Empirical Tests for Stochastic Dominance Efficiency

We derive empirical tests for the stochastic dominance efficiency of a given portfolio with respect to all possible portfolios constructed from a set of assets. The tests can be computed using straightforward linear programming. Bootstrapping techniques and asymptotic distribution theory can approximate the sampling properties of the test results and allow for statistical inference. Our results could provide a stimulus to the further proliferation of stochastic dominance for the problem of portfolio selection and evaluation. Using our tests, the Fama and French market portfolio is significantly inefficient relative to benchmark portfolios formed on market capitalization and book‐to‐market equity ratio.     

Do Socially Responsible Index Investors Incur an Opportunity Cost?

We construct index‐tracking portfolios using integer programming and then compare the tracking errors and performances of portfolios formed from an unrestricted and socially screened stock universe. We find that one can construct a portfolio of socially responsible stocks that deliver market performance. Thus, the exclusion of a set of stocks from consideration does not exhaust the existence of efficient index‐tracking portfolios, especially when the exclusionary screen is for nonfinancial reasons. Our results are robust to various specifications in constructing the portfolio, for example, number of stocks included in the portfolio and weighting schemes, and robust to alternative tracking error measurement; we show that the difference induced from conducting socially responsible screen is never statistically significant.     

TRADING OF NASDAQ STOCKS ON THE CHICAGO STOCK EXCHANGE

We use a linear programming model to form two portfolios with approximately equal levels of attributes such as financial leverage. One portfolio comprises stocks that trade exclusively on NASDAQ and the other, stocks that trade on both the Chicago Stock Exchange (CSE) and NASDAQ (CSE/NASDAQ). We find that spreads are lower for the CSE/NASDAQ portfolio, but so is the percentage of quotes at spreads of $0.125. In fact, the lower spreads observed for the CSE/NASDAQ portfolio arise from fewer quotes with spreads of more than $0.25.     

Measuring fund style,performance and activity: a new style‐profiling approach

We construct new measures of fund style, performance and activity from linear combinations of off‐the‐shelf stock‐market indices. A fund's benchmark portfolio is a linear combination of two or more reference portfolios that in a least‐squares sense most closely approximates the fund's portfolio. The resulting linear combination scalar is itself a measure of fund style and the distance between a fund and its benchmark is a measure of fund activity. Our approach has a number of advantages over existing characteristic‐matching methods. We illustrate our approach using a data set of US institutional funds.     

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.     

Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.     

Volatility timing: How best to forecast portfolio exposures

This paper investigates how best to forecast optimal portfolio weights in the context of a volatility timing strategy. It measures the economic value of a number of methods for forming optimal portfolios on the basis of realized volatility. These include the traditional econometric approach of forming portfolios from forecasts of the covariance matrix. Both naïve forecasts using simple historical averages, and those generated from econometric models are considered. A novel method, where a time series of optimal portfolio weights are constructed from observed realized volatility and direct forecast is also proposed. A number of naïve forecasts and the approach of directly forecasting portfolio weights show a great deal of merit. Resulting portfolios are of similar economic benefit to a number of competing approaches and are more stable across time. These findings have obvious implications for the manner in which volatility timing is undertaken in a portfolio allocation context.     

Comparison of Mean-Risk Efficient Portfolios in Asia-Pacific Capital Markets

In order to analyze the performance of mean-risk efficient portfolios, several methods of portfolio comparison have been developed. In this paper we analyze the second-order stochastic dominance efficiency of portfolios on the mean-risk efficient frontier assuming that the risk is represented by standard deviations and concordance matrices set up on the basis of Pearson's linear correlation, Spearman's rho, or Kendall's tau. Empirical analysis of the market returns of selected Asia-Pacific stock markets is carried out considering both the U.S. dollar and euro as reference currencies, and different periods: before and during the subprime crisis. Measures and portfolios on the mean-risk efficiency frontier that should be of interest to at least one risk-averse investor are empirically documented.     

INTERNATIONAL DIVERSIFICATION OF EQUITIES AND FIXED-INCOME SECURITIES

Portfolio selection models have been applied principally to common stocks traded in the United States and in foreign stock markets. This study examines the efficient set of portfolios selected from a choice set that includes returns derived from domestic and international corporate bond and government bond indices as well as domestic and international stock indices. To assess the benefits of international multi-asset diversification, the authors examine the following issues: (1) the extent to which international and domestic fixed-income securities are included in efficient portfolios; (2) the effect on efficient set composition of using the Sharpe portfolio selection model as compared to the Markowitz portfolio selection model; (3) the sensitivity of efficient set characteristics produced from a single-index based portfolio selection model to alternative world market indices; and (4) the correspondence between expected and realized portfolio risk and return for the different portfolio selection models.     

A conditional asset-pricing model with the optimal orthogonal portfolio

This paper employs a conditional asset-pricing model based on the optimal orthogonal portfolio approach to construct a factor portfolio that embodies all the latent factors important for pricing a given set of test assets. The advantage of this portfolio to the anomaly related mimicking portfolios is its ability to separate out the components of average return that are not related to the return covariation. The performance of this portfolio is evaluated against several conventional factors, using both cross-sectional and time-series regression approaches, as well as the Hansen and Jagannathan (1997) distance measure. Its strong out-of-sample results indicate that our suggested methodology may have important applications in risk management, portfolio selection and performance evaluation.     

Portfolio analysis of asset and liability management in small-, medium- and large-sized banks

The paper presents an analysis of the commercial banking firm based on Markowitz portfolio analysis. A bank is treated as a portfolio of five banking assets and three banking liabilities. The average rate of return and risk of each asset and liability is estimated empirically for groups of banks categorized by size — small, medium and large. Banks' rates return on equity are defined as the weighted average of the assets' rates of return less the liabilities' rates of return. Quadratic programming is used to delineate the set of banking portfolios which have the maximum rate of return on equity at each level of risk.     

Mean-variance versus utility maximization revisited: The case of constant relative risk aversion

We examine if mean-variance (M-V) is a good proxy for portfolios based on the Constant Relative Risk Aversion (CRRA) utility function. M-V portfolios are considered good proxies for portfolios from several utility functions which is why they are routinely used in the portfolio theory literature as the benchmark. Our results clearly show this is not the case. Low risk CRRA portfolios are in many cases very different to M-V portfolios, especially with respect to downside risk. If a risk-free asset is available, in many cases, no M-V portfolio is an adequate proxy for CRRA portfolios. The implications of our findings are that: i) M-V portfolios are a poor proxy for investors with CRRA preferences, ii) CRRA portfolios are more suited to investors who care about downside risk than M-V portfolios, and iii) the efficacy of M-V to proxy for utility maximization should be examined more thoroughly.     

Minimizing CVaR and VaR for a portfolio of derivatives

Value at risk (VaR) and conditional value at risk (CVaR) are frequently used as risk measures in risk management. Compared to VaR, CVaR is attractive since it is a coherent risk measure. We analyze the problem of computing the optimal VaR and CVaR portfolios. We illustrate that VaR and CVaR minimization problems for derivatives portfolios are typically ill-posed. We propose to include cost as an additional preference criterion for the CVaR optimization problem. We demonstrate that, with the addition of a proportional cost, it is possible to compute an optimal CVaR derivative investment portfolio with significantly fewer instruments and comparable CVaR and VaR. A computational method based on a smoothing technique is proposed to solve a simulation based CVaR optimization problem efficiently. Comparison is made with the linear programming approach for solving the simulation based CVaR optimization problem.     

How to build a factor portfolio: Does the allocation strategy matter?

Factor-based allocation embraces the idea of factors, as opposed to asset classes, as the ultimate building blocks of investment portfolios. We examine whether there is a superior way of combining factors in a portfolio and provide a comparison of factor-based allocation strategies within a multiple testing framework. Factor-based allocation is profitable beyond exploiting genuine risk premia, even when applying multiple testing corrections. Investment portfolios can be efficiently diversified using factor-based allocation strategies, as demonstrated by robust economic performance over various economic scenarios. The naïve equally weighted factor portfolio, albeit simple and cost-efficient, cannot be outperformed by more sophisticated allocation strategies.     

Correlation risk,cross-market derivative products and portfolio performance*

We consider portfolios whose returns depend on at least three variables and show the effect of the correlation structure on the probabilities of the extreme outcomes of the portfolio return, using a multivariate binomial approximation. the portfolio risk is then managed by using derivatives. We illustrate this risk management both with simple options, whose payoff depends upon only one of the underlying variables, and with more complex instruments, whose payoffs (and values) depend upon the correlation structure The question of benchmarking portfolio performance is complicated by the use of derivatives, especially complex derivatives, since these instruments fundamentally alter the distribution of returns. We use the multivariate binomial model to set performance benchmarks for multicurrency, international portfolios. Our model is illustrated using a simple example where a German institution invests a proportion of its funds in Germany equities and the remainder in UK equities. Portfolio performance is measured in Deutsche Marks and depends upon (1) the DAX index, (2) the FTSE index and (3) the Deutsche Mark-Sterling exchange rate. The output of the model is a simulation of possible outcomes from the portfolio hedging strategy. the difference in our methodology is that we are able to retain the simplicity of the binomial distribution, used extensively in the analysis of options, in a multivariate context. This is achieved by building three (or more) binomial trees for the individual variables and capturing the correlation structure with the use of varying conditional probabilities.     

Non-Linear Value-at-Risk

Value-at-risk methods which employ a linear ("delta only") approximationto the relation between instrument values and the underlyingrisk factors are unlikely to be robust when applied to portfolioscontaining non-linear contracts such as options. The most widelyused alternative to the delta-only approach involves revaluingeach contract for a large number of simulated values of theunderlying factors. In this paper we explore an alternativeapproach which uses a quadratic approximation to the relationbetween asset values and the risk factors. This method (i) islikely to be better adapted than the linear method to the problemof assessing risk in portfolios containing non-linear assets,(ii) is less computationally intensive than simulation usingfull-revaluation and (iii) in common with the delta-only method,operates at the level of portfolio characteristics (deltas andgammas) rather than individual instruments.     

Estimating a covariance matrix for market risk management and the case of credit default swaps

We analyze covariance matrix estimation from the perspective of market risk management, where the goal is to obtain accurate estimates of portfolio risk across essentially all portfolios—even those with small standard deviations. We propose a simple but effective visualisation tool to assess bias across a wide range of portfolios. We employ a portfolio perspective to determine covariance matrix loss functions particularly suitable for market risk management. Proper regularisation of the covariance matrix estimate significantly improves performance. These methods are applied to credit default swaps, for which covariance matrices are used to set portfolio margin requirements for central clearing. Among the methods we test, the graphical lasso estimator performs particularly well. The graphical lasso and a hierarchical clustering estimator also yield economically meaningful representations of market structure through a graphical model and a hierarchy, respectively.     

A comparison of MAD and CVaR models with real features

In this paper we consider two different mixed integer linear programming models for solving the single period portfolio selection problem when integer stock units, transaction costs and a cardinality constraint are taken into account. The first model has been formulated by using the maximization of the worst conditional expectation as objective function. The second model is based on the maximization of the safety measure corresponding to the mean absolute deviation. Extensive computational results are provided to compare the financial characteristics of the optimal portfolios selected by the two models on real data from European stock exchange markets. Some simple heuristics are also introduced that provide efficient and effective solutions when an optimal integer solution cannot be found in a reasonable amount of time.     

Optimal commodity asset allocation with a coherent market risk modeling

This paper fills a fundamental gap in commodity price risk management and optimal portfolio selection literatures by contributing a thorough reflection on trading risk modeling with a dynamic asset allocation process and under the supposition of illiquid and adverse market settings. This paper analyzes, from a portfolio managers' perspective, the performance of liquidity adjusted risk modeling in obtaining efficient and coherent investable commodity portfolios under normal and adverse market conditions. As such, the author argues that liquidity risk associated with the uncertainty of liquidating multiple commodity assets over given holding periods is a key factor in formalizing and measuring overall trading risk and is thus an important component to model, particularly in the wake of the repercussions of the recent 2008 financial crisis. To this end, this article proposes a practical technique for the quantification of liquidity trading risk for large portfolios that consist of multiple commodity assets and whereby the holding periods are adjusted according to the specific needs of each trading portfolio. Specifically, the paper proposes a robust technique to commodity optimal portfolio selection, in a liquidity-adjusted value-at-risk (L-VaR) framework, and particularly from the perspective of large portfolios that have both long and short positions or portfolios that consist of merely pure long trading positions. Moreover, in this paper, the author develops a portfolio selection model and an optimization-algorithm which allocates commodity assets by minimizing the L-VaR subject to applying credible operational and financial constraints based on fundamental asset management considerations. The empirical optimization results indicate that this alternate L-VaR technique can be regarded as a robust portfolio management tool and can have many uses and applications in real-world asset management practices and predominantly for fund managers with large commodity portfolios.     

Portfolio optimization under Expected Shortfall: contour maps of estimation error

The contour maps of the error of historical and parametric estimates of the global minimum risk for large random portfolios optimized under the Expected Shortfall (ES) risk measure are constructed. Similar maps for the VaR of the ES-optimized portfolio are also presented, along with results for the distribution of portfolio weights over the random samples and for the out-of-sample and in-sample estimates for ES. The contour maps allow one to quantitatively determine the sample size (the length of the time series) required by the optimization for a given number of different assets in the portfolio, at a given confidence level and a given level of relative estimation error. The necessary sample sizes invariably turn out to be unrealistically large for any reasonable choice of the number of assets and the confidence level. These results are obtained via analytical calculations based on methods borrowed from the statistical physics of random systems, supported by numerical simulations.