Robust state-dependent mean–variance portfolio selection: a closed-loop approach

Finance and Stochastics - This paper studies a class of robust mean–variance portfolio selection problems with state-dependent risk aversion. Model uncertainty, in the sense of considering...     

Dynamic mean–VaR portfolio selection in continuous time

The value-at-risk (VaR) is one of the most well-known downside risk measures due to its intuitive meaning and wide spectra of applications in practice. In this paper, we investigate the dynamic mean–VaR portfolio selection formulation in continuous time, while the majority of the current literature on mean–VaR portfolio selection mainly focuses on its static versions. Our contributions are twofold, in both building up a tractable formulation and deriving the corresponding optimal portfolio policy. By imposing a limit funding level on the terminal wealth, we conquer the ill-posedness exhibited in the original dynamic mean–VaR portfolio formulation. To overcome the difficulties arising from the VaR constraint and no bankruptcy constraint, we have combined the martingale approach with the quantile optimization technique in our solution framework to derive the optimal portfolio policy. In particular, we have characterized the condition for the existence of the Lagrange multiplier. When the opportunity set of the market setting is deterministic, the portfolio policy becomes analytical. Furthermore, the limit funding level not only enables us to solve the dynamic mean–VaR portfolio selection problem, but also offers a flexibility to tame the aggressiveness of the portfolio policy.     

Gram–Charlier densities: a multivariate approach

This paper introduces a new family of multivariate distributions based on Gram–Charlier and Edgeworth expansions. This family encompasses many of the univariate semi-non-parametric densities proposed in financial econometrics as marginal of its different formulations. Within this family, we focus on the analysis of the specifications that guarantee positivity to obtain well-defined multivariate semi-non-parametric densities. We compare two different multivariate distributions of the family with the multivariate Edgeworth–Sargan, Normal, Student's t and skewed Student's t in an in- and out-of-sample framework for financial returns data. Our results show that the proposed specifications provide a reasonably good performance, and would therefore be of interest for applications involving the modelling and forecasting of heavy-tailed distributions.     

Optimal tax policy and expected longevity: a mean and variance utility approach

This paper studies the normative problem of redistribution between agents who can influence their survival probability through private health spending, but who differ in their attitude towards the risks involved in the lotteries of life to be chosen. For that purpose, a two-period model is developed, where agents’ preferences on lotteries of life can be represented by a mean and variance utility function allowing, unlike the expected utility form, some sensitivity to what Allais (Econometrica 21(4), 503–546, 1953) calls the ‘dispersion of psychological values’. It is shown that if agents ignore the impact of health spending on the return of their savings, the decentralization of the first-best utilitarian optimum requires intergroup lump sum transfers and group-specific positive taxes on health spending. Under asymmetric information, a differentiated taxation across agents is still required, but subsidizing health spending may be optimal as a way to solve the incentive problem.     

Conditional Value-at-Risk,spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis

We study portfolio selection under Conditional Value-at-Risk and, as its natural extension, spectral risk measures, and compare it with traditional mean–variance analysis. Unlike the previous literature that considers an investor’s mean-spectral risk preferences for the choice of optimal portfolios only implicitly, we explicitly model these preferences in the form of a so-called spectral utility function. Within this more general framework, spectral risk measures tend towards corner solutions. If a risk free asset exists, diversification is never optimal. Similarly, without a risk free asset, only limited diversification is obtained. The reason is that spectral risk measures are based on a regulatory concept of diversification that differs fundamentally from the reward-risk tradeoff underlying the mean–variance framework.     

Investor sentiment and the mean–variance relation

This study shows the influence of investor sentiment on the market's mean–variance tradeoff. We find that the stock market's expected excess return is positively related to the market's conditional variance in low-sentiment periods but unrelated to variance in high-sentiment periods. These findings are consistent with sentiment traders who, during the high-sentiment periods, undermine an otherwise positive mean–variance tradeoff. We also find that the negative correlation between returns and contemporaneous volatility innovations is much stronger in the low-sentiment periods. The latter result is consistent with the stronger positive ex ante relation during such periods.     

Mean–variance dominant trading strategies

The paper examines the relative importance of ten anomaly-based trading strategies. We employ Mean Variance spanning methodologies in a classical unconditional setting and a novel conditional setting. Fixed-weight optimal portfolios stemming from the unconditional methodology indicate that all the strategies are needed to enhance the mean–variance tradeoff. This conclusion is completely reversed when we allow for time-varying portfolio weights as a nonlinear function of lagged economic indicators. The overall results suggest that diversified anomaly-based holdings are of limited benefit to sophisticated investors who employ dynamic trading strategies.     

Value-at-risk capital requirement regulation,risk taking and asset allocation: a mean–variance analysis

In this study, the mean–variance framework is employed to analyze the impact of the Basel value-at-risk (VaR) market risk regulation on the institution's optimal investment policy, the stockholders’ welfare, as well as the tendency of the institution to change the risk profile of the held portfolio. It is shown that with the VaR regulation, the institution faces a new regulated capital market line, which induces resource allocation distortion in the economy. Surprisingly, only when a riskless asset is available does VaR regulation induce the institution to reduce risk. Otherwise, the regulation may induce higher risk, accompanied by asset allocation distortion. On the positive side, the regulation implies an upper bound on the risk the institution takes and it never induces the firm to select an inefficient portfolio. Moreover, when the riskless asset is available, tightening the regulation always increases the amount of maintained eligible capital and decreases risk.     

Mean–variance convergence around the world

In this paper, we show (i) that the risk-return characteristics of our sample of 17 developed stock markets of the world have converged significantly toward each other during our study period 1974–2007, and (ii) that this international convergence in risk-return characteristics is driven mainly by the declining ‘country effect’, rather than the rising ‘industry effect’, suggesting that the convergence is associated with international market integration. Specifically, we first compute the risk-return distance among international stock markets based on the Euclidean distance and find that the distance thus computed has been decreasing significantly over time, implying a mean–variance convergence. In particular, the average risk-return distance has decreased by about 50% over our sample period. We also document that the risk-return characteristics of our sample of 14 emerging markets have been converging rapidly toward those of developed markets in recent years. This development notwithstanding, emerging markets still remain as a distinct asset class. Lastly, we show that the convergence in risk-return characteristics has exerted a negative impact on the efficiency of international investment during our sample period.     

Dynamic mean–variance problem with frictions

Finance and Stochastics - We study a dynamic mean–variance portfolio selection problem with return predictability and trading frictions from price impact. Applying mean-field type control...     

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.     

Time-consistent mean–variance asset-liability management in a regime-switching jump-diffusion market

Financial Markets and Portfolio Management - This paper investigates the time-consistent optimal control of a mean–variance asset-liability management problem in a regime-switching...     

Searching for a listed infrastructure asset class using mean–variance spanning

This study examines the portfolio-diversification benefits of listed infrastructure stocks. We employ three different definitions of listed infrastructure and tests of mean–variance spanning. The evidence shows that viewing infrastructure as an asset class is misguided. We employ different schemes of infrastructure asset selection (both traditional asset classes and factor exposures) and discover that they do not provide portfolio-diversification benefits to existing asset allocation choices. We also find that defining and selecting infrastructure investments by business model as opposed to industrial sectors can reveal a very different investment profile, albeit one that improves the mean–variance efficient frontier since the global financial crisis. This study provides new insights into defining and benchmarking infrastructure equity investments in general, as well as into the extent to which public markets can be used to proxy the risk-adjusted performance of privately held infrastructure investments.     

Global financial crisis and emerging stock market contagion: A multivariate FIAPARCH–DCC approach

This paper empirically investigates the contagion effects of the global financial crisis in a multivariate Fractionally Integrated Asymmetric Power ARCH (FIAPARCH) dynamic conditional correlation (DCC) framework during the period 1997–2012. We focus on five most important emerging equity markets, namely Brazil, Russia, India, China and South Africa (BRICS), as well as USA during different phases of the crisis. The length and the phases of the crisis are identified based on both an economic and a statistical approach. The empirical evidence does not confirm a contagion effect for most BRICS during the early stages of the crisis, indicating signs of isolation or decoupling. However, linkages reemerged (recoupled) after the Lehman Brothers collapse, suggesting a shift on investors' risk appetite. Moreover, correlations among all BRICS and USA are increased from early 2009 onwards, implying that their dependence is larger in bullish than in bearish markets. These findings do not show a pattern of contagion for all BRICSs' markets that could be attributed to their common trade and financial characteristics and provide important implications for international investors and policymakers.     

Investor preferences and portfolio selection: is diversification an appropriate strategy?

This paper analyzes the relationship between diversification and several distributional characteristics that have risk implications for stock returns. We develop a flexible three-parameter distribution to model the stock returns. Using data on the current 30 DJIA stocks, we show that an investor's strategy on diversification depends on the measures of risk for particular concerns. For example, investors who desire to increase positive skewness would hold a less diversified portfolio, while those who care more about extreme losses would hold a more diversified portfolio. Experimenting with a more general pool of stocks yields the same conclusions.     

Does country risks predict stock returns and volatility? Evidence from a nonparametric approach

We use the k-th order nonparametric causality test at monthly frequency over the period of 1984:1–2015:12 to analyze whether aggregate country risk, and its components (economic, financial and political) can predict movements in stock returns and volatility of eighty-three developed and developing economies. The nonparametric approach controls for the existing misspecification of a linear framework of causality, and hence, the weak evidence of causality obtained under the standard Granger tests cannot be relied upon. When we apply the nonparametric test, we find that, while there is no evidence of predictability of squared stock returns barring one case, at times, there are nearly 50 percent of the countries where the aggregate risks and its components tend to predict stock returns and realized volatility.     

Equity prices and fundamentals: a DDM–APT mixed approach

This paper focuses on the linkage between equity prices and fundamentals for 27 individual shares belonging to the French stock price index (CAC40). To assess fundamental value, the traditional dividend discount model (DDM) is coupled with the arbitrage pricing theory (APT), which assumes that investors hold efficient portfolios. This yields a simple equity valuation relationship for which the APT determines the long-term risk premium included in the DDM. Accordingly, equity risk premia are determined by common factors reflecting the non diversifiable risk. These factors are not a priori identified by the theory, and therefore must be exhibited through an empirical analysis. Four domestic and three international common factors are found, all being among those identified by empirical analyses of the APT in the literature. While studies related to stock price indices showed that DDM fundamental values are very smooth compared to stock indices, our DDM–APT model reproduces both trends and major fluctuations of share prices. Further, as for studies based on stock indices, a mean-reverting process of equity prices towards fundamentals is highlighted, but the linear error correction model that was considered contains shortcomings suggesting a more complex adjustment process.     

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.