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We show that the prices of risk for factors that are nonlinear in the market return can be obtained using index option prices. The price of coskewness risk corresponds to the market variance risk premium, and the price of cokurtosis risk corresponds to the market skewness risk premium. Option-based estimates of the prices of risk lead to reasonable values of the associated risk premia. An analysis of factor models with coskewness risk indicates that the new estimates of the price of risk improve the models’ performance compared with regression-based estimates.

This paper shows that low‐risk anomalies in the capital asset pricing model and in traditional factor models arise when investors require compensation for coskewness risk. Empirically, we find that option‐implied ex ante skewness is strongly related to ex post residual coskewness, which allows us to construct coskewness factor‐mimicking portfolios. Controlling for skewness renders the alphas of betting‐against‐beta and betting‐against‐volatility insignificant. We also show that the returns of beta‐ and volatility‐sorted portfolios are driven largely by a single principal component, which in turn is explained largely by skewness.

Purpose The purpose of this study is to update the investment literature by providing latest evidence of performance of Islamic mutual funds by using global sample mutual funds data to support with empirical facts. Design/methodology/approach This study analyzes the comparative performance of Islamic and conventional mutual funds by using capital asset pricing model, Fama & French’s three-factor model and Carhart’s four-factor model. Further, the study tested the coskenwness effect by using data envelopment analysis approach. Findings The authors find evidence that when size of the funds is controlled, Islamic investment underperform the conventional mutual funds in four out of six models. The size of underperformance varies from model to model: from 32 basis points in the Carhart’s four-factor model with the skewness factor to two basis points at the Fama and French’s three-factor model. Also the study finds that alpha(s) are only insignificant for conventional mutual funds when the skewness factor is included in the regression. While comparing the loading on Islamic mutual funds, results show that Islamic mutual funds are less risky than conventional mutual funds when they are controlled for skewness. Originality/value This study uses the different factor models of performance evolution which help in overcoming weakness of measuring the Islamic mutual funds’ performance.

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.

Principal skewness analysis (PSA) has been introduced for feature extraction in hyperspectral imagery. As a thirdorder generalization of principal component analysis (PCA), its solution of searching for the local maximum skewness direction is transformed into the problem of calculating the eigenpairs (the eigenvalues and the corresponding eigenvectors) of a coskewness tensor. By combining a fixed-point method with an orthogonal constraint, the new eigenpairs are prevented from converging to the same previously determined maxima. However, in general, the eigenvectors of the supersymmetric tensor are not inherently orthogonal, which implies that the results obtained by the search strategy used in PSA may unavoidably deviate from the actual eigenpairs. In this paper, we propose a new nonorthogonal search strategy to so lve this problem and the new algorithm is named nonorthogonal principal skewness analysis (NPSA). The contribution of NPSA lies in the finding that the search space of the eigenvector to be determined can be enlarged by using the orthogonal complement of the Kronecker product of the previous eigenvector with itself, instead of its orthogonal complement space. We also give a detailed theoretical proof on why we can obtain the more accurate eigenpairs through the new search strategy by comparison with PSA. In addition, after some algebraic derivations, the complexity of the presented algorithm is also greatly reduced. Experiments with both simulated data and real multi/hyperspectral imagery demonstrate its validity in feature extraction.

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 euro zone equity returns from 2005 to 2014 shows that contagion operated mainly through higher order moment channels during the GFC and the European debt crisis, which were not necessarily detected by traditional tests based on correlations. The empirical results have important implications for pricing risk and constructing well diversified portfolios.

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.

Bakgrund I snart ett halvt sekel har aktier med lågt beta visat sig generera hög avkastning i förhållande till risk. Denna observation brukar benämnas lågriskanomalin och ända sedan fenomenet uppmärksammades av Black 1972 har olika studier försökt förklara orsaken till dess förekomst. Empiriska resultat har inte bara visat på att lågriskaktier presterat bättre än vad teorin förutspår, utan till och med visat på ett negativt samband mellan risk och avkastning. Detta är i rak motsats till traditionella avkastningsmodeller som exempelvis CAPM, vilken hävdar att avkastning är en direkt funktion av systematisk risk – beta. Syfte Syftet med denna uppsats är att undersöka förekomsten av lågriskanomalin på den svenska aktiemarknaden och analysera huruvida anomalin kan förklaras av den tredje ordningens centralmoment, skevhet. Vidare syftar uppsatsen till att testa och analysera möjligheten att hantera skevhetsrisk genom att inkludera denna som en variabel i en tredimensionell optimeringsmodell. Genomförande Studien bygger på insamlad kurshistorik mellan åren 1998–2018 för samtliga aktier som har ingått i indexet OMXSPI. Totalt har 9650 risksorterade portföljer skapats, där loggning genomförts av portföljegenskaper och analysmått. Sambandet mellan lågriskanomalin och skevhetsrisk har testats genom hypotestester baserat på inkluderandet av en tredimensionell optimeringsmodell samt Three-moment CAPM. Slutsats Resultaten visar att aktier med lägre beta i genomsnitt har presterat signifikant bättre än högbetaaktier sett till både riskjuterad- samt faktiskt avkastning. Förhållandet mellan risk och avkastning har således varit negativt för den undersökta perioden. Vidare påvisas en signifikant riskaversion mot skevhetsrisk, men trots detta tyder samtliga av studiens tester på att skevhet är otillräckligt för att förklara detta fenomen. Genom tredimensionell optimering visas även hur portföljspecifik skevhet kan hanteras utan att ge signifikant försämrad avkastning. Dessa resultat faller i linje med att lågriskanomalin uppstår som en konsekvens av ett ineffektivt utbud- och efterfrågesamband och kan därmed ses som ett argument mot den effektiva marknadshypotesen Background For nearly half a century, stocks with low beta has shown to generate high return relative to risk. This observation is called the low risk anomaly and ever since it was observed by Black in 1972, different studies have tried to find an explanation for its presence. Empirical results have not only found that low risk stocks outperform in terms of riskadjusted returns, but also that the relationship between risk and return seem to have a negative correlation. This is the exact opposite of what is suggested by traditional financial models, such as CAPM, which claim that return on assets is a direct function of the its systematic risk – beta. Purpose The purpose of this study is to investigate the presence of the low risk anomaly on the Stockholm stock exchange and analyse if it can be explained by the third central moment, skewness. Further we intend to test and analyse if it is possible to control skewness risk by including it as a variable in three-dimensional optimization. Methodology The thesis is conducted by acquiring historical stock prices for the years 1998–2018 for all shares included in the index OMXSPI. To answer the underlying research questions, 9650 risk-sorted portfolios are created where portfolio performance indicators are being logged. Furthermore, the relationship between the low risk anomaly and skewness-based risk is examined through hypothesis testing, which depend on a three-dimensional optimization model as well as the Three-moment CAPM. Results The results of this study show that stocks with low beta has significantly outperformed high-beta stocks in terms of both risk-adjusted as well as actual return. This implies that the relationship between risk and return has been negative during the time period investigated. Furthermore, the results show a significant aversion towards skewness risk. However, all of the tests indicate that skewness is insufficient in the explanation of the low risk anomaly. It has been shown by three-dimensional optimization that it is possible to control portfolio skewness, without a significant loss in return. These results are in line with the conclusion that the low risk anomaly is an effect of inefficiency in supply and demand and can therefore be seen as an argument against the efficient market hypothesis.

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).

A flexible multivariate model of a time-varying joint distribution of asset returns is developed which allows for regime switching and a joint skew-normal distribution. A suite of tests for linear and nonlinear financial market contagion is developed within the framework. The model is illustrated through an application to contagion between US and European equity markets during the Global Financial Crisis. The results show that correlation contagion dominates coskewness contagion, but that coskewness contagion is significant for Greece. A flight to safety to the US is also evident in the significance of breaks in the skewness parameter in the crisis regime. Comparison to the Asian crisis shows that similar patterns emerge, with a flight to safety to Japan, and Malaysia affected by coskewnes contagion with Hong Kong.

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.

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.

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.

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.

In this letter, we present a new feature extraction approach based on third-order statistics (coskewness tensor) called principal skewness analysis (PSA). PSA is the natural extension of principal components analysis from second-order statistics to third-order statistics. The result of PSA is equivalent to that of FastICA when skewness is considered as a non-Gaussian index. Similar to FastICA, PSA also applies the fixed-point method to search the skewness extreme directions. However, when calculating the new projected direction in each iteration, PSA only requires a coskewness tensor, whereas FastICA requires all the pixels to be involved. Therefore, PSA has an advantage over FastICA in speed.

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.

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.

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.

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.

The Margrabe formula is used extensively by theorists and practitioners not only on exchange options, but also on executive compensation schemes, real options, weather and commodity derivatives, etc. However, the crucial assumption of a bivariate normal distribution is not fully satisfied in almost all applications. The impact of nonnormality on exchange options is studied by using a bivariate Gram-Charlier approximation. For near-the-money exchange options, skewness and coskewness induce price corrections which are linear in moneyness, while kurtosis and cokurtosis induce quadratic price corrections. The nonnormality helps to explain the implied correlation smile observed in practice.

We present hedge fund performance estimates that adjust for stale prices, Fama-French risk factors and skewness. We contrast these new performance estimates with traditional performance measures. Using three-factor models to adjust for staleness in prices and to incorporate Fama-French factors along with the Harvey-Siddique (2000) two-factor model that incorporates skewness, we find that for the period 1990–2003, all hedge fund categories achieve above average performance when measured against an aggregate market index. More significantly, however, when we estimate performance at the individual hedge fund level, we discover that only 40 to 47% of the funds are shown to achieve an above average performance over that time period depending on the model used. These results have important implications for investors, endowments and pensions when they choose hedge fund managers.

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.

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.

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.

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.

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.

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.

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...

We show theoretically that lower tail dependence ( χ ), a measure of the probability that a portfolio will suffer large losses given that the market does, contains important information for risk-averse investors. We then estimate χ for a sample of DJIA stocks and show that it differs systematically from other risk measures including variance, semi-variance, skewness, kurtosis, beta, and coskewness. In out-of-sample tests, portfolios constructed to have low values of χ outperform the market index, the mean return of the stocks in our sample, and portfolios with high values of χ . Our results indicate that χ is conceptually important for risk-averse investors, differs substantially from other risk measures, and provides useful information for portfolio selection.

In this thesis, we investigate some aspects of the interplay between economic regulation and the risk of the regulated firm. In the first chapter, the main goal is to understand the implications a mainstream regulatory model (Laffont and Tirole, 1993) have on the systematic risk of the firm. We generalize the model in order to incorporate aggregate risk, and find that the optimal regulatory contract must be severely constrained in order to reproduce real-world systematic risk levels. We also consider the optimal profit-sharing mechanism, with an endogenous sharing rate, to explore the relationship between contract power and beta. We find results compatible with the available evidence that high-powered regimes impose more risk to the firm. In the second chapter, a joint work with Daniel Lima from the University of California, San Diego (UCSD), we start from the observation that regulated firms are subject to some regulatory practices that potentially affect the symmetry of the distribution of their future profits. If these practices are anticipated by investors in the stock market, the pattern of asymmetry in the empirical distribution of stock returns may differ among regulated and non-regulated companies. We review some recently proposed asymmetry measures that are robust to the empirical regularities of return data and use them to investigate whether there are meaningful differences in the distribution of asymmetry between these two groups of companies. In the third and last chapter, three different approaches to the capital asset pricing model of Kraus and Litzenberger (1976) are tested with recent Brazilian data and estimated using the generalized method of moments (GMM) as a unifying procedure. We find that ex-post stock returns generally exhibit statistically significant coskewness with the market portfolio, and hence are sensitive to squared market returns. However, while the theoretical ground for the preference for skewness is well established and fairly intuitive, we did not find supporting evidence that investors require a premium for supporting this risk factor in Brazil. Essa tese investiga alguns aspectos da relação entre regulação econômica e risco da empresa regulada. No primeiro capítulo, o objetivo é entender as implicações do modelo tradicional de regulação por incentivos (Laffont e Tirole, 1993) sobre o risco sistemático da firma. Generalizamos o modelo de forma a incorporar risco agregado ao lucro da atividade, e descobrimos que o contrato ótimo deve ser severamente restringido para que reproduza betas (CAPM) próximos aos observados em setores regulados. Usamos um caso particular do modelo, de regulação por repartição de lucro (profit-sharing regulation), para avaliar a relação entre a potência do contrato e o nível de risco não diversificável. Encontramos resultados compatíveis com a evidência disponível, de que regimes com alta potência impõem mais risco sobre a firma. No segundo capítulo, escrito em co-autoria com Daniel Lima da Universidade da Califórnia em San Diego (UCSD), partimos da constatação de que empresas reguladas podem estar sujeitas a práticas regulatórias que potencialmente afetam a simetria da distribuição de seus lucros futuros. Se essas práticas forem antecipadas pelos investidores no mercado secundário de ações, poderemos identificar diferenças no padrão da assimetria da distribuição empírica de retornos das empresas reguladas com relação às não-reguladas. Nesse capítulo revisamos alguns métodos de mensuração de assimetria propostos recentemente na literatura, que são robustos à características comuns em séries de retornos financeiros (caudas pesadas e correlação serial), e investigamos se existem diferenças significativas na distribuição de assimetria entre empresas reguladas e não-reguladas. No terceiro e último capítulo, três diferentes abordagens empíricas do modelo de apreçamento de ativos de Kraus e Litzenberger (1976) são testadas com dados do mercado brasileiro de ações. Descobrimos que a distribuição empírica de retornos costuma exibir co-assimetria significativa com relação à carteira de mercado, e que portanto os retornos das ações são sensíveis à volatilidade (retornos quadráticos) do mercado. No entanto, apesar da base teórica para a preferência por retornos assimétricos esteja bem estabelecida e seja bastante intuitiva, não encontramos evidência que suporte a hipótese de que os investidores requeiram um prêmio para aceitar esse tipo de risco no mercado local.

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.

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.

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 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.

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.

We present a framework for modeling and estimating dynamics of variance and skewness from time-series data using a maximum likelihood approach assuming that the errors from the mean have a non-central conditional t distribution. We parameterize conditional variance and conditional skewness in an autoregressive framework similar to that of GARCH models and estimate the parameters in a conditional noncentral t distribution. The likelihood function has two time-varying parameters, the degrees of freedom and the noncentrality parameter. We apply this methodology to daily and monthly equity returns data from the U.S., Germany and Japan, concurrently estimating conditional mean, variance and skewness. We find that there is significant conditional skewness. We then use this model to understand how the inclusion of conditional skewness affects some of the well-known stylized facts about conditional variance and the relation between returns and conditional variance. Two important stylized facts about conditional variance we examine are persistence and asymmetry in variance. Persistence refers to the tendency where high conditional variance is followed by high conditional variance. Asymmetry in variance, i.e., the observation that conditional variance depends on the sign of the innovation to the conditional mean has been documented in asymmetric variance models used in Glosten, Jagannathan, and Runkle (1993) and Engle and Ng (1993). We find that the evidence of asymmetric variance is really just conditional skewness. Inclusion of conditional skewness also impacts the persistence in conditional variance. However, we also find that there are significant seasonalities in variance and the results also depend on how the seasonal effects are accommodated in the estimation methodology. We also examine the relation between expected returns and volatility.

In this paper, the authors employ a nonlinear formulation to examine empirically the structural content of the three moment capital asset pricing model (CAPM). Whereas previous research focused on the coefficients of beta and co-skewness, this paper presents empirical results on the market risk premium and elasticity coefficient components of these two coefficients. The results indicate that although the estimated coefficient of coskewness gives important information on the marginal rate of substitution between skewness and expected return, the elasticity coefficient can provide additional (albeit different) information on skewness preference that is independent of the effects of the market risk premium. This research also shows how the non-linear formulation provides a direct linkage between the twomoment and three-moment CAPM versions and thus provides an empirical test of the theoretical conditions under which skewness preference is consistent with the two-moment CAPM empiricial results.

Multivariate statistical analysis relies heavily on moment assumptions of second order and higher. With increasing interest in heavy-tailed distributions, however, it is desirable to describe dispersion, skewness, and kurtosis under merely first order moment assumptions. Here, the univariate L-moments of Hosking [L-moments: analysis and estimation of distributions using linear combinations of order statistics, J. Roy. Statist. Soc. Ser. B 52 (1990) 105–124] are extended to “L-comoments” analogous to covariance. For certain models, the second order case yields correlational analysis coherent with classical correlation but also meaningful under just first moment assumptions. We develop properties and estimators for L-comoments, illustrate for several multivariate models, examine behavior of sample multivariate L-moments with heavy-tailed data, and discuss applications to financial risk analysis and regional frequency analysis.

The quadratic form of the covariance-co-skewness model by Kraus and Litzenberger and arbitrage pricing theory are used for an empirical investigation of market equilibrium with skewed seecurity returns. Empirical tests similar to the ones in Black-Jensen-Scholes and Gibbons are discussed. The empirical estimates give some support to the Kraus-Litzenberger hypothesis on skewness preference. However, there is some evidence that the tested arbitrage equilibrium is not a complete description of security pricing.

This paper tests the Kraus-Litzenberger (1976) three-moment capital asset pricing model using Hansen's (1982) generalized method-of-moments (GMM). The GMM approach does not impose strong distributional assumptions on the asset returns. This is an interest? ing issue since there is no obvious multivariate distribution for returns that also exhibits co-skewness. Using monthly stock returns to test the model, there is some evidence that systematic skewness is priced.