15 research outputs found
Principal Regression Analysis and the index leverage effect
We revisit the index leverage effect, that can be decomposed into a
volatility effect and a correlation effect. We investigate the latter using a
matrix regression analysis, that we call `Principal Regression Analysis' (PRA)
and for which we provide some analytical (using Random Matrix Theory) and
numerical benchmarks. We find that downward index trends increase the average
correlation between stocks (as measured by the most negative eigenvalue of the
conditional correlation matrix), and makes the market mode more uniform. Upward
trends, on the other hand, also increase the average correlation between stocks
but rotates the corresponding market mode {\it away} from uniformity. There are
two time scales associated to these effects, a short one on the order of a
month (20 trading days), and a longer time scale on the order of a year. We
also find indications of a leverage effect for sectorial correlations as well,
which reveals itself in the second and third mode of the PRA.Comment: 10 pages, 7 figure
Individual and collective stock dynamics: intra-day seasonalities
We establish several new stylised facts concerning the intra-day
seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the
volatility, we find that the average correlation between stocks increases
throughout the day, leading to a smaller relative dispersion between stocks.
Somewhat paradoxically, the kurtosis (a measure of volatility surprises)
reaches a minimum at the open of the market, when the volatility is at its
peak. We confirm that the dispersion kurtosis is a markedly decreasing function
of the index return. This means that during large market swings, the
idiosyncratic component of the stock dynamics becomes sub-dominant. In a
nutshell, early hours of trading are dominated by idiosyncratic or sector
specific effects with little surprises, whereas the influence of the market
factor increases throughout the day, and surprises become more frequent.Comment: 9 pages, 7 figure
The fine-structure of volatility feedback I: multi-scale self-reflexivity
We attempt to unveil the fine structure of volatility feedback effects in the
context of general quadratic autoregressive (QARCH) models, which assume that
today's volatility can be expressed as a general quadratic form of the past
daily returns. The standard ARCH or GARCH framework is recovered when the
quadratic kernel is diagonal. The calibration of these models on US stock
returns reveals several unexpected features. The off-diagonal (non ARCH)
coefficients of the quadratic kernel are found to be highly significant both
In-Sample and Out-of-Sample, but all these coefficients turn out to be one
order of magnitude smaller than the diagonal elements. This confirms that daily
returns play a special role in the volatility feedback mechanism, as postulated
by ARCH models. The feedback kernel exhibits a surprisingly complex structure,
incompatible with models proposed so far in the literature. Its spectral
properties suggest the existence of volatility-neutral patterns of past
returns. The diagonal part of the quadratic kernel is found to decay as a
power-law of the lag, in line with the long-memory of volatility. Finally,
QARCH models suggest some violations of Time Reversal Symmetry in financial
time series, which are indeed observed empirically, although of much smaller
amplitude than predicted. We speculate that a faithful volatility model should
include both ARCH feedback effects and a stochastic component
Quantifying the behavior of stock correlations under market stress
Understanding correlations in complex systems is crucial in the face of turbulence, such as the ongoing financial crisis. However, in complex systems, such as financial systems, correlations are not constant but instead vary in time. Here we address the question of quantifying state-dependent correlations in stock markets. Reliable estimates of correlations are absolutely necessary to protect a portfolio. We analyze 72 years of daily closing prices of the 30 stocks forming the Dow Jones Industrial Average (DJIA). We find the striking result that the average correlation among these stocks scales linearly with market stress reflected by normalized DJIA index returns on various time scales. Consequently, the diversification effect which should protect a portfolio melts away in times of market losses, just when it would most urgently be needed. Our empirical analysis is consistent with the interesting possibility that one could anticipate diversification breakdowns, guiding the design of protected portfolios
Index Cohesive Force Analysis Reveals That the US Market Became Prone to Systemic Collapses Since 2002
BACKGROUND: The 2007-2009 financial crisis, and its fallout, has strongly emphasized the need to define new ways and measures to study and assess the stock market dynamics. METHODOLOGY/PRINCIPAL FINDINGS: The S&P500 dynamics during 4/1999-4/2010 is investigated in terms of the index cohesive force (ICF--the balance between the stock correlations and the partial correlations after subtraction of the index contribution), and the Eigenvalue entropy of the stock correlation matrices. We found a rapid market transition at the end of 2001 from a flexible state of low ICF into a stiff (nonflexible) state of high ICF that is prone to market systemic collapses. The stiff state is also marked by strong effect of the market index on the stock-stock correlations as well as bursts of high stock correlations reminiscence of epileptic brain activity. CONCLUSIONS/SIGNIFICANCE: The market dynamical states, stability and transition between economic states was studies using new quantitative measures. Doing so shed new light on the origin and nature of the current crisis. The new approach is likely to be applicable to other classes of complex systems from gene networks to the human brain
Emerging interdependence between stock values during financial crashes
To identify emerging interdependencies between traded stocks we investigate the behavior of the stocks of FTSE 100 companies in the period 2000-2015, by looking at daily stock values. Exploiting the power of information theoretical measures to extract direct influences between multiple time series, we compute the information flow across stock values to identify several different regimes. While small information flows is detected in most of the period, a dramatically different situation occurs in the proximity of global financial crises, where stock values exhibit strong and substantial interdependence for a prolonged period. This behavior is consistent with what one would generally expect from a complex system near criticality in physical systems, showing the long lasting effects of crashes on stock markets
Correlation of financial markets in times of crisis
Using the eigenvalues and eigenvectors of correlations matrices of some of
the main financial market indices in the world, we show that high volatility of
markets is directly linked with strong correlations between them. This means
that markets tend to behave as one during great crashes. In order to do so, we
investigate several financial market crises that occurred in the years 1987
(Black Monday), 1989 (Russian crisis), 2001 (Burst of the dot-com bubble and
September 11), and 2008 (Subprime Mortgage Crisis), which mark some of the
largest downturns of financial markets in the last three decades.Comment: 33 pages, 46 figure
Principal Regression Analysis and the index leverage effect
We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call `Principal Regression Analysis' (PRA) and for which we provide some analytical (using Random Matrix Theory) and numerical benchmarks. We find that downward index trends increase the average correlation between stocks (as measured by the most negative eigenvalue of the conditional correlation matrix), and makes the market mode more uniform. Upward trends, on the other hand, also increase the average correlation between stocks but rotates the corresponding market mode {\it away} from uniformity. There are two time scales associated to these effects, a short one on the order of a month (20 trading days), and a longer time scale on the order of a year. We also find indications of a leverage effect for sectorial correlations as well, which reveals itself in the second and third mode of the PRA.