Portfolio Selection and Optimization with Higher Moments: Evidence from the Indian Stock Market

The Markowitz portfolio optimization model, popularly known as the Mean-Variance model, assumes that stockreturns follow normal distribution. But when stock returns do not follow normal distribution, this model wouldbe inadequate as it would prescribe sub-optimal portfolios. Stock market literature often deliberates that stock returns are non-normal. In such context the Markowitz model would not be sufficient to estimate the portfolio risks. The purpose of this paper is to expand the original Markowitz portfolio theory (mean-variance) via adding the higher order moments like skewness (third moment about the mean) and kurtosis (fourth moment about the mean) in the return characteristics. The research paper investigates the impact of including higher moments using multi-objective programming model for portfolio stock selection and optimization. The empirical results indicate that the inclusion of higher moments had a considerable impact in estimating the returns behavior of portfolios. The portfolios optimized using all the four moments, generated higher returns for the given level of risk in comparison to the returns of the Markowitz model during the study period 2000–2011. The results of this study would be immensely useful to fund managers, portfolio managers and investors as it would help them in understanding the Indian stock market behavior better and also in selecting alternative portfolio selection models.     

Optimal investments in volatility

Volatility has evolved as an attractive new asset class of its own. The most common instruments for trading volatility are variance swaps. Mean returns of DAX and ESX variance swaps over the time period of 1995 to 2004 are strongly negative, and only part of the negative premium can be explained by the negative correlation of variance swap returns with stock market indices. We analyze the implications of this observation for optimal portfolio composition. Mean-variance efficient portfolios are characterized by sizable short positions in variance swaps. Typically, the stock index is also sold short to achieve a better portfolio diversification. To capture heterogeneous preferences for higher moments, we use a variant of the polynomial goal programming method. We assume that investors strive for a high Sharpe ratio, high skewness, and low kurtosis. Our analysis reveals that it is often not possible to achieve a balanced tradeoff between Sharpe ratio and skewness. Investors are advised to hold the extreme portfolios (Sharpe ratio driven, skewness driven, or kurtosis driven) and avoid the middle ground. This “all-or-nothing” characteristic is reflected in jumps of asset weights when certain thresholds of preference parameters are crossed. These empirical findings can explain why many investors are so reluctant to implement option-based short-selling strategies.

Stability of international stock market relationships across month of the year and different holding intervals

Potential benefits from international diversification depend upon the stability in stock market relationships. Using monthly data of 11 international stock markets, this paper examines the stability in stock market relationships across month of the year and across different holding intervals. Empirical results show that the correlation structure is more stable than the covariance structure. While empirical evidence supports the hypothesis that the correlation structure is very stable across different holding intervals, the empirical support for the stability in correlation structure across month of the year is much weaker.     

Causality in volatility and volatility spillover effects between US, Japan and four equity markets in the South China Growth Triangular

In examining co-movement across international stock markets, previous researchers usually pre-determine the direction of causation and neglect the Chinese equity markets. In this study, we examine the spillover effects of volatility among the two developed markets and four emerging markets in the South China Growth Triangular using Chueng and Ng's causality-in-variance test. Several findings deserve mention: (1) the Japanese stock market affects the US stock market and there is a feedback relationship between the Hong Kong and US stock market. (2) Markets of the SCGT are contemporaneously correlated with the return volatility of the US market. (3) Econometric models constructed according to the results of variance-in-causality tests have greater explanatory power than the conventional GARCH(1,1) model. (4) Using the return volatility of foreign exchange as a proxy for informational arrival can explain excess kurtosis of a stock return series, especially for the less open emerging market. (5) Geographic proximity and economic ties do not necessarily lead to a strong relationship in volatility across markets.     

Accounting Ratios and the Cross‐section of Expected Stock Returns

Under clean‐surplus accounting, the log return on a stock can be decomposed into a linear function of the contemporaneous log return on equity, the contemporaneous log dividend–price ratio (if the stock pays a dividend), and both the contemporaneous and lagged values of the log book‐to‐market equity ratio. This paper studies the implications of this decomposition for the cross‐section of conditional expected stock returns. The empirical analysis reveals that the log accounting ratios capture cross‐sectional variation in both the conditional mean and conditional variance of log stock returns, which is consistent with the decomposition. It also brings fresh insights to the relation between firm size (market equity) and conditional expected stock returns. The evidence indicates that the conditional median return increases with firm size, while the conditional return skewness decreases with firm size. Empirically, the skewness effect outweighs the median effect, leading to the well‐documented inverse relation between size and average returns. The results of out‐of‐sample tests suggest that investors could use the information provided by the observed values of the log accounting ratios to formulate more effective portfolio strategies.     

The impact of portfolio diversification on mean reverting components of stock indices

Positive autocorrelations are introduced into stock index portfolios when they are formed from individual stock indices while negative autocorrelations are induced in returns by increasing the investment horizon. Using monthly data of six international stock indices, this paper examines the diversification effect with different investment horizons on autocorrelations of stock index portfolios. The results show that portfolio diversification does not alter the impact of the investment horizon on autocorrelations. Different investment horizons, however, have great impact on the diversification effect on autocorrelations. With short (long) horizons, the average autocorrelation coefficient increases (decreases) with an increase in the portfolio size, suggesting that mean-reverting component dominates the delayed adjustment effect in long horizons and vice versa in short horizons. Our results are robust across two 10-year sub-periods.The author would like to thank an anonymous referee of this Journal for the comments on an earlier version of this paper and the Research Committee of Hong Kong Baptist University for the financial support in this research.     

Portfolio selection, diversification and fund-of-funds: a note

The present paper examines the performance and diversification properties of active Australian equity fund‐of‐funds (FoF). Simulation analysis is employed to examine portfolio performance as a function of the number of funds in the portfolio. The present paper finds that as the number of funds in an FoF portfolio increases, performance improves in a mean–variance setting; however, measures of skewness and kurtosis behave less favourably given an investor's preferences for the higher moments of the return distribution. The majority of diversification benefits are realized when a portfolio of approximately 6 active equity funds are included in the FoF portfolio.     

Possibility versus feasibility: International portfolio diversification under financial liberalization

Financial liberalization may have double-edged impacts on international portfolio diversification since it increases financial market integration and market correlation simultaneously. Financial market integration enhances the possibility of diversifying portfolios internationally, while financial market correlation reduces the feasibility of such a diversification benefit. Using a dataset of stock market across 35 countries over the period 2001–2021, this paper examines the “possibility versus feasibility” puzzle arising from international portfolio diversification under financial liberalization. The empirical results show that financial liberalization has a positive (negative or no) impact on diversification benefits in its early (medium or developed) stage respectively due to its dual effects. Moreover, market integration positively affects diversification benefits only in the early stage of financial liberalization, while market correlation consistently has a negative impact on diversification benefits. Furthermore, this paper proposes an integration-correlation-oriented (ICO) diversification strategy to address the “possibility versus feasibility” puzzle, enabling international investors to make appropriate decisions on international portfolio diversification under financial liberalization.     

Portfolio selection and skewness: Evidence from international stock markets

This paper finds that the returns of the world's 14 major stock markets are not normally distributed, and that the correlation matrix of these stock markets was stable during the January 1988–December 1993 time period. Polynomial goal programming, in which investor preferences for skewness can be incorporated, is utilized to determine the optimal portfolio consisting of the choices of 14 international stock indexes. The empirical findings suggest that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of the optimal portfolio. The evidence also indicate that investors trade expected return of the portfolio for skewness.     

Liquidity and asset pricing: Evidence from the Hong Kong stock market

This study investigates the role of liquidity in pricing stock returns in the Hong Kong stock market. Our results show that liquidity is an important factor for pricing returns in Hong Kong after taking well-documented asset pricing factors into consideration. The results are robust to adding portfolio residuals and higher moment factor in the factor models. The results are also robust to seasonality, and conditional-market tests. We also compare alternative factor models and find that the liquidity four-factor model (market excess return, size, book-to-market ratio, and liquidity) is the best model to explain stock returns in the Hong Kong stock market, while the momentum factor is not found to be priced.     

Risk transmission between Islamic and conventional stock markets: A return and volatility spillover analysis

This paper contributes to the current debate on the empirical validity of the decoupling hypothesis of the Islamic stock market from its mainstream counterparts by examining return and volatility spillovers across the global Islamic stock market, three main conventional national stock markets (the US, the UK and Japan) and a number of influential macroeconomic and financial variables over the period from July 1996 to June 2016. To that end, the VAR-based spillover index approach based on the generalized VAR framework developed by Diebold and Yilmaz (2012) is applied. The empirical analysis shows strong interactions in return and volatility among the global Islamic stock market, the conventional stock markets and the set of major risk factors considered. This finding means that the Islamic equity universe does not constitute a viable alternative for investors who wish to hedge their investments against the vagaries of stock markets, but it is exposed to the same global factors and risks hitting the conventional financial system. Therefore, this evidence leads to the rejection of the decoupling hypothesis of the Islamic stock market from conventional stock markets, which has significant implications for faith-based investors and policy makers in terms of portfolio diversification, hedging strategies and contagion risk.     

International asset allocation under regime switching, skew, and kurtosis preferences

This paper investigates the international asset allocation effectsof time-variations in higher-order moments of stock returnssuch as skewness and kurtosis. In the context of a four-momentInternational Capital Asset Pricing Model (ICAPM) specificationthat relates stock returns in five regions to returns on a globalmarket portfolio and allows for time-varying prices of covariance,co-skewness, and co-kurtosis risk, we find evidence of distinctbull and bear regimes. Ignoring such regimes, an unhedged USinvestor's optimal portfolio is strongly diversified internationally.The presence of regimes in the return distribution leads toa substantial increase in the investor's optimal holdings ofUS stocks, as does the introduction of skewness and kurtosispreferences.     

Does the US-China trade war affect co-movements between US and Chinese stock markets?

This paper investigates the impact of the US-China Trade War on co-movements between US and Chinese stock markets. It particularly examines the time-varying stock market co-movement between the United States and China at market level, as well as at sector level, over the period from 3rd January 2017 to 23rd January 2020. The ‘event study’ analysis is employed to investigate the effect of US-China trade disputes news on co-movement dynamics, and the news announcement effects before and after the official start of the US-China Trade War (regarded as 6th July 2018) are examined separately in light of this phenomenon. We also identify structural breaks and spillover patterns of cross-market co-movements during different phases. The results indicate that co-movements amongst mainland China, Hong Kong and US stock markets are positively affected by news releases and, after 6th July 2018, are enhanced significantly. More precisely, there is also empirical evidence of positive announcement effects in stock market co-movements between the US and mainland China in specific sectors (particularly, Industrials and Information Technology). For international investors, this evidence suggests that the US-China Trade War has reduced the benefit of portfolio diversification in managing risk.     

Does Trading Volume Contain Information to Predict Stock Returns? Evidence from China's Stock Markets

This paper examines empirical contemporaneous and causal relationships between trading volume, stock returns and return volatility in China's four stock exchanges and across these markets. We find that trading volume does not Granger-cause stock market returns on each of the markets. As for the cross-market causal relationship in China's stock markets, there is evidence of a feedback relationship in returns between Shanghai A and Shenzhen B stocks, and between Shanghai B and Shenzhen B stocks. Shanghai B return helps predict the return of Shenzhen A stocks. Shanghai A volume Granger-causes return of Shenzhen B. Shenzhen B volume helps predict the return of Shanghai B stocks. This paper also investigates the causal relationship among these three variables between China's stock markets and the US stock market and between China and Hong Kong. We find that US return helps predict returns of Shanghai A and Shanghai B stocks. US and Hong Kong volumes do not Granger-cause either return or volatility in China's stock markets. In short, information contained in returns, volatility, and volume from financial markets in the US and Hong Kong has very weak predictive power for Chinese financial market variables.     

The information content of implied skewness and kurtosis changes prior to earnings announcements for stock and option returns

We use option prices to examine whether changes in stock return skewness and kurtosis preceding earnings announcements provide information about subsequent stock and option returns. We demonstrate that changes in jump risk premiums can lead to changes in implied skewness and kurtosis and are also associated with the mean and variability of the stock price response to the earnings announcement. We find that changes in both moments have strong predictive power for future stock returns, even after controlling for implied volatility. Additionally, changes in both moments predict call returns, while put return predictability is primarily linked to changes in skewness.     

Changing conditions in the Hong Kong new issues market

This paper examines the Hong Kong IPO market from August 1995 to July 1999 and finds that the time of the June 30 1997 political handover coincides with the transition in the IPO market from ‘hot’ to ‘cold’. Although the handover was an anticipated event, an explanation for the change in market is that the political handover created uncertainty among investors; a type of information asymmetry where all investors faced greater uncertainty. Our finding provides empirical support to literature which proposes that events in the months preceding the October 27 1997 correction in Asian stock markets facilitated a decline in confidence in financial markets, subsequently characterised as the ‘Asia Financial Crisis’. In addition, we find initial returns of newly listed stocks in the Hong Kong market are associated with market condition but not associated with any particular industry (i.e., PROPERTY) or geographic location (i.e., ‘H’ SHARES) suggesting that the prevailing market condition was spread more generally across issues.     

Strategic International Diversification and Monthly Seasonality

To the author's knowledge no other studies have dealt with the effect of international diversification on stock market monthly seasonality. The aim of this study is to investigate this effect in various ways: stock market monthly seasonality is analyzed by incorporating exchange rates and trading costs in international portfolio returns. The variance of the world portfolio is decomposed into six components. Stochastic dominance approach is used to show the robustness of the results. Five trading strategies are compared to help international investors be more informed. All the results show that monthly seasonality is clearly present in an economic sense and robust. Particularly, when exchange rates are incorporated into portfolio returns. January has the highest return and the lowest risk in the world portfolio.     

On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation

Recent studies in the empirical finance literature have reportedevidence of two types of asymmetries in the joint distributionof stock returns. The first is skewness in the distributionof individual stock returns. The second is an asymmetry in thedependence between stocks: stock returns appear to be more highlycorrelated during market downturns than during market upturns.In this article we examine the economic and statistical significanceof these asymmetries for asset allocation decisions in an out-of-samplesetting. We consider the problem of a constant relative riskaversion (CRRA) investor allocating wealth between the risk-freeasset, a small-cap portfolio, and a large-cap portfolio. Weuse models that can capture time-varying moments up to the fourthorder, and we use copula theory to construct models of the time-varyingdependence structure that allow for different dependence duringbear markets than bull markets. The importance of these twoasymmetries for asset allocation is assessed by comparing theperformance of a portfolio based on a normal distribution modelwith a portfolio based on a more flexible distribution model.For investors with no short-sales constraints, we find thatknowledge of higher moments and asymmetric dependence leadsto gains that are economically significant and statisticallysignificant in some cases. For short sales-constrained investorsthe gains are limited.     

Is international diversification really beneficial?

Previous research claims that low constant correlations among international stock indices create substantial risk-reduction from diversification. We contend that only using constant correlations is too simplistic an approach. We examine international diversification by: (1) using conditional correlations, (2) evaluating tail risk, including the effect of skewness and kurtosis, and (3) examining the possible tradeoffs of standard deviation with correlation, skewness, and kurtosis. We show that conclusions concerning diversification based solely on constant correlations across markets can be misleading, since the diversification benefits are time-varying, are affected by non-normality, and depend on the benchmark (country) employed. Finally, tradeoffs do exist between standard deviation and the other risk factors.     

资本市场开放与股权资本成本——基于沪港通、深港通的实证研究

本文基于沪港通和深港通研究资本市场开放对中国内地股权资本成本的影响。研究发现,受政策风险和市场环境等因素所限,沪港通在初始阶段并未对沪市公司的股权资本成本产生显著影响,但随着政策进一步完善、市场逐渐稳定和交易不断活跃,其对股权资本成本的降低效果于实施两年后开始显现;深港通建立在沪港通的制度基础和运行经验上,其在开通后显著降低了标的公司的股权资本成本。本文还进一步分析了资本市场开放影响股权资本成本的竞争渠道和信息渠道,发现深港通对股权资本成本的降低作用主要集中在投资者竞争程度较高,或是公开信息质量较高、信息不对称程度较低的股票样本。