Mean-variance portfolio theory requires the restrictive quadratic utility assumption.

Evidence

Unless the changes in prices of securities followed a joint normal distribution (which was regarded as ruled out, because it would imply, as Samuelson had noted, a non-zero probability of negative prices), mean-variance analysis seemed to rest on a specific form of the “utility function” characterizing the relationship between the return, y, on an investor’s portfolio and his or her preferences. Mean-variance analysis seemed to imply that investors’ utility functions were quadratic: that is, they contained only terms my andy2. Special cases aside, a rational investor with a utility function whose mathematical form differed from this would not be guided by the expected mean and variance alone. — Donald MacKenzie, An Engine, Not a Camera, 588

Categorization

• DEFINE: Defines what quadratic utility means and why it is the mathematical load-bearing assumption behind mean-variance analysis.
• XREF: connects to: Expected-value-only investing logically implies holding a single stock, not a diversified portfolio — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 207; Adding risk to portfolio selection makes the optimization problem nonlinear and mathematically novel. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 211; Computational and data limits, not theory, made early portfolio selection unusable. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 230 (+4 more)

Broader Connections

• Classical utility theory defines value by final wealth with diminishing marginal returns #qualifies (0.82) — John T. Jost and Jim Sidanius, Political Psychology, 2412
• Arbitrage pricing theory generalizes CAPM to multiple unspecified risk factors #responds-to (0.78) — Donald MacKenzie, An Engine, Not a Camera, 1542