Pi Portfolio Management: Reaching Goals While Avoiding Losses

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