Equivalent Expectation Measures for Risk and Return Analysis of Contingent Claims

Vol. 22, No. 3, 2024
Sanjay K. Nawalkha and Xiaoyang Zhuo

Nearly half-a-century after the advent of equivalent martingale measures (EMMs), Nawalkha and Zhuo (2022, 2023) generalize these measures to obtain equivalent expectation measures (EEMs) for analyzing risk and return of portfolios of contingent claims over a finite horizon date. The new measures allow the derivation of analytical solutions of the physical moments and co-moments of contingent claim returns until before the horizon date, and serve as pricing measures on or after that date. This novel approach allows Markowitz’s (1952) mean–variance optimization to be applied to equity portfolios embedded with options as well as fixed-income portfolios with or without options. This is useful in the investment management of equity funds, bond funds, and hedge funds, for managing risk–return trade-offs more effectively over finite planning horizons.