Adding risk to portfolio selection makes the optimization problem nonlinear and mathematically novel.

Evidence

Markowitz quickly saw that once risk as well as return was brought into the picture the problem of finding efficient portfolios was not a linear one. The formula for the standard deviation or variance of returns involves squaring rates of return, so the problem could not be solved using existing linear programming techniques: it fell into what was then the little-explored domain of quadratic programming. Koopmans liked Markowitz’s term paper, giving it a grade of A, and encouraged him to take the problem further, telling him: “It doesn’t seem that hard. Why don’t you solve it?” (Markowitz interview) Solve the problem of selecting efficient portfolios was precisely what Markowitz went on to do. — Donald MacKenzie, An Engine, Not a Camera, 211

Categorization

• XREF: Charts the early technical history of the very models whose performativity the book examines; connects to the broader theme of quantitative finance’s intellectual origins. — connects to: Mean-variance portfolio theory requires the restrictive quadratic utility assumption. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 588; Value-at-risk quantifies portfolio exposure through estimated loss probabilities. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 995; Concave utility curves mathematically imply risk-averse choices.

Broader Connections

• Mean-variance portfolio theory requires the restrictive quadratic utility assumption. #qualifies (0.80) — Donald MacKenzie, An Engine, Not a Camera, 588
• Concave utility curves mathematically imply risk-averse choices. #exemplifies (0.75)
• Value-at-risk quantifies portfolio exposure through estimated loss probabilities. #expands (0.72) — Donald MacKenzie, An Engine, Not a Camera, 995