A basket is a set of instruments that are held together because its statistical profile delivers a desired goal, such as hedging or trading, which cannot be achieved through the individual constituents or even subsets of them. Multiple procedures have been proposed to compute hedging and trading baskets, among which balanced baskets have attracted significant attention in recent years. Unlike Principal Component Analysis (PCA) style of methods, balanced baskets spread risk or exposure across their constituents without requiring a change of basis. Practitioners typically prefer balanced baskets because their output can be understood in the same terms for which they have developed an intuition.We review three methodologies for determining balanced baskets, analyze the features of their respective solutions and provide Python code for their calculation. We also introduce a new method for reducing the dimension of a covariance matrix, called Covariance Clustering, which addresses the problem of numerical ill-conditioning without requiring a change of basis.
{"title":"Balanced Baskets: A New Approach to Trading and Hedging Risks","authors":"D. Bailey, Marcos M. López de Prado","doi":"10.2139/ssrn.2066170","DOIUrl":"https://doi.org/10.2139/ssrn.2066170","url":null,"abstract":"A basket is a set of instruments that are held together because its statistical profile delivers a desired goal, such as hedging or trading, which cannot be achieved through the individual constituents or even subsets of them. Multiple procedures have been proposed to compute hedging and trading baskets, among which balanced baskets have attracted significant attention in recent years. Unlike Principal Component Analysis (PCA) style of methods, balanced baskets spread risk or exposure across their constituents without requiring a change of basis. Practitioners typically prefer balanced baskets because their output can be understood in the same terms for which they have developed an intuition.We review three methodologies for determining balanced baskets, analyze the features of their respective solutions and provide Python code for their calculation. We also introduce a new method for reducing the dimension of a covariance matrix, called Covariance Clustering, which addresses the problem of numerical ill-conditioning without requiring a change of basis.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"415 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77493295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
High rates of government investment in public sector capital forecast high risk premiums both at the aggregate and firm-level. This result is in sharp contrast with the well-documented negative relationship between the private sector investment rate and risk premiums. To explain the empirical findings, we extend the neoclassical q-theory model of investment and specify public sector capital as an additional input in the firm's technology. We show that the model can quantitatively replicate the empirical facts with reasonable parameter values if public sector capital increases the marginal productivity of private inputs.
{"title":"Government Investment and the Stock Market","authors":"F. Belo, Jianfeng Yu","doi":"10.2139/ssrn.1508120","DOIUrl":"https://doi.org/10.2139/ssrn.1508120","url":null,"abstract":"High rates of government investment in public sector capital forecast high risk premiums both at the aggregate and firm-level. This result is in sharp contrast with the well-documented negative relationship between the private sector investment rate and risk premiums. To explain the empirical findings, we extend the neoclassical q-theory model of investment and specify public sector capital as an additional input in the firm's technology. We show that the model can quantitatively replicate the empirical facts with reasonable parameter values if public sector capital increases the marginal productivity of private inputs.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"302 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83443573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We analyze the quality of macroeconomic survey forecasts. Recent findings indicate that they are anchoring biased. This irrationality would challenge the results of a wide range of empirical studies, e.g., in asset pricing, volatility clustering or market liquidity, which rely on survey data to capture market participants' expectations. We contribute to the existing literature in two ways. First, we show that the cognitive bias is a statistical artifact. Despite highly significant anchoring coefficients a bias adjustment does not improve forecasts' quality. To explain this counterintuitive result we take a closer look at macroeconomic analysts' information processing abilities. We find that analysts benefit from the use of an extensive information set, neglected in the anchoring bias test. Exactly this information advantage drives the misleading anchoring bias test results. Second, we find that the superior information aggregation capabilities enable analysts to easily outperform sophisticated timeseries forecasts and therefore survey forecasts should clearly be favored.
{"title":"Irrationality or Efficiency of Macroeconomic Survey Forecasts? Implications from the Anchoring Bias Test","authors":"D. Hess, Sebastian Orbe","doi":"10.2139/ssrn.1669587","DOIUrl":"https://doi.org/10.2139/ssrn.1669587","url":null,"abstract":"We analyze the quality of macroeconomic survey forecasts. Recent findings indicate that they are anchoring biased. This irrationality would challenge the results of a wide range of empirical studies, e.g., in asset pricing, volatility clustering or market liquidity, which rely on survey data to capture market participants' expectations. We contribute to the existing literature in two ways. First, we show that the cognitive bias is a statistical artifact. Despite highly significant anchoring coefficients a bias adjustment does not improve forecasts' quality. To explain this counterintuitive result we take a closer look at macroeconomic analysts' information processing abilities. We find that analysts benefit from the use of an extensive information set, neglected in the anchoring bias test. Exactly this information advantage drives the misleading anchoring bias test results. Second, we find that the superior information aggregation capabilities enable analysts to easily outperform sophisticated timeseries forecasts and therefore survey forecasts should clearly be favored.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74249483","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We extend the Consumption-based CAPM (C-CAPM) model to representative agents with different risk attitudes. We first use the concept of expectation dependence and show that for a risk averse representative agent, it is the first-degree expectation dependence (FED) rather than the covariance that determines C-CAPM’s riskiness. We extend the assumption of risk aversion to prudence and propose the measure of second-degree expectation dependence (SED) to obtain the values of asset price and equity premium. These theoretical results are linked to the equity premium puzzle. Using the same dataset as in Campbell (2003), the estimated measures of relative risk aversion from FED and SED approximations are much lower than those obtained in the original study and correspond to the theoretical values often discussed in the literature. The theoretical model is then generalized to higher-degree risk changes and higher-order risk averse representative agents.
{"title":"An Extension of the Consumption-Based CAPM Model","authors":"G. Dionne, Jingyuan Li, Cédric Okou","doi":"10.2139/ssrn.2018476","DOIUrl":"https://doi.org/10.2139/ssrn.2018476","url":null,"abstract":"We extend the Consumption-based CAPM (C-CAPM) model to representative agents with different risk attitudes. We first use the concept of expectation dependence and show that for a risk averse representative agent, it is the first-degree expectation dependence (FED) rather than the covariance that determines C-CAPM’s riskiness. We extend the assumption of risk aversion to prudence and propose the measure of second-degree expectation dependence (SED) to obtain the values of asset price and equity premium. These theoretical results are linked to the equity premium puzzle. Using the same dataset as in Campbell (2003), the estimated measures of relative risk aversion from FED and SED approximations are much lower than those obtained in the original study and correspond to the theoretical values often discussed in the literature. The theoretical model is then generalized to higher-degree risk changes and higher-order risk averse representative agents.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79073002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Trying to perform non-parametric change point tests for multivariate data using empirical processes is much more difficult that in the univariate case, since the limiting distribution depends on the unknown joint distribution function or its associated copula. In order to solve this problem, we extend the multiplier central limit theorem to empirical processes of pseudo-observations to build asymptotically independent copies of these processes. Examples of applications to change point problems for i.i.d observations and innovations of dynamic models are given, both for the full distribution and the associated copula.
{"title":"Non-Parametric Change Point Problems Using Multipliers","authors":"B. Rémillard","doi":"10.2139/ssrn.2043632","DOIUrl":"https://doi.org/10.2139/ssrn.2043632","url":null,"abstract":"Trying to perform non-parametric change point tests for multivariate data using empirical processes is much more difficult that in the univariate case, since the limiting distribution depends on the unknown joint distribution function or its associated copula. In order to solve this problem, we extend the multiplier central limit theorem to empirical processes of pseudo-observations to build asymptotically independent copies of these processes. Examples of applications to change point problems for i.i.d observations and innovations of dynamic models are given, both for the full distribution and the associated copula.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77620799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Large one-off events cause large changes in prices, but may not affect the volatility and correlation dynamics as much as smaller events. In such cases, standard volatility models may deliver biased covariance forecasts. We propose a multivariate volatility forecasting model that is accurate in the presence of large one-off events. The model is an extension of the dynamic conditional correlation (DCC) model. In our empirical application to forecasting the covariance matrix of the daily EUR/USD and Yen/USD return series, we find that our method produces more precise out-of-sample covariance forecasts than the DCC model. Furthermore, when used in portfolio allocation, it leads to portfolios with similar return characteristics but lower turnovers, and hence higher profits.
{"title":"Robust Forecasting of Dynamic Conditional Correlation GARCH Models","authors":"Kris Boudt, Jón Dańıelsson, S. Laurent","doi":"10.2139/ssrn.1717796","DOIUrl":"https://doi.org/10.2139/ssrn.1717796","url":null,"abstract":"Large one-off events cause large changes in prices, but may not affect the volatility and correlation dynamics as much as smaller events. In such cases, standard volatility models may deliver biased covariance forecasts. We propose a multivariate volatility forecasting model that is accurate in the presence of large one-off events. The model is an extension of the dynamic conditional correlation (DCC) model. In our empirical application to forecasting the covariance matrix of the daily EUR/USD and Yen/USD return series, we find that our method produces more precise out-of-sample covariance forecasts than the DCC model. Furthermore, when used in portfolio allocation, it leads to portfolios with similar return characteristics but lower turnovers, and hence higher profits.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"33 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89250487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ane and Geman (2000) observed that market returns appear to follow a conditional Gaussian distribution where the conditioning is a stochastic clock based on cumulative transaction count. The existence of long range dependence in the squared and absolute value of market returns is a ‘stylized fact’ and researchers have interpreted this to imply that the stochastic clock is self-similar, multi-fractal (Mandelbrot, Fisher and Calvet, 1997) or mono-fractal (Heyde, 1999). We model the market stochastic clock as the stochastic integrated intensity of a doubly stochastic Poisson (Cox) point process of the cumulative transaction count of stocks traded on the New York Stock Exchange (NYSE). A comparative empirical analysis of a self-normalized version of the stochastic integrated intensity is consistent with a mono-fractal market clock with a Hurst exponent of 0.75.
{"title":"Fractal Market Time","authors":"James McCulloch","doi":"10.2139/ssrn.1803888","DOIUrl":"https://doi.org/10.2139/ssrn.1803888","url":null,"abstract":"Ane and Geman (2000) observed that market returns appear to follow a conditional Gaussian distribution where the conditioning is a stochastic clock based on cumulative transaction count. The existence of long range dependence in the squared and absolute value of market returns is a ‘stylized fact’ and researchers have interpreted this to imply that the stochastic clock is self-similar, multi-fractal (Mandelbrot, Fisher and Calvet, 1997) or mono-fractal (Heyde, 1999). We model the market stochastic clock as the stochastic integrated intensity of a doubly stochastic Poisson (Cox) point process of the cumulative transaction count of stocks traded on the New York Stock Exchange (NYSE). A comparative empirical analysis of a self-normalized version of the stochastic integrated intensity is consistent with a mono-fractal market clock with a Hurst exponent of 0.75.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"2033 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91318988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Disaggregate demand in the marketplace exists on a grid determined by the package sizes offered by manufacturers and retailers. Although consumers may want to purchase a continuous-valued amount of a product, realized purchases are constrained by available packages. This constraint might not be problematic for high-volume demand, but it is potentially troubling when demand is small. Despite the prevalence of packaging constraints on choice, economic models of choice have been slow to deal with their effects on parameter estimates and policy implications. In this paper we propose a general framework for dealing with indivisible demand in economic models of choice, and we show how to estimate model parameters using Bayesian methods. Analyses of simulated data and a scanner-panel data set of yogurt purchases indicate that ignoring packaging constraints can bias parameter estimates and measures of model fit, which results in the inaccurate measures of metrics such as price elasticity and compensating value. We also show that a portion of nonpurchase in the data e.g., 2.27% for Yoplait Original reflects the restriction of indivisibility, not the lack of preference. The importance of demand indivisibility is also highlighted by the counterfactual study where the removal of the smallest package size i.e., 4 oz mainly results in nonpurchase in the yogurt category instead of switching to larger package sizes.
{"title":"Modeling Indivisible Demand","authors":"Sanghak Lee, Greg M. Allenby","doi":"10.2139/ssrn.1809136","DOIUrl":"https://doi.org/10.2139/ssrn.1809136","url":null,"abstract":"Disaggregate demand in the marketplace exists on a grid determined by the package sizes offered by manufacturers and retailers. Although consumers may want to purchase a continuous-valued amount of a product, realized purchases are constrained by available packages. This constraint might not be problematic for high-volume demand, but it is potentially troubling when demand is small. Despite the prevalence of packaging constraints on choice, economic models of choice have been slow to deal with their effects on parameter estimates and policy implications. In this paper we propose a general framework for dealing with indivisible demand in economic models of choice, and we show how to estimate model parameters using Bayesian methods. Analyses of simulated data and a scanner-panel data set of yogurt purchases indicate that ignoring packaging constraints can bias parameter estimates and measures of model fit, which results in the inaccurate measures of metrics such as price elasticity and compensating value. We also show that a portion of nonpurchase in the data e.g., 2.27% for Yoplait Original reflects the restriction of indivisibility, not the lack of preference. The importance of demand indivisibility is also highlighted by the counterfactual study where the removal of the smallest package size i.e., 4 oz mainly results in nonpurchase in the yogurt category instead of switching to larger package sizes.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"131 9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82944389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article describes the expectation and measure groups of the quadratic Gaussian algebra, and consider their application in the pricing of interest rate and cross asset derivatives. The discussion is motivated by the desire to construct consistent, arbitrage-free, term structure pricing models, that incorporate multi-factor decorrelation and credible smile dynamics in a robust and easy to implement framework. The article concludes with the application of symmetry techniques in the construction of the quadratic Gaussian Libor model.
{"title":"Symmetry Methods for the Quadratic Gaussian Libor Model (Slides)","authors":"P. Mccloud","doi":"10.2139/ssrn.1584849","DOIUrl":"https://doi.org/10.2139/ssrn.1584849","url":null,"abstract":"This article describes the expectation and measure groups of the quadratic Gaussian algebra, and consider their application in the pricing of interest rate and cross asset derivatives. The discussion is motivated by the desire to construct consistent, arbitrage-free, term structure pricing models, that incorporate multi-factor decorrelation and credible smile dynamics in a robust and easy to implement framework. The article concludes with the application of symmetry techniques in the construction of the quadratic Gaussian Libor model.","PeriodicalId":11485,"journal":{"name":"Econometrics: Applied Econometrics & Modeling eJournal","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2012-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77681540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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