Pi Portfolio Management: Reaching Goals While Avoiding Losses

48 Pages Posted: 7 Sep 2019 Last revised: 3 Sep 2020

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 new objective for portfolio optimization: a weighted average of the probabilities
of achieving specific target levels and avoiding specific loss levels. The objective is relatively easy
to understand by non-experts, making it easier to calibrate to individuals’ risk profiles. Moreover,
our approach is consistent with both standard and non-standard risk preferences, such as those
of prospect theory. Comparing the associated optimal portfolio to the optimal mean-variance and
Merton’s portfolios, in our setting the one-fund theorem still holds, but the holdings in the risky
assets are nonlinear in their risk premium and/or their return rates. Our model helps explain
the complicated risk seeking and risk aversion behavior as the level of wealth and time change,
observed for fund managers.

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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