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.     

Behavioral portfolio selection and optimization: an application to international stocks

The behavioral approach of decision making has emerged as a diversified solution in the presence of risk and uncertainty. Using the popular cumulative prospect theory as an objective function for portfolio selection, this study implements the classical mean–variance model to compare the portfolio performance of high behavioral stocks with that of stocks with lower behavioral values. Based on a sample of 37 international stocks over the period from October 1998 to November 2017, empirical results from D-vine pair copula GARCH-GEV indicate that the portfolio of high behavioral prospect stocks outperforms the portfolio of stocks with low behavioral scores. This finding may suggest that portfolios with high behavioral values coincide with rational efficiency sets.     

Downside risk and asset pricing

We analyze if the value-weighted stock market portfolio is stochastic dominance (SD) efficient relative to benchmark portfolios formed on size, value, and momentum. In the process, we also develop several methodological improvements to the existing tests for SD efficiency. Interestingly, the market portfolio seems third-order SD (TSD) efficient relative to all benchmark sets. By contrast, the market portfolio is inefficient if we replace the TSD criterion with the traditional mean–variance criterion. Combined these results suggest that the mean–variance inefficiency of the market portfolio is caused by the omission of return moments other than variance. Especially downside risk seems to be important for explaining the high average returns of small/value/winner stocks.     

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.     

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.     

Portfolio selection: An extreme value approach

We show theoretically that lower tail dependence (χ), a measure of the probability that a portfolio will suffer large losses given that the market does, contains important information for risk-averse investors. We then estimate χ for a sample of DJIA stocks and show that it differs systematically from other risk measures including variance, semi-variance, skewness, kurtosis, beta, and coskewness. In out-of-sample tests, portfolios constructed to have low values of χ outperform the market index, the mean return of the stocks in our sample, and portfolios with high values of χ. Our results indicate that χ is conceptually important for risk-averse investors, differs substantially from other risk measures, and provides useful information for portfolio selection.     

Is gold good for portfolio diversification? A stochastic dominance analysis of the Paris stock exchange

This paper aims to assess the role of gold quoted in Paris in the diversification of French portfolios from 1949 to 2012 using the stochastic dominance (SD) approach. The principal advantage of this method is that there is no restriction on the distribution of the returns. Our results show that stock portfolios including gold stochastically dominate those without gold at the second and third orders. This implies that risk-averse investors would be better off by including gold in their stock portfolios to maximize their expected utilities. The study on sub-periods shows that this result holds especially in unstable or crisis times. However, these results do not hold for bond or risk-free portfolios, for which the portfolios without gold dominate those with gold. To check the robustness of our results, our SD analysis of a mixed portfolio (50% stocks, 30% bonds and 20% the risk-free asset) provides results similar to those for portfolios with stocks only, except from 1971 to 1983. Portfolios including gold quoted in London show results similar to those from Paris. The results of mean–variance performance measures confirm the findings of previous studies that gold is good for the diversification of stock portfolios but not for bond portfolios.     

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.     

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.     

Risk optimizations on basis portfolios: The role of sorting

This paper investigates the mean–variance and diversification properties of risk-based strategies executed on style or basis portfolios. We show that the performance of these risk strategies is highly sensitive to the sorting procedure used to form the basis assets. Whereas the extant literature provides mixed support for the outperformance of smart beta strategies based on scientific diversification, our designed strategies outperform both the market model and multifactor model. Our testing framework is based on bootstrapped mean–variance spanning tests and shows valid conclusions when controlling for multiple testing, transaction costs, and luck from random basis portfolio construction rules. Economically, our results are supported by diversification-based properties.     

Art as an investment: risk, return and portfolio diversification in major painting markets

The present paper examines risk, return and the prospects for portfolio diversification among major painting and financial markets over the period 1976–2001. The art markets examined are Contemporary Masters, French Impressionists, Modern European, 19th Century European, Old Masters, Surrealists, 20th Century English and Modern US paintings. The financial markets comprise US Treasury bills, corporate and government bonds and small and large company stocks. In common with the published literature in this area, the present study finds that the returns on paintings are much lower and the risks much higher than conventional investment markets. Moreover, while low correlations of returns suggest that opportunities for portfolio diversification in art works alone and in conjunction with equity markets exist, the construction of Markowitz mean‐variance efficient portfolios indicates that no diversification gains are provided by art in financial asset portfolios. However, diversification benefits in portfolios comprised solely of art works are possible, with Contemporary Masters, 19th Century European, Old Masters and 20th Century English paintings dominating the efficient frontier during the period in question.     

Portfolio performance of linear SDF models: an out-of-sample assessment

We evaluate linear stochastic discount factor models using an ex-post portfolio metric: the realized out-of-sample Sharpe ratio of mean–variance portfolios backed by alternative linear factor models. Using a sample of monthly US portfolio returns spanning the period 1968–2016, we find evidence that multifactor linear models have better empirical properties than the CAPM, not only when the cross-section of expected returns is evaluated in-sample, but also when they are used to inform one-month ahead portfolio selection. When we compare portfolios associated to multifactor models with mean–variance decisions implied by the single-factor CAPM, we document statistically significant differences in Sharpe ratios of up to 10 percent. Linear multifactor models that provide the best in-sample fit also yield the highest realized Sharpe ratios.     

Safety-first portfolio optimization for US investors in emerging global,Asian and Latin American markets

Risk averse US investors with safety-first objectives in portfolio optimization hold small weights (maximum 10%) in emerging markets when constructing portfolios of the Standard and Poor's 500 (SP), and the Emerging Markets Composite Global (CG), Asia (AS) and Latin American (LA) indexes, respectively. The Composite Global and Asia weights are even smaller than their minimum variance weights. Yet, these optimal safety-first portfolios are dominant in terms of risk and return over the global minimum or higher variance portfolios. In contrast, safety-first optimization for Latin America is hardly different from the minimum variance and not clearly dominant over other mean–variance portfolios. Overall, safety-first limits portfolio losses associated with infrequent catastrophic events and otherwise optimize performance.     

Comment on “A note on the returns from minimum variance investing”

In Scherer (2011) the author, analyzing minimum variance investing, shows that “the minimum variance tends to hold low beta and low residual risk stocks.”The conclusion that low residual risk assets and assets with a low β (below one) create a positive portfolio weight in the minimum variance portfolio does not prove the paper's “conjecture that the minimum variance portfolio is likely to pick up low beta and low residual risk stocks.”     

Are Euro Area Small Cap Stocks an Asset Class? Evidence from Mean‐Variance Spanning Tests

In this paper we perform regression‐based tests for mean‐variance spanning in order to detect the effect of investing in euro area small capitalisation stocks on the minimum variance frontier, and apply different measures to assess the extent of diversification gains. Empirical analysis shows that euro area small and mid cap stocks, as classified by size quartile and quintile rankings, arise as truly autonomous asset classes. This result is robust to different methodologies used to form size‐based portfolios, and holds relative to both euro area large cap stocks and other international asset classes, US small capitalisation stocks included.     

Idiosyncratic volatility and the pricing of poorly-diversified portfolios

This article examines the role of idiosyncratic volatility in explaining the cross-sectional variation of size- and value-sorted portfolio returns. We show that the premium for bearing idiosyncratic volatility varies inversely with the number of stocks included in the portfolios. This conclusion is robust within various multifactor models based on size, value, past performance, liquidity and total volatility and also holds within an ICAPM specification of the risk–return relationship. Our findings thus indicate that investors demand an additional return for bearing the idiosyncratic volatility of poorly-diversified portfolios.     

Multi-scale variation,path risk and long-term portfolio management

Mean–variance analysis is constrained to weight the frequency bands in a return time series equally. A more flexible approach allows the user to assign preference weightings to short or longer run frequencies. Wavelet analysis provides further flexibility, removing the need to assume asset returns are stationary and encompassing alternative return concepts. The resulting portfolio choice methodology establishes a reward–energy efficient frontier that allows the user to trade off expected reward against path risk, reflecting preferences as between long or short run variation. The approach leads to dynamic analogues of mean–variance such as band pass portfolios that are more sensitive to variability at designated scales.     

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.     

基于余弦相似度(CS)和最小生成树(MST)的基金市场复杂网络研究

以中国基金市场中123家基金公司持有的投资组合为样本,综合运用余弦相似度(CS)和最小生成树(MST)方法,考量基金市场复杂网络。结果显示：各家基金公司持有股票组合的相似程度比持有债券组合的相似程度更高,表明他们持有的债券组合较之股票组合更加多元化,基金公司持有的股票相对集中于市值大、成长性高的公司。同时,全部资产投资组合、股票投资组合和债券投资组合等三类基金MST网络的节点度均服从幂律分布,表明大多数基金公司以少数强影响力基金公司为中心聚集起来,彼此之间具有较强的业务关联。此种网络结构特征可能导致市场风险向基金聚集团体集中,其抵御系统性风险的能力偏弱,也不利于满足投资者的理财多元化需求。     

The return premiums to accruals quality

Using a battery of look-ahead-bias free measures of accruals quality (AQ), we find a strong and long-lasting negative relation between future returns and AQ. In decile portfolios that rank on AQ, a hedge portfolio that goes long in the lowest decile and short in the highest decile generates an annualized, risk-adjusted return of 4–12 % over 1-month to 5-year horizons, depending on the AQ measure and the portfolio weighting scheme. The return premiums associated with AQ are, (1) robust to a wide range of AQ measures, (2) robust to a battery of return-informative variables, and (3) not driven by low-priced or small stocks, earnings shocks, or the fourth-quarter effect. The documented premiums are consistent with the information uncertainty effect where firm uncertainty is negatively related to future returns.