Excluding sum stable distributions as an explanation of second moment condition failure - the Australian evidence (original) (raw)
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Moment Condition Failure Australian Evidence
SSRN Electronic Journal, 2000
This paper examines the existence of stock return moments in the less liquid Australian market. We initially find conflicting results. Characteristic exponent point estimates of approximately 1.5 are found for Australian stocks, in line with previous US research findings. This would imply that the population variance is infinite. On the other hand, Hill-estimates, are above 2 for all stocks indicating that second moments do exist. This conflicting result is resolved by setting up a simulation experiment in which we show that combinations of the Hill-estimate and the characteristic exponent, produced by the real data, are extremely unlikely for sum stables. These results provide further evidence for the existence of second moments. However, the determination of the existence of fourth moments still remains unresolved.
An investigation of higher order moments of empirical financial data and the implications to risk
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Here, we analyse the behaviour of the higher order standardised moments of financial time series when we truncate a large data set into smaller and smaller subsets, referred to below as time windows. We look at the effect of the economic environment on the behaviour of higher order moments in these time windows. We observe two different scaling relations of higher order moments when the data sub sets’ length decreases; one for longer time windows and another for the shorter time windows. These scaling relations drastically change when the time window encompasses a financial crisis. We also observe a qualitative change of higher order standardised moments compared to the gaussian values in response to a shrinking time window. We extend this analysis to incorporate the effects these scaling relations have upon risk. We decompose the return series within these time windows and carry out a Value-at-Risk calculation. In doing so, we observe the manifestation of the scaling relations thro...
An investigation of higher order moments of empirical financial data and their implications to risk
Heliyon, 2022
Higher order standardised moments Value-at-risk Gaussian mixtures Here, we analyse the behaviour of the higher order standardised moments of financial time series when we truncate a large data set into smaller and smaller subsets, referred to below as time windows. We look at the effect of the economic environment on the behaviour of higher order moments in these time windows. We observe two different scaling relations of higher order moments when the data sub sets' length decreases; one for longer time windows and another for the shorter time windows. These scaling relations drastically change when the time window encompasses a financial crisis. We also observe a qualitative change of higher order standardised moments compared to the gaussian values in response to a shrinking time window. Moreover, we model the observed scaling laws by analysing the hierarchy of rare events on higher order moments. We extend the analysis of the scaling relations to incorporate the effects these scaling relations have upon risk. We decompose the return series within these time windows and carry out a Value-at-Risk calculation. In doing so, we observe the manifestation of the scaling relations through the change in the Value-at-Risk level.
An investigation of higher order moments of empirical financial data series
2021
Here we analyse the behaviour of the higher order moments of financial series when we truncate a large data set into smaller and smaller subsets, referred to below as time windows. Additionally, we look at the effect of the economic environment on the behaviour of higher order moments in these time windows. We observe two different nontrivial scaling relations of higher order moments when the data sub sets' length decreases; one for longer time windows and another for the shorter time windows. The scaling relations drastically change when the time window encompasses a financial crisis. We also observe a qualitative change of higher order standardised moments compared to the gaussian values in response to a shrinking time window.
Stock Return Distributions: Tests of Scaling and Universality from Three Distinct Stock Markets
We examine the validity of the power-law tails of the distributions of stock returns P͕R Ͼ x͖ϳx − R using trade-by-trade data from three distinct markets. We find that both the negative as well as the positive tails of the distributions of returns display power-law tails, with mutually consistent values of R Ϸ 3 for all three markets. We perform similar analyses of the related microstructural variable, the number of trades N ϵ N ⌬t over time interval ⌬t, and find a power-law tail for the cumulative distribution P͕N Ͼ x͖ϳx − N , with values of N that are consistent across all three markets analyzed. Our analysis of U.S. stocks shows that the exponent values R and N do not display systematic variations with market capitalization or industry sector. Moreover, since R and N are remarkably similar for all three markets, our results support the possibility that the exponents R and N are universal.
Uncertainty in Second Moments: Implications for Portfolio Allocation
SSRN Electronic Journal, 2003
This paper investigates the uncertainty in variance and covariance of asset returns. It is commonly believed that these second moments can be estimated very accurately. However, time varying volatility and nonnormality of asset returns can lead to imprecise variance estimates. Using CRSP value weighted monthly returns from 1926 to 2001, this 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 variance estimation can be shown to be as large as the loss due to the expected return estimation. Moreover, as the number of assets in the portfolio increases, the loss due to the variance uncertainty becomes larger. This provides a possible explanation to the home bias puzzle.
2008
Setup and first-order asymptotic theory 2.1 Setup 98 2.2 The realized covariance matrix 99 2.3 The realized covariance 2.4 The realized correlation 101 ix 2.5 The realized regression 102 2.6 Monte Carlo resuits for the first-order asymptotic theory 103 3 The bootstrap 3.1 The bootstrap realized covariance matrix. 3.2 The bootstrap realized covariance 108 3.3 The bootstrap realized correlation 108 3.4 The bootstrap realized regression 109 3.5 Ivlonte Carlo resuits for the bootstrap 109 4 A detailed study of realized regressions 111 4.1 The first order asymptotic theory revisited 4.2 First order asymptotic properties of the pairwise bootstrap 113 4.3 Second order asymptotic properties of the pairwise bootstrap 5 Empirical application 118 6 Conclusion 3.1 Asymptotic expansions of the curnulants of T,3,h 3.2 Asymptotic expansions of the bootstrap cumulants of. . .
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2004
Testing for normality is of paramount importance in many areas of science since the Gaussian distribution is a key hypothesis in many models. As the use of semi–moments is increasing in physics, economics or finance, often to judge the distributional properties of a given sample, we propose a test of normality relying on such statistics. This test is proposed in three different versions and an extensive study of their power against various alternatives is conducted in comparison with a number of powerful classical tests of normality. We find that semi–moments based tests have high power against leptokurtic and asymmetric alternatives. This new test is then applied to stock returns, to study the evolution of their normality over different horizons. They are found to converge at a “log-log” speed, as are moments and most semi–moments. Moreover, the distribution does not appear to converge to a real Gaussian.
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