Portfolio Return Distributions: Sample Statistics With Stochastic Correlations

Chetalova, Desislava; Schmitt, Thilo A.; Schäfer, Rudi; Guhr, Thomas

doi:10.1142/s0219024915500120

Cited by 13 publications

(20 citation statements)

References 36 publications

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“…In particular, we investigate the stability of their corresponding correlation structures. We address this question by means of a random matrix approach introduced in [4,5]. It models the non-stationarity of the correlations by an ensemble of random matrices.…”

Section: Introductionmentioning

confidence: 99%

Zooming into market states

Chetalova¹,

Schäfer²,

Guhr³

2015

J. Stat. Mech.

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We analyze the daily stock data of the Nasdaq Composite index in the 22-year period 1992 − 2013 and identify market states as clusters of correlation matrices with similar correlation structures. We investigate the stability of the correlation structure of each state by estimating the statistical fluctuations of correlations due to their non-stationarity. Our study is based on a random matrix approach recently introduced to model the non-stationarity of correlations by an ensemble of random matrices. This approach reduces the complexity of the correlated market to a single parameter which characterizes the fluctuations of the correlations and can be determined directly from the empirical return distributions. This parameter provides an insight into the stability of the correlation structure of each market state as well as into the correlation structure dynamics in the whole observation period. The analysis reveals an intriguing relationship between average correlation and correlation fluctuations. The strongest fluctuations occur during periods of high average correlation which is the case particularly in times of crisis.

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Section: Introductionmentioning

confidence: 99%

Zooming into market states

Chetalova¹,

Schäfer²,

Guhr³

2015

J. Stat. Mech.

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“…A K component vector r = r 1 , ..., r K with elements r k , k = 1, ..., K, normalized to zero mean and unit variance, follows a multivariate K distribution [16,17], if its probability density is given by…”

Section: Bivariate K Copula Densitymentioning

confidence: 99%

Local fluctuations of the signed traded volumes and the dependencies of demands: a copula analysis

Wang¹,

Guhr²

2018

J. Stat. Mech.

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We investigate how the local fluctuations of the signed traded volumes affect the dependence of demands between stocks. We analyze the empirical dependence of demands using copulas and show that they are well described by a bivariate K copula density function. We find that large local fluctuations strongly increase the positive dependence but lower slightly the negative one in the copula density. This interesting feature is due to cross-correlations of volume imbalances between stocks. Also, we explore the asymmetries of tail dependencies of the copula density, which are moderate for the negative dependencies but strong for the positive ones. For the latter, we reveal that large local fluctuations of the signed traded volumes trigger stronger dependencies of demands than of supplies, probably indicating a bull market with persistent raising of prices.

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“…on short time horizons where the covariance matrix Σ st for this time interval can be viewed as stationary, see [22]. We recall that we receive the average return distribution by averaging Eq.…”

Section: Empirical Return Distributionmentioning

confidence: 99%

“…Importantly, the covariance and correlation matrix of asset values changes in time [18,19,20,21]. We assume that the asset values are distributed according to a correlation averaged multivariate distribution, which we recently introduced [22]. The validity of this assumption is verified by an extensive empirical study of the asset returns.…”

Section: Introductionmentioning

confidence: 99%

Credit risk: taking fluctuating asset correlations into account

Schmitt¹,

afer²,

Guhr³

2015

JCR

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In structural credit risk models, default events and the ensuing losses are both derived from the asset values at maturity. Hence it is of utmost importance to choose a distribution for these asset values which is in accordance with empirical data. At the same time, it is desirable to still preserve some analytical tractability. We achieve both goals by putting forward an ensemble approach for the asset correlations. Consistently with the data, we view them as fluctuating quantities, for which we may choose the average correlation as homogeneous. Thereby we can reduce the number of parameters to two, the average correlation between assets and the strength of the fluctuations around this average value. Yet, the resulting asset value distribution describes the empirical data well. This allows us to derive the distribution of credit portfolio losses. With Monte-Carlo simulations for the Value at Risk and Expected Tail Loss we validate the assumptions of our approach and demonstrate the necessity of taking fluctuating correlations into account.

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Portfolio Return Distributions: Sample Statistics With Stochastic Correlations

Cited by 13 publications

References 36 publications

Zooming into market states

Zooming into market states

Local fluctuations of the signed traded volumes and the dependencies of demands: a copula analysis

Credit risk: taking fluctuating asset correlations into account

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