Standard Mean-variance Optimization Research Articles

Practical Improvements to Mean-Variance Optimization for Multi-Asset Class Portfolios

In the more than 70 years since Markowitz introduced mean-variance optimization for portfolio construction, academics and practitioners have documented numerous weaknesses in the approach. In this paper, we propose two easily understandable improvements to mean-variance optimization in the context of multi-asset class portfolios, each of which provides less extreme and more stable portfolio weights. The first method sacrifices a small amount of expected optimality for reduced weight concentration, while the second method randomly resamples the available assets. Additionally, we develop a process for testing the performance of portfolio construction approaches on simulated data assuming variable degrees of forecasting skill. Finally, we show that the improved methods achieve better out-of-sample risk-adjusted returns than standard mean-variance optimization for realistic investor skill levels.

Enhanced Portfolio Optimization

Portfolio optimization should provide large benefits for investors, but standard mean–variance optimization (MVO) works so poorly in practice that optimization is often abandoned. Many of the approaches developed to address this issue are surrounded by mystique regarding how, why, and whether they really work. So, we sought to simplify, unify, and demystify optimization. We identified the portfolios that cause problems in standard MVO, and we present here a simple “enhanced portfolio optimization” method. Applying this method to industry momentum and time-series momentum across equities and global asset classes, we found significant alpha beyond the market, the 1/N portfolio, and standard asset pricing factors.

Enhanced Portfolio Optimization

Portfolio optimization should provide large benefits to investors, but standard mean-variance optimization (MVO) works so poorly in practice that optimization is often abandoned. The approaches developed to address this issue are often surrounded by mystique regarding how, why, and whether they really work, so we seek to simplify, unify, and demystify optimization. We identify the portfolios that cause problems in standard MVO and present a simple enhanced portfolio optimization (EPO) method. Applying EPO to industry momentum and time series momentum across equities and global asset classes, we find significant alpha beyond the market, the 1/N portfolio, and standard asset pricing factors. Citation: Pedersen, Lasse Heje, Abhilash Babu, and Ari Levine, Enhanced Portfolio Optimization, Financial Analysts Journal, 2021, 77(2): 124-151. Available at SSRN: https://ssrn.com/abstract=3530390 Published version (open access) at https://doi.org/10.1080/0015198X.2020.1854543

The Black-Litterman Model: Extensions and Asset Allocation

The Black-Litterman Model (BLM), created by Fischer Black and Robert Litterman, is a sophisticated portfolio construction method that overcomes the problem of unintuitive, highly-concentrated portfolios, input-sensitivity, and estimation error maximization. The BLM uses a Bayesian approach to combine the subjective views of an investor regarding the expected returns of one or more assets with the market equilibrium vector of expected returns (the prior distribution) to form a new, mixed estimate of expected returns. The resulting new vector of returns (the posterior distribution), leads to intuitive portfolios with sensible portfolio weights. (Idzorek, 2004). BLM was first introduced in Black and Litterman (1990) and further explained in Black and Litterman (1991) and Black and Litterman (1992) It is an asset allocation model which has its roots in mean-variance (MV) optimization model and capital asset pricing model (CAPM). Model builds on MV optimization and CAPM by using a Bayesian framework that allows investors to incorporate their views on markets effectively into asset allocation process. Main contribution of BLM is that it enables investors to construct sensible portfolios without using unnecessary constraints which also reflect their views on markets. It is well known to both academics and practitioners that standard MV optimization is very sensitive to expected returns and often generates extreme portfolios (concentration in very few assets, large long and short positions). BLM overcomes these issues by choosing a neutral reference point, CAPM equilibrium. It also allows investors to express their views with varying confidence levels and integrate these views into CAPM prior by using a Bayesian framework. As a result, since its introduction BLM has been increasingly used among practitioners and allowed asset allocation decisions to be in more of a quantitative nature rather than qualitative because of the apparent shortcomings of MV optimization model.

How Costly Are Stale Prices? Illiquidity in Hedge Fund Returns and Its Implications for Asset Allocation

Diversification and low correlation are the primary reasons institutional investors cite for choosing to include hedge funds in a portfolio. However, there are a number of hidden biases in the reported returns which may overstate the attractiveness of hedge funds as an asset class. We review the literature on the stale pricing bias in hedge fund returns, propose an improved model for assessing the existence and extent of the stale pricing bias, and discuss potential causes of the pricing bias. We show how correcting hedge fund returns for stale pricing has a meaningful impact on the estimated volatility and correlation with other asset classes. From this, we demonstrate the degree to which asset allocation decisions relying on standard mean-variance optimization will mis-allocate to hedge funds when the stale pricing bias is not corrected.

A fuzzy compromise programming approach for the Black-Litterman portfolio selection model

In this paper, we examine advanced optimization approach for portfolio problem introduced by Black and Litterman to consider the shortcomings of Markowitz standard Mean-Variance optimization. Black and Litterman propose a new approach to estimate asset return. They present a way to incorporate the investor’s views into asset pricing process. Since the investor’s view about future asset return is always subjective and imprecise, we can represent it by using fuzzy numbers and the resulting model is multi-objective linear programming. Therefore, the proposed model is analyzed through fuzzy compromise programming approach using appropriate membership function. For this purpose, we introduce the fuzzy ideal solution concept based on investor preference and indifference relationships using canonical representation of proposed fuzzy numbers by means of their correspondingα-cuts. A real world numerical example is presented in which MSCI (Morgan Stanley Capital International Index) is chosen as the target index. The results are reported for a portfolio consisting of the six national indices. The performance of the proposed models is compared using several financial criteria.

Dynamic Hedge Fund Portfolio Construction: A Semi-Parametric Approach

In this paper, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. Using monthly hedge fund index returns for the period 1990 to 2011, we compare the standard mean-variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, in which we first model the marginal density of each hedge fund index using extreme value theory and construct the joint density of hedge fund index returns using a copula-based approach. We then simulate hedge fund returns from this joint density in order to compute CVaR, CDaR and Omega, which are used in the optimization process. We compare the semi-parametric approach with the standard, non-parametric approach, in which the quantiles of the marginal density of portfolio returns are estimated empirically and used to compute CVaR, CDaR and Omega. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the mean-variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.

Revisiting the Black–Litterman model: The case of hedge funds

The article provides an illustration of the Black–Litterman model. It shows how to combine an investor's views with the market equilibrium. This study also sheds light on the behaviour of hedge funds as an asset class. In this article, we re-examine a new optimization approach introduced by Black and Litterman to overcome the weaknesses of the standard mean-variance optimization model. We also consider the resampling technique to refine our results. Our results show that combining the resampling technique with the Black–Litterman model presents the most robust asset allocation. When we consider the case of hedge funds (HFs), we find that the integration of HFs into traditional investment categories indeed improves the portfolio's risk/return profile, for the period 2002–2007. The importance of HFs is less obvious, however, when using the Black–Litterman model with the resampling technique.

Real Estate in the Real World: Dealing with Non-Normality and Risk in an Asset Allocation Model

Executive Summary. Quantitative models of asset allocation are increasingly used by institutional commercial real estate investors as a guide for investment strategy. Real estate as an asset class, however, does not conform well to many of the assumptions underlying standard mean-variance optimization. This paper outlines a model of allocation that addresses two important “real world” violations of these assumptions. First, the assumption that returns are normally distributed is relaxed; instead, returns are modeled using a distribution that allows for both the “fat-tailed” behavior and skewness seen in asset returns. Second, an alternative to the traditional MPT optimizer is employed—the so called “downside deviation” model—that better reflects the observed behavior of investors.