Disentangling the role of variance and covariance information in portfolio selection problems

The covariation among financial asset returns is often a key ingredient used in the construction of optimal portfolios. Estimating covariances from data, however, is challenging due to the potential influence of estimation error, specially in high-dimensional problems, which can impact negatively the performance of the resulting portfolios. We address this question by putting forward a simple approach to disentangle the role of variance and covariance information in the case of mean-variance efficient portfolios. Specifically, mean-variance portfolios can be represented as a two-fund rule: one fund is a fully invested portfolio that depends on diagonal covariance elements, whereas the other is a long-short, self financed portfolio associated with the presence of non-zero off-diagonal covariance elements. We characterize the contribution of each of these two components to the overall performance in terms of out-of-sample returns, risk, risk-adjusted returns and turnover. Finally, we provide an empirical illustration of the proposed portfolio decomposition using both simulated and real market data.     

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.     

Improving Portfolio Performance with Option Strategies: Evidence from Switzerland

This paper investigates the performance of a global investment strategy that combines diversification and option strategies, in particular the covered call strategy, on the Swiss Exchange over the period 1989–96. As the return distributions of portfolios including options are possibly non-normal, the mean-variance framework may not be appropriate to assess the relative performance of such portfolios. Stochastic dominance and modified betas are the alternative approaches, robust to departure from normality, used in this paper to compare the performance of portfolios. The results show that the use of option strategies consistently improves the performance of stock portfolios, even in the presence of transaction costs.     

Do Sukuk provide diversification benefits to conventional bond investors? Evidence from Turkey

We investigate the contribution of Sukuk in diversification of bond portfolios. We do so by comparing Turkish bond funds that invest exclusively in conventional bonds (pure conventional bond funds), in Sukuk (pure Islamic bond funds), and in both (mixed bond funds) among each other for the period of 2014–2019. We employ tests of differences in means and variances of various risk-return measures as well as mean-variance spanning and intersection tests in order to uncover the diversification potentials of Sukuk in the portfolio management industry. Our results suggest that bond funds, of which the portfolios are composed of a combination of Sukuk and conventional bonds (i.e. mixed bond funds), have a relatively “lower risk-higher return” profile. Moreover, including Sukuk to conventional bond portfolios theoretically offers significant diversification opportunities for investors, particularly when the economy worsens.     

Orthogonal Frontiers and Alternative Mean-Variance Efficiency Tests

This paper catalogues properties of minimum norm orthogonal portfolios: portfolios which minimize a quadratic objective function and have returns uncorrelated with those of a candidate portfolio that is not mean-variance efficient. The analysis shows that the dollar versions of these portfolios correspond to estimators of zero beta rates based on alternative statistical criteria and grouping procedures while costless orthogonal portfolios represent candidate mean-variance efficiency tests. It also develops inference procedures for zero and unit net investment portfolios of individual securities (instead of grouped portfolios) that have zero expected betas. The resulting mean-variance efficiency tests are reasonably insensitive to the underlying statistical assumptions.     

The economic value of range-based covariance between stock and bond returns with dynamic copulas

The covariance between stock and bond returns plays important roles in the setting up of asset allocation strategies and portfolio diversification. In the present study, we propose a multivariate range-based volatility model incorporating dynamic copulas into a range-based volatility model to describe the volatility and dependence structures of stock and bond returns. We then go on to assess the economic value of the covariance forecasts based on our proposed model under a mean-variance framework. The out-of-sample forecasting performance reveals that investors would be willing to pay between 39 and 2081 basis points per year to switch from a dynamic trading strategy under the return-based volatility model to a dynamic trading strategy under the range-based volatility model, with more risk-averse investors being willing to pay even higher switching fees. Furthermore, additional economic gains of between 33 and 1471 annualized basis points are achieved when taking the leverage effect into consideration.     

Optimal asset allocation under linear loss aversion

We study the asset allocation of a linear loss-averse (LA) investor and compare it to the more traditional mean-variance (MV) and conditional value-at-risk (CVaR) investors. First we derive conditions under which the LA problem is equivalent to the MV and CVaR problems and solve analytically the two-asset problem of the LA investor for a risk-free and a risky asset. Then we run simulation experiments to study properties of the optimal LA and MV portfolios under more realistic assumptions. We find that under asymmetric dependence LA portfolios outperform MV portfolios, provided investors are sufficiently loss-averse and dependence is large. Finally, using 13 EU and US assets, we implement the trading strategy of a linear LA investor who reallocates his/her portfolio on a monthly basis. We find that LA portfolios clearly outperform MV and CVaR portfolios and that incorporating a dynamic update of the LA parameters significantly improves the performance of LA portfolios.     

The Opportunity Cost of a Mean-Variance Efficient Choice

The mean-variance criterion is one of the most frequently used methods for selecting investment portfolios. Yet, because it is an approximation of an investor's maximum expected utility choice, some theoreticians and practitioners have criticized the approach. This paper examines the investment loss that different investors experience by accepting a mean-variance efficient portfolio. Simulated security returns with extreme distributional characteristics are used to determine the extent of an investor's loss. The results indicate that even under very unreasonable investment distributional assumptions, an investor's loss by accepting a mean-variance efficient choice rarely exceeds a small fraction of one percent per invested dollar.     

Portfolio performance gauging in discrete time using a Luenberger productivity indicator

This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios over time. Integrating the shortage function (Luenberger, 1995) into a Luenberger portfolio productivity indicator (Chambers, 2002), this study estimates the changes in the relative positions of portfolios with respect to the traditional Markowitz mean-variance efficient frontier, as well as the eventual shifts of this frontier over time. Based on the analysis of local changes relative to these mean-variance and higher moment (in casu, mean-variance-skewness and mean-variance-skewness-kurtosis) frontiers, this methodology allows to neatly separate between on the one hand performance changes due to portfolio strategies and on the other hand performance changes due to the market evolution. This methodology is empirically illustrated using a mimicking portfolio approach (22 and 23) using US monthly data from January 1931 to August 2007.     

International portfolio selection and efficiency analysis

In the risk-return tradeoff, the traditional mean-variance analysis has been widely used for studies of international portfolio efficiency and diversification. Without prior knowledge about either the parametric structure of assets' return distributions or the form of investors' preference functions, the variance may no longer serve as a suitable risk proxy. This article examines international portfolio efficiency and diversification effects through mean-variance and various distribution-free (or less restrictive) risk-return measures. We show empirically that the mean-variance model is appropriate for large or well-diversified portfolios, but may provide biased results for single assets and less diversified portfolios. While stochastic dominance stands as theoretically the most appropriate method of international portfolio selection and efficiency analysis, the lack of optimal search algorithms reduces its practical usefulness. Very little gain is obtained by using the Gini-mean-difference risk measure as compared to the semivariance measure. The semivariance measure is a powerful and convenient discriminator of risky prospects, while stochastic dominance can serve as a benchmark to justify portfolio efficiency.     

Characteristic-based mean-variance portfolio choice

We study empirical mean-variance optimization when the portfolio weights are restricted to be direct functions of underlying stock characteristics such as value and momentum. The closed-form solution to the portfolio weights estimator shows that the portfolio problem in this case reduces to a mean-variance analysis of assets with returns given by single-characteristic strategies (e.g., momentum or value). In an empirical application to international stock return indexes, we show that the direct approach to estimating portfolio weights clearly beats a naive regression-based approach that models the conditional mean. However, a portfolio based on equal weights of the single-characteristic strategies performs about as well, and sometimes better, than the direct estimation approach, highlighting again the difficulties in beating the equal-weighted case in mean-variance analysis. The empirical results also highlight the potential for ‘stock-picking’ in international indexes using characteristics such as value and momentum with the characteristic-based portfolios obtaining Sharpe ratios approximately three times larger than the world market.     

General Tests of Latent Variable Models and Mean-Variance Spanning

The methods of Gibbons and Ferson (1985) are extended, relaxing the assumption that expected returns are linear functions of predetermined instruments. A model of conditional mean-variance spanning generalizes Huberman and Kandel (1987). The empirical results indicate that more than a single risk premium is needed to model expected stock and bond returns, but the number of common factors in the expected returns is small. However, when size-based common stock portfolios proxy for the risk factors, we reject the hypothesis that four of them describe the conditional expected returns of the other assets.     

Mean-variance vs. stochastic dominance some empirical findings on efficient sets

The study attempts to shed additional light on the issue of the costs and benefits of using the mean-variance criterion as opposed to stochastic dominance criteria for investment decisions. Relevant probabilities which facilitate measurement of these costs and benefits are identified. The mean-variance criterion is shown to be useful to some extent in identifying potentially optimal portfolios. However, it is shown that the informationally less demanding mean-variance criterion admits two types of errors: (i) including portfolios that no expected utility maximizing risk averters would choose, and (ii) excluding portfolios which some risk averters would find optimal. The empirical investigation also indicates that although the composition of the efficient sets appears to be unstable over time, the relationships between the efficient sets are persistent over time.     

Short-term market timing using the bond–equity yield ratio

This paper takes a new look at the market-timing ability of the bond–equity yield ratio (BEYR). We compare the short-term profitability of a naive strategy based on the extreme values of the BEYR to the short-term profitability of a sophisticated strategy relying on regime switches. In contrast to previous studies, we do not document any major international evidence that these dynamic strategies deliver significantly higher risk-adjusted returns than the buy-and-hold portfolios. Moreover, the profitability of these active strategies is not improved when the equity yield, instead of the BEYR, is used as a criterion to time the market.     

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.     

The performance of international asset allocation strategies using conditioning information

The existence of predictable components in conditional expected returns has been widely reported. We propose a test of the economic significance of this phenomenon by designing dynamic international allocation strategies based on a conditioning information set. We compare the performance of these dynamic strategies with some market portfolio benchmark and with unconditionally efficient portfolios (among the set of primitive assets). We find the performance of the dynamic strategies to be superior. The difference is not only statistically significant, it is economically large.     

A relaxation algorithm for building undominated portfolios

Stochastic dominance methods which have been developed in recent years are generally more valid than mean-variance (EV) and higher moment methods for selecting a portfolio from a given finite set of possible portfolios. One of the limitations of these methods is the lack of procedures for building portfolios from a given set of securities and the probability distribution of their returns. Markowitz has developed an algorithm based on the restriction method in linear programming to build undominated portfolios. In this paper a more efficient method based on the relaxation method of linear programming is developed and tested for efficiency. Computational results justify its use as a practical tool for portfolio building.     

Is there a real estate factor premium?

In this paper, we study the variation of expected returns on five different asset portfolios in a multi-factor model. We found the presence of a real estate factor, in addition to both a stock factor and a bond factor in asset pricing. This suggests that mutual fund managers should seriously consider including real estate assets in their portfolios, since one cannot capture the real estate factor premium without having some kind of real estate exposure. Another result is that the market segmentation found in previous studies disappears in a more general model of asset pricing in which we allow for multi-factors other than the market factor to affect asset returns. This implies that real estate assets can be treated just like other assets as far as mean-variance efficient asset allocations are concerned. We also have some preliminary evidence that equity REITs and the Russell-NCREIF index are driven by the same underlying real estate factor.     

The Economic Value of Volatility Timing

Numerous studies report that standard volatility models have low explanatory power, leading some researchers to question whether these models have economic value. We examine this question by using conditional mean-variance analysis to assess the value of volatility timing to short-horizon investors. We find that the volatility timing strategies outperform the unconditionally efficient static portfolios that have the same target expected return and volatility. This finding is robust to estimation risk and transaction costs.