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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.

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.

This study examines contagion across general equity and securitized real estate markets of China, Hong Kong and the US during the Chinese financial crisis. This is the first study to combine the case-resampling bootstrap method with the coskewness and cokurtosis test. Thus the new method works well on data with a non-normal distribution or non-constant variance. Additional channels of contagion may also be detected to reflect a more precise pattern of contagion. In contrast to Hatemi-J and Hacker, Applied Financial Economics Letters, 1(6), 343-347 (2005)‘s result, we find that the case-resampling bootstrap method diminishes the overall effect of contagion. In particular, no additional channels of contagion can be found when the case-resampling bootstrap method is applied on the coskewness test, but when the case-resampling bootstrap method is applied on the cokurtosis test, additional channels of contagion are detected. Furthermore, the overall effect of contagion is greater on the general equity markets than on the securitized real estate markets. This study has useful implications to investors, regulators and policy makers.

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.

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.

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.

This study presents an improved model for estimating life insurer cost of capital with the inclusion of upside and downside risk factors and controlling for life insurer characteristics. Although various asymmetric measures of market risk have been shown to be priced factors for the broader equity market, life insurer realized equity returns include a much larger premium for bearing downside risk, even after controlling for firm characteristics and other measures of risk. Cross-sectional regression analysis finds a positive (negative) premium for downside (upside) betas, conditional on down and up markets, respectively. Coskewness and cokurtosis are also priced factors.

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.

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.

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.

This paper aims to investigate the contagion across European securitised real estate markets during the European sovereign debt crisis by the Forbes–Rigobon test, the coskewness test and the cokurtosis test. The new cokurtosis test is constructed by extending the method of constructing the coskewness test to further higher order moments. The results reveal that the cokurtosis test can show additional channels of contagion of which the other tests fail to show, and hence can provide more information on the direction of contagion, and reflect a more complete picture of the contagion pattern. This study has implications to investors and policy-makers. During a crisis, investors should reallocate their portfolio to reduce their loss. Policy-makers should cooperate with other authorities and act accordingly in order to stabilise the economy.

Javier Estrada has argued that differences attributable to the bifurcation of beta on either side of mean returns, at least in emerging markets, are too substantial to ignore.1 We should likewise expect to find considerable differences in financial performance arising from the deployment of a four-moment CAPM, the proper specification of this augmented CAPM according to cross moments, and the bifurcation of coskewness and cokurtosis along the upside and downside of mean 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 derive pricing kernels in which the market volatility is endogenously determined. Using the Taylor expansion series of the representative investor's marginal utility, I show that the price of market volatility risk is restricted by the investor's risk aversion and skewness preference. The risk aversion is estimated to be between two and five and is significant. The price of the market volatility is negative. Consistent with economic theory, I find that the pricing kernel decreases in the market index return and increases in market volatility. The projection of the estimated pricing kernel onto a polynomial function of the market return produces puzzling behaviors, which can be observed in the pricing kernel and absolute risk aversion functions. The inclusion of additional terms in the Taylor expansion series of the investor's marginal utility produces a pricing kernel function of market stochastic volatility, stochastic skewness, and stochastic kurtosis. The prices of risk of these moments are restricted by the investor's risk aversion, skewness preference, and kurtosis preference. The prices of risk of these moments should not be confused with the price of risk of powers of the market return, such as coskewness and cokurtosis. This paper was accepted by Wei Xiong, finance.

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 examines whether additional risk factors such as the variance, skewness, and coskewness of returns offer an appropriate explanation of company returns in less developed capital markets. Arguments for considering some additional factors in pricing models to better deal with such situations are presented. Using individual company returns from a range of developing Asian capital markets, empirical tests examine the importance of these extra risk factors. Results indicate that both individually and when in combination, variance and coskewness are significantly related to returns in these markets. Skewness is less consistently important. Robustness tests confirm that these measures tend not to capture size or book to market factors.

A new class of tests of contagion is proposed identifying transmission channels of financial market crises through changes in higher order moments of the distribution of returns such as coskewness. Applying the framework to test for contagion in real estate and equity markets following the Hong Kong crisis in 1997–1998 and the U.S. subprime crisis in 2007 shows that the coskewness-based tests of contagion detect additional channels not identified by the correlation-based tests. Implications of contagion in pricing exchange options where there is a change in higher order comoments of returns on the underlying assets are also investigated.

We develop a one-period model of investor asset holdings where investors have heterogeneous preference for skewness. Introducing heterogeneous preference for skewness allows the model's investors, in equilibrium, to underdiversify. We find suppport for our model's three key implications using a dataset of 60,000 individual investor accounts. First, we document that the portfolio returns of underdiversified investors are substantially more positively skewed than those of diversified investors. Second, we show that the apparent mean-variance inefficiency of underdiversified investors can be largely explained by the fact that investors sacrifice mean-variance efficiency for higher skewness exposure. Furthermore, contrary to the asset-pricing predictions of models that incorporate return skewness in the context of full diversification, we show that idiosyncratic skewness, and not just coskewness, can impact equilibrium prices. Third, the underdiversification of investors does not appear to be coincidentally related to skewness. Stocks most often selected by underdiversified investors have substantially higher average skewness -- especially idiosyncratic skewness -- than stocks most often selected by diversified investors.

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.

This article shows how the market coskewness model of Rubinstein (1973) and Kraus and Litzenberger (1976) is altered when a nonredundant call option is optimally traded. Owing to the option's nonredundancy, the economy's stochastic discount factor (SDF) depends not only on the market return and the square of the market return but also on the option return, the square of the option return, and the product of the market and option returns. This leads to an asset pricing model in which the expected return on any risky asset depends explicitly on the asset's coskewness with option returns. The empirical results show that the option coskewness model outperforms several competing benchmark models. Furthermore, option coskewness captures some of the same risks as the Fama--French factors small minus big (SMB) and high minus low (HML). These results suggest that the factors that drive the pricing of nonredundant options are also important for pricing risky equities.(JEL G11, G12, D61) Copyright 2006, Oxford University Press.

In this article we investigate portfolio coskewness using a quadratic market model as a return-generating process. We show that the portfolios of small (large) firms have negative (positive) coskewness with the market. We test an asset pricing model including coskewness by checking the validity of the restrictions that it imposes on the return-generating process. We find evidence of an additional component in expected excess returns, which is not explained by either covariance or coskewness with the market. However, this unexplained component is homogeneous across portfolios in our sample and modest in magnitude. Finally, we investigate the implications of erroneously neglecting coskewness for testing asset pricing models, with particular attention to the empirically detected explanatory power of firm size.

In this paper we examine the variables that explain the cross-section of UK stock returns. Previous studies have found that the CAPM beta has moderate or even insignificant explanatory power once the Fama French factors are included. However, we control for different realised risk premia in up and down markets by using the same methodology as Pettengill, Sundaram and Mathur (1995). Unlike previous work, we find that beta is highly significant in explaining the cross-section of UK stock returns and more importantly remains significant even when the Fama French factors are included in the cross-sectional regressions. We also investigate whether higher co-moments (co-skewness and co-kurtosis) have any explanatory power but find that empirical support is weaker.

This paper is an empirical study of asset pricing with the systematic skewness in the pricing model. We adopt the Fama-French three-factor model, which incorporates the firm-size and book-to-market ratio in asset pricing as the base case, and then includes the skewness factor used by Harvey and Siddique in the pricing model. The evidence shows that systematic skewness is significant and might be important in asset pricing when portfolios are formed by industry, firm-size, book-to-market, or momentum strategies. When portfolios are constructed by momentum or coskewness strategies, lower momentum, or lower coskewness portfolios exhibit higher skewness and higher kurtosis. When portfolios are grouped by excess returns, it is seen that the average excess return is positively correlated with size and coskewness. Thus the systematic skewness is closely related to firm size. And the relationship between systematic skewness and excess return is obscured by the reverse firm-size effect.

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.

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 applies the methodology of Lambert and Hübner (2009) for creating fundamental risk factors and factor systematic variance, skewness, and kurtosis into returns from March 1989 to June 2008. The coskewness and cokurtosis premiums present significant monthly average returns of respectively 0.2% and 0.4% over the period. First, we show that our set of moment-related premiums consistently price 2 sets of 2x3 covariance/coskewness and of 2x3 covariance/cokurtosis portfolios. The model delivers for all portfolios low levels of specification errors, high levels of R2, and beta loadings consistent with the portfolio rankings. Second, we perform Fama and MacBeth (1973) cross-sectional regressions made of higher-moment market premiums and/or Fama and French (1993) factors on 25 and 100 two-dimensional portfolios sorted on size and bookto- market. Used separately, a four-moment factor model and a four-factor Fama and French (1993) and Carhart (1997) model have been shown to deliver similar model specification errors (alphas) for the size/BTM portfolios. The Four-Moment Asset Pricing Model captures however a higher proportion of the portfolio variability of size/BTM portfolios than an empirical Capital Asset Pricing Model. Finally, our study demonstrates that moment and empirical premiums present complementary significance over the period.

This paper revisits some recently found evidence in the literature on the cross-section of stock returns for a carefully constructed dataset of euro area stocks. First, we confirm recent results for US data and find evidence of a negative cross-sectional relation between extreme positive returns and average returns after controlling for characteristics such as momentum, book-to-market, size, liquidity and short term return reversal. We argue that this is the case because these stocks have lottery-like characteristics, which is attractive to certain investors. Also, these stocks tend to be very volatile so that arbitrageurs are discouraged from correcting potential mispricing. As a consequence, these stocks are often overpriced and hence face lower expected returns. Second, when we control for extreme returns, the recently found negative relationship between idiosyncratic risk and future returns is less robust. In our models, after adding maximum returns, the relationship is insignificant and sometimes even positive. We also find that idiosyncratic skewness and coskewness play an important role for asset pricing, as predicted by several theoretical models.

The aim of this paper is to investigate the contagion across real estate markets of four countries: Hong Kong, China, U.S. and U.K., during the financial tsunami in 2008. We use the Forbes-Rigobon test, the coskewness test and the cokurtosis test. We propose a new cokurtosis test constructed by extending the method of constructing the coskewness test to further higher order moments. It can show additional channels of contagion that other tests fail to show, and hence can provide more information on the direction of contagion, and reflect a more complete picture of the contagion pattern. The coskewness and cokurtosis tests show that contagion exists between the four countries, and the contagion effect is stronger between Hong Kong and China, and between U.S. and U.K. This provides clues for investors on how to diversify their investment to reduce their risk. This paper bridges the gap that previous works on contagion across real estate markets give mixed results, and gives a first insight into the contagion pattern of global real estate markets during the financial tsunami. First Publish Online: 2 Oct 2012

This paper examines whether investors receive compensation for holding crash-sensitive stocks. We capture the crash sensitivity of stocks by their lower tail dependence (LTD) with the market based on copulas. We find that stocks with weak LTD serve as a hedge during crises, but, overall, stocks with strong LTD have higher average future returns. This effect cannot be explained by traditional risk factors and is different from the impact of beta, downside beta, coskewness, and cokurtosis. Our findings are consistent with results from the empirical option pricing literature and support the notion that investors are crash-averse.

In an intertemporal equilibrium asset pricing model featuring disappointment aversion and changing macroeconomic uncertainty, we show that besides the market return and market volatility, three disappointment related factors are also priced. They can be interpreted as a disappointment, a market downside, and a volatility downside factor, respectively. We find that stock returns reflect premiums for bearing undesirable exposures to these factors. The signs of estimated risk premiums are consistent with the theoretical predictions. Economic magnitudes suggest that long/short strategies on associated exposures earn more than 5% per annum, and these rewards are not explained by the coskewness, size, value, and momentum factors.

Bond skewness and coskewness (i.e., bond return comovement with market volatility) are both time varying, with cross-sectional variation driven by maturity and credit rating. Other things being equal, longer maturity bonds have lower skewness, and lower coskewness with respect to the bond market index; lower quality bonds have lower skewness, and higher coskewness with respect to the bond market index. Three-moment bond alphas (which account for coskewness effects) are time varying and predictable by market default spread. They are significantly different from, and often are closer to zero than, two-moment alphas (which ignore coskewness effects).

This study explores the impact of systematic risk (beta) and systematic coskewness on EREIT returns. The test uses the Skewness Preference CAPM, which includes the impact of the third moment on ret...

The objective of this study is to investigate turnover information and to test whether this information affects asset returnｓ. We explore the relationship between turnover and price momentum (reversalｓ) for Japanese stocks. In the Japanese stock market, the return reversal effect is known to be stronger than in other developed capital markets and most preceding studies show that price momentum cannot be found in the Japanese stock market. In this study, we investigate the relationship between price momentum and turnover, particularly, conditional upon the level of turnover; we find that high turnover tends to induce momentum in short-term periods. The study also investigates whether the coskewness premium affects price momentum effects, like the findings in previous studies of U.S. data, which demonstrated that coskewness helps explain some of the profitability of momentum-based trading strategies. Our results show that the coskewness of past losers is larger than that of past winners. This indicates that negative coskewness stock has a coskewness premium and that investors require a premium for negative coskewness stocks. Furthermore, the coskewness premium helps enhance price momentum as the turnover level increases and depresses return reversal effects for the highest turnover stock group.

Managed portfolios are subject to tail risks, which can be either index level (systematic) or fund-specific. Examples of fund-specific extreme events include those due to big bets or fraud. This paper studies the two components in relation to compensation structure in managed portfolios. A simple model generates fund-specific tail risk and its asymmetric dependence on the market, and makes predictions for where such risks should be concentrated. The model predicts that systematic tail risks increase with an increased weight on systematic returns in compensation and idiosyncratic tail risks increase with the degree of convexity in contracts. The model predictions are supported with empirical results. Hedge funds are subject to higher idiosyncratic tail risks and Exchange Traded Funds exhibit higher systematic tail risks. In skewness and kurtosis decompositions, I find that coskewness is an important source for fund skewness, but fund kurtosis is driven by cokurtosis, as well as volatility comovement and residual kurtosis, with the importance of these components varying across fund types. Investors are subject to different sources of skewness and fat tail risks through delegated investments. Volatility based tail risk hedging is not effective for all fund styles and types.

I investigate a pricing kernel in which coskewness and the market volatility risk factors are endogenously determined. I show that the price of coskewness and market volatility risk are restricted by investor risk aversion and skewness preference. The risk aversion is estimated to be between two and five and significant. The price of volatility risk ranges from -1.5% to -0.15% per year. Consistent with theory, I find that the pricing kernel is decreasing in the aggregate wealth and increasing in the market volatility. When I project my estimated pricing kernel on a polynomial function of the market return, doing so produces the puzzling behaviors observed in pricing kernel. Using pricing kernels, I examine the sources of the idiosyncratic volatility premium. I find that nonzero risk aversion and firms' non-systematic coskewness determine the premium on idiosyncratic volatility risk. 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, different measures of market volatility and firm characteristics.

Using a very large dataset that spans the period 1996 to 2007 and contains transaction prices for all reported auctions at the Chicago Wine Company, we analyze how the prices of high-end wines have evolved over the last decade. We characterize the returns for different wine categories and show that characteristics like vintage, rating and ranking have an impact not only on the pricing of wines but also on their subsequent returns. The best wines according to these characteristics earn higher returns and tend to have either a lower or a similar variance than less good wines. Nevertheless, the different categories of wines seem to follow a similar trend over the long run. This essentially means that the market for Bordeaux wines is not segmented. To address the issue of diversification, we consider a realistic setting that accounts for covariance between equities and wines and also for coskewness and cokurtosis. We employ a polynomial goal programming model to investigate how investor preferences affect the portfolio allocation and the return distribution. Wine returns are only slightly correlated with other assets and as such they can be used to reduce the risk of an equity portfolio. Wines look even more attractive when the investor also has concerns about the skewness of his portfolio. However, the part to be invested in wines is reduced if we include the kurtosis into the analysis. Finally, it seems advisable to diversify across the range of wine categories as their moves in the short-run are partially independent of each other. First growths and wines rated as extraordinary by Robert Parker deliver the best tradeoff in terms of portfolio expected returns, variance, skewness and kurtosis for most investor preference settings considered.

Equity returns are more dependent in bear markets than in bull markets. Previous studies have argued that a multivariate GARCH model or a regime switching (RS) model based on normal innovations could reproduce this asymmetric extreme dependence. We show analytically that it cannot be the case. We propose an alternative model that allows for tail dependence in lower returns and keeps tail independence for upper returns. This model is applied to international equity and bond markets to investigate their dependence structure. It includes one normal regime in which dependence is symmetric and a second regime characterized by a symmetric dependence. Empirical results show that the dependence between equities and bonds is low even in the same country, while the dependence between international assets of the same type is large in both regimes. The cross-country dependence is especially large in the asymmetric regime. Exchange rate volatility seems to be a factor contributing to asymmetric dependence. With the introduction of a fixed exchange rate the dependence between France and Germany becomes less asymmetric and more normal than before. High exchange rate volatility is associated with a high level of asymmetry. Empirical phenomena such as home bias investment and flight to safety are amplified by asymmetric dependence through coskewness. For a US investor who holds US and Canadian bonds and equities, the share invested in Canada increases with the asymmetric dependence since the Canadian market in our sample is less risky. However, when the adjustment for perceived risk is made to take into account the asymmetric information the result changes and asymmetric dependence increases the home investment. A similar behavior is observed for the bond and equity trade-off. In the asymmetric dependence regime, the very risk-averse agent increases the fraction of its wealth in bonds.

We propose a measure for extreme downside risk (EDR) to investigate whether bearing such a risk is rewarded by higher expected stock returns. Constructing an EDR proxy with the left tail index in the classical generalized extreme value distribution, we document a significantly positive premium on firm-specific EDR in cross-section of stock returns even after controlling for market, size, value, momentum, and liquidity effects. The EDR premium is more prominent among glamour stocks and when high market returns are expected. High-EDR stocks generally have high idiosyncratic risk, large downside beta, lower coskewness and cokurtosis, and high bankruptcy risk. The EDR premium persists after these characteristics are controlled for. EDR is also closely related to firm-specific Value at Risk (VaR) which substantially impacts EDR’s effect on expected stock returns. EDR supplements VaR in predicting stock returns by exhibiting additional explanatory power.

A growing literature shows evidence that supports higher-moment CAPM. We conduct cross-sectional tests of the four-moment CAPM on returns of portfolios formed from combining stocks in international markets and portfolios invested locally in the U.K. and the U.S. We find that coskewness and cokurtosis are significant in explaining the cross-section of returns of beta-gamma-delta sequential sorts, one-way and two-way momentum and size portfolios. Secondly, we investigate whether higher-moment-CAPM nonlinear market models can explain and predict time-series of portfolio returns. We find that non-linear market terms are significant in explaining time-series returns of the winner and smallest size deciles and that the quadratic market model has the smallest prediction error among models.

This study examines the impact of negative skewness to preferences and asset pricing. Furthermore, it shows how intertemporal risk premia can be interpreted as negative skewness. Hence, a new performance measure, the intercept of the Harvey-Siddique two-factor asset pricing model is proposed for prudent, long-term investors. Using this model, the performance of UK unit trusts is examined over the period 1991-2005. Despite exhibiting significantly negative managerial ability, trust managers were successful in reaping part of the coskewness premium, which was, on average, 2.09% p.a.

We investigate more than a dozen of factors formed on firm characteristics and risk measures that have been claimed to be able to explain cross-sectional asset returns in the literature. In accordance to Fama and French (1993, 1996a), we use these factors in asset pricing, and show that the market portfolio, liquidity and coskewness explain the stock returns as well as the famous Fama-French three factors with momentum. In particular, in most sample periods tested, individual stocks' alphas are insignificant with only two factors, market portfolio and liquidity; in addition, many factors are redundant in asset pricing and are likely to come from data-mining.

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 (1999) (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 (1993) 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 develop a three-moment international asset-pricing model (TM-IAPM) that prices coskewness and embeds the standard IAPMs as special cases. We use the model to investigate the time-series behavior of market, size, value, and momentum premiums in the United States, Japan, and the United Kingdom equity markets. We find that the model explains most of the variation of these premiums during the 1980s and 1990s and that the coskewness risk is more important than covariance risk.

The CAPM model is hard put to explain the superior performance of hedge funds in the past. We argue that the Markowitz mean-variance criterion underpinning the traditional CAPM may fail to capture systematic features characterizing hedge fund performance. Thus, we extend the two-moment market model to a higher-moment model to accommodate coskewness and cokurtosis. The higher-moment approach is more appropriate for capturing the non-linear relation between hedge fund and market returns and accounting for the specific risk-return payoffs of each hedge fund investment strategy. The key result is that the use solely of the two-moment pricing model may be misleading and may wrongly indicate insufficient compensation for the investment risk. First Version: July 23, 2002 This Version: July 14, 2005 JEL Classification : C29; G12 Keywords : Hedge Funds, Higher Moments, Skewness, Kurtosis, Coskewness, and Cokurtosis. α Angelo Ranaldo, Swiss National Bank, Research Department, Borsenstrasse 15, P.O. Box 2800, Zurich, Switzerland. E-mail: angelo.ranaldo@snb.ch, Phone: ++41.44.6313826, Fax: ++41.44.6313901.

I derive the beta-pricing representation of Harvey and Siddique (2000) conditional 3M-CAPM and estimate it using returns on the Fama and French (1995) 30 US industry portfolios from 1952 to 2002 and Lettau and Ludvigson (2001) consumption-wealth ratio as a conditioning variable. The parameter estimates imply an inverse S-shaped utility function and the gamma premium turns out to be insignificant when risk aversion and non-increasing absolute risk aversion are imposed. However, if we accept some risk seeking over gains, my 3-moment beta pricing representation is surprisingly successful at explaining the cross-section of average industry returns.

Most theoretical models in finance measure risk as variance or covariance. However, many financial decision-makers seem to regard risk as the volatility of below-target returns and treat the volatility of above-target returns as a sweetener. Using simple metrics of downside risk and upside potential, constructed from conditional covariances, I test for the empirical content of this asymmetry. I introduce a new composite metric of semidimensional risks which reveals that the nonlinearity in the covariation of stock returns with bearish and bullish conditions of the market is priced in the cross-section of stock returns. In particular, I find that stocks that have concave characteristic regression lines against the market earn higher average returns than stocks that have convex characteristic regression lines. This new metric captures the relevant information in returns asymmetry or nonlinearity better than either coskewness or the square-coefficient from quadratic regression. I also present results that are consistent with a semidimensional risk-based explanation for the twin puzzles of return momentum and reversal. The primitive representation of the security pricing kernel as the negative of covariance between marginal utility of consumption and security returns lends theoretical support for semidimensional risks and provides a unifying perspective for seemingly disparate literature on semivariances, skewness and behavioral finance.

VIRTUALLY ALL OF THE early studies of the Sharpe-Lintner capital asset pricing model (CAPM) found the predicted linear relationship between return and the non-diversifiable risk of risky assets, generally represented by common stocks listed on the New York Stock Exchange (NYSE). However, they also found that this return-risk relationship seemed to imply for most periods a riskless market rate of return substantially above any reasonable measure of the actual risk-free rates of return. Recent papers point to a similar result if the market portfolio of risky assets is represented by an appropriately weighted portfolio of common stocks and bonds instead of common stocks alone.1 Thus, it is noteworthy that a study by Kraus and Litzenberger finds that a measure6 of co-skewness can be used as a supplement to the co-variance measure of risk to explain the returns on individual NYSE stocks, and in the process to explain the otherwise observed discrepancies between these returns and the returns on NYSE stocks as a whole.2 In other words, they extend capital asset pricing theory to incorporate the effect of skewness in return distributions, making the assumption that investors have a preference for positive return skewness in their portfolios (and therefore positive or negative co-skewness in individual assets depending on the skewness in the market portfolio).3 As a consequence Kraus and Litzenberger are apparently able to explain observed returns in the stock market without the substitution of a non-observable zerobeta construct for the risk-free rate. Kraus and Litzenberger assume that just as investors are averse to variance in their portfolios, and therefore beta in individual assets, they prefer positive skewness in their portfolios. Hence, since they also assume that all investors hold the market portfolio, investors would be willing to pay a premium for assets which possess positive co-skewness with the market if