COMMENT ON “SKEWNESS‐AWARE ASSET ALLOCATION”

This paper discusses risk measures proposed by Low et al. One of their new risk measures is skewness‐aware deviation, which is closely related to constant absolute risk aversion utility functions. This measure captures downside risk more effectively than traditional variance does. The authors also propose a second measure, skewness‐aware variance, which is derived from skewness‐aware deviation. This measure simplifies asset allocation problems and empirical results indicate that it captures risk better than traditional variance. However, this measure is also found to be inconsistent due to factor selection. Additionally, in the aspect of skewness‐aware deviation, optimal portfolios based upon skewness‐aware variance are sometimes less efficient than optimal portfolios that base themselves on traditional variance.     

Emerging markets,downside risk and the asset allocation decision

This study examines the use of downside risk measures in the construction of an optimal international portfolio, with particular reference to the estimated allocations in emerging markets and the out-of-sample performance of the optimal portfolios. The use of downside risk measures is assessed due to the problems of using a conventional mean-variance analysis approach in the presence of the non-normality often found to be present in emerging market data. The data set used consists of the MSCI indices for developed equity markets and the IFC data set on emerging markets. The primary component of the paper consists of the construction of optimal portfolios under both mean-variance and downside risk frameworks. In addition, the use of Bayes–Stein estimators is also assessed, in an attempt to reduce estimation error. The resulting estimated allocations are then used to assess the out-of-sample performance of the optimal portfolios. The results indicate that for risk-averse investors the use of downside risk measures can result in significant improvements in performance.     

The Effect of Diversification on Tail Risk: Evidence from US Equity Mutual Fund Portfolios

This paper examines the effect of diversification on the tail risk of US equity mutual fund portfolios by utilizing classical higher‐moment measures and robust tail weight measures. Empirical results show that market standard portfolios based on the mean‐variance framework are exposed to greater tail risk than benchmark portfolios are and diversification further intensifies this exposure.     

Ability parity model for optimal fund allocation: Evidence from China's mutual fund markets

We propose in this article a novel ability parity model for optimal fund allocation. Compared with the traditional portfolio selection methods which directly work on asset returns and/or risk (volatility), the proposed ability parity method focuses mainly on the allocation between the stock selection ability and market timing ability of fund managers, which essentially determines fund performance (Fama, 1972). Using the data of China's mutual fund markets, we find strong and robust evidence that the proposed ability parity model delivers significantly higher return, skewness, and Sharpe ratio than traditional models and the benchmark index, while having volatilities comparable with traditional models.     

A note on the relationships between some risk‐adjusted performance measures

Assuming portfolio returns are normally distributed, it is shown that both Sortino ratio (SR) and upside potential ratio (UPR) are monotonically increasing functions of the Sharpe ratio. As a result, all three risk‐adjusted performance measures provide identical ranking among investment alternatives. The effects of skewness and kurtosis are then evaluated within the Edgeworth‐Sargan density family. For the Sortino ratio, the above conclusion remains valid in the presence of negative skewness or excessive kurtosis. Similar results apply to the UPR with modifications. For all other cases, both SR and UPR provide exactly opposite ranking among investment alternatives to that suggested by the Sharpe ratio when the Sharpe ratio is large. Applications to futures hedging are discussed. Specifically, it is found that the Sharpe ratio may frequently lead to a smaller futures position than the other two ratios. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:483–495, 2002     

Measuring the financial and social performance of French mutual funds: A data envelopment analysis approach

Socially responsible investors pursue both financial and non-financial goals. In this paper, we attempt to assess the performance of French socially responsible mutual funds (SRMFs). We consider the data envelopment analysis (DEA) approach, which allows us to assign a unique efficiency score while combining financial and social characteristics, using various combinations within different types of risk (total risk, market risk, and downside risk). We report the list of funds found to be DEA efficient using various output-oriented models. We also compare our obtained results with the traditional and modern measures used in the literature (Sharpe, Treynor, and the information ratio). We contribute to the literature by testing the validity of the DEA methodology in the financial context. The findings have important implications for fund selection processes and would be mainly of interest to investors and fund managers who integrate environmental, social, and governance criteria into their investment choices.     

Disagreement in a Multi‐Asset Market

This paper provides a simple framework to study the effect of disagreement in a multi‐asset market equilibrium by considering two agents who disagree about expected returns, variances, and correlation of returns of two risky assets. When agents' subjective beliefs are characterized by mean preserving spreads of a benchmark homogeneous belief, we show that the effect of the disagreement does not cancel out in general and the effect in a multi‐asset market can be very different from a single asset market. In particular, the market risk premium can increase and the risk‐free rate can decrease significantly even when the market is overoptimistic and overconfident.     

Are Sharia stocks,gold and U.S. Treasury hedges and/or safe havens for the oil-based GCC markets?

This study examines whether the Sharia-compliant stocks measured by Dow Jones Islamic World Emerging Market index (DJIWEM), gold and the U.S. Treasury bills (T-bills) can serve as a hedge and/or a safe-haven asset in the six GCC stock markets, by using a vine copula approach. The results show that GCC and global investors can realize both risk diversification benefits and downside risk reductions during tranquil and downturn periods by including gold or DJIWEM in their portfolios but not the T-bills.     

A Markowitz Optimization of Commodity Futures Portfolios

We examine the diversification benefits of using individual futures contracts instead of simply a commodity index. We determine the ex‐ante, ex‐post, and stability results for optimal Markowitz portfolios, investigate the instability between the ex‐ante and ex‐post results, and compare our results to traditional and naïve portfolios. The ex‐ante complete futures portfolio dominates the traditional and naive portfolios and the ex‐post portfolio outperforms the naïve portfolio. The instability between the ex‐ante and ex‐post results is primarily driven by the time‐varying returns of the individual assets rather than by risk. Finally, the Sharpe portfolio results are essentially identical to the Markowitz results. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:343‐368, 2013     

The limits of leverage

When trading incurs proportional costs, leverage can scale an asset's return only up to a maximum multiple, which is sensitive to its volatility and liquidity. In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long‐term returns given average volatility. As leverage increases, rising rebalancing costs imply declining Sharpe ratios. Beyond a critical level, even returns decline. Holding the Sharpe ratio constant, higher asset volatility leads to superior returns through lower costs.     

ROBUST ASSET ALLOCATION WITH BENCHMARKED OBJECTIVES

In this paper, we introduce a new approach for finding robust portfolios when there is model uncertainty. It differs from the usual worst‐case approach in that a (dynamic) portfolio is evaluated not only by its performance when there is an adversarial opponent (“nature”), but also by its performance relative to a stochastic benchmark. The benchmark corresponds to the wealth of a fictitious benchmark investor who invests optimally given knowledge of the model chosen by nature, so in this regard, our objective has the flavor of min–max regret. This relative performance approach has several important properties: (i) optimal portfolios seek to perform well over the entire range of models and not just the worst case, and hence are less pessimistic than those obtained from the usual worst‐case approach; (ii) the dynamic problem reduces to a convex static optimization problem under reasonable choices of the benchmark portfolio for important classes of models including ambiguous jump‐diffusions; and (iii) this static problem is dual to a Bayesian version of a single period asset allocation problem where the prior on the unknown parameters (for the dual problem) correspond to the Lagrange multipliers in this duality relationship. This dual static problem can be interpreted as a less pessimistic alternative to the single period worst‐case Markowitz problem. More generally, this duality suggests that learning and robustness are closely related when benchmarked objectives are used.     

HEDGING STRATEGIES AND MINIMAL VARIANCE PORTFOLIOS FOR EUROPEAN AND EXOTIC OPTIONS IN A LÉVY MARKET

This paper presents hedging strategies for European and exotic options in a Lévy market. By applying Taylor’s theorem, dynamic hedging portfolios are constructed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importance as such other derivatives might be readily available. Moment swaps or power jump assets are not typically liquidly traded. It is shown how minimal variance portfolios can be used to hedge the higher order terms in a Taylor expansion of the pricing function, investing only in a risk‐free bank account, the underlying asset, and potentially variance swaps. The numerical algorithms and performance of the hedging strategies are presented, showing the practical utility of the derived results.     

ROBUST PORTFOLIOS AND WEAK INCENTIVES IN LONG‐RUN INVESTMENTS

When the planning horizon is long, and the safe asset grows indefinitely, isoelastic portfolios are nearly optimal for investors who are close to isoelastic for high wealth, and not too risk averse for low wealth. We prove this result in a general arbitrage‐free, frictionless, semimartingale model. As a consequence, optimal portfolios are robust to the perturbations in preferences induced by common option compensation schemes, and such incentives are weaker when their horizon is longer. Robust option incentives are possible, but require several, arbitrarily large exercise prices, and are not always convex.     

Performance Analysis of Sustainable Investments in the Brazilian Stock Market: A Study About the Corporate Sustainability Index (ISE)

In this article, we studied the Corporate Sustainability Index (ISE) of the Brazilian Mercantile, Futures and Stock Exchange (BM&FBOVESPA), with the main objective of analyzing the performance of sustainable investments in the Brazilian stock market, during the period from December 2005 to December 2010. To achieve this aim, we characterized ISE portfolios and we compared its performance with the IBOVESPA (representing the market portfolio) and other BM&FBOVESPA sectoral indices. In the performance comparison, we used level of liquidity, return and risk indicators, as well as the following measures: Sharpe, Treynor, Sortino, and Omega. Our results show that although sustainable investments have presented some interesting characteristics, such as increasing liquidity and low diversifiable risk, they did not achieve satisfactory financial performance in the analysis period. This indicates that the constraints imposed by this type of investment in capital allocation in Brazil may be harming their return and risk attractiveness.     

Does downside risk matter more in asset pricing? Evidence from China

This study examines if downside risk matters in asset pricing. Using a comprehensive sample of 3658 companies listed on the Chinese stock market from 1998 to 2017, evidence shows a positive reward for holding stocks with high downside risk, and this reward is not explained by other cross-sectional effects and remains robust across robustness tests. Downside beta is also found to be useful in the implementation of successful trading strategies in the medium and long term. By contrast, mixed results are found on the premiums robustness of total risk and semi-deviation, while no evidence of beta effect could be found.     

RISK HORIZON AND REBALANCING HORIZON IN PORTFOLIO RISK MEASUREMENT

This paper analyzes portfolio risk and volatility in the presence of constraints on portfolio rebalancing frequency. This investigation is motivated by the incremental risk charge (IRC) introduced by the Basel Committee on Banking Supervision. In contrast to the standard market risk measure based on a 10‐day value‐at‐risk calculated at 99% confidence, the IRC considers more extreme losses and is measured over a 1‐year horizon. More importantly, whereas 10‐day VaR is ordinarily calculated with a portfolio’s holdings held fixed, the IRC assumes a portfolio is managed dynamically to a target level of risk, with constraints on rebalancing frequency. The IRC uses discrete rebalancing intervals (e.g., monthly or quarterly) as a rough measure of potential illiquidity in underlying assets. We analyze the effect of these rebalancing intervals on the portfolio’s profit and loss distribution over a risk‐measurement horizon. We derive limiting results, as the rebalancing frequency increases, for the difference between discretely and continuously rebalanced portfolios; we use these to approximate the loss distribution for the discretely rebalanced portfolio relative to the continuously rebalanced portfolio. Our analysis leads to explicit measures of the impact of discrete rebalancing under a simple model of asset dynamics.     

Optimal close-to-home biases in asset allocation

This article studies optimal portfolio decisions with (long-term) liabilities for small open economy based investors, including the optimality of currency hedging (Walker (2008a). Chile is the home country of the representative investor, but results are likely to hold more generally. The problem is set up as in [Sharpe & Tint, 1990] and [Hoevenaars et al., 2007]. Hedging the liabilities and the consumption currency may imply optimal close-to-home biases, defined as overweighting asset classes which are highly correlated with local ones. The implementation challenges include: developing a methodology to estimate expected returns in local (real) currency; estimating the covariance matrix allowing for serial and crossed-serial correlations; and checking the results' robustness using a resampling method. The findings are: (i) portfolios always have optimal close-to-home biases, beyond the investment in local fixed income to hedge liabilities; (ii) currency hedging reduces investment in close-to-home asset classes, (iii) but has ambiguous effects on welfare — detected with the resampling method; (iv) currency hedged long-term US bonds are useful for hedging local interest rate risk; and (v) liabilities give access to high risk-return portfolios, not affecting otherwise the overall shape of the efficient regions. This article can be useful to investors based on small open economies, including pension funds, insurance companies, sovereign wealth funds and Central Banks.     

Cross‐commodity analysis and applications to risk management

The understanding of joint asset return distributions is an important ingredient for managing risks of portfolios. Although this is a well‐discussed issue in fixed income and equity markets, it is a challenge for energy commodities. In this study we are concerned with describing the joint return distribution of energy‐related commodities futures, namely power, oil, gas, coal, and carbon. The objective of the study is threefold. First, we conduct a careful analysis of empirical returns and show how the class of multivariate generalized hyperbolic distributions performs in this context. Second, we present how risk measures can be computed for commodity portfolios based on generalized hyperbolic assumptions. And finally, we discuss the implications of our findings for risk management analyzing the exposure of power plants, which represent typical energy portfolios. Our main findings are that risk estimates based on a normal distribution in the context of energy commodities can be statistically improved using generalized hyperbolic distributions. Those distributions are flexible enough to incorporate many characteristics of commodity returns and yield more accurate risk estimates. Our analysis of the market suggests that carbon allowances can be a helpful tool for controlling the risk exposure of a typical energy portfolio representing a power plant. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:197–217, 2009     

Robust Markowitz mean‐variance portfolio selection under ambiguous covariance matrix

This paper studies a robust continuous‐time Markowitz portfolio selection problem where the model uncertainty affects the covariance matrix of multiple risky assets. This problem is formulated into a min–max mean‐variance problem over a set of nondominated probability measures that is solved by a McKean–Vlasov dynamic programming approach, which allows us to characterize the solution in terms of a Bellman–Isaacs equation in the Wasserstein space of probability measures. We provide explicit solutions for the optimal robust portfolio strategies and illustrate our results in the case of uncertain volatilities and ambiguous correlation between two risky assets. We then derive the robust efficient frontier in closed form, and obtain a lower bound for the Sharpe ratio of any robust efficient portfolio strategy. Finally, we compare the performance of Sharpe ratios for a robust investor and for an investor with a misspecified model.     

Nonparametric Kernel Method to Hedge Downside Risk

We propose a nonparametric kernel estimation method (KEM) that determines the optimal hedge ratio by minimizing the downside risk of a hedged portfolio, measured by conditional value‐at‐risk (CVaR). We also demonstrate that the KEM minimum‐CVaR hedge model is a convex optimization. The simulation results show that our KEM provides more accurate estimations and the empirical results suggest that, compared to other conventional methods, our KEM yields higher effectiveness in hedging the downside risk in the weather‐sensitive markets.