Pi Portfolio Management: Reaching Goals While Avoiding Losses

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