left Unanswered
In Part 1, we applied mean-variance optimization to five S&P 500 universes and found that the math works exactly as advertised. Given a set of stocks and a sample period, Markowitz finds the portfolio with the highest historical Sharpe ratio on the efficient frontier.
The healthcare portfolio illustrates what mean-variance optimization actually produces in practice. Out of the available stocks, the Max Sharpe portfolio collapsed into two names: AbbVie (ABBV) at 71.9% and Boston Scientific (BSX) at 27.6%, with Agilent Technologies (A) receiving a token 0.6%. The remaining stocks — including names like Amgen (AMGN), Baxter International (BAX), and Biogen (BIIB) — received zero allocation. The optimizer found that ABBV and BSX delivered the best risk-adjusted returns over the sample period and had no reason to look elsewhere. This is not diversification across healthcare. It is a concentrated bet on two companies.
The technology portfolio tells a similar story. Out of twelve available stocks, the Max Sharpe portfolio concentrated in just four: Broadcom (AVGO) at 43.1%, Amphenol (APH) at 32.2%, Alphabet (GOOG) at 18.1%, and Apple (AAPL) at 6.7%.
This is not a flaw in the implementation; it is the expected behavior of an optimizer that sees only one dimension of risk: variance. When a stock has dominated a sector’s risk-adjusted returns over the sample period, the model has no reason to hold back. It bets the portfolio on that historical signal.
But why did those stocks win? Once we understand the sources of return, we can build portfolios that are more balanced without sacrificing much performance. That understanding runs through the Fama-French three-factor model.
II. Fama-French Three-Factor Model
In 1992, Eugene Fama and Kenneth French published findings that permanently changed how academics and practitioners think about equity returns. Building on the Capital Asset Pricing Model (CAPM), they showed that two simple stock characteristics — company size and book-to-market ratio — explained a large share of cross-sectional return variation that the single market factor left unaccounted for.
Their model expresses a portfolio’s excess return as a linear combination of three systematic factors:
The central insight is that a portfolio’s return is not a single undifferentiated number. It is the sum of compensated exposures to systematic risks. A tech-heavy portfolio that rose 40% over five years may have done well mostly because tech stocks in general were booming, not because its specific stocks were uniquely well-chosen. A financial sector portfolio may be delivering a value premium that other, less concentrated instruments could replicate just as well.
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For portfolio construction, this matters because factor exposures are, to a significant degree, interchangeable within a sector. If two stocks share nearly identical HML and SMB loadings, concentrating the entire portfolio in one of them delivers no factor diversification benefit that the other would not provide. The Markowitz optimizer cannot see this. Factor analysis can.
III. Factor Fingerprints Across Sectors
We ran FF3 regressions on equal-weight versions of each sector portfolio using daily returns from January 2020 through December 2024, with factor data sourced from Kenneth French’s data library. Running the regression on an equal-weight portfolio rather than the optimized one lets us characterize the sector’s underlying factor structure without the circular problem of using optimized weights to explain why the optimizer behaved the way it did.
Technology’s beta HML of -0.28 confirms its growth character. The portfolio loads on stocks with low book-to-market ratios, and companies like Broadcom, Apple, and Alphabet, whose value lies in future earnings and intangible assets. Financials carry the strongest factor signal in the sample, with an HML beta of +0.61. Insurance companies, banks, and asset managers like the ones in our universe are textbook value stocks with high book-to-market ratios and mature cash flows. Healthcare sits almost exactly at zero on HML (-0.006), reflecting that the sector spans high-growth biotech and mature large pharma, and those exposures largely cancel each other out.
Large Cap is the only portfolio with a statistically significant alpha at +5.5%. A 5-year sample is short, and we are cautious about reading too much into it, but the result is consistent with the idea that a cross-sector, quality-tilted, large-cap universe may capture return sources that the three factors do not fully explain.
Each sector has a distinct factor fingerprint, and that fingerprint explains a lot about why the optimizer behaves the way it does. Healthcare concentrates because its low R² means idiosyncratic stock performance, not systematic factors, drives returns; AbbVie delivered in that race over the sample period. Technology concentrates in Broadcom and Amphenol (APH) because those two names delivered the best growth-tilted, market-sensitive returns without the optimizer needing anything else.
IV. What the Factors Reveal
Once you understand what the optimizer is actually chasing, you can give it more informed constraints. The table below shows what happens when portfolios are rebuilt with factor targets derived from the regressions above and a 40% cap on any single stock.
The Sharpe cost of diversification is small across the board. Technology gives up 0.03, Large Cap gives up 0.01, and Diversified barely moves. The biggest drop is in Financials, where forcing weight away from Arthur J. Gallagher (AJG) has a real cost because that stock genuinely dominated the sample. But in every case, the maximum weight drops from something operationally problematic to something an actual portfolio manager could defend.
V. Conclusion
Factor analysis reframes the concentration problem. What looks like an optimizer making an aggressive bet on a single stock is, underneath, an optimizer efficiently acquiring a specific set of return exposures. The issue is that it found one vehicle for those exposures when several were available. Spreading weight across equivalent factor exposures costs almost nothing in Sharpe terms but produces a portfolio that is actually manageable in practice.
The numbers make the case quietly. Across five different universes, the Sharpe ratio barely moved while maximum single-stock weights dropped from the 50–80% range to 40%. That gap between the theoretical optimum and the practical portfolio is where factor awareness earns its keep.
