Distribution Characteristics of Multivariate Financial Assets Return based on Mathematical Model

For the non-normality and time variability of the distribution of multivariate financial assets return, a dynamic model of the distribution of multivariate financial assets return based on mathematical model is constructed in this paper. AR(1)-DCC(1,1)-GARCH(1,1) model reflects dynamic characteristics of conditional expectation and conditional variance of multivariate financial assets return. It solves the problem that restricts the in-depth research on high order dynamic portfolio optimization, which is the estimation of conditional coskewness matrix and conditional cokurtosis matrix. By constructing a multi-dimensional fluctuation model with biased t distribution, conditional asymmetric parameter and conditional free degree parameter, the distribution of multivariate financial assets return is researched. Experimental results show that the proposed model can reasonably reflect the time-varying characteristics of the multivariate stock return distribution in China’s stock market.

Contrasting Cryptocurrencies with Other Assets: Full Distributions and the COVID Impact

We investigate any similarity and dependence based on the full distributions of cryptocurrency assets, stock indices and industry groups. We characterize full distributions with entropies to account for higher moments and non-Gaussianity of returns. Divergence and distance between distributions are measured by metric entropies, and are rigorously tested for statistical significance. We assess the stationarity and normality of assets, as well as the basic statistics of cryptocurrencies and traditional asset indices, before and after the COVID-19 pandemic outbreak. These assessments are not subjected to possible misspecifications of conditional time series models which are also examined for their own interests. We find that the NASDAQ daily return has the most similar density and co-dependence with Bitcoin daily return, generally, but after the COVID-19 outbreak in early 2020, even S&P500 daily return distribution is statistically closely dependent on, and indifferent from Bitcoin daily return. All asset distances have declined by 75% or more after the COVID-19 outbreak. We also find that the highest similarity before the COVID-19 outbreak is between Bitcoin and Coal, Steel and Mining industries, and after the COVID-19 outbreak is between Bitcoin and Business Supplies, Utilities, Tobacco Products and Restaurants, Hotels, Motels industries, compared to several others. This study shed light on examining distribution similarity and co-dependence between cryptocurrencies and other asset classes.

Distributional Replication

A function which transforms a continuous random variable such that it has a specified distribution is called a replicating function. We suppose that functions may be assigned a price, and study an optimization problem in which the cheapest approximation to a replicating function is sought. Under suitable regularity conditions, including a bound on the entropy of the set of candidate approximations, we show that the optimal approximation comes close to achieving distributional replication, and close to achieving the minimum cost among replicating functions. We discuss the relevance of our results to the financial literature on hedge fund replication; in this case, the optimal approximation corresponds to the cheapest portfolio of market index options which delivers the hedge fund return distribution.

Kurtosis and Skewness on Lagged Market Risk Premium in Indonesian Market During Covid 19 Pandemic

This study investigates the impact of return distribution such as skewness and kurtosis on lagged market risk premium to risk premium in Indonesia capital market during COVID-19 pandemic. Data are monthly, from january to December 2020, and 674 firms. Panel data predictive regression is used The method For this study, I first looked for market risk premium and risk premium desripitives. Second, I used monthly panel data predictive regression from lagged market risk premium and risk premium in 2020. Third, I incorporate skewness and kurtosis simultaneously. Fourth, I exclude kurtosis or skewness in previous model. The results are market risk premium and risk premium having negative return. Risk premium has lower returns than market risk premium. The beta lagged market risk premium is significant to risk premium. The skewness and kurtosis market risk premium do not signify to risk premium together but significant separately. I can clonclude that the movement market risk premim and risk premium during COVID-19 pandemic are average negative. Beta lagged market risk premium can explain the future monthly risk premium. Contrary skewness and kurtosis, those can not be run together. When the model used to beta lagged market risk premium and skewness, partially the skewness was significant and the direction was positive. However, only beta lagged market risk premium and kurtosis were staying negative to the previous model. Incorporating lagged assumptive distribution only explain the risk premium under 1 % about 0.24%.

Crowded Trades, Market Clustering, and Price Instability

Crowded trades by similarly trading peers influence the dynamics of asset prices, possibly creating systemic risk. We propose a market clustering measure using granular trading data. For each stock, the clustering measure captures the degree of trading overlap among any two investors in that stock, based on a comparison with the expected crowding in a null model where trades are maximally random while still respecting the empirical heterogeneity of both stocks and investors. We investigate the effect of crowded trades on stock price stability and present evidence that market clustering has a causal effect on the properties of the tails of the stock return distribution, particularly the positive tail, even after controlling for commonly considered risk drivers. Reduced investor pool diversity could thus negatively affect stock price stability.

Asset Liability Management for the Parliamentary Pension Scheme of Uganda by Stochastic Programming

We develop a model for asset liability management of pension funds, which is solved by stochastic programming techniques. Using data provided by the Parliamentary Pension Scheme of Uganda, we obtain the optimal investment policies.Randomly sampled scenario trees using the mean, and covariance structure of the return distribution are used for generating the coefficients of the stochastic program. Liabilities are modelled by remaining years of life expectancy and guaranteed period for monthly pension.We obtain the funding situation of the scheme at each stage under three different asset investment limits.

GARCH with generalized Pareto tail

This paper proposes the use of a spliced distribution with generalized Pareto tail for financial risk management. The proposed distribution is tailored to flexibly capture the heavy tail in asset return distribution. The parameters of the distribution can be estimated jointly with a conditional heteroskedasticity model. The estimated parameters can then be used to produce tail risk forecasts for risk management purposes. The use of the proposed distribution is illustrated by evaluating tail risk forecasts for a number of major stock indices.