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.     

Optimal portfolio positioning within generalized Johnson distributions

Many empirical studies have shown that financial asset returns do not always exhibit Gaussian distributions, for example hedge fund returns. The introduction of the family of Johnson distributions allows a better fit to empirical financial data. Additionally, this class can be extended to a quite general family of distributions by considering all possible regular transformations of the standard Gaussian distribution. In this framework, we consider the portfolio optimal positioning problem, which has been first addressed by Brennan and Solanki [J. Financial Quant. Anal., 1981, 16, 279–300], Leland [J. Finance, 1980, 35, 581–594] and further developed by Carr and Madan [Quant. Finance, 2001, 1, 9–37] and Prigent [Generalized option based portfolio insurance. Working Paper, THEMA, University of Cergy-Pontoise, 2006]. As a by-product, we introduce the notion of Johnson stochastic processes. We determine and analyse the optimal portfolio for log return having Johnson distributions. The solution is characterized for arbitrary utility functions and illustrated in particular for a CRRA utility. Our findings show how the profiles of financial structured products must be selected when taking account of non Gaussian log-returns.     

Robustness of the inference procedures for the global minimum variance portfolio weights in a skew-normal model

In this paper, we study the influence of skewness on the distributional properties of the estimated weights of optimal portfolios and on the corresponding inference procedures derived for the optimal portfolio weights assuming that the asset returns are normally distributed. It is shown that even a simple form of skewness in the asset returns can dramatically influence the performance of the test on the structure of the global minimum variance portfolio. The results obtained can be applied in the small sample case as well. Moreover, we introduce an estimation procedure for the parameters of the skew-normal distribution that is based on the modified method of moments. A goodness-of-fit test for the matrix variate closed skew-normal distribution has also been derived. In the empirical study, we apply our results to real data of several stocks included in the Dow Jones index.     

An exact test on structural changes in the weights of the global minimum variance portfolio

In the paper, a finite sample test is suggested for detecting changes in the composition of the global minimum variance portfolio. The exact density of the test statistic is calculated. It appears that under the null hypothesis of no change, it is independent of the parameters of the asset returns distribution. The testing procedure is implemented in a situation that is practically relevant. We show that ignoring the uncertainty about the estimated weights of the holding portfolio leads to misleading results, i.e. to a more frequent reallocation of the investor's wealth.     

Dynamic portfolio optimization across hidden market regimes

Regime-based asset allocation has been shown to add value over rebalancing to static weights and, in particular, reduce potential drawdowns by reacting to changes in market conditions. The predominant approach in previous studies has been to specify in advance a static decision rule for changing the allocation based on the state of financial markets or the economy. In this article, model predictive control (MPC) is used to dynamically optimize a portfolio based on forecasts of the mean and variance of financial returns from a hidden Markov model with time-varying parameters. There are computational advantages to using MPC when estimates of future returns are updated every time a new observation becomes available, since the optimal control actions are reconsidered anyway. MPC outperforms a static decision rule for changing the allocation and realizes both a higher return and a significantly lower risk than a buy-and-hold investment in various major stock market indices. This is after accounting for transaction costs, with a one-day delay in the implementation of allocation changes, and with zero-interest cash as the only alternative to the stock indices. Imposing a trading penalty that reduces the number of trades is found to increase the robustness of the approach.     

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.     

Deciphering robust portfolios

Robust portfolio optimization has been developed to resolve the high sensitivity to inputs of the Markowitz mean–variance model. Although much effort has been put into forming robust portfolios, there have not been many attempts to analyze the characteristics of portfolios formed from robust optimization. We investigate the behavior of robust portfolios by analytically describing how robustness leads to higher dependency on factor movements. Focusing on the robust formulation with an ellipsoidal uncertainty set for expected returns, we show that as the robustness of a portfolio increases, its optimal weights approach the portfolio with variance that is maximally explained by factors.     

Investing for the Long-run in European Real Estate

We calculate optimal portfolio choices for a long-horizon, risk-averse investor who diversifies among European stocks, bonds, real estate, and cash, when excess asset returns are predictable. Simulations are performed for scenarios involving different risk aversion levels, horizons, and statistical models capturing predictability in risk premia. Importantly, under one of the scenarios, the investor takes into account the parameter uncertainty implied by the use of estimated coefficients to characterize predictability. We find that real estate ought to play a significant role in optimal portfolio choices, with weights between 12 and 44%. Under plausible assumptions, the welfare costs of either ignoring predictability or restricting portfolio choices to traditional financial assets only are found to be in the order of 150–300 basis points per year. These results are robust to changes in the benchmarks and in the statistical framework.      

The augmented Black–Litterman model: a ranking-free approach to factor-based portfolio construction and beyond

The Fama and French factor-ranking approach (1992, 1993, etc.) has been extensively applied in quantitative fund management. However, this approach suffers from hidden factor view, information inefficiency, etc. issues. Based on the Black–Litterman model (1992; as explained in Cheung 2010b Cheung, W. 2010b. The Black–Litterman model explained. J. Asset Mgmt., 11: 229–243. [Crossref] , [Google Scholar]), we develop a technique that endogenizes the ranking process and elegantly resolves these issues. This model explicitly seeks forward-looking factor views and smoothly blends them to deliver robust allocation to securities. Our numerical experiments show this is an intuitive and practical framework for factor-based portfolio construction, and beyond. This article features: (1) a new and unified framework for strategy combination, factor mimicking and security-specific bets; (2) an elegant and ranking-free approach to factor style construction; (3) worked examples based on the FTSE EUROTOP 100 universe; (4) insight into the classic issue of confidence parameter setting; and (5) implementation guidance in an appendix.     

A jackknife-type estimator for portfolio revision

This article proposes a novel approach to portfolio revision. The current literature on portfolio optimization uses a somewhat naïve approach, where portfolio weights are always completely revised after a predefined fixed period. However, one shortcoming of this procedure is that it ignores parameter uncertainty in the estimated portfolio weights, as well as the biasedness of the in-sample portfolio mean and variance as estimates of the expected portfolio return and out-of-sample variance. To rectify this problem, we propose a jackknife procedure to determine the optimal revision intensity, i.e. the percent of wealth that should be shifted to the new, in-sample optimal portfolio. We find that our approach leads to highly stable portfolio allocations over time, and can significantly reduce the turnover of several well established portfolio strategies. Moreover, the observed turnover reductions lead to statistically and economically significant performance gains in the presence of transaction costs.     

On pricing barrier control in a regime-switching regulated market

We study a pricing barrier control problem in a regime-switching regulated market. In doing so, we analyze a class of one-dimensional reflected regime-switching diffusion processes. Such diffusion models arise as the key approximating processes in a regulated financial market system with the presence of regime changes. Our main goal is to determine optimal pricing barriers as solutions of long-run average mean–variance optimization problems. More precisely, the optimal barrier, if exists, will be to maximize the long-run average expected return (i.e. steady-state mean) subject to a selected level of long-run average risk (i.e. steady-state variance).     

Multi-asset portfolio optimization and out-of-sample performance: an evaluation of Black–Litterman,mean-variance,and naïve diversification approaches

The Black–Litterman model aims to enhance asset allocation decisions by overcoming the problems of mean-variance portfolio optimization. We propose a sample-based version of the Black–Litterman model and implement it on a multi-asset portfolio consisting of global stocks, bonds, and commodity indices, covering the period from January 1993 to December 2011. We test its out-of-sample performance relative to other asset allocation models and find that Black–Litterman optimized portfolios significantly outperform naïve-diversified portfolios (1/N rule and strategic weights), and consistently perform better than mean-variance, Bayes–Stein, and minimum-variance strategies in terms of out-of-sample Sharpe ratios, even after controlling for different levels of risk aversion, investment constraints, and transaction costs. The BL model generates portfolios with lower risk, less extreme asset allocations, and higher diversification across asset classes. Sensitivity analyses indicate that these advantages are due to more stable mixed return estimates that incorporate the reliability of return predictions, smaller estimation errors, and lower turnover.