Portfolio Construction Via Convex Optimization
A portfolio is a collection of investments, such as stocks, bonds, and other alternatives assets that an investor holds, in addition to short positions, where the investor borrows an asset, sells it immediately, and assumes the obligation to repurchase it later. Portfolio construction, also known as...
Saved in:
| Main Author: | |
|---|---|
| Format: | Dissertation |
| Language: | English |
| Published: |
ProQuest Dissertations & Theses
01-01-2024
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | A portfolio is a collection of investments, such as stocks, bonds, and other alternatives assets that an investor holds, in addition to short positions, where the investor borrows an asset, sells it immediately, and assumes the obligation to repurchase it later. Portfolio construction, also known as portfolio optimization, refers to the choice of assets to include and the amount to be invested (possibly negative, meaning a short position). The goal of portfolio construction is at a high level to maximize the return of the portfolio, while controlling the risk of losses.Since the seminal work of Markowitz in the 1950s, portfolio construction has been a cornerstone of financial theory and practice. It has also been a fertile ground for the development and application of optimization techniques. This thesis contributes to the field by developing new problems formulations and methodologies for portfolio construction under novel settings, risk measures, and utility functions.The following sections provide a brief overview of each chapter, highlighting the core contributions and methodologies developed.1.1Strategic asset allocation with illiquid alternativesChapter 2 is based on the paper [72]. We address the problem of strategic asset allocation (SAA) with portfolios that include illiquid alternative asset classes. The main challenge in portfolio construction with illiquid asset classes is that we do not have direct control over our positions, as we do in liquid asset classes. Instead we can only make commitments; the position builds up over time as capital calls come in, and reduces over time as distributions occur, neither of which the investor has direct control over. The effect on positions of our commitments is subject to a delay, typically of a few years, and is also unknown or stochastic. A further challenge is the requirement that we can meet the capital calls, with very high probability, with our liquid assets.We formulate the illiquid dynamics as a random linear system, and propose a convex optimization based model predictive control (MPC) policy for allocating liquid assets and making new illiquid commitments in each period. Despite the challenges of time delay and uncertainty, we show that this policy attains performance surprisingly close to a fictional setting where we pretend the illiquid asset classes are completely liquid, and we can arbitrarily and immediately adjust our positions. In this chapter we focus on the growth problem, with no external liabilities or income, but the method is readily extended to handle this case.Portfolio construction with Gaussian mixture returns and exponential utilityChapter 3 is based on the paper [71]. We consider the problem of choosing an optimal portfolio, assuming the asset returns have a Gaussian mixture (GM) distribution, with the objective of maximizing expected exponential utility. In this chapter we show that this problem is convex, and readily solved exactly using domain-specific languages for convex optimization, without the need for sampling or scenarios. We then show how the closely related problem of minimizing entropic value at risk can also be formulated as a convex optimization problem.1.2 Portfolio construction with cumulative prospect theory utilityChapter 4 is based on the paper [73]. We consider the problem of choosing a portfolio that maximizes the cumulative prospect theory (CPT) utility on an empirical distribution of asset returns. We show that while CPT utility is not a concave function of the portfolio weights, it can be expressed as a difference of two functions. |
|---|---|
| ISBN: | 9798384337751 |