Risk Preference Smoothness and the APT
Attitudes of risk aversion and diversification preference are closely linked to the degree of smoothness of the underlying preference relation over monetary risks, represented in terms of the first and second variations of the preference functional in the direction of incremental risks, evaluated at an initial portfolio. Under general maintained assumptions, "exact" and "approximate" versions of the Arbitrage Pricing Theory (APT) may be derived respectively from first and second-degree smoothness of risk preferences among investors in a competitive, finite asset market.
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