A Stein-type shrinkage estimator of the covariance matrix for portfolio selections

The covariance matrix plays a crucial role in portfolio optimization problems as the risk and correlation measure of asset returns. An improved estimation of the covariance matrix can enhance the performance of the portfolio. In this paper, based on the Cholesky decomposition of the covariance matrix, a Stein-type shrinkage strategy for portfolio weights is constructed under the mean-variance framework. Furthermore, according to the agent’s maximum expected utility value, a portfolio selection strategy is proposed. Finally, simulation experiments and an empirical study are used to test the feasibility of the proposed strategy. The numerical results show our portfolio strategy performs satisfactorily.     

Selecting a discrete portfolio

We study the problem of selecting an optimal portfolio out of a finite set of available assets. Assets are characterized by their expected returns and the covariance matrix, and investors are assumed to have a mean–variance utility, that is, their utility function is linear in the mean and variance of the portfolio they hold.When assets are negatively correlated, or even when a slightly more general condition is satisfied, we provide an algorithm for selecting an optimal portfolio. We illustrate the usefulness of this algorithm by some comparative statics result. When assets can be positively correlated, we deliver a negative result regarding the existence of useful algorithms for selecting an optimal portfolio.     

Optimal investment decisions when time-horizon is uncertain

Many investors do not know with certainty when their portfolio will be liquidated. Should their portfolio selection be influenced by the uncertainty of exit time? In order to answer this question, we consider a suitable extension of the familiar optimal investment problem of Merton [Merton, R.C., 1971. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373–413], where we allow the conditional distribution function of an agent’s time-horizon to be stochastic and correlated to returns on risky securities. In contrast to existing literature, which has focused on an independent time-horizon, we show that the portfolio decision is affected.     

Does investor sentiment impact the returns and volatility of Islamic equities?

In this paper, we estimate generalized autoregressive conditional heteroskedasticity (GARCH) and vector autoregressive (VAR) models to examine whether investor sentiment impacts the returns and volatility of various U.S. Dow Jones Islamic equity indices. The results from GARCH estimations show that changes in investor sentiment are positively correlated with the returns of the Shari’ah-compliant market portfolio. In addition, we find similar results for the three Shari’ah-compliant firm-size portfolios (i.e., large-, medium-, and small-cap). However, this relationship is stronger for harder to arbitrage Shari’ah-compliant stocks; that is, investor sentiment has a greater influence on small-cap equities. Additionally, estimations from the vector autoregressive model confirm the aforementioned results. In terms of volatility, GARCH estimations suggest that bullish shifts in investor sentiment in the current period are accompanied by lower conditional volatility in the ensuing period. In general, our findings suggest that as noise traders create more risk the market seems to reward them with higher expected returns.     

Impact of diversification on the distribution of stock returns: International evidence

In the past, stock returns are often assumed to be normally distributed. Potential gains from international portfolio diversification are thus based on a mean-variance framework. However, numerous empirical results reveal that stock returns are actually not normally distributed. Although previous studies found that both skewness and kurtosis can be rapidly diversified away, these results are only valid for a random sample of a given portfolio size. This paper studies the joint effect of diversification and intervaling on the skewness and kurtosis of eleven international stock market indexes with a holding period spanning from one to six months. A complete set of all possible combinations of portfolios is used. It is found that diversification does not reduce either skewness or kurtosis. As the portfolio size increases, portfolio returns become more negatively skewed and more leptokurtic. As a result, a rational investor may not gain from international diversification.     

An Empirical Test of Pricing Kernel Monotonicity

A large class of asset pricing models predicts that securities which have high payoffs when market returns are low tend to be more valuable than those with high payoffs when market returns are high. More generally, we expect the projection of the stochastic discount factor on the market portfolio—that is, the discounted pricing kernel evaluated at the market portfolio—to be a monotonically decreasing function of the market portfolio. Numerous recent empirical studies appear to contradict this prediction. The non‐monotonicity of empirical pricing kernel estimates has become known as the pricing kernel puzzle. In this paper we propose and apply a formal statistical test of pricing kernel monotonicity. We apply the test using 17 years of data from the market for European put and call options written on the S&P 500 index. Statistically significant violations of pricing kernel monotonicity occur in a substantial proportion of months, suggesting that observed non‐monotonicities are unlikely to be the product of statistical noise. Copyright © 2014 John Wiley & Sons, Ltd.     

Multivariate semi-nonparametric distributions with dynamic conditional correlations

This paper generalizes the Dynamic Conditional Correlation (DCC) model of Engle (2002), incorporating a flexible non-Gaussian distribution based on Gram-Charlier expansions. The resulting semi-nonparametric-DCC (SNP-DCC) model allows estimation in two stages and deals with the negativity problem which is inherent in truncated SNP densities. We test the performance of a SNP-DCC model with respect to the (Gaussian)-DCC through an empirical application of density forecasting for portfolio returns. Our results show that the proposed multivariate model provides a better in-sample fit and forecast of the portfolio returns distribution, and thus is useful for financial risk forecasting and evaluation.     

Portfolio selection based on semivariance and distance correlation under minimum variance framework

In the minimum variance model, the covariance matrix plays an important role because it measures the risk and relationship of asset returns simultaneously under the normality assumption. However, in practice, the distribution of asset returns is nonnormal and has an obvious fat‐tail nature. In addition, the risk is one‐sided. In this paper, the main objective is to propose a better tool to replace the covariance matrix. The covariance matrix can be decomposed into two parts: a diagonal variance matrix and a square matrix with its elements being the Pearson correlation coefficient. A substitution of the covariance matrix is presented by replacing the variance and Pearson correlation coefficient in the decomposition of the covariance matrix with a semivariance and distance correlation coefficient, respectively. The proposed portfolio optimization strategy is applied to empirical data, and the numerical studies show the strategy performs well.     

Asymptotic behavior of the estimated weights and of the estimated performance measures of the minimum VaR and the minimum CVaR optimal portfolios for dependent data

In this paper we derive the asymptotic distributions of the estimated weights and of estimated performance measures of the minimum value-at-risk portfolio and of the minimum conditional value-at-risk portfolio assuming that the asset returns follow a strictly stationary process. It is proved that the estimated weights as well as the estimated performance measures are asymptotically multivariate normally distributed. We also present an asymptotic test for the weights and a joint test for the characteristics of both portfolios. Moreover, the asymptotic densities of the estimated performance measures are compared with the corresponding exact densities. It is shown that the asymptotic approximation performs well even for the moderate sample size.     

Gradual information diffusion and contrarian strategies

Various rational and behavioral models have been proposed to explain contrarian portfolio returns. In this article, I test the gradual information diffusion model of Hong and Stein [Hong, H., & Stein J. C. (1999). A unified theory of underreaction, momentum trading, and overreaction in asset markets. Journal of Finance, 54, 2143–2184]. Specifically, I study contrarian strategies based on past long-term returns and fundamental value-to-price ratios. Using ex post returns as a proxy for expected returns and size-controlled analyst coverage as a proxy for the rate of information diffusion, I show that contrarian portfolio returns decline monotonically with increasing rates of information diffusion. These results are consistent with the predictions of the Hong and Stein model. In addition, I show that analyst coverage is more important among glamour than value stocks, supporting the view that investors are more prone to decision biases when it comes to pricing hard-to-value glamour stocks for which information is relatively more ambiguous.     

The translog production function: Some evidence from establishment data

This paper uses cross-section data from individual establishments to estimate directly, i.e., without using side conditions, translog functions for 44 four-digit ISIC Chilean manufacturing industries. Main results are: (1) The null hypothesis that the production function is Cobb-Douglas cannot be rejected for 39 out of 44 four-digit ISIC industries. (2) The null hypothesis of constant returns to scale cannot be rejected for 35 out of 44 industries; the remaining 9 sectors show evidence of increasing returns to scale.     

Value‐at‐risk for long and short trading positions

In this paper we model Value‐at‐Risk (VaR) for daily asset returns using a collection of parametric univariate and multivariate models of the ARCH class based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, VaR for traders having both long and short positions is not adequately modelled using usual normal or Student distributions. We suggest using an APARCH model based on the skewed Student distribution (combined with a time‐varying correlation in the multivariate case) to fully take into account the fat left and right tails of the returns distribution. This allows for an adequate modelling of large returns defined on long and short trading positions. The performances of the univariate models are assessed on daily data for three international stock indexes and three US stocks of the Dow Jones index. In a second application, we consider a portfolio of three US stocks and model its long and short VaR using a multivariate skewed Student density. Copyright © 2003 John Wiley & Sons, Ltd.     

Day-of-the-week effect on the VIX. A parsimonious representation

The study of significant deterministic seasonal patterns in financial asset returns is of high importance to academia and investors. This paper analyzes the presence of seasonal daily patterns in the VIX and S&P 500 returns series using a trigonometric specification. First, we show that, given the isomorphism between the trigonometrical and alternative seasonality representations (i.e., daily dummies), it is possible to test daily seasonal patterns by employing a trigonometrical representation based on a finite sum of weighted sines and cosines. We find a potential evolutive seasonal pattern in the daily VIX that is not in the daily S&P 500 log-returns series. In particular, we find an inverted Monday effect in the VIX level and changes in the VIX, and a U-shaped seasonal pattern in the changes in the VIX when we control for outliers. The trigonometrical representation is more robust to outliers than the one commonly used by literature, but it is not immune to them. Finally, we do not find a day-of-the-week effect in S&P 500 returns series, which suggests the presence of a deterministic seasonal pattern in the relation between VIX and S&P 500 returns.     

Robustness of stable volatility strategies

The paper analyzes the robustness of stable volatility strategies, i.e. strategies in which the portfolio weight of the stock is inversely proportional to its local volatility. These strategies are optimal for a CRRA investor if the stock follows a diffusion process, the expected excess return is proportional to its volatility, and the hedging demand is zero. We assess the performance of stable volatility strategies when these restrictive assumptions do not hold, in particular, when the risk premium is not proportional to volatility and when the stock price is subject to jumps. We find that stable volatility strategies are indeed robust or close to robust under a maxmin decision rule. In addition to our theoretical results, we perform a simulation analysis to evaluate strategies that scale the portfolio weight by the volatility, variance or a constant portfolio weight, and also analyze the strategies using empirical excess returns. Both analyses confirm the robustness of stable volatility strategies.     

Fractal statistical measure and portfolio model optimization under power-law distribution

An effective portfolio selection model is constructed on the premise of measuring accurately the risk and return on assets. According to the reality that the tail of returns on assets obey power-law distribution, this paper firstly builds two fractal statistical measures, fractal expectation and fractal variance, to measure the asset returns and risks, inspired by the method of measuring curve length in the fractal theory. Then, by incorporating the fractal statistical measure into the return-risk criterion, a portfolio selection model based on fractal statistical measure is established, namely the fractal portfolio selection model, and the closed-form solution of the model is given. Finally, through empirical analysis we find that the fractal portfolio selection model is effective and can improve investment performance.     

Defensive acquisitions in the banking industry: The takeover premium hypothesis

We define defensive acquisitions as takeovers made by a firm so as to become so large that it becomes an unattractive target itself. A sample of defensive acquisitions in the banking industry is used to test the takeover premium hypothesis. Under this hypothesis, the defensive acquirers lose because a takeover premium that previously existed in their prices is deflated while the takeover premium increases for smaller competitors because they become more likely targets. We find that the defensive acquirers experience significant negative abnormal returns on the announcement day, and that smaller competitors have positive abnormal returns on the announcements of defensive acquisitions. In contrast, larger competitors do not react to the announcements. The results are consistent with the takeover premium hypothesis.     

Searching hedging instruments against diverse global risks and uncertainties

We evaluate the influence of five major risk and uncertainty factors on four asset classes. Our time-varying findings suggest that each asset hedges only a particular uncertainty factor, whereas gold does more than one factor, especially during COVID-19. Our frequency-based quantile regression (QR) results show that in the raw frequency, gold and Islamic stock can better hedge various uncertainty factors than Bitcoin and crude oil, depending on the market conditions. Additionally, using the frequency bands (e.g., short, medium, and long term) data, we further notice that, depending on the market circumstances and investment horizons, gold and Islamic stock returns are still better hedges for the various risks and uncertainties than Bitcoin and crude oil returns. Our findings have crucial risk and portfolio management implications for investors, portfolio managers, and policymakers.     

Testing out-of-sample portfolio performance

This paper studies the quality of portfolio performance tests based on out-of-sample returns. By disentangling the components of the out-of-sample performance, we show that the observed differences are driven largely by the differences in estimation risk. Our Monte Carlo study reveals that the puzzling empirical findings of inferior performances of theoretically superior strategies result mainly from the low power of these tests. Thus, our results provide an explanation as to why the null hypothesis of equal performance of the simple equally-weighted portfolio compared to many theoretically-superior alternative strategies cannot be rejected in many out-of-sample horse races. Our findings turn out to be robust with respect to different designs and the implementation strategies of the tests.For the applied researcher, we provide some guidance as to how to cope with the problem of low power. In particular, we make use of a novel pretest-based portfolio strategy to show how the information regarding performance tests can be used optimally.     

Individual versus institutional investors and the weekend effect

Since the late 1980’s, considerable research has focused on the behavior of individual versus institutional investors and the potential patterns which may emerge from their trading activities. Miller (1988) and Abraham and Ikenberry (1994) posit that the tendency for negative Monday returns on equity (i.e., the weekend effect) is at least partially explained by the trading behavior of individual investors. Sias and Starks (1995), on the other hand, present empirical evidence showing a dominant role played by institutional traders. This study contributes to the literature by distinguishing between individual versus institutional trading as it relates to the weekend effect. We find that the information-processing hypothesis is consistent with observed institutional trading patterns, thus supporting the results of Sias and Starks (1995). In addition, these results are shown to be robust with respect to market type (i.e., auction and dealer markets).     

A residual-based multivariate constant correlation test

We propose a new multivariate constant correlation test based on residuals. This test takes into account the whole correlation matrix instead of the considering merely marginal correlations between bivariate data series. In financial markets, it is unrealistic to assume that the marginal variances are constant. This motivates us to develop a constant correlation test which allows for non-constant marginal variances in multivariate time series. However, when the assumption of constant marginal variances is relaxed, it can be shown that the residual effect leads to nonstandard limit distributions of the test statistics based on residual terms. The critical values of the test statistics are not directly available and we use a bootstrap approximation to obtain the corresponding critical values for the test. We also derive the limit distribution of the test statistics based on residuals under the null hypothesis. Monte Carlo simulations show that the test has appealing size and power properties in finite samples. We also apply our test to the stock returns in Euro Stoxx 50 and integrate the test into a binary segmentation algorithm to detect multiple break points.