We model the joint risk neutral distribution of the euro-sterling and the dollar-sterling exchang... more We model the joint risk neutral distribution of the euro-sterling and the dollar-sterling exchange rates using option-implied marginal distributions that are connected via a copula function that satisfies the triangular no-arbitrage condition. We then derive a univariate distribution for a simplified sterling effective exchange rate index (ERI). Our results indicate that standard parametric copula functions, such as the commonly used Normal and Frank copulas, fail to capture the degree of asymmetry observed in the data. We overcome this problem by using a non-parametric dependence function in the form of a Bernstein copula which is shown to produce a very close fit. We further give an example of how our approach can be used to price currency index options accounting for strike-dependent implied volatilities. We would like to thank Michael Bennett, Andrew Patton and Alessio Sancetta, participants at the CEF 2005 in Washington and the GFC 2005 in Dublin, as well as seminar participants at the Bank of England for useful comments and discussion. Any remaining mistakes are our own. This paper represents the views of the authors and should not be thought to represent those of the Bank of England and members of the Monetary Policy Committee.
A trading strategy is generally optimised for a given market regime. If it takes too long to swit... more A trading strategy is generally optimised for a given market regime. If it takes too long to switch from one trading strategy to another, then a sub-optimal trading strategy may be adopted. This paper proposes the first FPGA-based framework which supports multiple trend-following trading strategies to obtain accurate market characterisation for various financial market regimes. The framework contains a trading strategy kernel library covering a number of well-known trend-following strategies, such as "triple moving average". Three types of design are targeted: a static reconfiguration trading strategy (SRTS), a full reconfiguration trading strategy (FRTS), and a partial reconfiguration trading strategy (PRTS). Our approach is evaluated using both synthetic and historical market data. Compared to a fully optimised CPU implementation, the SRTS design achieves 11 times speedup, the FRTS design achieves 2 times speedup, while the PRTS design achieves 7 times speedup. The FRTS and PRTS designs also reduce the amount of resources used on chip by 29% and 15% respectively, when compared to the SRTS design.
... Christian Gourieroux and Joana Jasiak, (2000) Financial Econometrics, Princeton University Pr... more ... Christian Gourieroux and Joana Jasiak, (2000) Financial Econometrics, Princeton University Press. ... Asea P. and Mthuli Ncube, (1997), Heterogeneous Information arrival and Option Pricing, NBER Working Paper 5950, available in full text mode on the web at http://netec.mcc.ac ...
We investigate asset returns using the concept of beta herding, which measures crosssectional var... more We investigate asset returns using the concept of beta herding, which measures crosssectional variations in betas due to changes in investors' confidence about their market outlook. Overconfidence causes beta herding (compression of betas towards the market beta), while under-confidence leads to adverse beta herding (dispersion of betas from the market beta). We show that the low-beta anomaly can be explained by a return reversal following adverse beta herding, as high beta stocks underperform low beta stocks exclusively following periods of adverse beta herding. This result is robust to investors' preferences for lottery-like assets, sentiment, and return reversals, and beta herding leads time variation in betas.
ABSTRACT The paper approaches the modeling of the yield curve from a stochastic volatility perspe... more ABSTRACT The paper approaches the modeling of the yield curve from a stochastic volatility perspective based on time deformation. The way in which we model time deformation is new and differs from alternatives that currently exist in the literature and is based on market microstructure theory of the impact of information flow on a market. We model the stochastic volatility process by modeling the instantaneous volatility as a function of price intensity in the spirit of Cho and Frees (1988), Engle and Russell (1998) and Gerhard and Hautsch (2002). One contribution of the paper therefore lies with the introduction of a new transaction level approach to the econometric modelling of stochastic volatility in a multivariate framework exploiting intensity-based point processes previously used by Bowsher (2003), Hall and Haustch (2003). We find that the individual yields of U.S. treasury notes and bonds appear to be driven by different operational clocks as suggested by the market segmentation theory of the Term Structure but these are related to each other through a multivariate Hawkes model which effectively coordinates activity along the yield curve. The results offer some support to the Market Segmentation or Preferred Habitat models as the univariate Hawkes models we have found at each maturity are statistically significantly different from each other and the major impact on each maturity is activity at that maturity. However there are flows between the different maturities that die away relatively quickly which indicates that the markets are not completely segmented. Diagnostic tests show that the point process models are relatively well specified and a robustness comparison with realized volatility indicates the close relationship between the two estimators of integrated volatility but also some differences between the structural intensity model and the model free realized volatility. We have also shown that bond returns standardized by the instantaneous volatility estimated from our Hawkes model are Gaussian which is consistent with the theory of time deformation for security prices quite generally.
Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability dist... more Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability distribution from a given distribution, thus effectively giving the upper bound of the approximation error which can be represented as the expectation of a Stein's operator. Hosking (1990, 1992) proposes the concept of L-moment which better summarizes the characteristics of a distribution than conventional moments (C-moments). The purpose of the paper is to propose new tests for conditional parametric distribution functions with weakly dependent and strictly stationary data generating processes (DGP) by constructing a set of the Stein equations as the L-statistics of conceptual ordered sub-samples drawn from the population sample of distribution; hereafter are referred to as the L-moment (GMLM) tests. The limiting distributions of our tests are nonstandard, depending on test criterion functions used in conditional L-statistics restrictions; the covariance kernel in the tests reflects parametric dependence specification. The GMLM tests can resolve the choice of orthogonal polynomials remaining as an identification issue in the GMM tests using the Stein approximation (Bontemps and Meddahi, 2005, 2006) because L-moments are simply the expectations of quantiles which can be linearly combined in order to characterize a distribution function. Thus, our test statistics can be represented as functions of the quantiles of the conditional distribution under the null hypothesis. In the broad context of goodness-of-fit tests based on order statistics, the methodologies developed in the paper differ from existing methods such as tests based on the (weighed) distance between empirical distribution and a parametric distribution under the null or the tests based on likelihood ratio of Zhang (2002) in two respects: 1) our tests are motivated by the L-moment theory and Stein's method; 2) offer more flexibility because we can select an optimal number of L-moments so that the sample size necessary for a test to attain a given level of power is minimal. Finally, we provide some Monte-Carlo simulations for IID data to examine the size, the power and the robustness of the GMLM test and compare with both existing moment-based tests and tests based on order statistics.
ABSTRACT This paper aims to provide an introductory review of copulae and their potential applica... more ABSTRACT This paper aims to provide an introductory review of copulae and their potential application finance, in particular in capturing the dependence between financial assets that follow non-gaussian distributions and hence for modelling credit risk, pricing options and portfolio design. We briefy review the failure of methods based on multivariate normality and where dependency is measured by correlation. Using a copula approach enables us to measure the different relationships that may exist between financial assets in different ranges of their behaviour- for instance do assets exhibit similar dependency patterns in the tails of their distributions as they do around their means? We review different measures of association and show that when these dependency measures can be expressed simply as functions of a copula they will be invariant to strictly monotone transformations of the random variables and hence the units in which we choose to express our data. The standard Pearson Correlation statistic is not in general invariant to scale changes in the data. We then discuss several statistical issues relating to the estimation of Copulae and their empirical application through both parametric and non parametric methods. An important issue lies in the statistical discrimination between copulae and we propose a encompassing framework based on simulation for discriminating between what are effectively separate statistical families. We then consider several applications, modelling default risk, tail dependence, quantile regression and portfolio design for non-gaussian assets.
Although geometry has always aided intuition in econometrics, more recently differential geometry... more Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000, this volume was an early example of the application of these techniques to econometrics. An introductory chapter provides a brief tutorial for those unfamiliar with the tools of Differential Geometry. The topics covered in the following chapters demonstrate the power of the geometric method to provide practical solutions and insight into problems of econometric inference.
We investigate asset returns using the concept of beta herding, which measures cross-sectional va... more We investigate asset returns using the concept of beta herding, which measures cross-sectional variations in betas induced by investors whose beliefs about the market are biased due to changes in confidence or sentiment. Overconfidence or optimistic sentiment causes beta herding (compression of individual assets' betas towards the market beta), while underconfidence or pessimistic sentiment leads to adverse beta herding (dispersion of betas away from the market beta). We find that beta herding is related to the low-beta anomaly, as high beta stocks underperform low beta stocks on a risk-adjusted basis exclusively following periods of adverse beta herding. As an explanation of the low-beta anomaly, we propose the persistence of bias in betas (i.e., a large difference in betas) that lasts for more than one year as market uncertainty continues.
In this paper we test whether investors are uncertainty averse during a reallife trading process ... more In this paper we test whether investors are uncertainty averse during a reallife trading process in the foreign exchange market. We do this through an agent-based model in which fundamentalist and chartist beliefs of the exchange rate are allowed to be either uncertainty neutral or uncertainty averse. The uncertainty aversion is modelled via the maxmin expected utility approach. We find that traders are uncertainty averse in the FX market. The estimation results show that the inclusion of uncertainty averse agents improves the performance of the model and the uncertainty aversion parameter is significantly different from zero. Fundamentalists are found to be uncertainty neutral and chartists-mainly uncertainty averse.
In this paper, two non-linear hypotheses are tested on the controversial time-series relationship... more In this paper, two non-linear hypotheses are tested on the controversial time-series relationship between investor sentiment and market returns: i) an interaction, subject to abrupt regime shifts, and ii) a gradual sentiment effect, which alters the influences of other factors, such as the volatility premium, as a sentiment threshold is exceeded. Both hypotheses are supported by the data (vs. the corresponding linear alternatives) for the SP500 index and institutional (but not individual) sentiment over the period 1965-2003, and after controlling for various risk factors. A mutual influence, significant both in statistical and economic terms, exists between monthly returns and institutional sentiment, during a dominant market regime with occurrence probability 80%. Instead, individual sentiment exerts no significant effect on SP500 returns, although it responds positively to them. Institutional and individual investors are influenced by each others' sentiment, but they interpret these as opposite signals, contrarian and momentum respectively. Similarly, they perceive past volatility as a source of optimism / pessimism. Interestingly, aggregate idiosyncratic volatility, a proxy for total arbitrage cost, exerts a positive impact on both subsequent returns and institutional sentiment, indicating that institutions correctly predict higher returns as this cost increases (e.g. due to an anticipated correction of a mispricing) or possibly, that they partially contribute to this pattern via their own trading. A smooth-transition regression specification reveals that, in a similar way that sentiment alters, at the individual stock level, the effects of firm characteristics on returns (Baker and Wurgler, 2006), institutional sentiment alters, at the market level, the sign and magnitude of the volatility effect. This indicates a compensation for sentiment risk, as implied by De Long et al. (1990). Accounting for regime shifts seems critical for return prediction over month-ahead horizons.
ABSTRACT The time-series relationship between investor sentiment and market returns, in particula... more ABSTRACT The time-series relationship between investor sentiment and market returns, in particular the direction and size of the effects, remains ambiguous, being assessed under the restrictive assumption of linearity. This paper reveals the presence of four, intuitive, regimes in price and sentiment formation in the US stock market at the monthly level over the period 1965-2003, even after controlling for various economic and financial factors. An optimistic state of high returns (occurrence probability: 44%) alternates with a pessimistic state of low returns (35%), while two infrequent, highly volatile states capture temporal irregularities: episodes of extreme negative returns and strong pessimism (13%) and a reversal phase of intense optimism (8%). Five main findings arise: i) In the high return (low return) state, only individual (institutional) sentiment is influential, being a contrarian (momentum) signal for the subsequent return and responding positively (negatively) but weakly to its lagged value. In the former case, the impact of sentiment is consistent with correction of a previous mispricing, possibly induced by individuals, while in the latter, it indicates institutions' correct predictive ability. ii) The impact of institutional sentiment is substantial but constrained in the pessimistic state, while the effect of individual sentiment is moderate but augmented substantially at irregular times. iii) Individuals interpret institutional optimism as a positive signal, whereas institutions perceive individuals' optimism as a contrarian indicator. iv) Total arbitrage cost exerts a positive impact on both subsequent returns and institutional optimism. v) Interest rates' reductions amplify investors' optimism at irregular times, most evidently during the market reversal phase.
This paper considers how trading activity at one maturity of the yield curve a¤ects and is a¤ecte... more This paper considers how trading activity at one maturity of the yield curve a¤ects and is a¤ected by trading at other maturities. We approach the modelling of bond prices from a stochastic volatility perspective based on time deformation. We put forward a new, continuous time, multivariate time deformation model which is coherent with the market microstructure theory of price discovery and captures information ‡ow in the market. We model the stochastic volatility process by estimating the instantaneous volatility as a function of the price intensity in the spirit of Cho and Frees (1988) and Gerhard and Hautsch (2002). The point process model, a Hawkes model, that we use to model the price intensity allows for both the self and cross excitation e¤ects of trading at di¤erent maturities. Univariate and multivariate models are estimated using transaction level data from BrokerTec, a highly liquid and widely traded electronic platform for US securities. We …nd that the integrated price intensity is statistically supported as an appropriate directing process in the US bond market suggesting that private information is revealed indirectly through trades in the presence of information asymmetry and heterogeneous agents. We also …nd that the individual yields on US treasury notes and bonds appear to be driven by di¤erent 'market clocks' as suggested perhaps by the market segmentation theory of the term structure. These separate market time scales are then related to each other through a multivariate Hawkes model which e¤ectively coordinates activity along the yield curve. We also show that bond returns standardized by the instantaneous volatility estimated from our Hawkes model are Gaussian which is consistent with the theory of time deformation for security prices quite generally.
This paper examines the predictability of exchange rates on a transaction level basis using both ... more This paper examines the predictability of exchange rates on a transaction level basis using both past transaction prices and the structure of the order book. In contrast to the existing literature we also recognise that the trader may be subject to (Knightian) uncertainty as opposed to risk regarding the structure by which exchange rates are determined and hence regarding both the model he employs to make predictions and the reliability of any conditioning information. The trader is faced with a two stage decision problem due to this uncertainty; first he needs to resolve a question of market timing as to when to enter the market and then secondly how to trade. We provide a formalisation for this two stage decision problem. Statistical tests indicate the significance of out of sample ability to predict directional changes and the economic value of predictability using one week of tick-by-tick data on the USD-DM exchange rate drawn from Reuters DM2002 electronic trading system. These conclusions rest critically on the frequency of trading which is controlled by an inertia parameter reflecting the degree of uncertainty; trading too frequently significantly reduces profitability taking account of transaction costs.
This study proposes a new measure and test of herding which is based on the crosssectional disper... more This study proposes a new measure and test of herding which is based on the crosssectional dispersion of factor sensitivity of assets within a given market. This new measure enables us to evaluate the directions towards which the market may be herding and separate these from movements in fundamentals. We apply the test to an analysis of the US, UK, and South Korean stock markets and somewhat surprisingly, …nd statistically signi…cant evidence of herding towards ”the market portfolio ” during relatively quiet periods rather than when the market is under stress. The approach also allows us to investigate herding towards other factors beyond the market factor and we …nd that the US market shows signi…cant herding towards “value ” after the Russian Crisis in 1998.
[email protected]. We would like to thank Alistair Sayer of J.P.Morgan, London for several disc... more [email protected]. We would like to thank Alistair Sayer of J.P.Morgan, London for several discussions relating to the practical implementation of performance We have carried out a detailed comparison of the statistical properties and the relationships between a set of five performance measures using 14 UK based Investment Trusts over a sample period ranging from 1980 to 2001. Our results suggest very clearly that there is almost no difference between Jensen’s Alpha, the Treynor-Mazuy (TM) measure and the Positive Period Weighting(PPW) measure over our sample period and amongst our set of Investment Trusts. This would seem to indicate that there is no timing ability within these fund managers. The Sharpe Ratio clearly provides different signals regarding performance than the other measures and is the only absolute measure in the set of measures we have considered. While simple correlation analysis suggests that there is a high degree of dependence between most of the measures we h...
Abstract: We model the joint risk neutral distribution of the euro-sterling and the dollar-sterli... more Abstract: We model the joint risk neutral distribution of the euro-sterling and the dollar-sterling ex-change rates using option-implied marginal distributions that are connected via a copula function that satisfies the triangular no-arbitrage condition. We then derive a univariate distribution for a simplified sterling effective exchange rate index (ERI). Our results indicate that standard parametric copula func-tions, such as the commonly used Normal and Frank copulas, fail to capture the degree of asymmetry observed in the data. We overcome this problem by using a non-parametric dependence function in the form of a Bernstein copula which is shown to produce a very close fit. We further give an example of how our approach can be used to price currency index options accounting for strike-dependent implied volatilities. We would like to thank Michael Bennett, Andrew Patton and Alessio Sancetta, participants at the CEF 2005 in Washington and the GFC 2005 in Dublin, as well as seminar...
Multivariate options are widely used when there is a need to hedge against a number of risks simu... more Multivariate options are widely used when there is a need to hedge against a number of risks simultaneously; such as when there is an exposure to several currencies or the need to provide cover against an index such as the FTSE100, or indeed any portfolio of assets. In the case of a basket option the payoff depends on the value of the entire portfolio or basket of assets where the basket is some weighted average of the underlying assets. The principal reason for using basket options is that they are cheaper to use for portfolio insurance than a corresponding portfolio of plain vanilla options on the individual assets. This cost saving depends on the correlation structure between the assets; the lower the correlation between currency pairs in a currency portfolio for instance, the greater the cost saving.
We model the joint risk neutral distribution of the euro-sterling and the dollar-sterling exchang... more We model the joint risk neutral distribution of the euro-sterling and the dollar-sterling exchange rates using option-implied marginal distributions that are connected via a copula function that satisfies the triangular no-arbitrage condition. We then derive a univariate distribution for a simplified sterling effective exchange rate index (ERI). Our results indicate that standard parametric copula functions, such as the commonly used Normal and Frank copulas, fail to capture the degree of asymmetry observed in the data. We overcome this problem by using a non-parametric dependence function in the form of a Bernstein copula which is shown to produce a very close fit. We further give an example of how our approach can be used to price currency index options accounting for strike-dependent implied volatilities. We would like to thank Michael Bennett, Andrew Patton and Alessio Sancetta, participants at the CEF 2005 in Washington and the GFC 2005 in Dublin, as well as seminar participants at the Bank of England for useful comments and discussion. Any remaining mistakes are our own. This paper represents the views of the authors and should not be thought to represent those of the Bank of England and members of the Monetary Policy Committee.
A trading strategy is generally optimised for a given market regime. If it takes too long to swit... more A trading strategy is generally optimised for a given market regime. If it takes too long to switch from one trading strategy to another, then a sub-optimal trading strategy may be adopted. This paper proposes the first FPGA-based framework which supports multiple trend-following trading strategies to obtain accurate market characterisation for various financial market regimes. The framework contains a trading strategy kernel library covering a number of well-known trend-following strategies, such as "triple moving average". Three types of design are targeted: a static reconfiguration trading strategy (SRTS), a full reconfiguration trading strategy (FRTS), and a partial reconfiguration trading strategy (PRTS). Our approach is evaluated using both synthetic and historical market data. Compared to a fully optimised CPU implementation, the SRTS design achieves 11 times speedup, the FRTS design achieves 2 times speedup, while the PRTS design achieves 7 times speedup. The FRTS and PRTS designs also reduce the amount of resources used on chip by 29% and 15% respectively, when compared to the SRTS design.
... Christian Gourieroux and Joana Jasiak, (2000) Financial Econometrics, Princeton University Pr... more ... Christian Gourieroux and Joana Jasiak, (2000) Financial Econometrics, Princeton University Press. ... Asea P. and Mthuli Ncube, (1997), Heterogeneous Information arrival and Option Pricing, NBER Working Paper 5950, available in full text mode on the web at http://netec.mcc.ac ...
We investigate asset returns using the concept of beta herding, which measures crosssectional var... more We investigate asset returns using the concept of beta herding, which measures crosssectional variations in betas due to changes in investors' confidence about their market outlook. Overconfidence causes beta herding (compression of betas towards the market beta), while under-confidence leads to adverse beta herding (dispersion of betas from the market beta). We show that the low-beta anomaly can be explained by a return reversal following adverse beta herding, as high beta stocks underperform low beta stocks exclusively following periods of adverse beta herding. This result is robust to investors' preferences for lottery-like assets, sentiment, and return reversals, and beta herding leads time variation in betas.
ABSTRACT The paper approaches the modeling of the yield curve from a stochastic volatility perspe... more ABSTRACT The paper approaches the modeling of the yield curve from a stochastic volatility perspective based on time deformation. The way in which we model time deformation is new and differs from alternatives that currently exist in the literature and is based on market microstructure theory of the impact of information flow on a market. We model the stochastic volatility process by modeling the instantaneous volatility as a function of price intensity in the spirit of Cho and Frees (1988), Engle and Russell (1998) and Gerhard and Hautsch (2002). One contribution of the paper therefore lies with the introduction of a new transaction level approach to the econometric modelling of stochastic volatility in a multivariate framework exploiting intensity-based point processes previously used by Bowsher (2003), Hall and Haustch (2003). We find that the individual yields of U.S. treasury notes and bonds appear to be driven by different operational clocks as suggested by the market segmentation theory of the Term Structure but these are related to each other through a multivariate Hawkes model which effectively coordinates activity along the yield curve. The results offer some support to the Market Segmentation or Preferred Habitat models as the univariate Hawkes models we have found at each maturity are statistically significantly different from each other and the major impact on each maturity is activity at that maturity. However there are flows between the different maturities that die away relatively quickly which indicates that the markets are not completely segmented. Diagnostic tests show that the point process models are relatively well specified and a robustness comparison with realized volatility indicates the close relationship between the two estimators of integrated volatility but also some differences between the structural intensity model and the model free realized volatility. We have also shown that bond returns standardized by the instantaneous volatility estimated from our Hawkes model are Gaussian which is consistent with the theory of time deformation for security prices quite generally.
Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability dist... more Stein (1972, 1986) provides a flexible method for measuring the deviation of any probability distribution from a given distribution, thus effectively giving the upper bound of the approximation error which can be represented as the expectation of a Stein's operator. Hosking (1990, 1992) proposes the concept of L-moment which better summarizes the characteristics of a distribution than conventional moments (C-moments). The purpose of the paper is to propose new tests for conditional parametric distribution functions with weakly dependent and strictly stationary data generating processes (DGP) by constructing a set of the Stein equations as the L-statistics of conceptual ordered sub-samples drawn from the population sample of distribution; hereafter are referred to as the L-moment (GMLM) tests. The limiting distributions of our tests are nonstandard, depending on test criterion functions used in conditional L-statistics restrictions; the covariance kernel in the tests reflects parametric dependence specification. The GMLM tests can resolve the choice of orthogonal polynomials remaining as an identification issue in the GMM tests using the Stein approximation (Bontemps and Meddahi, 2005, 2006) because L-moments are simply the expectations of quantiles which can be linearly combined in order to characterize a distribution function. Thus, our test statistics can be represented as functions of the quantiles of the conditional distribution under the null hypothesis. In the broad context of goodness-of-fit tests based on order statistics, the methodologies developed in the paper differ from existing methods such as tests based on the (weighed) distance between empirical distribution and a parametric distribution under the null or the tests based on likelihood ratio of Zhang (2002) in two respects: 1) our tests are motivated by the L-moment theory and Stein's method; 2) offer more flexibility because we can select an optimal number of L-moments so that the sample size necessary for a test to attain a given level of power is minimal. Finally, we provide some Monte-Carlo simulations for IID data to examine the size, the power and the robustness of the GMLM test and compare with both existing moment-based tests and tests based on order statistics.
ABSTRACT This paper aims to provide an introductory review of copulae and their potential applica... more ABSTRACT This paper aims to provide an introductory review of copulae and their potential application finance, in particular in capturing the dependence between financial assets that follow non-gaussian distributions and hence for modelling credit risk, pricing options and portfolio design. We briefy review the failure of methods based on multivariate normality and where dependency is measured by correlation. Using a copula approach enables us to measure the different relationships that may exist between financial assets in different ranges of their behaviour- for instance do assets exhibit similar dependency patterns in the tails of their distributions as they do around their means? We review different measures of association and show that when these dependency measures can be expressed simply as functions of a copula they will be invariant to strictly monotone transformations of the random variables and hence the units in which we choose to express our data. The standard Pearson Correlation statistic is not in general invariant to scale changes in the data. We then discuss several statistical issues relating to the estimation of Copulae and their empirical application through both parametric and non parametric methods. An important issue lies in the statistical discrimination between copulae and we propose a encompassing framework based on simulation for discriminating between what are effectively separate statistical families. We then consider several applications, modelling default risk, tail dependence, quantile regression and portfolio design for non-gaussian assets.
Although geometry has always aided intuition in econometrics, more recently differential geometry... more Although geometry has always aided intuition in econometrics, more recently differential geometry has become a standard tool in the analysis of statistical models, offering a deeper appreciation of existing methodologies and highlighting the essential issues which can be hidden in an algebraic development of a problem. Originally published in 2000, this volume was an early example of the application of these techniques to econometrics. An introductory chapter provides a brief tutorial for those unfamiliar with the tools of Differential Geometry. The topics covered in the following chapters demonstrate the power of the geometric method to provide practical solutions and insight into problems of econometric inference.
We investigate asset returns using the concept of beta herding, which measures cross-sectional va... more We investigate asset returns using the concept of beta herding, which measures cross-sectional variations in betas induced by investors whose beliefs about the market are biased due to changes in confidence or sentiment. Overconfidence or optimistic sentiment causes beta herding (compression of individual assets' betas towards the market beta), while underconfidence or pessimistic sentiment leads to adverse beta herding (dispersion of betas away from the market beta). We find that beta herding is related to the low-beta anomaly, as high beta stocks underperform low beta stocks on a risk-adjusted basis exclusively following periods of adverse beta herding. As an explanation of the low-beta anomaly, we propose the persistence of bias in betas (i.e., a large difference in betas) that lasts for more than one year as market uncertainty continues.
In this paper we test whether investors are uncertainty averse during a reallife trading process ... more In this paper we test whether investors are uncertainty averse during a reallife trading process in the foreign exchange market. We do this through an agent-based model in which fundamentalist and chartist beliefs of the exchange rate are allowed to be either uncertainty neutral or uncertainty averse. The uncertainty aversion is modelled via the maxmin expected utility approach. We find that traders are uncertainty averse in the FX market. The estimation results show that the inclusion of uncertainty averse agents improves the performance of the model and the uncertainty aversion parameter is significantly different from zero. Fundamentalists are found to be uncertainty neutral and chartists-mainly uncertainty averse.
In this paper, two non-linear hypotheses are tested on the controversial time-series relationship... more In this paper, two non-linear hypotheses are tested on the controversial time-series relationship between investor sentiment and market returns: i) an interaction, subject to abrupt regime shifts, and ii) a gradual sentiment effect, which alters the influences of other factors, such as the volatility premium, as a sentiment threshold is exceeded. Both hypotheses are supported by the data (vs. the corresponding linear alternatives) for the SP500 index and institutional (but not individual) sentiment over the period 1965-2003, and after controlling for various risk factors. A mutual influence, significant both in statistical and economic terms, exists between monthly returns and institutional sentiment, during a dominant market regime with occurrence probability 80%. Instead, individual sentiment exerts no significant effect on SP500 returns, although it responds positively to them. Institutional and individual investors are influenced by each others' sentiment, but they interpret these as opposite signals, contrarian and momentum respectively. Similarly, they perceive past volatility as a source of optimism / pessimism. Interestingly, aggregate idiosyncratic volatility, a proxy for total arbitrage cost, exerts a positive impact on both subsequent returns and institutional sentiment, indicating that institutions correctly predict higher returns as this cost increases (e.g. due to an anticipated correction of a mispricing) or possibly, that they partially contribute to this pattern via their own trading. A smooth-transition regression specification reveals that, in a similar way that sentiment alters, at the individual stock level, the effects of firm characteristics on returns (Baker and Wurgler, 2006), institutional sentiment alters, at the market level, the sign and magnitude of the volatility effect. This indicates a compensation for sentiment risk, as implied by De Long et al. (1990). Accounting for regime shifts seems critical for return prediction over month-ahead horizons.
ABSTRACT The time-series relationship between investor sentiment and market returns, in particula... more ABSTRACT The time-series relationship between investor sentiment and market returns, in particular the direction and size of the effects, remains ambiguous, being assessed under the restrictive assumption of linearity. This paper reveals the presence of four, intuitive, regimes in price and sentiment formation in the US stock market at the monthly level over the period 1965-2003, even after controlling for various economic and financial factors. An optimistic state of high returns (occurrence probability: 44%) alternates with a pessimistic state of low returns (35%), while two infrequent, highly volatile states capture temporal irregularities: episodes of extreme negative returns and strong pessimism (13%) and a reversal phase of intense optimism (8%). Five main findings arise: i) In the high return (low return) state, only individual (institutional) sentiment is influential, being a contrarian (momentum) signal for the subsequent return and responding positively (negatively) but weakly to its lagged value. In the former case, the impact of sentiment is consistent with correction of a previous mispricing, possibly induced by individuals, while in the latter, it indicates institutions' correct predictive ability. ii) The impact of institutional sentiment is substantial but constrained in the pessimistic state, while the effect of individual sentiment is moderate but augmented substantially at irregular times. iii) Individuals interpret institutional optimism as a positive signal, whereas institutions perceive individuals' optimism as a contrarian indicator. iv) Total arbitrage cost exerts a positive impact on both subsequent returns and institutional optimism. v) Interest rates' reductions amplify investors' optimism at irregular times, most evidently during the market reversal phase.
This paper considers how trading activity at one maturity of the yield curve a¤ects and is a¤ecte... more This paper considers how trading activity at one maturity of the yield curve a¤ects and is a¤ected by trading at other maturities. We approach the modelling of bond prices from a stochastic volatility perspective based on time deformation. We put forward a new, continuous time, multivariate time deformation model which is coherent with the market microstructure theory of price discovery and captures information ‡ow in the market. We model the stochastic volatility process by estimating the instantaneous volatility as a function of the price intensity in the spirit of Cho and Frees (1988) and Gerhard and Hautsch (2002). The point process model, a Hawkes model, that we use to model the price intensity allows for both the self and cross excitation e¤ects of trading at di¤erent maturities. Univariate and multivariate models are estimated using transaction level data from BrokerTec, a highly liquid and widely traded electronic platform for US securities. We …nd that the integrated price intensity is statistically supported as an appropriate directing process in the US bond market suggesting that private information is revealed indirectly through trades in the presence of information asymmetry and heterogeneous agents. We also …nd that the individual yields on US treasury notes and bonds appear to be driven by di¤erent 'market clocks' as suggested perhaps by the market segmentation theory of the term structure. These separate market time scales are then related to each other through a multivariate Hawkes model which e¤ectively coordinates activity along the yield curve. We also show that bond returns standardized by the instantaneous volatility estimated from our Hawkes model are Gaussian which is consistent with the theory of time deformation for security prices quite generally.
This paper examines the predictability of exchange rates on a transaction level basis using both ... more This paper examines the predictability of exchange rates on a transaction level basis using both past transaction prices and the structure of the order book. In contrast to the existing literature we also recognise that the trader may be subject to (Knightian) uncertainty as opposed to risk regarding the structure by which exchange rates are determined and hence regarding both the model he employs to make predictions and the reliability of any conditioning information. The trader is faced with a two stage decision problem due to this uncertainty; first he needs to resolve a question of market timing as to when to enter the market and then secondly how to trade. We provide a formalisation for this two stage decision problem. Statistical tests indicate the significance of out of sample ability to predict directional changes and the economic value of predictability using one week of tick-by-tick data on the USD-DM exchange rate drawn from Reuters DM2002 electronic trading system. These conclusions rest critically on the frequency of trading which is controlled by an inertia parameter reflecting the degree of uncertainty; trading too frequently significantly reduces profitability taking account of transaction costs.
This study proposes a new measure and test of herding which is based on the crosssectional disper... more This study proposes a new measure and test of herding which is based on the crosssectional dispersion of factor sensitivity of assets within a given market. This new measure enables us to evaluate the directions towards which the market may be herding and separate these from movements in fundamentals. We apply the test to an analysis of the US, UK, and South Korean stock markets and somewhat surprisingly, …nd statistically signi…cant evidence of herding towards ”the market portfolio ” during relatively quiet periods rather than when the market is under stress. The approach also allows us to investigate herding towards other factors beyond the market factor and we …nd that the US market shows signi…cant herding towards “value ” after the Russian Crisis in 1998.
[email protected]. We would like to thank Alistair Sayer of J.P.Morgan, London for several disc... more [email protected]. We would like to thank Alistair Sayer of J.P.Morgan, London for several discussions relating to the practical implementation of performance We have carried out a detailed comparison of the statistical properties and the relationships between a set of five performance measures using 14 UK based Investment Trusts over a sample period ranging from 1980 to 2001. Our results suggest very clearly that there is almost no difference between Jensen’s Alpha, the Treynor-Mazuy (TM) measure and the Positive Period Weighting(PPW) measure over our sample period and amongst our set of Investment Trusts. This would seem to indicate that there is no timing ability within these fund managers. The Sharpe Ratio clearly provides different signals regarding performance than the other measures and is the only absolute measure in the set of measures we have considered. While simple correlation analysis suggests that there is a high degree of dependence between most of the measures we h...
Abstract: We model the joint risk neutral distribution of the euro-sterling and the dollar-sterli... more Abstract: We model the joint risk neutral distribution of the euro-sterling and the dollar-sterling ex-change rates using option-implied marginal distributions that are connected via a copula function that satisfies the triangular no-arbitrage condition. We then derive a univariate distribution for a simplified sterling effective exchange rate index (ERI). Our results indicate that standard parametric copula func-tions, such as the commonly used Normal and Frank copulas, fail to capture the degree of asymmetry observed in the data. We overcome this problem by using a non-parametric dependence function in the form of a Bernstein copula which is shown to produce a very close fit. We further give an example of how our approach can be used to price currency index options accounting for strike-dependent implied volatilities. We would like to thank Michael Bennett, Andrew Patton and Alessio Sancetta, participants at the CEF 2005 in Washington and the GFC 2005 in Dublin, as well as seminar...
Multivariate options are widely used when there is a need to hedge against a number of risks simu... more Multivariate options are widely used when there is a need to hedge against a number of risks simultaneously; such as when there is an exposure to several currencies or the need to provide cover against an index such as the FTSE100, or indeed any portfolio of assets. In the case of a basket option the payoff depends on the value of the entire portfolio or basket of assets where the basket is some weighted average of the underlying assets. The principal reason for using basket options is that they are cheaper to use for portfolio insurance than a corresponding portfolio of plain vanilla options on the individual assets. This cost saving depends on the correlation structure between the assets; the lower the correlation between currency pairs in a currency portfolio for instance, the greater the cost saving.
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Papers by Mark Salmon