Physica A: Statistical Mechanics and its Applications, 2004
Financial correlations play a central role in financial theory and also in many practical applica... more Financial correlations play a central role in financial theory and also in many practical applications. From theoretical point of view, the key interest is in a proper description of the structure and dynamics of correlations. From practical point of view, the emphasis is on the ability of the developed models to provide the adequate input for the numerous portfolio and risk management procedures used in the financial industry. This is crucial, since it has been long argued that correlation matrices determined from financial series contain a relatively large amount of noise and, in addition, most of the portfolio and risk management techniques used in practice can be quite sensitive to the inputs. In this paper we introduce a model (simulation)-based approach which can be used for a systematic investigation of the effect of the different sources of noise in financial correlations in the portfolio and risk management context. To illustrate the usefulness of this framework, we develop several toy models for the structure of correlations and, by considering the finiteness of the time series as the only source of noise, we compare the performance of several correlation matrix estimators introduced in the academic literature and which have since gained also a wide practical use. Based on this experience, we believe that our simulation-based approach can also be useful for the systematic investigation of several other problems of much interest in finance.
Physica A: Statistical Mechanics and its Applications, 2001
We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. B... more We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution function, which is an important feature of financial data. Nevertheless, it was commonly found that RiskMetrics performs satisfactorily well, and therefore the technique has become widely used in the financial industry. We find, however, that the success of RiskMetrics is the artifact of the choice of the risk measure. First, the outstanding performance of volatility estimates is basically due to the choice of a very short (one-period ahead) forecasting horizon. Second, the satisfactory performance in obtaining Value-at-Risk by simply multiplying volatility with a constant factor is mainly due to the choice of the particular significance level.
Modelling and Simulation in Materials Science and Engineering, 1998
A two-dimensional dislocation system on a triangular lattice is studied by Monte Carlo simulation... more A two-dimensional dislocation system on a triangular lattice is studied by Monte Carlo simulations with special emphasis on the effect of external stress applied to the system. For fixed values of the stress, only pairs of dislocations with opposite Burgers vectors are present to a considerable extent in the system at low temperatures, while with increasing temperature unbinding of the
The European Physical Journal B - Condensed Matter, 2002
Recent studies inspired by results from random matrix theory found that covariance matrices deter... more Recent studies inspired by results from random matrix theory found that covariance matrices determined from empirical financial time series appear to contain such a high amount of noise that their structure can essentially be regarded as random. This seems, however, to be in contradiction with the fundamental role played by covariance matrices in finance, which constitute the pillars of modern investment theory and have also gained industry-wide applications in risk management. Our paper is an attempt to resolve this embarrassing paradox. The key observation is that the effect of noise strongly depends on the ratio r = n/T , where n is the size of the portfolio and T the length of the available time series. On the basis of numerical experiments and analytic results for some toy portfolio models we show that for relatively large values of r (e.g. 0.6) noise does, indeed, have the pronounced effect suggested by [1, 2, 3] and illustrated later by in a portfolio optimization context, while for smaller r (around 0.2 or below), the error due to noise drops to acceptable levels. Since the length of available time series is for obvious reasons limited in any practical application, any bound imposed on the noise-induced error translates into a bound on the size of the portfolio. In a related set of experiments we find that the effect of noise depends also on whether the problem arises in asset allocation or in a risk measurement context: if covariance matrices are used simply for measuring the risk of portfolios with a fixed composition rather than as inputs to optimization, the effect of noise on the measured risk may become very small.
We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of... more We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate the spectrum of large exponentially weighted random matrices (whose upper band edge needs to be known for the implementation of the estimation) analytically, by a procedure analogous to that used for standard random matrices. Finally, we illustrate, on empirical data, the superiority of the newly introduced estimator in a portfolio optimization context over both the method of exponentially weighted moving averages and the uniformly-weighted random-matrix-theory-based filtering.
We study empirical covariance matrices in finance. Due to the limited amount of available input i... more We study empirical covariance matrices in finance. Due to the limited amount of available input information, these objects incorporate a huge amount of noise, so their naive use in optimization procedures, such as portfolio selection, may be misleading. In this paper we investigate a recently introduced filtering procedure, and demonstrate the applicability of this method in a controlled, simulation environment.
Physica A: Statistical Mechanics and its Applications, 2004
Financial correlations play a central role in financial theory and also in many practical applica... more Financial correlations play a central role in financial theory and also in many practical applications. From theoretical point of view, the key interest is in a proper description of the structure and dynamics of correlations. From practical point of view, the emphasis is on the ability of the developed models to provide the adequate input for the numerous portfolio and risk management procedures used in the financial industry. This is crucial, since it has been long argued that correlation matrices determined from financial series contain a relatively large amount of noise and, in addition, most of the portfolio and risk management techniques used in practice can be quite sensitive to the inputs. In this paper we introduce a model (simulation)-based approach which can be used for a systematic investigation of the effect of the different sources of noise in financial correlations in the portfolio and risk management context. To illustrate the usefulness of this framework, we develop several toy models for the structure of correlations and, by considering the finiteness of the time series as the only source of noise, we compare the performance of several correlation matrix estimators introduced in the academic literature and which have since gained also a wide practical use. Based on this experience, we believe that our simulation-based approach can also be useful for the systematic investigation of several other problems of much interest in finance.
Physica A: Statistical Mechanics and its Applications, 2001
We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. B... more We analyze the performance of RiskMetrics, a widely used methodology for measuring market risk. Based on the assumption of normally distributed returns, the RiskMetrics model completely ignores the presence of fat tails in the distribution function, which is an important feature of financial data. Nevertheless, it was commonly found that RiskMetrics performs satisfactorily well, and therefore the technique has become widely used in the financial industry. We find, however, that the success of RiskMetrics is the artifact of the choice of the risk measure. First, the outstanding performance of volatility estimates is basically due to the choice of a very short (one-period ahead) forecasting horizon. Second, the satisfactory performance in obtaining Value-at-Risk by simply multiplying volatility with a constant factor is mainly due to the choice of the particular significance level.
Modelling and Simulation in Materials Science and Engineering, 1998
A two-dimensional dislocation system on a triangular lattice is studied by Monte Carlo simulation... more A two-dimensional dislocation system on a triangular lattice is studied by Monte Carlo simulations with special emphasis on the effect of external stress applied to the system. For fixed values of the stress, only pairs of dislocations with opposite Burgers vectors are present to a considerable extent in the system at low temperatures, while with increasing temperature unbinding of the
The European Physical Journal B - Condensed Matter, 2002
Recent studies inspired by results from random matrix theory found that covariance matrices deter... more Recent studies inspired by results from random matrix theory found that covariance matrices determined from empirical financial time series appear to contain such a high amount of noise that their structure can essentially be regarded as random. This seems, however, to be in contradiction with the fundamental role played by covariance matrices in finance, which constitute the pillars of modern investment theory and have also gained industry-wide applications in risk management. Our paper is an attempt to resolve this embarrassing paradox. The key observation is that the effect of noise strongly depends on the ratio r = n/T , where n is the size of the portfolio and T the length of the available time series. On the basis of numerical experiments and analytic results for some toy portfolio models we show that for relatively large values of r (e.g. 0.6) noise does, indeed, have the pronounced effect suggested by [1, 2, 3] and illustrated later by in a portfolio optimization context, while for smaller r (around 0.2 or below), the error due to noise drops to acceptable levels. Since the length of available time series is for obvious reasons limited in any practical application, any bound imposed on the noise-induced error translates into a bound on the size of the portfolio. In a related set of experiments we find that the effect of noise depends also on whether the problem arises in asset allocation or in a risk measurement context: if covariance matrices are used simply for measuring the risk of portfolios with a fixed composition rather than as inputs to optimization, the effect of noise on the measured risk may become very small.
We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of... more We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate the spectrum of large exponentially weighted random matrices (whose upper band edge needs to be known for the implementation of the estimation) analytically, by a procedure analogous to that used for standard random matrices. Finally, we illustrate, on empirical data, the superiority of the newly introduced estimator in a portfolio optimization context over both the method of exponentially weighted moving averages and the uniformly-weighted random-matrix-theory-based filtering.
We study empirical covariance matrices in finance. Due to the limited amount of available input i... more We study empirical covariance matrices in finance. Due to the limited amount of available input information, these objects incorporate a huge amount of noise, so their naive use in optimization procedures, such as portfolio selection, may be misleading. In this paper we investigate a recently introduced filtering procedure, and demonstrate the applicability of this method in a controlled, simulation environment.
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Papers by Szilard Pafka