Robustness of the inference procedures for the global minimum variance portfolio weights in a skew-normal model

In this paper, we study the influence of skewness on the distributional properties of the estimated weights of optimal portfolios and on the corresponding inference procedures derived for the optimal portfolio weights assuming that the asset returns are normally distributed. It is shown that even a simple form of skewness in the asset returns can dramatically influence the performance of the test on the structure of the global minimum variance portfolio. The results obtained can be applied in the small sample case as well. Moreover, we introduce an estimation procedure for the parameters of the skew-normal distribution that is based on the modified method of moments. A goodness-of-fit test for the matrix variate closed skew-normal distribution has also been derived. In the empirical study, we apply our results to real data of several stocks included in the Dow Jones index.     

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.     

Do commodities add value in multi-asset portfolios? An out-of-sample analysis for different investment strategies

An essential motive for investing in commodities is to enhance the performance of portfolios traditionally including only stocks and bonds. We analyze the in-sample and out-of-sample portfolio effects resulting from adding commodities to a stock-bond portfolio for commonly implemented asset allocation strategies such as equally- and strategically-weighted portfolios, risk-parity, minimum-variance as well as reward-to-risk timing, mean-variance and Black–Litterman. We analyze different commodity groups such as agricultural and livestock commodities that currently are critically discussed. The out-of-sample portfolio analysis indicates that the attainable benefits of commodities are much smaller than suggested by previous in-sample studies. Hence, in-sample analyses, such as spanning tests, might exaggerate the advantages of commodities. Moreover, the portfolio gains greatly vary between different types of commodities and sub-periods. While aggregate commodity indices, industrial and precious metals as well as energy improve the performance of a stock-bond portfolio for most asset allocation strategies, we hardly find positive portfolio effects for agriculture and livestock. Consequently, investments in food commodities are not essential for efficient asset allocation.     

Modern portfolio management with conditioning information

This paper studies models in which active portfolio managers utilize conditioning information unavailable to their clients to optimize performance relative to a benchmark. We derive explicit solutions for the optimal strategies with multiple risky assets, with or without a risk-free asset, and consider various constraints on portfolio risks or weights. The optimal strategies feature a mean–variance efficient component (to minimize portfolio variance), and a hedging demand for the benchmark portfolio (to maximize correlation with the benchmark). A currency portfolio example shows that the optimal strategies improve the measured performance by 53% out of sample, compared with portfolios ignoring conditioning information.     

A comparison of static and dynamic portfolio policies

Garleanu and Pedersen (2013) show that the optimal static portfolio policy in light of quadratic transaction costs is a weighted average of the existing portfolio and the target portfolio. In this paper, we demonstrate the importance of the robust target portfolio in the static portfolio policy that considers quadratic transaction costs. By using both empirical and simulated data, we find no evidence that the optimal dynamic portfolio policy proposed by Garleanu and Pedersen (2013) is superior to the static portfolio policy that trades towards the robust target portfolio. The robust target portfolio is achieved by either introducing time-varying covariances or restricting portfolio weights. Furthermore, the static portfolio with time-varying covariances and the short sale-constrained static portfolio are both very efficient in reducing portfolio turnover. The good performance of the static portfolio policy is robust to parameter uncertainty and trading parameters.     

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.     

Factor based index tracking

Stock index tracking requires to build a portfolio of stocks (a replica) whose behavior is as close as possible to that of a given stock index. Typically, much fewer stocks should appear in the replica than in the index, and there should be no low frequency or integrated (persistent) components in the tracking error. The latter property is not satisfied by many commonly used methods for index tracking. These are based on the in-sample minimization of a loss function, but do not take into account the dynamic properties of the index components. Moreover, most existing methods do not take into account the known structure of the index weight system. In this paper we represent the index components with a dynamic factor model. In this model the price of each stock in the index is driven by a set of common and idiosyncratic factors. Factors can be either integrated or stationary. We develop a procedure that, in a first step, builds a replica that is driven by the same persistent factors as the index. This procedure is grounded in recent results which suggest the application of principal component analysis for factor estimation even for integrated processes. In a second step, it is also possible to refine the replica so that it minimizes a specific loss function, as in the traditional approach. In both steps the replica weights depend on the existing information on the index weights system. An extended set of Monte Carlo simulations and an application to the most widely used index in the European stock market, the EuroStoxx50 index, provide substantial support for our approach.     

Convex risk measures based on generalized lower deviation and their applications

Considering the implementability and the properties that a reasonable and realistic risk measure should satisfy, we propose a new class of risk measures based on generalized lower deviation with respect to a chosen benchmark. Besides convexity and monotonicity, our new risk measure can reflect the investor's degree of risk aversion as well as the fat-tail phenomenon of the loss distribution with the help of different benchmarks and weighted functions. Based on the new risk measure, we establish a realistic portfolio selection model taking market frictions into account. To examine the influence of the benchmarks and weighted functions on the optimal portfolio and its performance, we carry out a series of empirical studies in Chinese stock markets. Our in-sample and out-of-sample results show that the new risk measure and the corresponding portfolio selection model can reflect the investor's risk averse attitude and the impact of different trading constraints. Most importantly, with the new risk measure we can obtain an optimal portfolio which is more robust and superior to the optimal portfolios obtained with the traditional expected shortfall risk measures.     

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.     

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.     

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.     

Optimal Asset Allocation Over the Business Cycle

Utilizing a broadly diversified portfolio of nine equity and debt assets, we show our portfolio's in-sample Markowitz return/risk profile considerably improved by keying asset proportions to cyclical changes in economic activity. For comparative purposes, we use the same assets in a hypothetical buy-and-hold benchmark portfolio. We find the variance/covariance structure of our portfolio to be considerably altered by the phase of the business cycle, with the diversification benefits enjoyed during expansions substantially diluted during recessions. Thus, cyclical reallocation appears to be more important in maintaining Markowitz efficiency during recessions vis-a-vis expansions. In the latter case we find expansion reallocation producing a 3.53% increase in our portfolio's return-to-risk ratio (relative to a buy-and-hold position), while for recessions optimal reallocation leads to a 79.14% increase.     

Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps

Green and Hollifield (1992) argue that the presence of a dominant factor would result in extreme negative weights in mean‐variance efficient portfolios even in the absence of estimation errors. In that case, imposing no‐short‐sale constraints should hurt, whereas empirical evidence is often to the contrary. We reconcile this apparent contradiction. We explain why constraining portfolio weights to be nonnegative can reduce the risk in estimated optimal portfolios even when the constraints are wrong. Surprisingly, with no‐short‐sale constraints in place, the sample covariance matrix performs as well as covariance matrix estimates based on factor models, shrinkage estimators, and daily data.     

Fama–French factor timing: The long-only integrated approach

There is ample evidence that factor momentum exists in the standard long–short mixed approach to factor investing. However, the excess returns are put under scrutiny due to the high implementation costs. We present a novel real-life approach that relies on the long-only integrated approach to factor investing. Instead of exploiting the potential momentum in factor portfolios, our strategy builds on the momentum of the optimal factor score weights in the integrated approach, which allows us to additionally profit from the serial dependence in the factors' interaction effects. One limitation of short-term timing strategies is their high turnover. By including the information of the covariance matrix and minimising the strategy's risk to the market portfolio, we can substantially reduce turnover. The resulting timing alpha remains significant even after transaction costs in a robust statistical test framework across the major stock markets.     

Limits to mutual funds' ability to rely on mean/variance optimization

Our evidence suggests that estimation error in the required statistics is an important factor inhibiting investors' ability to rely on mean/variance analysis. We compare the returns reported by mutual funds to the returns obtained from a mean/variance optimized portfolio of fund holdings. The results suggest that funds tend to outperform the optimized portfolio out-of-sample (when means/variances/covariances are unknown), but under-perform in-sample (when the required statistics in the optimization are known). Therefore, a popular assumption in asset pricing models that investors rely on a basic mean/variance analysis with known underlying statistics is likely to be grossly violated in the case of mutual funds.     

The index revision party

This paper examines the annual revision of the AEX index in the Netherlands. This particular index is interesting because the revision rules enable investors to anticipate changes in both constituents and index weights long in advance. Our results suggest that attention and temporary price pressure play a role in the observed revision effect. A portfolio containing those stocks expected to benefit from the index revision is showing an outperformance of up to 7% in the weeks before the revision, while losers are unaffected. Around the revision day, we find indications of temporary price pressure for winners as well as losers.     

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.     

Forecasting variance using stochastic volatility and GARCH

This paper estimates the conditional variance of daily Swedish OMX-index returns with stochastic volatility (SV) models and GARCH models and evaluates the in-sample performance as well as the out-of-sample forecasting ability of the models. Asymmetric as well as weekend/holiday effects are allowed for in the variance, and the assumption that errors are Gaussian is released. Evidence is found of a leverage effect and of higher variance during weekends. In both in-sample and out-of-sample comparisons SV models outperform GARCH models. However, while asymmetry, weekend/holiday effects and non-Gaussian errors are important for the in-sample fit, it is found that these factors do not contribute to enhancing the forecasting ability of the SV models.     

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.     

Portfolio optimisation with jumps: Illustration with a pension accumulation scheme

In this paper, we address portfolio optimisation when stock prices follow general Lévy processes in the context of a pension accumulation scheme. The optimal portfolio weights are obtained in quasi-closed form and the optimal consumption in closed form. To solve the optimisation problem, we show how to switch back and forth between the stochastic differential and standard exponentials of the Lévy processes. We apply this procedure to both the Variance Gamma process and a Lévy process whose arrival rate of jumps exponentially decreases with size. We show through a numerical example that when jumps, and therefore asymmetry and leptokurtosis, are suitably taken into account, then the optimal portfolio share of the risky asset is around half that obtained in the Gaussian framework.