Pi Portfolio Management: Reaching Goals While Avoiding Losses

59 Pages Posted: 7 Sep 2019 Last revised: 5 Apr 2023

See all articles by Jaksa Cvitanic

Jaksa Cvitanic

California Institute of Technology - Division of the Humanities and Social Sciences

Steven Kou

Boston University

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management

Karyn Williams

Hightree Advisors LLC

Date Written: August 30, 2019

Abstract

We propose a general framework for portfolio optimization by using a new objective function:
a weighted average of the probabilities of achieving specific target levels and avoiding specific
loss levels. The framework can explicitly take into account investors’ constraints on profit and
loss probabilities and on portfolio weights. It is relatively easy to understand the objective
by non-experts. Moreover, the objective function can approximate arbitrary utility functions
and is consistent with both standard and some non-standard risk preferences. Comparing the
associated optimal portfolio to the optimal mean-variance and Merton’s portfolios, the one-fund
theorem still holds in our setting, but the holdings in the risky assets are nonlinear in their risk
premium and/or their return rates.

Keywords: portfolio selection, portfolio management, goal investing, mean-variance, prospect theory

JEL Classification: G11, G40, G50

Suggested Citation

Cvitanic, Jaksa and Kou, Steven and Wan, Xiangwei and Williams, Karyn L., Pi Portfolio Management: Reaching Goals While Avoiding Losses (August 30, 2019). Available at SSRN: https://ssrn.com/abstract=3444836 or http://dx.doi.org/10.2139/ssrn.3444836

Jaksa Cvitanic (Contact Author)

California Institute of Technology - Division of the Humanities and Social Sciences ( email )

1200 East California Blvd.
Pasadena, CA 91125
United States

HOME PAGE: http://www.hss.caltech.edu/~cvitanic/

Steven Kou

Boston University ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
6173583318 (Phone)

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management ( email )

No.1954 Huashan Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200030
China
+86-21-52301570 (Phone)

HOME PAGE: http://sites.google.com/view/wanxiangwei/research

Karyn L. Williams

Hightree Advisors LLC ( email )

100 Wilshire Boulevard Suite 700
Santa Monica, CA 90401
United States

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