Search

We study the impact of dependence uncertainty on the expectation of the product of $d$ random variables, $\mathbb{E}(X_1X_2\cdots X_d)$ when $X_i \sim F_i$ for all~$i$. Under some conditions on the $F_i$, explicit sharp bounds are obtained and a numerical method is provided to approximate them for arbitrary choices of the $F_i$. The results are applied to assess the impact of dependence uncertainty on coskewness. In this regard, we introduce a novel notion of "standardized rank coskewness," which is invariant under strictly increasing transformations and takes values in $[-1,\ 1]$.

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.

This study investigates whether contagion occurred during the recent global financial crisis across European and US financial markets. The methodologies used to test for contagion are based on changes in correlation, coskewness, cokurtosis and covolatility. These tests are applied to a set of bank sector CDS, insurance sector CDS, sovereign bonds, equity and volatility indices. The findings indicate significant evidence of contagion, especially through the channels of higher order moments.

We reexamine the role of systematic skewness in asset pricing. We begin by replicating Harvey and Siddique (2000) for the extended period of July 1926 to December 2019. Their coskewness measure provides mixed results in pricing the cross-section of U.S. stocks, suggesting the need for less noisy measures. We explore the persistent systematic skewness (PSS) measure of Langlois (2020) and a modified measure (mPSS) that we construct by conditioning only on market data. These measures are better at capturing coskewness and appear to be priced in the data, highlighting the importance of proper measures of systematic skewness.

Financial integration is East Asia and the ASEAN nations is investigated using a new approach based on entropy theory. An important advantage of the proposed framework is that it takes into account changes in integration arising from higher order moments including coskewness and cokurtosis as well as more traditional measures based on second order moments. The analysis focusses on the role of the U.S. in understanding changes in global integration over time, as well as changes in regional integration arising from China. Using daily stock returns from 1997 to 2016, the empirical results show an overall trend to improvements in financial integration over time with deviations from the trend occurring during periods of financial crises in Asia in 1997–98, the U.S. in 2007–10 and the recent European debt crisis. The influence of the Chinese economy mainly through its trading linkages is found to be an important determinant of financial integration over time both regionally as well as globally.

In this paper, we derive higher-moment liquidity risks theoretically and examine whether they are empirically priced. We discover that when investors add trading cost to the utility function, the expected return of a stock should contain premia related to three higher-moment liquidity risks. We show that one of our higher-moment liquidity risks, or liquidity coskewness risk, measures an individual stock's marginal contribution to the skewness of portfolio liquidity and is consistently priced. In addition, our analysis of the Hansen-Jagannathan distance and the maximum Sharpe ratio show that the liquidity coskewness risk plays a substantial role in asset pricing and portfolio management.

This paper uses tests drawn from the literature on financial market contagion measured by changes in higher-order comoments to establish the patterns in the interdependence between equity markets in Shanghai and Shenzhen with Hong Kong as mainland China liberalized their capital market. On the announcement of the opening of the Shanghai market correlations rise, but subside by the launch. Following the launch changes in coskewness, cokurtosis and covolatility emerge. The liberalization process is complete by mid-September 2016.

When using daily mutual fund returns to study the market timing, heavy tails and heteroscedasticity significantly challenge the existing methods. We to accommodate them, we propose a new measure and an efficient test for market timing ability and find that the traditional test misclassifies about 50% of funds. Excluding funds withvzero timing ability, we find that that higher timing ability is associated with lower stock picking skill, this conclusion is robust to different benchmark models. Examining theholding characteristics of the funds with different levels of timing ability, we find that funds with a positive timing ability hold stocks with lower trading frictions.

We examine whether the renminbi (RMB) is a safe-haven currency in terms of its effectiveness in hedging financial stress for global equity investors. The coskewness of the RMB (the covariance between the RMB premium and equity volatility) is mostly negative, implying that the RMB is not a good hedge in times of market volatility. Moreover, the positive cokurtosis of the RMB (the covariance between the RMB premium and equity skewness) implies that the RMB is unable to hedge against stock market crashes. Neither the coskewness nor the cokurtosis of the RMB is priced, suggesting that equity investors with skewness and kurtosis preferences would not use the RMB to hedge against financial stress. Therefore, the RMB is not yet a safe-haven currency.

We report the results of regressing the Sharpe ratios of 72 cryptocurrencies on first, second and third co-moments of their returns. Our general aim is to examine the risk-return trade-off characteristics of cryptocurrencies. In other words, to determine whether the returns of cryptocurrencies justify their huge volatility especially with regard to the higher moment components of their systemic risk? We find that adjusted Sharpe ratios of the cryptocurrencies and traditional indexes do not differ significantly in this respect.

The paper develops a novel econometric approach to estimate abnormal returns and systematic risk of private equity investments from observable investment cash flows. A unique feature of the method is that it gives closed-form estimators for systematic risk and abnormal returns. In addition, unlike previous studies that derive estimates based on the standard CAPM, the method employs a generalized CAPM that is based on the equilibrium model of Rubinstein (1976).This generalized CAPM accurately takes into account that private equity returns typically deviate from a normal distribution. The methodology is validated using numerical examples and is applied to a unique and comprehensive sample of 12,565 (7,732 venture capital and 4,833 buyout) fully realized portfolio company investments by private equity funds. The outperformance of venture capital investments documented is lower than found in previous studies that estimate a standard CAPM, which is consistent with the theory that investors require an additional premium for the negative coskewness reported for the sample investments. In contrast, we find a similar outperformance and systematic risk of buyout investments than previously documented, which is in line with the observation that the sample buyout investments do not exhibit significant coskewness. In addition, the results highlight that the log-utility CAPM, which provides estimates that are consistent with the standard PME, typically overstates the alpha from large beta assets, like venture capital investments, whereas it provides a good approximation for assets that have betas relatively close to one, like buyout investments.

There is ample evidence that stock returns exhibit non-normal distributions with high skewness and excess kurtosis. Experimental evidence has shown that investors like positive skewness, dislike extreme losses and show high levels of prudence. This has motivated the introduction of the four-moment capital asset pricing model (CAPM). This extension, however, has not been able to successfully explain average returns. Our paper argues that a number of pitfalls may have contributed to the weak and conflicting empirical results found in the literature. We investigate whether conditional models, whether models that use individual stocks rather than portfolios and whether models that extend both the moment and factor dimension can improve on more traditional static, portfolio-based, mean–variance models. More importantly, we find that the use of a scaled coskewness measure in cross-section regression is likely to be spurious because of the possibility for the market skewness to be close to zero, at least for some periods. We provide a simple solution to this problem.

We develop a strategy for testing endogenously contagion within banking sector, stock market indices and Credit Default Swap Spreads. We present evidence of strong contagion in several cases and markets. Contagion seems to be widespread during the Global Financial Crisis and the recent European Sovereign Debt Crisis. Our results are important for a better understanding of contagion and the development of macroprudential tools for financial stability surveillance.

This study investigates contagion among securitized real estate and general equity indices of the U.K., France, Germany, the U.S., Hong Kong and Japan, after the Brexit referendum in June 2016. We combine the case-resampling bootstrap method with the coskewness and cokurtosis test, and apply a new approach by taking the interquartile mean as the estimator. The interquartile mean has advantages over both mean and median that it is insensitive to outliers and is a distinct parameter based on a large number of observations from the dataset. The case-resampling bootstrap method shows less significant evidence of contagion than the normal methods do. If we take the interquartile mean as the estimator, the effect of contagion is further diminished when compared with the method of taking the median as the estimator. Moreover, the effect of contagion is larger on the western economies than on the Asian economies, and there is more significant evidence of contagion on the general equity markets than on the securitized real estate markets. This has an important implication to investors that they should diversify their portfolio to reduce risk.

The ability of mutual fund managers to time coskewness successfully can help them manage their portfolio’s exposure to potential losses and improve their fund’s performance. This study assesses whether mutual fund managers are able to manage the market exposure of their investment portfolios given a change in coskewness. We demonstrate that fund managers investing in Small Blend and Small Growth stocks possess the ability to time coskewness. On average, the fund managers of these two investment objectives increase the market exposures of their portfolios about 2.749 % and 1.340 %, respectively, based on their anticipations on future coskewness. Superiority is driven from the fact that the fund managers in small capitalization stocks are successfully able to manage the tail risk of their funds’ portfolios. The fund-by-fund results confirm that the number of individual funds succeeding in timing market skewness of the Small Blend and Small Growth investment objectives is larger than the remaining types. The main findings are robust when controlling for other types of timing ability, the periods of financial turbulence, and the construction of coskewness.

Consistent with flight-to-quality, the coskewness between developed market sovereign bonds and global equity markets can help explain bond returns. A coskewness factor, defined as the return difference between the most negative coskewness bond portfolio and the most positive coskewness bond portfolio, carries a statistically significant unit price of risk of 43.8 basis points per month. Decreases in coskewness are also significantly associated with declines in bond yields. Coskewness declines during recessions when interest rates become low. Moreover, countries with a monetary policy regime which explicitly targets monetary aggregates have lower coskewness.

Many asset pricing studies assume that a stock's coskewness or idiosyncratic skewness is priced because of the characteristic's influence on portfolio skewness. From empirical returns, we show that the number of stocks in a portfolio is the most important determinant of portfolio skewness, while component stocks' coskewness or idiosyncratic skewness has marginal effects. This result indicates that individual stock skewness does not well represent portfolio skewness.

Because levered equity is an option on the firm, variations in asset idiosyncratic risk (ivol) induces a negative relationship between equity ivol and expected returns. We show that the effect is caused by the nonlinear payoff of equity and the law of one price, and is present in all but risk-neutral economies. We test the cross-sectional predictions of our theory by contrasting the ivol-return relationship at the equity and asset levels. The ivol-return relationship is stronger for equity than for assets, and stronger for more levered firms — consistent with the theory. We test also the timeseries implications of the theory. Time variation in asset ivol causes time variation in the option value of equity that translates into time varying risk factor loadings. Unconditional alpha subsequently becomes biased when asset ivol correlates with the market price of risk. We show empirically that a conditional CAPM that accounts for time variation in equity nonlinearity helps explain earlier findings that high-minuslow ivol-portfolios generate negative unconditional alpha.

We provide a new methodology to empirically investigate the respective roles of systematic and idiosyncratic skewness in explaining expected stock returns. Using a large number of predictors, we forecast the cross-sectional ranks of systematic and idiosyncratic skewness which are easier to predict than their actual values. Compared to other measures of ex ante systematic skewness, our forecasts create a significant spread in ex post systematic skewness. A predicted systematic skewness risk factor carries a significant risk premium that ranges from 7% to 12% per year and is robust to the inclusion of downside beta, size, value, momentum, profitability, and investment factors. In contrast to systematic skewness, the role of idiosyncratic skewness in pricing stocks is less robust. Finally, we document how the determinants of systematic and idiosyncratic skewness differ.

There exists extant evidence which shows risk-return trade-offs within stock markets cannot be rationalized by assumptions of global risk aversion. The extent to which dearth of global risk aversion is evidence of transitions between risk averse and risk seeking preferences, or interactions between risk averse and risk seeking preferences remains, however, a matter of conjecture. This note demonstrates application of the single crossing property to risk premiums that are output of one-factor and two-factor Capital Asset Pricing Models (CAPMs) enables inferences as to presence or absence within stock markets of agents characterized primarily by risk seeking preferences. The framework proposed not only allows for qualitative inferences, but enables parameterization of effects of risk seeking agents on risk premiums which obtain within stock markets.

A general procedure is proposed to identify changes in asset return interdependence over time using entropy theory. The approach provides a decomposition of interdependence in terms of comoments including coskewness, cokurtosis and covolatility as well as more traditional measures based on second order moments such as correlations. A new diagnostic test of independence is also developed which incorporates these higher order comoments. The properties of the entropy interdependence measure are demonstrated using a number of simulation experiments, as well as applying the methodology to euro zone equity markets over the period 1990 to 2017.

In this study, we investigate the mutual fund managers’ ability to time market coskewness. Analyzing nine investment styles of US equity fund, we find strong evidence to support that between 1973 and 2018, mutual fund managers investing in Small-Blend and Small-Growth schemes demonstrate the ability to time the market coskewness. On average fund managers of the Small-Blend and Small-Growth fund increase their portfolio beta by about 2.79%, and 1.34% based on their expectation of market coskewnewss, respectively.

The coskewness–cokurtosis pricing model is equivalent to absence of any positive-alpha return for which the residual risk has positive coskewness and negative cokurtosis with the market. This parallels the CAPM and also the fundamental theorem of asset pricing.

This study examines contagion across equity and securitized real estate markets of Hong Kong, US and UK during the global financial crisis by the Forbes–Rigobon, coskewness and cokurtosis tests. In particular, this is the first study to use the cokurtosis test to examine contagion between real estate and equity markets. The results show that the cokurtosis test can detect additional channels of contagion, and hence is a more powerful test. In contrary to Fry et al. (2010), we find that the cokurtosis test shows a highly significant evidence of contagion between the equity and real estate markets in both directions. In particular, the contagion between US’s equity and real estate markets is the most significant. This reflects that US is the centre of shock of the global financial crisis.

In this paper we evaluate the intertemporal pricing performance of stock return determinants over the periods surrounding, and outside of, financial crises. The analysis focuses on the variables of size, book-to-market ratio, momentum, liquidity, and higher-order systematic co-moments. The evidence reveals that over non-crisis periods the market beta plays an important role in determining the cross-section of stock returns. Size, value, momentum, and liquidity also exhibit associations with the cross-section of stock returns. However, over crisis periods most of the variables we examined lose their explanatory power, suggesting that their usefulness is limited for investment purposes when financial markets experience crises. There is some evidence of coskewness pricing surrounding market crashes. Practitioners may consider coskewness over crisis periods.

In this paper, we show that augmenting the consumption CAPM with sentiment, and thus allowing for systematic investor error in forming beliefs, helps reconcile investors’ optimizing behaviour with the cross-section of average stock returns. The fit of specifications that do not include sentiment-related factors, instead, crucially hinges on parameters estimates that are inconsistent with standard risk aversion assumptions, as formulated for example by Kimball (1993). This implies that investors must either commit systematic errors, at least ex-post, in assessing the joint distribution of stock returns and aggregate consumption or they must behave in a way that, at the aggregate level, is inconsistent with expected utility maximization under Kimball’s (1993) standard risk aversion.

Despite the fact that it is easy to see intuitively why skewness and coskewness should matter for asset pricing, it is difficult to build a model that links analytically skewness premia to deep structural parameters governing preferences and the distribution of shocks. This paper takes up the challenge and studies the effect of skewness and coskewness on asset valuation. To reach this important goal, asset returns skewness is modeled with promising Azzalini’s [1985. Scandinavian Journal of Statistics 12, 171–178] skew-normal distribution. With this assumption, we are now able to derive explicit expressions of assets skewness premiums and to shed a new light on asset valuation.

A moment method for the three parameter multivariate asymmetric Laplace distribution is considered. It is based on the star product of both the coskewness and cokurtosis tensors. It improves on an earlier moment method by Visk (2009) and shows that the covariance matrix of this multivariate distribution is functionally dependent upon coskewness and cokurtosis.

Superior to the variance, "swap variance (SwV)" summarizes the entire probability distribution of returns and is unbiased to distributional asymmetry. Retaining the same simplicity as mean-variance (MV) model, the efficiency of mean-swap variance (MSwV) is necessary and sufficient conditions for that of stochastic dominance. The SwV is composed of a quadratic volatility and a proxy of asymmetric variation (A). The mean-variance-asymmetry (MVA) analysis, a three-dimensional extension of the classical MV portfolio theory and the CAPM, is consistent with expected utility maximization for all risk-averse investors and those who are downside loss-averse but prefer the prospect of potential upside gains.

Joint tests of contagion are derived which are designed to have power where contagion operates simultaneously through coskewness, cokurtosis and covolatility. Finite sample properties of the new tests are evaluated and compared with existing tests of contagion that focus on a single channel. Applying the tests to daily Eurozone equity returns from 2005 to 2014 shows that contagion operates through higher order moment channels during the GFC and the European debt crisis, which are not necessarily detected by traditional tests based on correlations.

Intuition suggests that constraint investment strategies will result in losses due to a limited portfolio allocation. Two types of constrained assets have been particularly growing over the last few decades: Islamic Mutual Funds and Socially Responsible Mutual Funds. Although research regarding the performance of these types of constrained investments has been performed, little attention has been given to their relative performance. In this paper we assess, and rank, the relative performance of Islamic, Socially Responsible, and conventional mutual funds from 11 Islamic markets and the United States by expanding the traditional mean-variance frontier to account for higher moments; constrained assets tend to be smaller and skewed in nature, thus violating the normality assumption under the mean-variance frontier. We find that controlling for skewness risk, by using an unconditional coskewness measure, has the power to improve asset pricing tests by expanding the mean-variance frontier specification. We find supporting evidence suggesting that Islamic mutual funds perform better than Socially Responsible Investing, which in turn outperform conventional mutual funds.

Full Paper is available at: https://ssrn.com/abstract=2839781 In the supplementary appendix to the paper Boudt, Cornilly, and Verdonck (2018) we discuss the impact of autocorrelation and a time-varying structure on the estima- tion of coskewness matrices and provide more explanation about structured estima- tion. We go into more detail about our approach of optimizing the targets and provide several examples of other coskewness matrices in the literature. In particular, we pro- vide guidance how to use the latent single-factor coskewness matrix of Simaan (1993) in a shrinkage setting and correct the estimators provided in Martellini and Ziemann (2010) to estimate C(Φ ,T) for their observed single-factor and constant correlation coskewness estimators. The simulation setting discussed in the main paper is explored into more detail and we study three additional data generating processes. Further- more, we provide details on the empirical application studied in the main paper and extend the empirical study of Martellini and Ziemann (2010). Finally, we introduce the R code, publicly available in the PerformanceAnalytics package of Peterson and Carl (2018), for all single- and multi-target shrinkage estimators.

This study investigates the role of higher co-moments in explaining stock returns in the China and UK stock markets. In China, investors price only coskewness risk, while UK investors price both coskewness and cokurtosis risks. China investors use a two-year window period to evaluate coskewness risk, while UK investors utilize a five-year window period to evaluate. In addition, the significant coskewness risk premium in China is driven mainly by the sub-period after the split share structure reform. We argue that differences in market infrastructure and stage of development contribute to explaining the different higher co-moments pricing behavior in the two markets.

This study examines the asset pricing implications of preferences over the higher moments of returns’ distributions. We show that in a market populated by risk-averse, prudent and temperate investors, firms whose returns exhibit negative coskewness or positive cokurtosis should yield higher premia relative to counterpart firms with positive coskewness and negative cokurtosis respectively. These theoretical predictions are empirically tested using a comprehensive dataset of shares listed on the London Stock Exchange during the period 1986–2008. Our empirical results confirm that coskewness and cokurtosis premia are genuinely priced in the UK market, over and above what covariance risk, size, value and momentum factors can explain. We also show that a theoretically motivated, higher co-moment asset pricing model has significant explanatory ability over the cross-section of coskewness and cokurtosis portfolio returns.

This paper derives a liquidity-adjusted conditional two-moment capital asset pricing model (CAPM) and a liquidity-adjusted conditional three-moment CAPM respectively based on theory of stochastic discount factor. The liquidity-adjusted conditional two-moment CAPM shows that a security's conditional expected excess return consists of three parts: its conditional expected liquidity cost, the systemic risk premium and the liquidity risk premium. The liquidity-adjusted conditional three-moment CAPM shows that a security's conditional expected excess return depends on its conditional expected liquidity cost, the conditional covariance between its return and the market return, the conditional covariance between its liquidity cost and the market liquidity cost, and the conditional coskewness of its return and the market return.

I use Stochastic Discount Factors to examine the sources of the idiosyncratic volatility premium. I find that non-zero risk aversion and firms’ non-systematic coskewness determine the premium on idiosyncratic volatility risk. The firm’s non-systematic coskewness measures the comovement of the asset’s volatility with the market return. When I control for the non-systematic coskewness factor, I find no significant relation between idiosyncratic volatility and stock expected returns. My results are robust across different sample periods and firm characteristics.

This paper develops exact distribution-free tests of unconditional mean-variance efficiency. These new tests allow for unknown forms of non-normalities, conditional heteroskedasticity, and other non-linear temporal dependencies among the absolute values of the error terms in the asset pricing model. Exactness here rests on the assumption that the joint temporal error density is symmetric around zero. This still leaves open the possibility of return distribution asymmetry via coskewness with the benchmark portfolio. A simulation study shows that the new tests have very good power relative to that of many commonly used tests. The inference procedures developed are further illustrated by tests of the mean-variance efficiency of a market index using a 42-year sample of monthly returns on ten U.S. equity portfolios.

The coskewness matrix is a (p)x(p^2) parameter matrix useful for studying the third-order interactions between variables and computing the skewness of linear combinations of variables. The classical sample estimator of the coskewness matrix performs poorly in terms of mean squared error (MSE) when the sample size is small, even in moderate dimensions. A possible approach to improve estimation is to use shrinkage estimators that offer a compromise between the (unbiased) sample coskewness matrix and a (possibly biased) target matrix (with lower estimation variance) with the aim of minimizing the MSE. We improve upon the existing literature by proposing unbiased estimators, using multivariate k-statistics and polykays, for the MSE loss function and by including the possibility of having multiple target matrices. Simulations show the superiority of our estimators in both the single-target and the multi-target setting for skewed data. Accurate coskewness estimation is highly valued in the field of portfolio optimization (among others) where we show that the out-of-sample skewness of the maximum skewness optimized portfolio is higher when using the proposed shrinkage coskewness matrix estimates.

We explore the empirical usefulness of conditional coskewness to explain the cross-section of equity returns. We find that coskewness is an important determinant of the returns to equity, and that the pricing relationship varies through time. In particular we find that when the conditional market skewness is positive investors are willing to sacrifice 7.87% annually per unit of gamma (a standardized measure of coskewness risk) while they only demand a premium of 1.80% when the market is negatively skewed. A similar picture emerges from the coskewness factor of Harvey and Siddique (Harvey, C., Siddique, A., 2000a. Conditional skewness in asset pricing models tests. Journal of Finance 65, 1263–1295.) (a portfolio that is long stocks with small coskewness with the market and short high coskewness stocks) which earns 5.00% annually when the market is positively skewed but only 2.81% when the market is negatively skewed. The conditional two-moment CAPM and a conditional Fama and French (Fama, E., French, K., 1992. The cross-section of expected returns. Journal of Finance 47,427465.) three-factor model are rejected, but a model which includes coskewness is not rejected by the data. The model also passes a structural break test which many existing asset pricing models fail.

We consider the robustness of the least-squares inference of linear asset pricing models. We evaluate the asymptotic covariance matrices of the least-squares estimator of alphas and betas when the joint distribution of factors and error terms is independently and identically distributed without making any specific distributional assumptions. When the standard assumption of conditional homoskedasticity for the conditional covariance matrix of error terms given factors does not hold, we show the asymptotic covariance matrix for betas depends only on cokurtosis of factors and error terms while the asymptotic covariance matrix for alphas depends on cokurtosis as well as coskewness of factors and error terms. This implies the inference of betas is not affected by skewness of the underlying joint distribution. Numerical examples are provided using Fama and French's benchmark portfolio returns and factors.

We measure risk preferences for decisions that involve more than a single monetary attribute. According to theory, the multivariate risk preferences correlation aversion, cross-prudence (coskewness preference) and cross-temperance (cokurtosis aversion) determine how univariate risk preferences over attributes co-vary and interact. We obtain model-free measurements of these multivariate risk preferences in three economic domains, viz., time preferences, social preferences, and preferences over waiting time. This first systematic empirical exploration of multivariate risk preferences provides evidence for assumptions made in economic models on inequality, labor, time preferences, saving, and insurance.

This research adds cokurtosis risk factor as a new factor into Moreno and Rodriguez (2009) five-factor model to be six-factor model to evaluate the equity mutual fund performance both unconditionally and conditionally, and between up and down market of three selected countries in Asia - China, Singapore, and Thailand as representatives of fast growing Asian countries. The result shows some empirical evidence for the difference in the performance of mutual funds between the positive excess market return period and negative excess market return period. The higher moment six factor model fits better and shows more explanation power in negative excess return market period. The predetermined public information variables used in conditional model do not help explain the equity mutual fund return in these countries. The bootstrap technique shows that many of the significance alphas that are shown in least square method are from sampling variability.

This research adds cokurtosis risk factor as a new factor into Moreno and Rodriguez (2009) five-factor model to be six-factor model to evaluate the equity mutual fund performance of three selected countries in Asia — China, Singapore, and Thailand as representatives of fast growing Asian countries. To my knowledge, this is the first research to incorporate both coskewness and cokurtosis risk factors into Carhart (1997) four-factor model, to become a six-factor model, to explain the equity mutual fund returns. The result shows that coskewness and cokurtosis risk factors show some significance in some countries in Asia. Adding coskewness and cokurtosis risk factors in both CAPM and four-factor model, show some increment in the explanatory power of the models.

Mutual funds seek alpha, but residual coskewness is also an important performance attribute. Alpha and residual coskewness relative to the market are negatively correlated in theory, so funds may generate undesirable residual coskewness in the pursuit of alpha. Empirically, the trade-off exists for mutual funds and is driven by both fund composition and actions of managers. Sorting funds by proxies for active management generates positive alpha, but also undesirable coskewness. Investment styles also carry skewness consequences, but only partially explain the trade-off in funds. A minority of funds overcome the trade-off. Thus, seeking alpha generally comes at a skewness cost.

Ang, Chen and Xing have shown in "Downside Risk" that stocks that covary strongly with the market during market declines have high average returns. The reward for bearing downside risk is not simply compensation for regular market beta, nor is it explained by coskewness or liquidity risk, or by size, value, and momentum characteristics. The downside beta premium is not for free. The drawdown is considerable amplified in times of market troubles. This working paper combines the results of Ang, Chen and Xing with a signal based approach developed in a previous working-paper. The implied-volatility-term-structure (IVTS) classifies market regimes. One invests only in the favorable regime fully into stocks with high downside beta. Due to this classification the downside beta premium is (almost) a free lunch.

The coskewness-cokurtosis pricing model is equivalent to there not being any return for which the alpha is positive and for which the residual risk has positive coskewness and negative cokurtosis with the market. Such returns would be extremely attractive to investors with mean-variance-skewness-kurtosis preferences who hold the market portfolio. This result establishes a parallel to the CAPM, which is equivalent to the absence of positive alpha returns. It also establishes a parallel to the fundamental theorem of asset pricing, because it relates absence of portfolios with unusually good costs/payoffs to the existence of a stochastic discount factor of a particular type.

We investigate the dynamic and asymmetric dependence structure between equity portfolios from the US and UK. We demonstrate the statistical significance of dynamic asymmetric copula models in modelling and forecasting market risk. First, we construct "high-minus-low" equity portfolios sorted on beta, coskewness, and cokurtosis. We find substantial evidence of dynamic and asymmetric dependence between characteristic-sorted portfolios. Second, we consider a dynamic asymmetric copula model by combining the generalized hyperbolic skewed t copula with the generalized autoregressive score (GAS) model to capture both the multivariate non-normality and the dynamic and asymmetric dependence between equity portfolios. We demonstrate its usefulness by evaluating the forecasting performance of Value-at-Risk and Expected Shortfall for the high-minus-low portfolios. From backtesting, we find consistent and robust evidence that our dynamic asymmetric copula model provides the most accurate forecasts, indicating the importance of incorporating the dynamic and asymmetric dependence structure in risk management.

This paper examines the empirical performance of a global conditional three-moment CAPM. We employ monthly Finnish stock market data for 1987–1995. To explore the robustness of the three-moment model, we also examine whether local equity market returns, exchange rate fluctuations and movements in overall stock market turnover come into play after accounting for global market portfolio risk exposures. Our findings indicate that these additional factors are not generally able to detect deviations from the three-moment CAPM and time-varying global coskewness affects the cross-section of expected returns on local size portfolios even after accounting for other factors.

I derive an equilibrium asset pricing model incorporating both systematic and idiosyncratic return asymmetries, and show their respective impact on expected returns. With systematic return asymmetry, investors allocate their wealth between the risk-free security, the market portfolio, and a factor which overweights assets with high systematic asymmetry. Investors who prefer positive asymmetry remain underdiversified from a mean-variance perspective to preserve skewness in their portfolio, and idiosyncratic asymmetry therefore is priced in equilibrium. I find that a systematic asymmetry factor and a factor capturing idiosyncratic asymmetry help explain the cross-sectional variation of expected returns across U.S. equities, international equity markets, government bonds, currencies, and commodities. My results offer a risk-based explanation of expected returns that contributes to our understanding of asset pricing across multiple markets.

This paper focuses on portfolio selection with a systematic skewness constraint within the mean-variance framework. We derive the composition of efficient portfolios in our model, and analyze the properties of these efficient portfolios. We show that the required systematic skewness is achieved at the expense of mean-variance efficiency, and find that the more stringent the constraint, the greater the loss in efficiency. Our numerical analysis indicates that the systematic skewness constraint helps enhance the skewness of efficient portfolios over the skewness of traditional efficient portfolios. In addition, investors with a greater skewness preference impose a more stringent coskewness constraint, and at the same time are willing to accept a higher risk. Finally, we establish the relationship between our model and the three-moment asset pricing model, and analyze the determinants of market prices of systematic variance and skewness implied by our model.