On a dynamic adaptation of the Distribution Builder approach to investment decisions

TL;DR

This paper extends the Distribution Builder approach from a single-period to a continuous-time setting, enabling dynamic investment decision-making based on desired future wealth distributions.

Contribution

It adapts the distribution-based investor preference elicitation method to continuous time, analyzing feasibility, risk preferences, and optimal policies over investment horizons.

Findings

Desired distributions influence feasibility and risk preferences

The approach determines optimal policies in various scenarios

Examples illustrate practical application of the method

Abstract

Sharpe et al. proposed the idea of having an expected utility maximizer choose a probability distribution for future wealth as an input to her investment problem instead of a utility function. They developed a computer program, called The Distribution Builder, as one way to elicit such a distribution. In a single-period model, they then showed how this desired distribution for terminal wealth can be used to infer the investor's risk preferences. We adapt their idea, namely that a risk-averse investor can choose a desired distribution for future wealth as an alternative input attribute for investment decisions, to continuous time. In a variety of scenarios, we show how the investor's desired distribution combines with her initial wealth and market-related input to determine the feasibility of her distribution, her implied risk preferences, and her optimal policies throughout her investment horizon. We then provide several examples.