In 1952, a 25-year-old graduate student published a 14-page paper that changed Wall Street forever. Harry Markowitz’s "Portfolio Selection" laid the mathematical foundation for modern quantitative finance and earned him a Nobel Prize.

In this inaugural episode of Finance Papers, we strip away the fluff and do a section-by-section deep dive into the actual math and mechanics of Markowitz's original text.

Key Topics Covered:

• ​The Concentration Trap: Why trying to purely maximize returns mathematically forces you to put 100% of your money into a single stock.
• ​The Myth of Large Numbers: Why holding 60 railway stocks isn't true diversification when a systemic market crash hits.
• ​The Magic of Covariance: How the interaction between assets—not their individual volatility—defines true portfolio risk.
• ​The Computing Bottleneck: How the sheer impossibility of calculating 125,000 covariance pairs by hand in 1952 eventually led to the creation of Beta and CAPM.
• ​The Math of Gambling: Why rational humans willingly buy lottery tickets (the statistical concept of Skewness).

Paper Explored: Markowitz, H. (1952), PORTFOLIO SELECTION*. The Journal of Finance, 7: 77-91.

🔗 Read the full paper here: https://doi.org/10.1111/j.1540-6261.1952.tb01525.x

Finance Papers is conceptualized and curated by Luiz Gidrão, CFA, CAIA (founder of stock.cash and goa.capital). Hit play, open the paper PDF, and learn with us.

Following up on Harry Markowitz’s foundational concept of diversification, William Sharpe’s 1964 paper took Modern Portfolio Theory to the next level.

This seminal work is the practical key that unlocked MPT for the investing world, introducing the Capital Asset Pricing Model (CAPM) and fundamentally changing how we evaluate investment returns in relation to risk. Like Markowitz, Sharpe also received a Nobel Prize for this foundational contribution to finance.

Join Finance Papers for a focused breakdown of Sharpe's masterwork. We strip away the textbook simplifications to analyze how the model truly works from its original source text, section-by-section.

Key Topics Covered in This Deep Dive:

• The Risk-Free Addition: How introducing a risk-free borrowing and lending asset collapses the complex Efficient Frontier into a single, elegant visual: The Capital Market Line (CML).

• The Separation Theorem: Understanding why the "efficient" portfolio is identical for every investor, regardless of their personal risk tolerance.

• Defining Beta (β): The exact mathematical meaning of Sharpe’s original metric for systematic risk and its relationship to the total market portfolio.

• The Undiversifiable Problem: Why diversification (as taught by Markowitz) cannot eliminate market risk—only firm-specific risk.

• Market Equilibrium: How collective investor behavior forces asset prices to adjust to a state of balance based on risk premiums.

Paper Explored: Sharpe, W.F. (1964), CAPITAL ASSET PRICES: A THEORY OF MARKET EQUILIBRIUM UNDER CONDITIONS OF RISK*. The Journal of Finance, 19: 425-442.

🔗 Read the full paper here

Finance Papers is conceptualized and curated by Luiz Gidrão, CFA, CAIA (founder of stock.cash and goa.capital). Hit play, open the PDF, and learn with us.