Optimal portfolio allocation with higher moments

We model the risky asset as driven by a pure jump process, with non-trivial and tractable higher moments. We compute the optimal portfolio strategy of an investor with CRRA utility and study the sensitivity of the investment in the risky asset to the higher moments, as well as the resulting wealth loss from ignoring higher moments. We find that ignoring higher moments can lead to significant overinvestment in risky securities, especially when volatility is high.      

Realised higher moments: theory and practice

This paper examines the incorporation of higher moments in portfolio selection problems utilising high-frequency data. Our approach combines innovations from the realised volatility literature with a portfolio selection methodology utilising higher moments. We provide an empirical study of the measurement of higher moments from tick by tick data and implement the model for a selection of stocks from the DOW 30 over the time period 2005–2011. We demonstrate a novel estimator for moments and co-moments in the presence of microstructure noise.     

Second and higher moments of fundamentals: A literature review

This literature review outlines the recent progress in fundamental second and higher moments of research. We survey the moments’ existence, formation, and financial market and macroeconomic implications. Research shows that time‐varying volatility and non‐Gaussian shocks exist throughout all measures of fundamentals at both the micro‐ and macro levels. In addition, the granular network among firms helps explain the origin of fundamental second and higher moments. Empirical evidence shows that the moments have strong predictive power on asset prices and macroeconomic variables. We also highlight several areas where more research is needed to better understand the moments.     

Effects of market default risk on index option risk-neutral moments

We investigate the relative importance of market default risk in explaining the time variation of the S&P 500 Index option-implied risk-neutral moments. The results demonstrate that market default risk is positively (negatively) related to the index risk-neutral volatility and skewness (kurtosis). These relations are robust in the presence of other factors relevant to the dynamics and microstructure nature of the spot and option markets. Overall, this study sheds light on a set of economic determinants which help to understand the daily evolution of the S&P 500 Index option-implied risk-neutral distributions. Our findings offer explanations of why theoretical predictions of option pricing models are not consistent with what is observed in practice and provide support that market default risk is important to asset pricing.     

Integral and differential equations for the moments of multistate models in health insurance

The moments of the random future liabilities of health insurance policies are key quantities for studying distributional properties of the future liabilities. Assuming that the randomness of the future health status of individual policyholders can be described by a semi-Markovian multistate model, integral and differential equations are derived for moments of any order and for the moment generating function. Different representations are derived and discussed with a view to numerical solution methods.     

Some results on relocation policies

In this paper, we derive general results concerning optimal relocation policy under some assumptions. We consider a firm that is located in a specific location, producing at a certain level of efficiency. With time, the firm can decide to change its location to a new and more efficient site, paying relocation costs. Moreover, we assume that these new sites become available according to a Poisson process, and that the levels of efficiency improvement inherent to each one of these sites are random variables. With this framework, we characterise certain parameters of the optimal relocation policy. In particular, we characterise the expected relocation time and we prove that it depends on the distribution of the level of efficiency improvement only through an expected value. Therefore, the optimal policy shows a kind of robustness in terms of the stochastic assumptions of the problem, which has a major impact in the application of relocation policies. In addition, we also characterise the optimal relocation time. Impacts on the final results driven by the characteristics of the firm's original location site, the market environment and the way in which risk is modelled are studied numerically. The overall results are in line with economic intuition.     

Diversification benefits of NFTs for conventional asset investors: Evidence from CoVaR with higher moments and optimal hedge ratios

This study investigates the risk and returns on one of the newest digital asset classes instruments, non-fungible tokens (NFTs), by accounting for tail dependence of higher-order moments and portfolio characteristics. We used a wide range of asset classes, encompassing equites, fixed income securities, and commodities, and document the desirable hedging and portfolio attributes of NFTs by employing Conditional Value-at-Risk (CoVaR) and ∆CoVaRs with various copula functions. We found that NFTs exhibit beneficial investment and hedging attributes under all market conditions, including the Covid-19 pandemic. Our findings have important implications for investors, risk managers, and regulators.     

Some results on the compound Markov binomial model

Abstract

Some years ago, in the course of an analysis of upper and lower limits for incomplete moments of statistical distributions I established an elementary summation formula¹ which proved rather useful for the purpose I had in view. Subsequently the formula was generalized by professor Steffensen, who showed² that the formula in question could be looked upon as giving the first term of an expansion in a certain type of series. Professor Steffensen established recurrence formulae for the coefficients of the series and computed the second, third and fourth term and the corresponding remainders¹, but did not arrive at a general, explicite expression for the coefficient of the n-th term and the corresponding remainder. A year later I found these expressions accidentally while I was working on some other problem. I also discovered the real nature of the procedure in question which proved to be a certain kind of least square fitted polynomial approximation. I did not, however, at the time publish the result. Taking the question up again later I found that the whole problem could be considerably generalized. The type of generalization in question is analogous to the generalization from polynomials to arbitrary functions.     

The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics

This paper investigates the role of stochastic volatility and return jumps in reproducing the volatility dynamics and the shape characteristics of the Korean Composite Stock Price Index (KOSPI) 200 returns distribution. Using efficient method of moments and reprojection analysis, we find that stochastic volatility models, both with and without return jumps, capture return dynamics surprisingly well. The stochastic volatility model without return jumps, however, cannot fully reproduce the conditional kurtosis implied by the data. Return jumps successfully complement this gap. We also find that return jumps are essential in capturing the volatility smirk effects observed in short-term options.

Recursions and fast Fourier transforms for a new bivariate aggregate claims model

Insurance companies typically face multiple sources (types) of claims. Therefore, modelling dependencies among different types of risks is extremely important for evaluating the aggregate claims of an insurer. In this paper, we first introduce a multivariate aggregate claims model, which allows dependencies among claim numbers as well as dependencies among claim sizes. For this proposed model, we derive recursive formulas for the joint probability functions of different types of claims. In addition, we extend the concept of exponential tilting to the multivariate fast Fourier transform and use it to compute the joint probability functions of the various types of claims. We provide numerical examples to compare the accuracy and efficiency of the two computation methods.     

Interest rates and exchange rates: Some new empirical results

This paper presents indirect evidence on the behavior on the real interest rate by studying the correlations between changes in nominal interest rates and in exchange rates. These correlations are examined both before and after October 6, 1979. The empirical evidence supports the views that monetary shocks affect the real rate and that the change in Fed monetary policy on October 6 led to greater variation in the real rate.     

Equilibrium compound distributions and stop-loss moments

A convolution representation is derived for the equilibrium or integrated tail distribution associated with a compound distribution. This result allows for the derivation of reliability properties of compound distributions, as well as an explicit analytic representation for the stop-loss premium, of interest in connection with insurance claims modelling. This result is extended to higher order equilibrium distributions, or equivalently to higher stop-loss moments. Special cases where the counting distribution is mixed Poisson or discrete phase-type are considered in some detail. An approach to handle more general counting distributions is also outlined.     

Black-market exchange-rate expectations and the domestic demand for money: Some empirical results

This paper analyzes the effects of expectations about future exchange-rate adjustments on the demand for money. These effects are studied empirically for the case of countries which have imposed foreign-exchange restrictions. The results obtained for Brazil, Chile, and Colombia indicate that the demand for money is significantly reduced when expectations of black-market depreciation intensify; and that when this variable (for which the proxy used is the divergence of the black-market exchange rate from purchasing power parity) is omitted from the demand-for-money function, the response of the demand for money to changes in the expected rate of domestic inflation tends to be overestimated.     

Performance evaluation with high moments and disaster risk

Traditional performance evaluation measures do not account for tail events and rare disasters. To address this issue, we reinterpret the riskiness measures of Aumann and Serrano (2008) and Foster and Hart (2009) as performance indices. We derive the moment properties of these indices and their sensitivity to rare disasters and show that they are consistent with the asset pricing literature. As applications, we show that “anomalous” investment strategies such as “momentum” or investment in private equity lose much of their glamour when accounting for high moments and rare events. Furthermore, using the indices to select mutual funds results in desirable high-moment properties out of sample.     

Monthly Pattern and Portfolio Effect on Higher Moments of Stock Returns: Empirical Evidence from Hong Kong

Using a direct test, this paper studies the month-of-the-year effect on the higher moments of six industrial stock indices of the Hong Kong market. We also examine the portfolio effect on skewness and kurtosis across month of the year to see if such an anomaly exists. The empirical results support a weak month-of-the-year effect in higher moments of stock returns. Using a complete sample of all possible combinations for each portfolio size, we show that portfolio effect varies across month of the year for both skewness and kurtosis. In particular, our results show that diversification does not necessarily provide benefits to rational investors when the stock return distribution is non-normal, even though portfolio formation can reduce standard deviation. In June, August and October, diversification across industrial sectors results in a more negatively skewed and leptokurtic return distribution, which is not preferred by investors with risk-aversion. Two (one) possible explanations for the portfolio effect on skewness (kurtosis) are also provided. Our empirical results add new evidence to the existence of anomalies in the Hong Kong stock market. This revised version was published online in August 2006 with corrections to the Cover Date.     

Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging

In this paper, we analyze properties of multinomial lattices that model general stochastic dynamics of the underlying stock by taking into account any given cumulants (or moments). First, we provide a parameterization of multinomial lattices, and demonstrate that mean, variance, skewness, and kurtosis of the underlying may be matched using five branches. Then, we investigate the convergence of the multinomial lattice when the basic time period approaches zero, and prove that the limiting process of the multinomial lattice that matches annualized mean, variance, skewness and kurtosis is given by a compound Poisson process. Finally, we illustrate the effect of higher order moments in the underlying asset process on the price of derivative securities through numerical experiments using the multinomial lattice, and provide a comparison with jump-diffusion models.     

S -Convex Extrema,Taylor-Type Expansions and Stochastic Approximations

The present work studies s -convex orders using a remarkable probabilistic generalization of Taylor's theorem obtained by Massey & Whitt (1993) and further discussed by Lin (1994). We propose two methods for approximating a given risk with known first moments by means of s -convex extremal distributions. The goodness of those approximations is explored using stop-loss distances. Several applications show the interest of this approach in actuarial sciences.     

资产评估与审计关系的综述及思考

西方国家在长期资本市场发展过程中,评估与审计行业已经形成了相互独立、相对稳定、分工明确的两大阵营。随着我国经济日益发展、业务逐渐规范以及行业格局变革,早期的研究主要从目的、性质、原则、职能、方法等诸多方面阐述资产评估与审计的关系,侧重理论引导,成果多见于高校资产评估学教材,也有些研究性文章专题论述了特定经济环境下两者之间的关系;近年的研究主要探讨在国企改制、上市重组、债转股等方面两者的业务协同、工作顺序等问题,侧重于实务推动。本文拟通过对文献的整理,旨在厘清思路、梳理业务协作边界、提出问题及建议。