Non-normality Of Returns Research Articles

Spillover in higher‐order moments across carbon and energy markets: A portfolio view

AbstractMotivated by the occurrence of extreme events and nonnormality of returns, we examine the spillovers among the conditional volatility, skewness and (excess) kurtosis of European Union allowances (EUA), Brent oil, natural gas, coal, electricity and clean energy markets. The jointly estimated spillover index in the system of the three higher‐order moments is notably high, exceeding the spillover index estimated for each individual moment separately. This suggests that spillovers across moments in the carbon‐energy system are important for the sake of completeness of the spillover analysis, and should not be ignored. The performance of the portfolio improves after considering higher‐order moments.

Higher-order moments and co-moments' contribution to spillover analysis and portfolio risk management

Unlike volatility, the skewness and kurtosis of asset returns are often neglected in the analysis of spillovers and risk management, although they capture the return asymmetry and fat-tailedness, respectively, arising from the non-normality of returns. In this paper, we provide evidence of the relevance and utility of considering spillovers in volatility and higher-order moments (skewness, and kurtosis) and co-moments (covariance, co-skewness, and co-kurtosis), and their implications for hedging. Using high-frequency data on the US stock, crude oil, and gold markets, a time-varying spillover approach and portfolio analysis, we reveal the following results. Firstly, besides volatility and covariance, co-skewness and co-kurtosis are relevant spillover transmitters across the stock, crude oil, and gold markets. Secondly, the level of total spillover increases when including not only covariance but also co-skewness and co-kurtosis, suggesting the relevance of considering higher order co-moments beyond volatility when studying spillovers. Thirdly, the inclusion of co-moments in the spillover analysis generates a significant improvement in hedging for all pairs, which is reflected in the significant increase in the utility function when co-skewness and co-kurtosis are considered. This result is noted when the COVID-19 sub-period is considered separately, except for oil‑gold. Overall, the findings matter for the system of interconnectivity across various assets and emphasize the implications and contributions of higher-order moments and co-moments to portfolio allocation and financial risk management.

Ex-ante real estate Value at Risk calculation method

The computation of Value at Risk (VaR) has long been a problematic issue in commercial real estate. Difficulties mainly arise from the lack of appropriate data, the lack of transactions, the non-normality of returns, and the inapplicability of many of the traditional methodologies. In addition, specific risks remain latent in investors’ portfolios and thus risk measurements based on market index do not represent the risks of a specific portfolio. Following a spate of new regulations such as Basel II, Basel III, NAIC and Solvency II, financial institutions have increasingly been required to estimate and control their exposure to market risk. Hence, financial institutions now commonly use “internal” VaR (or Expected Shortfall) models in order to assess their market risk exposure. This paper proposes the first model designed especially for static real estate VaR computation. The proposal accounts for specific real estate characteristics such that the lease structures or the vacancies. The paper contributes to the real estate risk management literature by proposing for the first time a model that incorporates characteristics of real estate investments. It allows more precise real estate risk measurements and is derived from a regulators’ approach.

Cornish-Fisher Expansion for Commercial Real Estate Value at Risk

The computation of Value at Risk has traditionally been a troublesome issue in commercial real estate. Difficulties mainly arise from the lack of appropriate data, the non-normality of returns, and the inapplicability of many of the traditional methodologies. As a result, calculation of this risk measure has rarely been done in the real estate field. However, following a spate of new regulations such as Basel II, Basel III, NAIC and Solvency II, financial institutions have increasingly been required to estimate and control their exposure to market risk. As a result, financial institutions now commonly use “internal” Value at Risk (V a R) models in order to assess their market risk exposure. The purpose of this paper is to estimate distribution functions of real estate V a R while taking into account non-normality in the distribution of returns. This is accomplished by the combination of the Cornish-Fisher expansion with a certain rearrangement procedure. We demonstrate that this combination allows superior estimation, and thus a better V a R estimate, than has previously been obtainable. We also show how the use of a rearrangement procedure solves well-known issues arising from the monotonicity assumption required for the Cornish-Fisher expansion to be applicable, a difficulty which has previously limited the useful of this expansion technique. Thus, practitioners can find a methodology here to quickly assess Value at Risk without suffering loss of relevancy due to any non-normality in their actual return distribution. The originality of this paper lies in our particular combination of Cornish-Fisher expansions and the rearrangement procedure.

Initial public offerings: an asset allocation decision based on nonnormal returns

This study analyses whether the inclusion of initial public offering (IPO) stocks as part of an optimal asset allocation strategy can reduce the systematic risk of an investment portfolio. The asset allocation framework takes account of nonnormality of returns from a universe of eight asset classes using 240 monthly returns between January 1992 and December 2011. AR-GJR-GARCH models resolve the tail dependence and heteroscedasticity in the return series. Generalized Pareto distributions help to fit the heavy-tailed return distributions, while copula functions help to calibrate the dependence structure between the asset returns. The optimization algorithm persistently includes IPO stocks as part of an optimal asset allocation strategy. Their portfolio inclusion reduces the conditional value-at-risk and improves the risk-return trade-off.

Explaining the Volatility Surface: A Closed-Form Solution to Option Pricing in a Fractional Jump-Diffusion Market

This paper prices European options in a framework that captures both non-normality of returns and serial correlation within financial time series. The underlying security dynamics are driven by a jump-diffusion process where the diffusion part is fractional Brownian motion while jumps exhibit a double-exponential distribution. These model characteristics suffice to overcome most of the evidentdrawbacks of the classical Black-Scholes setting, while the parsimony of my model still ensures analytical tractability.

Multivariate Downside Risk: Normal Versus Variance Gamma

Although several types of options on multiple assets are popular in today's financial markets, valuing multi-asset options is still a challenge in finance. The standard framework of multivariate normality is often inappropriate, since it ignores fat tails and other stylized facts of asset returns. The Variance Gamma (VG) model appears to be a promising alternative. In the univariate case, it has become a standard tool in the financial industry. One way to extend the model to the multivariate case is to subordinate a Brownian motion through a univariate subordinator. We study this model in a large-scale application with multi-asset options traded in an active market. Our database consists of 468 multivariate barrier reverse convertibles at the Swiss market for structured products. The Swiss market ranks among the largest in the world and is characterized by an exceptional popularity of multiple asset options. Apart from the empirical analysis of the multivariate VG model, our study aims to contribute to the literature on pricing of structured financial products. The existing studies typically derive fair values from the normal model, which might seriously bias the results on the degree of overpricing. We find that smile-consistent calibration is possible in 277 out of 468 cases in our sample. The estimated multivariate VG processes significantly differ from multivariate Brownian Motion. In particular, the VG model implies a higher probability of strongly negative returns with a final stock price below the barrier. The value difference to the normal model depends primarily on the time-to-maturity and the degree of skewness in the smile patterns. We conclude that non-normality of returns cannot be ignored when valuing multi-asset options, which is important for future studies on the overpricing of exotic structured products.

MaxVaR for non-normal and heteroskedastic returns¶

In this work we propose Monte Carlo simulation models for dynamically computing MaxVaR for a financial return series. This dynamic MaxVaR takes into account the time-varying volatility as well as non-normality of returns or innovations. We apply this methodology to five stock market indices. To validate the proposed methods we compute the number of MaxVaR violations and compare them with the expected number. We also compute the MaxVaR-to-VaR ratio and find that, on average, dynamic MaxVaR exceeds dynamic VaR by 5–7% at the 1% significance level, and by 12–14% at the 5% significance level for the selected indices. ¶This work was carried out when Nityanand Misra and Bharat Kodase were graduate students at the Indian Institute of Management Bangalore.

Short Term Predictability, Volume and Microstructure Effects in Stock Prices

This paper documents strong evidence for short term predictability of individual stocks in the London Stock Exchange. We find empirical evidence for price reversals after large price changes and price continuation after small price changes. Our results indicate that large companies seem to react more efficiently to previous price changes and that the effect has been robust over time. The results are robust to non-normality of returns and are not explained by market microstructure effects like nonsynchronous trading or bid-ask bounce. We further investigate whether the effect can be explained by rational asset-pricing theory or behavioral theories. In these investigations we employ volume as an additional explanatory variable. Finally when considering whether the predictability has any implications for market efficiency we show that the size of bid-ask spreads are highly related to previous price movements.

Volatility as an Asset Class: European Evidence

Volatility movements are known to be negatively correlated with stock index returns. Hence, investing in volatility appears to be attractive for investors seeking risk diversification. The most common instruments for investing in pure volatility are variance swaps, which now enjoy an active over-the-counter market. This paper investigates the risk-return tradeoff of variance swaps on the Deutscher Aktienindex (DAX) and EuroStoxx50 index (ESX) over the time period of 1995 to 2004. We synthetically derive variance swap rates from the smile in option prices. Using quotes from two large investment banks over two months, we validate that the synthetic values are close to OTC market prices. Our objective is to analyze the relationship between index and variance swap returns, including extreme events like September 11, 2001. We find that the variance swap return pattern shows a pronounced kink at zero index return. This not only highlights the importance of differentiating between up and down markets but also sheds new light on the leverage effect. Due to the option-like profile of returns it is crucial to account for the non-normality of returns in measuring the performance of variance swap investments. Based on the empirical analysis, we finally draw conclusions for investors. Our backtests result in significant short volatility positions in optimal portfolios during the sample period. Typically, the stock index weight is also negative, since the diversification gain exceeds the loss in expected return.

Stocks, bonds and the investment horizon: a test of time diversification on the French market

In this paper, we investigate the relative performance of stocks and bonds for various investment horizons on the French market. We use a new matched block bootstrap approach to take account of estimation risk. Furthermore, in the light of non-normality of returns, we use two different risk approaches as inputs in portfolio optimization: the traditional variance, and a downside risk measure, the semi-variance. Our results suggest that an investor should avoid bonds in the long run due to the time diversification effect.

Uncertainty in Second Moments: Implications for Portfolio Allocation

This paper investigates the uncertainty in second moments of asset returns. It is commonly believed that the second moments are accurately measured. However, time varying volatility and nonnormality of returns can lead to imprecise variance estimates. Using CRSP value weighted monthly returns from 1926 to 2001, the paper shows that the variance is less accurately estimated than the expected return. In addition, a mean variance investor will incur significant certainty equivalent loss due to the uncertainty in second moments. Applying the Fama French 3 factor model to 25 size, BE/ME sorted portfolios from 1963 to 2001, the loss due to the second moment estimation can be shown to be as large as the loss due to the first moment estimation. Moreover, as the number of assets in the portfolio increases, the loss due to the uncertainty in second moments becomes larger. This provides a possible explanation to the home bias puzzle.

Stocks, Bonds And The Investment Horizon : Another Look At Time Diversification On The French Market

In this paper, we investigate the relative performance of stocks and bonds for various investment horizons on the French Market. We use a new Markowian moving block bootstrap approach to take account for estimation risk. Furthermore, in the light of non normality of returns, we use two different risk approach as input in portfolio optimization - the traditional variance and a downside risk measure, the semi variance.

Accounting for Illiquidity and Non-Normality of Returns in the Performance Assessment

The present paper proposes a new family of performance measures for opaque asset portfolios, such as credit assets and alternative investment forms (CTA, managed commodity funds, etc.), where due to prevalent non-normality and/or lacking liquidity no capital market equilibrium-based performance measures apply. The considered performance measures center on the shape of the expected risky payoff available for consumpton, regardless of the underling's nature. The proposed methodology is based on the variance, skewness and kurtosis (omega-s-k) as risk components. Investors value risky payoffs with these terms, and compare them with other investment opportunities, looking for good-deals. Using optioned markets, it is also possible to create replicating payoff profiles, that is, investments with identical (omega-s-k) terms, and the expected return of this replicating portfolio serves as a natural benchmark for performance comparisons. We propose a multi-moment framework for creating and pricing the replicating optioned portfolios, on which a new family of performance measures is built up.