Distribution Of Asset Returns Research Articles

Generalized risk premia

This paper develops an optimal trading strategy explicitly linked to an agent׳s preferences and assessment of the distribution of asset returns. The price of this strategy is a portfolio of implied moments, and its expected excess returns naturally accommodate compensation for higher-order moment risk. Variance risk and the equity premium approximate it to first order and it nests cross-sectional asset pricing models such as the linear Capital Asset Pricing Model (CAPM). An empirical study in the US index market compares the investment behavior of an agent with recursive long-run risk preferences to one who merely uses an identically independently distributed time series model and takes market prices as given. The two agents exhibit very similar behavior during crises and can be distinguished mostly during calm periods.

ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails

It is well-known in empirical finance that virtually all asset returns, whether monthly, daily, or intraday, are heavy-tailed and, particularly for stock returns, are mildly but often significantly negatively skewed. However, the tail indices, or maximally existing moments of the returns, can differ markedly across assets. To accommodate these stylized facts when modeling the joint distribution of asset returns, an asymmetric extension of the meta-elliptical t distribution is proposed. While the likelihood is tractable, for high dimensions it will be impractical to use for estimation. To address this, a fast, two-step estimation procedure is developed, based on a saddlepoint approximation to the noncentral Student's t distribution. The model is extended to support a CCC-(I)GARCH structure and demonstrated by modeling and forecasting the return series comprising the DJIA. The techniques of shrinkage, time-varying tail dependence, and weighted likelihood are employed to further enhance the forecasting performance of the model with no added computational burden.

Multivariate Time-VaryingG-HCopula GARCH Model and Its Application in the Financial Market Risk Measurement

Taking full advantage of the strengths ofG-Hdistribution, Copula function, and GARCH model in depicting the return distribution of financial asset, we construct the multivariate time-varyingG-HCopula GARCH model which can comprehensively describe “asymmetric, leptokurtic, and heavy-tail” characteristics, the time-varying volatility characteristics, and the extreme-tail dependence characteristics of financial asset return. Based on the conditional maximum likelihood estimator and IFM method, we propose the estimation algorithm of model parameters. Using the quantile function and simulation method, we propose the calculation algorithm of VaR on the basis of this model. To apply this model on studying a real financial market risk, we select the SSCI (China), HSI (Hong Kong, China), TAIEX (Taiwan, China), and SP500 (USA) from January 3, 2000, to June 18, 2010, as the samples to estimate the model parameters and to measure the VaRs of various index risk portfolios under different confidence levels empirically. The results of the application example are in line with the actual situation and the risk diversification theory of portfolio. To a certain extent, these results also justify the feasibility and effectiveness of the multivariate time-varyingG-HCopula GARCH model in depicting the return distribution of financial assets.

Inference of Aggregational Gaussianity in Asset Returns Exhibiting a Paretian-distribution

Abstract Aggregational Gaussianity (AG) has long been considered a stylized fact of empirical asset return distributions. This research links existing work on the stable-Paretian Hypothesis with the Aggregational Gaussianity hypothesis and notes that the two are incompatible. We use simulation to show that under certain conditions, AG can be falsely inferred to hold in a data set exhibiting the stable-Paretian distribution.

BAYESIAN ESTIMATION OF ASYMMETRIC JUMP-DIFFUSION PROCESSES

The hypothesis that asset returns are normally distributed has been widely rejected. The literature has shown that empirical asset returns are highly skewed and leptokurtic. The affine jump-diffusion (AJD) model improves upon the normal specification by adding a jump component to the price process. Two important extensions proposed by Ramezani and Zeng (1998) and Kou (2002) further improve the AJD specification by having two jump components in the price process, resulting in the asymmetric affine jump-diffusion (AAJD) specification. The AAJD specification allows the probability distribution of the returns to be asymmetrical. That is, the tails of the distribution are allowed to have different shapes and densities. The empirical literature on the "leverage effect" shows that the impact of innovations in prices on volatility is asymmetric: declines in stock prices are accompanied by larger increases in volatility than the reverse. The asymmetry in AAJD specification indirectly accounts for the leverage effect and is therefore more consistent with the empirical distributions of asset returns. As a result, the AAJD specification has been widely adopted in the portfolio choice, option pricing, and other branches of the literature. However, because of their complexity, empirical estimation of the AAJD models has received little attention to date. The primary objective of this paper is to contribute to the econometric methods for estimating the parameters of the AAJD models. Specifically, we develop a Bayesian estimation technique. We provide a comparison of the estimated parameters under the Bayesian and maximum likelihood estimation (MLE) methodologies using the S&P 500, the NASDAQ, and selected individual stocks. Focusing on the most recent spectacular market bust (2007–2009) and boom (2009–2010) periods, we examine how the parameter estimates differ under distinctly different economic conditions.

Distributional Linkages between European Sovereign Bond and Bank Asset Returns

We analyse the dependence between sovereign bonds' and banks' asset return distributions with a large panel of European data from 2001 to 2013. Using quantile regressions, we identify nonlinear contemporaneous and lagged dependence. As a result, shocks to crisis-hit sovereign bonds have contemporaneous effects on the whole distribution of banks' returns, as well as a persistent impact in the tails. Our results offer relevant insights about the relationship between banking and sovereign crises. In particular, during the recent financial crisis, banks' asset return distributions have lower means and fatter tails than in the absence of a simultaneous sovereign crisis.

Risk-Adjusted Option-Implied Moments

Option-implied moments, like implied volatility, contain useful information about an underlying asset's return distribution but are derived under the risk-neutral probability measure. This paper provides a direct way of converting risk-neutral moments into the corresponding physical moments, which are required for many applications. The main result is a representation of physical moments in terms of observed option prices and a representative investor's preferences. As an empirical application of this result, we provide implied estimates of the representative stock market investor's disappointment aversion using S&P 500 index option prices. We find that disappointment aversion has a procyclical pattern. It is high in times of high index levels and declines when the index falls. We confirm the view that investors with high risk aversion and disappointment aversion leave the stock market during times of turbulence and reenter it after a period of high returns.

A Standardized Normal-Laplace Mixture Distribution Fitted to Symmetric Implied Volatility Smiles

This article proposes to use a standardized version of the normal-Laplace mixture distribution for the modeling of tail-fatness in an asset return distribution and for the fitting of volatility smiles implied by option prices. Despite the fact that only two free parameters are used, the proposed distribution allows arbitrarily high kurtosis and uses one shape parameter to adjust the density function within three standard deviations for any specified kurtosis. For an asset price model based on this distribution, the closed-form formulas for European option prices are derived, and subsequently the volatility smiles can be easily obtained. A regression analysis is conducted to show that the kurtosis, which is commonly used as an index of tail-fatness, is unable to explain the smiles satisfactorily under the proposed model, because the additional shape parameter also significantly accounts for the deviations revealed in smiles. The effectiveness of the proposed parsimonious model is demonstrated in the practical examples where the model is fitted to the volatility smiles implied by the NASDAQ market traded foreign exchange options.

Polynomial goal programming and the implicit higher moment preferences of US institutional investors in hedge funds

Polynomial goal programming (PGP) is a flexible method that allows investor preferences for different moments of the return distribution of financial assets to be included in the portfolio optimization. The method is intuitive and particularly suitable for incorporating investor preferences in higher moments of the return distribution. However, until now, PGP has not been able to meet its full potential because it requires quantification of “real” preference parameters towards those moments. To date, the chosen preference parameters have been selected somewhat “arbitrarily”. Our goal is to calculate implied sets of preference parameters using investors’ choices of and the importance they attribute to risk and performance measures. We use three groups of institutional investors—pension funds, insurance companies, and endowments—and derive implied sets of preference parameters in the context of a hedge fund portfolio optimization. To determine “real” preferences for the higher moments of the portfolio return distribution, we first fit implied preference parameters so that the PGP optimal portfolio is identical to the desired hedge fund portfolio. With the obtained economically justified sets of preference parameters, the well-established PGP framework can be employed more efficiently to derive allocations that satisfy institutional investor expectations for hedge fund investments. Furthermore, the implied preference parameters enable fund of hedge fund managers and other investment managers to derive optimal portfolio allocations based on specific investor expectations. Moreover, the importance of individual moments, as well as their marginal rates of substitution, can be assessed.

Generalized Risk Premia

This paper develops an optimal trading strategy explicitly linked to an agent's preferences and assessment of the distribution of asset returns. The price of this strategy is a portfolio of implied moments, and its expected excess returns naturally accommodate compensation for higher-order moment risk. Variance risk and the equity premium approximate it to first order and it nests cross-sectional asset pricing models such as the CAPM. An empirical study in the US index market compares the investment behavior of an agent with recursive long-run risk preferences to one who merely uses an i.i.d. time series model and takes market prices as given. The two agents exhibit very similar behavior during crises and can be distinguished mostly during calm periods.

Stock Liquidity, Microstructure and Kurtosis

This paper investigates the hypothesis that market microstructure is an important determinant of stock-return kurtosis. We first develop a simple model where an informed investor has private information about the firm's fundamentals and marketmaker has private information about the non-fundamentals, particularly concerning the structure of noise-traders' demand. The model shows that these market frictions can generate significant kurtosis in asset return distribution. Consistently, findings in our empirical analyses support this conjecture. We find a positive and causal association between liquidity cost in stock market and kurtosis in stock return. This association is robust to various specifications, and different proxies for liquidity cost and return kurtosis. It is even present when we control for the endogeneity and reverse causality concerns. Our findings have implications for research in asset pricing and corporate finance, and also add to the knowledge of practitioners, especially from risk management perspective.

Do stock returns have an Archimedean copula?

The flexible class of Archimedean copulas plays an important role in multivariate statistics. While there is a large number of goodness-of-fit tests for copulas and parametric families of copulas, the question if a given data set belongs to an arbitrary Archimedean copula or not has not yet received much attention in the literature. This paper suggests a new, straightforward method to test whether a copula is an Archimedean copula without the need to specify its parametric family. We conduct Monte Carlo simulations to assess the power of the test. The approach is applied to (bivariate) joint distributions of stock asset returns. We find that, in general, stock returns may have Archimedean copulas.

From Equity Volatility Skew to Firm Leverage

The leverage effect is widely considered to be the major contributor to volatility skew in the stock option market. This s tudy concentrates on explicit modeling of corporate leverage. The asset-equity relation is modeled by a perpetual American option, and the asymmetry of the asset return distribution is addressed by introducing a Constant Elasticity of Variance (CEV) asset dynamic. The model retains closed-form representation of firm equity wit h respect to asset and liability. This provides a convenient simplification to equity option pricing, so that the model can be calibrated to stock prices and the entire volatility structure. This mode l demonstrates how the volatility smile, as well as skew, can be accommodated by the structural model, and also successfully explains why low-leverage stocks could still have a non-trivial volatility structure . A cross-sectional study shows that the calibrated parameters effectively outline the financial characteristics of the leveraged firms. The cre dit quality measure generated from this model is also more informative in terms of explaining Credit Default Swap (CDS) spread movements.

Empirical competitiveness of deterministic option pricing models: Evidences from the recent waves of financial upheavals in India

It is acknowledged by the leading researchers that the fundamental force behind the emergence of advanced option pricing models was the result of abundant empirical research analysis, leading to the fact that the asset return distribution is non-log-normal. It obviously resulted in strong moneyness and maturity pricing biases of Black–Scholes (BS). The concept defined the assertive distributional assumptions for Nifty (benchmark index of India), because the stated view supported the idea and its implications majorly focused on establishing the well-protected alternative model. The core concept of almost all the option pricing models was substantially indicating towards the flexible distributional structure. Such behaviour not only correlated underlying stock returns and its volatility but also subdued the level of skewness and kurtosis. Therefore, this article endeavours to investigate empirically the out-of-sample moneyness–maturity forecasting performance of deterministic volatility option pricing models during the recent waves of economic imbalance. It forecasts S&P CNX Nifty 50 index options of India against significant BS option pricing model and also attempts to find out forecasting performances of a family of deterministic volatility option pricing models, namely, Practitioner Black-Scholes (PBS), Gram–Charlier (GC) and Constant Elasticity of Variance (CEV). The accuracy of models’ prices testify to the relative market price of Nifty index options using error metrics. For the purpose of this research, the prices are compared analytically through continuously updating the parameters of the models using cross-sectional option data, almost on a daily basis. The underlying focus of the article emphasizes on how to investigate the parameters of various models, pertaining specifically to a period of turbulence in the Indian economy. Eventually, while giving verdict to the results deduced, we measure out that the PBS model has smaller out-of-sample valuation errors in pricing Nifty Index options than the CEV and GC. However, it remains challenging to root out price bias completely out of all models we have framed out and applied.

A Regime Switching Skew-Normal Model for Measuring Financial Crisis and Contagion

A regime switching skew-normal model for …nancial crisis and contagion is proposed in which we develop a new class of multiple-channel crisis and contagion tests. Crisis channels are measured through changes in ‘own’moments of the mean, variance and skewness, while contagion is through changes in the correlation and co-skewness of the joint distribution of asset returns. In this framework: i) linear and non-linear dependence is allowed; ii) transmission channels are simultaneously examined; iii) crisis and contagion are distinguished and individually modeled; iv) the market that a crisis originates is endogenous; and v) the timing of a crisis is endogenous. In an empirical application, we apply the proposed model to equity markets during the Great Recession using Bayesian model comparison techniques to assess the multiple channels of crisis and contagion. The results generally show that crisis and contagion are pervasive across Europe and the US. The second moment channels of crisis and contagion are systematically more evident than the …rst and third moment channels.

Tailoring the Logistic Distribution to Fit the Empirical Distribution of Financial Asset Returns

Risk measures, including Value-at-Risk (VaR) and Conditional VaR (Expected Shortfall), turn out to be quite sensitive to the degree to which distributions are thick tailed and asymmetric. Lack of encoding information about asymmetry and leptokurtosis is a well-known drawback of the Gaussian law. This has led to a search for alternative distributions (Szego (2004)). In this paper, we will tackle the issue of accounting for asymmetry, (possibly severe) excess kurtosis and dependence by following the alternative approach of adjusting bell-shaped distributions using orthogonal polynomials as shape adapters. Our focus will be on polynomial transformations of parent symmetric probability density functions to match the empirical moments of target distributions characterized by possibly substantial heavy-tails and asymmetry. We will demonstrate a simple but powerful novel result, i.e. that the function that achieves the transformation from a given parent to a target distribution, depends on both the orthogonal polynomials associated to the former and the moment-differentials between these two distributions. We will then apply this result to the modelling of heavy-tailed and skewed distributions of financial asset returns.

Tailoring Density Functions via Orthogonal Polynomials

This paper re-examines the issue of how to tailor distributions to embody evidence of moments and dependence structure deviating from those of a given parent distribution. It is well known that the function that achieves the transformation from a given parent to a target distribution can be expressed as a linear combination of a set of orthogonal polynomials associated to parent distribution. We show that the coefficients of such linear combination are simple algebraic functions of the difference between the moments of the parent and target distributions. These results facilitate reshaping a considerably broader class of distributions than well-known approaches based on Hermite polynomials, which can be used only to reshape the normal distribution and allow to do so only to a limited extent. We provide applications to modeling distributions of financial asset returns, which are known to exhibit considerable skewness and fat tails.

Generalized Risk Premia -- The Economic Value of Predictability

This paper develops an optimal trading strategy explicitly linked to an agent's preferences and assessment of the distribution of asset returns. The price of this strategy is a portfolio of implied moments, and its expected excess returns naturally accommodate compensation for higher-order moment risk. Variance risk and the equity premium approximate it to first order and it nests cross-sectional asset pricing models such as the CAPM. An empirical study in the US index market compares the investment behavior of an agent with recursive long-run risk preferences to one who merely uses an i.i.d. time series model and takes market prices as given. The two agents exhibit very similar behavior during crises and can be distinguished mostly during calm periods.

A Heterogeneous Agent-based Asset Pricing Model and Simulation

Behavioral finance models can help to explain several stylized facts in financial markets. As one of the behavioral financial theory, prospect theory describes how „irrational investors‟ making decisions under uncertainty. In this paper, we present a heterogeneous agent-based asset pricing model, where parts of investors determine their demand for risky asset using prospect theory utility function. Time series generated from simulation show many stylized facts that can be observed in actual financial markets, such as abnormal distribution of asset returns, volatility clustering and equity premium. We also find that positive correlation between investors‟ performance and their market share, negative correlation between investors‟ performance and the loss aversion coefficient under certain market condition.

Portfolio Value-at-Risk Optimization for Asymmetrically Distributed Asset Returns

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using simulated data, the PVaR approach always generates better risk-return tradeoffs in the optimal portfolios when compared to traditional Markowitz mean-variance approach. When using real financial data, our approach also outperforms the Markowitz approach in the risk-return tradeoff. Given that the PVaR measure is also a robust risk measure, our new approach can be very useful for optimal portfolio allocations when asset return distributions are asymmetrical.