Modern portfolio management with conditioning information

This paper studies models in which active portfolio managers utilize conditioning information unavailable to their clients to optimize performance relative to a benchmark. We derive explicit solutions for the optimal strategies with multiple risky assets, with or without a risk-free asset, and consider various constraints on portfolio risks or weights. The optimal strategies feature a mean–variance efficient component (to minimize portfolio variance), and a hedging demand for the benchmark portfolio (to maximize correlation with the benchmark). A currency portfolio example shows that the optimal strategies improve the measured performance by 53% out of sample, compared with portfolios ignoring conditioning information.     

Portfolio selection based on the mean–VaR efficient frontier

Value-at-Risk (VaR) has become one of the standard measures for assessing risk not only in the financial industry but also for asset allocations of individual investors. The traditional mean–variance framework for portfolio selection should, however, be revised when the investor's concern is the VaR instead of the standard deviation. This is especially true when asset returns are not normal. In this paper, we incorporate VaR in portfolio selection, and we propose a mean–VaR efficient frontier. Due to the two-objective optimization problem that is associated with the mean–VaR framework, an evolutionary multi-objective approach is required to construct the mean–VaR efficient frontier. Specifically, we consider the elitist non-dominated sorting Genetic Algorithm (NSGA-II). From our empirical analysis, we conclude that the risk-averse investor might inefficiently allocate his/her wealth if his/her decision is based on the mean–variance framework.     

Portfolio construction incorporating asymmetric dependence structures: a user's guide

We outline a method of portfolio selection incorporating asymmetric dependency structures using copula functions. Assuming normally distributed marginal returns, we illustrate how asymmetric return correlations affect the efficient frontier and subsequent portfolio performance under a dynamic rebalancing framework. Implementing this methodology within the context of tactically allocating a small set of market indices, we demonstrate several key findings. First, we establish the manner by which the efficient frontier constructed under asymmetric dependence differs from a mean‐variance frontier. By establishing a paper portfolio based on these differences, we find that asymmetric correlation structures do have real economic value. The primary source of this economic value is the ability to better protect portfolio value and reduce the size of any erosion in return relative to the normal portfolio when asymmetric return correlations are accounted for.     

Portfolio selection with a drawdown constraint

When identifying optimal portfolios, practitioners often impose a drawdown constraint. This constraint is even explicit in some money management contracts such as the one recently involving Merrill Lynch’ management of Unilever’s pension fund. In this setting, we provide a characterization of optimal portfolios using mean–variance analysis. In the absence of a benchmark, we find that while the constraint typically decreases the optimal portfolio’s standard deviation, the constrained optimal portfolio can be notably mean–variance inefficient. In the presence of a benchmark such as in the Merrill Lynch–Unilever contract, we find that the constraint increases the optimal portfolio’s standard deviation and tracking error volatility. Thus, the constraint negatively affects a portfolio manager’s ability to track a benchmark.     

A dynamic model of active portfolio management with benchmark orientation

This paper studies optimal dynamic portfolios for investors concerned with the performance of their portfolios relative to a benchmark. Assuming that asset returns follow a multi-linear factor model similar to the structure of Ross (1976) [Ross, S., 1976. The arbitrage theory of the capital asset pricing model. Journal of Economic Theory, 13, 342–360] and that portfolio managers adopt a mean tracking error analysis similar to that of Roll (1992) [Roll, R., 1992. A mean/variance analysis of tracking error. Journal of Portfolio Management, 18, 13–22], we develop a dynamic model of active portfolio management maximizing risk adjusted excess return over a selected benchmark. Unlike the case of constant proportional portfolios for standard utility maximization, our optimal portfolio policy is state dependent, being a function of time to investment horizon, the return on the benchmark portfolio, and the return on the investment portfolio. We define a dynamic performance measure which relates portfolio’s return to its risk sensitivity. Abnormal returns at each point in time are quantified as the difference between the realized and the model-fitted returns. Risk sensitivity is estimated through a dynamic matching that minimizes the total fitted error of portfolio returns. For illustration, we analyze eight representative mutual funds in the U.S. market and show how this model can be used in practice.     

A note on the returns from minimum variance investing

Disappointed with the performance of market weighted benchmark portfolios yet skeptical about the merits of active portfolio management, investors in recent years turned to alternative index definitions. Minimum variance investing is one of these popular concepts. I show in this paper that the portfolio construction process behind minimum variance investing implicitly picks up risk-based pricing anomalies. In other words the minimum variance tends to hold low beta and low residual risk stocks. Long/short portfolios based on these characteristics have been associated in the empirical literature with risk adjusted outperformance. This paper shows that 83% of the variation of the minimum variance portfolio excess returns (relative to a capitalization weighted alternative) can be attributed to the FAMA/FRENCH factors as well as to the returns on two characteristic anomaly portfolios. All regression coefficients (factor exposures) are highly significant, stable over the estimation period and correspond remarkably well with our economic intuition. The paper also shows that a direct combination of market weighted benchmark portfolio and risk based characteristic portfolios will provide a statistically significant improvement over the indirect pickup via the minimum variance portfolio.     

Linear programing models for portfolio optimization using a benchmark

We consider the problem of constructing a perturbed portfolio by utilizing a benchmark portfolio. We propose two computationally efficient portfolio optimization models, the mean-absolute deviation risk and the Dantzig-type, which can be solved using linear programing. These portfolio models push the existing benchmark toward the efficient frontier through sparse and stable asset selection. We implement these models on two benchmarks, a market index and the equally-weighted portfolio. We carry out an extensive out-of-sample analysis with 11 empirical datasets and simulated data. The proposed portfolios outperform the benchmark portfolio in various performance measures, including the mean return and Sharpe ratio.     

A semi-parametric approach to risk management

Abstract

The benchmark theory of mathematical finance is the Black–Scholes–Merton (BSM) theory, based on Brownian motion as the driving noise process for stock prices. Here the distributions of financial returns of the stocks in a portfolio are multivariate normal. Risk management based on BSM underestimates tails. Hence estimation of tail behaviour is often based on extreme value theory (EVT). Here we discuss a semi-parametric replacement for the multivariate normal involving normal variance–mean mixtures. This allows a more accurate modelling of tails, together with various degrees of tail dependence, while (unlike EVT) the whole return distribution can be modelled. We use a parametric component, incorporating the mean vector μ and covariance matrix Σ, and a non-parametric component, which we can think of as a density on [0,∞), modelling the shape (in particular the tail decay) of the distribution. We work mainly within the family of elliptically contoured distributions, focusing particularly on normal variance mixtures with self-decomposable mixing distributions. We discuss efficient methods to estimate the parametric and non-parametric components of our model and provide an algorithm for simulating from such a model. We fit our model to several financial data series. Finally, we calculate value at risk (VaR) quantities for several portfolios and compare these VaRs to those obtained from simple multivariate normal and parametric mixture models.     

The premium of dynamic trading

It is well established that, in a market with inclusion of a risk-free asset, the single-period mean–variance efficient frontier is a straight line tangent to the risky region, a fact that is the very foundation of the classical CAPM. In this paper, it is shown that, in a continuous-time market where the risky prices are described by Itô processes and the investment opportunity set is deterministic (albeit time-varying), any efficient portfolio must involve allocation to the risk-free asset at any time. As a result, the dynamic mean–variance efficient frontier, although still a straight line, is strictly above the entire risky region. This in turn suggests a positive premium, in terms of the Sharpe ratio of the efficient frontier, arising from dynamic trading. Another implication is that the inclusion of a risk-free asset boosts the Sharpe ratio of the efficient frontier, which again contrasts sharply with the single-period case.     

Keeping up with the Joneses and optimal diversification

Peer-effects have been shown to affect behavior, and can generally lead to investments choices that are mean–variance inefficient. This paper analyzes optimal diversification with peer-effects. We show that if individuals have keeping-up with the Joneses preferences and they take their peer-group reference as the market portfolio, Markowitz’s mean–variance efficiency analysis and the CAPM equilibrium are intact. This holds for any keeping-up preferences, as well as heterogeneous combinations of such preferences. These results also extend to the Merton–Levy segmented-market model.     

A minimum variance benchmark to measure the performance of pension funds in Mexico

We propose the use of the minimum variance portfolio as weighting method in a strategy benchmark for pension funds performance in Mexico. By performing three discrete event simulations with daily data from January 2002 to May 2013, we test this benchmark's weighting method against the Max Sharpe ratio one and a linear combination of both benchmarks (minimum variance and Max Sharpe). With the Sharpe ratio, the Jensen's alpha significance test and the Huberman and Kandel’ (1987) spanning test, we found that the three benchmarks have a statistically equal performance. By using Bailey's (1992) risk exposure, market representativeness and turnover benchmark quality criteria, we found that the min variance is preferable for the publicly traded Mexican defined contribution pension funds.     

On the performance of the minimum VaR portfolio

Alexander and Baptista [2002. Economic implications of using a mean-value-at-risk (VaR) model for portfolio selection: A comparison with mean–variance analysis. Journal of Economic Dynamics and Control 26: 1159–93] develop the concept of mean-VaR efficiency for portfolios and demonstrate its very close connection with mean–variance efficiency. In particular, they identify the minimum VaR portfolio as a special type of mean–variance efficient portfolio. Our empirical analysis finds that, for commonly used VaR breach probabilities, minimum VaR portfolios yield ex post returns that conform well with the specified VaR breach probabilities and with return/risk expectations. These results provide a considerable extension of evidence supporting the empirical validity and tractability of the mean-VaR efficiency concept.     

Jump robust two time scale covariance estimation and realized volatility budgets

We estimate the daily integrated variance and covariance of stock returns using high-frequency data in the presence of jumps, market microstructure noise and non-synchronous trading. For this we propose jump robust two time scale (co)variance estimators and verify their reduced bias and mean square error in simulation studies. We use these estimators to construct the ex-post portfolio realized volatility (RV) budget, determining each portfolio component’s contribution to the RV of the portfolio return. These RV budgets provide insight into the risk concentration of a portfolio. Furthermore, the RV budgets can be directly used in a portfolio strategy, called the equal-risk-contribution allocation strategy. This yields both a higher average return and lower standard deviation out-of-sample than the equal-weight portfolio for the stocks in the Dow Jones Industrial Average over the period October 2007–May 2009.     

Multiobjective portfolio optimization with non-convex policy constraints: Evidence from the Eurostoxx 50

Our purpose in this paper is to depart from the intrinsic pathology of the typical mean–variance formalism, due to both the restriction of its assumptions and difficulty of implementation. We manage to co-assess a set of sophisticated real-world non-convex investment policy limitations, such as cardinality constraints, buy-in thresholds, transaction costs, particular normative rules, etc., within the frame of complex scenarios, which demand for simultaneous optimization of multiple investment objectives. In such a case, the portfolio selection process reflects a mixed-integer multiobjective portfolio optimization problem. On this basis, we meticulously develop all the corresponding modeling procedures and then solve the underlying problem by use of a new, fast and very effective algorithm. The value of the suggested framework is integrated with the introduction of two novel concepts in the field of multiobjective portfolio optimization, i.e. the security impact plane and the barycentric portfolio. The first represents a measure of each security's impact in the efficient surface of Pareto optimal portfolios. The second serves as the vehicle for implementing a balanced strategy of iterative portfolio tuning. Moreover, a couple of some very informative graphs provide thorough visualization of all empirical testing results. The validity of the attempt is verified through an illustrative application on the Eurostoxx 50. The results obtained are characterized as very encouraging, since a sufficient number of efficient or Pareto optimal portfolios produced by the model, appear to possess superior out-of-sample returns with respect to the underlying benchmark.     

Estimating correlation and covariance matrices by weighting of market similarity

We discuss a weighted estimation of correlation and covariance matrices from historical financial data. To this end, we introduce a weighting scheme that accounts for the similarity of previous market conditions to the present situation. The resulting estimators are less biased and show lower variance than either unweighted or exponentially weighted estimators. The weighting scheme is based on a similarity measure that compares the current correlation structure of the market to the structures at past times. Similarity is then measured by the matrix 2-norm of the difference of probe correlation matrices estimated for two different points in time. The method is validated in a simulation study and tested empirically in the context of mean–variance portfolio optimization. In the latter case we find an enhanced realized portfolio return as well as a reduced portfolio risk compared with alternative approaches based on different strategies and estimators.     

Dynamic portfolio choice without cash

We consider the dynamic mean–variance portfolio choice without cash under a game theoretic framework. The mean–variance criterion is investigated in the situation where an investor allocates the wealth among risky assets while keeping no cash in a bank account. The problem is solved explicitly up to solutions of ordinary differential equations by applying the extended Hamilton–Jacobi–Bellman equation system. Given a constant risk aversion coefficient, the optimal allocation without a risk-free asset depends linearly on the current wealth, while that with a risk-free asset turns out to be independent of the current wealth. We also study the minimum-variance criterion, which can be viewed as an extension of the mean–variance model when the risk aversion coefficient tends to infinity. Calibration exercises demonstrate that for large investments, the mean–variance model without cash yields the highest certainty equivalent return for both short-term and long-term investments. Furthermore, the mean–variance portfolio choices with and without cash yield almost the same Sharpe ratio for an investment with large initial wealth.     

A note on the geometry of Shanken's CSR T2 test for mean/variance efficiency

Shanken (1985) derives a test for the zero-beta capital asset pricing model (CAPM) which, as he points out, is equivalent to a test of the mean/variance efficiency of the market portfolio. This note illustrates the geometry of Shanken's test in the mean/variance space.     

THE MEAN‐GINI EFFICIENT PORTFOLIO FRONTIER

A main advantage of the mean‐variance (MV) portfolio frontier is its simplicity and ease of derivation. A major shortcoming, however, lies in its familiar restrictions, such as the quadraticity of preferences or the normality of distributions. As a workable alternative to MV, we present the mean‐Gini (MG) efficient portfolio frontier. Using an optimization algorithm, we compute MG and mean‐extended Gini (MEG) efficient frontiers and compare the results with the MV frontier. MEG allows for the explicit introduction of risk aversion in building the efficient frontier. For U.S. classes of assets, MG and MEG efficient portfolios constructed using Ibbotson (2000) monthly returns appear to be more diversified than MV portfolios. When short sales are allowed, distinct investor risk aversions lead to different patterns of portfolio diversification, a result that is less obvious when short sales are foreclosed. Furthermore, we derive analytically the MG efficient portfolio frontier by restricting asset distributions. The MG frontier derivation is identical in structure to that of the MV efficient frontier derivation. The penalty paid for simplifying the search for the MG efficient frontier is the loss of some information about the distribution of assets.     

Dynamic Investment Strategy with Factor Models Under Regime Switches

A model for dynamic investment strategy is developed where assets’ returns are represented by multiple factors. In a mean–variance framework with factor models under regime switches, we derive a semi-analytic solution for the optimal portfolio with transaction costs. Due to the existence of transaction costs, the optimal portfolio is characterized as a linear combination of current and target portfolios, the latter of which maximizes the value function in the current regime. For some special cases of interest, we also derive simplified analytical solutions. To see the effect of regime switches, the proposed model is applied to US equity market in which small minus big and high minus low are employed as factors. Investment strategy based on our model demonstrates empirically that the regime switching models exhibit superior performance over the single regime model for such performance measures as realized utility and Sharpe ratio which are of particular interest in practice. Taking a close look at the time series of portfolio returns, the result shows the usefulness of the regime switching model as investors flexibly optimize asset allocations depending on the state of the market.     

Capital Asset Pricing Compatible with Observed Market Value Weights

We show that the set of expected return vectors, for which an observed portfolio is mean variance (MV) efficient, is a two-parameter family. We identify ten ways to specify the time series behavior of the two parameters; the result highlights a number of inconsistencies involved in MV modelling. For each of the cases, it permits the inference of the time series of expected return vectors, as well as all the other Capital Asset Pricing Model (CAPM) variables, compatible with a known covariance matrix and the observed time series of market value weights. The empirical work shows that there are substantial case-to-case differences in the time series of mean vectors and many of them are quite different from the constant mean vector envisioned in tests of the CAPM.