Not long ago securities were traded by human traders in face-to-face markets. The ecosystem of an open outcry market was well-known, visible to a human eye, and rigidly prescribed. Now trading is increasingly done in anonymous electronic markets where traders do not have designated functions or mandatory roles. In fact, the traders themselves have been replaced by algorithms (machines) operating with little or no human oversight. While the process of electronic trading is not visible to a human eye, machine-learning methods have been developed to recognize persistent patterns in the data. In this study, we develop a dynamic machine-learning method that designates traders in an anonymous electronic market into five persistent categories: high frequency traders, market makers, opportunistic traders, fundamental traders, and small traders. Our method extends a plaid clustering technique with a smoothing framework that filters out transient patterns. The method is fast, robust, and suitable for a discovering trading ecosystems in a large number of electronic markets
{"title":"Discovering the Ecosystem of an Electronic Financial Market with a Dynamic Machine-Learning Method","authors":"Shawn Mankad, G. Michailidis, A. Kirilenko","doi":"10.2139/ssrn.1787577","DOIUrl":"https://doi.org/10.2139/ssrn.1787577","url":null,"abstract":"Not long ago securities were traded by human traders in face-to-face markets. The ecosystem of an open outcry market was well-known, visible to a human eye, and rigidly prescribed. Now trading is increasingly done in anonymous electronic markets where traders do not have designated functions or mandatory roles. In fact, the traders themselves have been replaced by algorithms (machines) operating with little or no human oversight. While the process of electronic trading is not visible to a human eye, machine-learning methods have been developed to recognize persistent patterns in the data. In this study, we develop a dynamic machine-learning method that designates traders in an anonymous electronic market into five persistent categories: high frequency traders, market makers, opportunistic traders, fundamental traders, and small traders. Our method extends a plaid clustering technique with a smoothing framework that filters out transient patterns. The method is fast, robust, and suitable for a discovering trading ecosystems in a large number of electronic markets","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122034997","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}
Equity risk premiums are a central component of every risk and return model in finance and are a key input in estimating costs of equity and capital in both corporate finance and valuation. Given their importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating equity risk premiums, historical returns are used, with the difference in annual returns on stocks versus bonds over a long time period comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. In the next section, we look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generated expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis.
{"title":"Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2011 Edition","authors":"A. Damodaran","doi":"10.2139/ssrn.1769064","DOIUrl":"https://doi.org/10.2139/ssrn.1769064","url":null,"abstract":"Equity risk premiums are a central component of every risk and return model in finance and are a key input in estimating costs of equity and capital in both corporate finance and valuation. Given their importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating equity risk premiums, historical returns are used, with the difference in annual returns on stocks versus bonds over a long time period comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. In the next section, we look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generated expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127683423","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}
Principal Component Analysis (PCA) is a common and popular tool for the analysis of financial market data, such as implied volatility smiles, interest rate curves and commodity future curves. We provide a critical view on PCA analysis and the corresponding results from empirical literature. In particular, it will be shown how PCA can produce patterned loading vectors if the correlation matrix just happens to belong to a particular matrix class. We will also provide evidence why the level factor is the dominating factor in virtually all empirical PCA analyses and question whether this reflects the true dynamics. In addition, we show how artifacts can be generated by PCA and how problematic the interpretation of PCA results can be, if a system is indeed driven by level, slope and curvature dynamics.
{"title":"Potential PCA Interpretation Problems for the Dynamics of Financial Market Data","authors":"Dimitri Reiswich, R. Tompkins","doi":"10.2139/ssrn.1757221","DOIUrl":"https://doi.org/10.2139/ssrn.1757221","url":null,"abstract":"Principal Component Analysis (PCA) is a common and popular tool for the analysis of financial market data, such as implied volatility smiles, interest rate curves and commodity future curves. We provide a critical view on PCA analysis and the corresponding results from empirical literature. In particular, it will be shown how PCA can produce patterned loading vectors if the correlation matrix just happens to belong to a particular matrix class. We will also provide evidence why the level factor is the dominating factor in virtually all empirical PCA analyses and question whether this reflects the true dynamics. In addition, we show how artifacts can be generated by PCA and how problematic the interpretation of PCA results can be, if a system is indeed driven by level, slope and curvature dynamics.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123035876","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}
It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite order VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t). We illustrate the findings with a small analysis of the term structure of interest rates.
{"title":"An Invariance Property of the Common Trends Under Linear Transformations of the Data","authors":"S. Johansen, K. Juselius","doi":"10.2139/ssrn.1701167","DOIUrl":"https://doi.org/10.2139/ssrn.1701167","url":null,"abstract":"It is well known that if X(t) is a nonstationary process and Y(t) is a linear function of X(t), then cointegration of Y(t) implies cointegration of X(t). We want to find an analogous result for common trends if X(t) is generated by a finite order VAR. We first show that Y(t) has an infinite order VAR representation in terms of its prediction errors, which are a linear process in the prediction error for X(t). We then apply this result to show that the limit of the common trends for Y(t) are linear functions of the common trends for X(t). We illustrate the findings with a small analysis of the term structure of interest rates.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133048445","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 investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observable covariates is required, like inverse probability weighting, kernel and other variants of matching, as well as different parametric models. The simulation design used is based on real data usually employed for the evaluation of labour market programmes in Germany. We vary several dimensions of the design that are of practical importance, like sample size, the type of the outcome variable, and aspects of the selection process. We find that trimming individual observations with too much weight as well as the choice of tuning parameters is important for all estimators. The key conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall, in particular when robustness to misspecifications of the propensity score is considered an important property.
{"title":"How to Control for Many Covariates? Reliable Estimators Based on the Propensity Score","authors":"M. Huber, M. Lechner, Conny Wunsch","doi":"10.2139/ssrn.1696892","DOIUrl":"https://doi.org/10.2139/ssrn.1696892","url":null,"abstract":"We investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observable covariates is required, like inverse probability weighting, kernel and other variants of matching, as well as different parametric models. The simulation design used is based on real data usually employed for the evaluation of labour market programmes in Germany. We vary several dimensions of the design that are of practical importance, like sample size, the type of the outcome variable, and aspects of the selection process. We find that trimming individual observations with too much weight as well as the choice of tuning parameters is important for all estimators. The key conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall, in particular when robustness to misspecifications of the propensity score is considered an important property.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116851969","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}
The aim of this paper is to investigate the ability of the Dynamic Variance Gamma model, recently proposed by Bellini and Mercuri (2010), to evaluate option prices on the S&P500 index. We also provide a simple relation between the Dynamic Variance Gamma model and the Vix index. We use this result to build a maximum likelihood estimation procedure and to calibrate the model on option data.
{"title":"Estimation and Calibration of a Dynamic Variance Gamma Model Using Vix Data","authors":"L. Mercuri","doi":"10.2139/ssrn.1695515","DOIUrl":"https://doi.org/10.2139/ssrn.1695515","url":null,"abstract":"The aim of this paper is to investigate the ability of the Dynamic Variance Gamma model, recently proposed by Bellini and Mercuri (2010), to evaluate option prices on the S&P500 index. We also provide a simple relation between the Dynamic Variance Gamma model and the Vix index. We use this result to build a maximum likelihood estimation procedure and to calibrate the model on option data.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114482556","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 paper develops basic algebraic concepts for instrumental variables (IV) regressions which are used to derive the leverage and influence of observations on the 2SLS estimate and compute alternative heteroskedasticity-consistent (HC1, HC2 and HC3) estimators for the 2SLS covariance matrix in a finite-sample context. Monte Carlo simulations and applications to growth regressions are used to evaluate the performance of these estimators. The results support the use of HC3 instead of White’s robust standard errors in small and unbalanced data sets. The leverage and influence of observations can be examined with the various measures derived in the paper.
{"title":"Leverage and Covariance Matrix Estimation in Finite-Sample IV Regressions","authors":"Andreas Steinhauer, T. Wuergler","doi":"10.2139/ssrn.1662459","DOIUrl":"https://doi.org/10.2139/ssrn.1662459","url":null,"abstract":"This paper develops basic algebraic concepts for instrumental variables (IV) regressions which are used to derive the leverage and influence of observations on the 2SLS estimate and compute alternative heteroskedasticity-consistent (HC1, HC2 and HC3) estimators for the 2SLS covariance matrix in a finite-sample context. Monte Carlo simulations and applications to growth regressions are used to evaluate the performance of these estimators. The results support the use of HC3 instead of White’s robust standard errors in small and unbalanced data sets. The leverage and influence of observations can be examined with the various measures derived in the paper.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120955668","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}
In missing data analysis, there is often a need to assess the sensitivity of key inferences to departures from untestable assumptions regarding the missing data process. Such sensitivity analysis often requires specifying a missing data model which commonly assumes parametric functional forms for the predictors of missingness. In this paper, we relax the parametric assumption and investigate the use of a generalized additive missing data model. We also consider the possibility of a non-linear relationship between missingness and the potentially missing outcome, whereas the existing literature commonly assumes a more restricted linear relationship. To avoid the computational complexity, we adopt an index approach for local sensitivity. We derive explicit formulas for the resulting semiparametric sensitivity index. The computation of the index is simple and completely avoids the need to repeatedly fit the semiparametric nonignorable model. Only estimates from the standard software analysis are required with a moderate amount of additional computation. Thus, the semiparametric index provides a fast and robust method to adjust the standard estimates for nonignorable missingness. An extensive simulation study is conducted to evaluate the effects of misspecifying the missing data model and to compare the performance of the proposed approach with the commonly used parametric approaches. The simulation study shows that the proposed method helps reduce bias that might arise from the misspecification of the functional forms of predictors in the missing data model. We illustrate the method in a Wage Offer dataset.
{"title":"A Semiparametric Approach for Analyzing Nonignorable Missing Data","authors":"Hui Xie, Y. Qian, Leming Qu","doi":"10.5705/SS.2009.252","DOIUrl":"https://doi.org/10.5705/SS.2009.252","url":null,"abstract":"In missing data analysis, there is often a need to assess the sensitivity of key inferences to departures from untestable assumptions regarding the missing data process. Such sensitivity analysis often requires specifying a missing data model which commonly assumes parametric functional forms for the predictors of missingness. In this paper, we relax the parametric assumption and investigate the use of a generalized additive missing data model. We also consider the possibility of a non-linear relationship between missingness and the potentially missing outcome, whereas the existing literature commonly assumes a more restricted linear relationship. To avoid the computational complexity, we adopt an index approach for local sensitivity. We derive explicit formulas for the resulting semiparametric sensitivity index. The computation of the index is simple and completely avoids the need to repeatedly fit the semiparametric nonignorable model. Only estimates from the standard software analysis are required with a moderate amount of additional computation. Thus, the semiparametric index provides a fast and robust method to adjust the standard estimates for nonignorable missingness. An extensive simulation study is conducted to evaluate the effects of misspecifying the missing data model and to compare the performance of the proposed approach with the commonly used parametric approaches. The simulation study shows that the proposed method helps reduce bias that might arise from the misspecification of the functional forms of predictors in the missing data model. We illustrate the method in a Wage Offer dataset.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126526206","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}
One of the pervasive issues in social and environmental research has been to improve the quality of socioeconomic data in developing countries. Because of the shortcoming of standard data sources, the present study examines luminosity (measures of nighttime lights) as a proxy for standard measures of output. The paper compares output and luminosity at the country levels and at the 1° x 1° grid-cell levels for the period 1992-2008. The results are that luminosity has very little value added for countries with high-quality statistical systems. However, it may be useful for countries with the lowest statistical grades, particularly for war-torn countries with no recent population or economic censuses. The results also indicate that luminosity has more value added for economic density estimates than for time-series growth rates.
{"title":"The Value of Luminosity Data as a Proxy for Economic Statistics","authors":"Xi Chen, W. Nordhaus","doi":"10.2139/ssrn.1666164","DOIUrl":"https://doi.org/10.2139/ssrn.1666164","url":null,"abstract":"One of the pervasive issues in social and environmental research has been to improve the quality of socioeconomic data in developing countries. Because of the shortcoming of standard data sources, the present study examines luminosity (measures of nighttime lights) as a proxy for standard measures of output. The paper compares output and luminosity at the country levels and at the 1° x 1° grid-cell levels for the period 1992-2008. The results are that luminosity has very little value added for countries with high-quality statistical systems. However, it may be useful for countries with the lowest statistical grades, particularly for war-torn countries with no recent population or economic censuses. The results also indicate that luminosity has more value added for economic density estimates than for time-series growth rates.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116588004","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}
R. Feenstra, R. Lipsey, Lee G. Branstetter, C. Foley, J. Harrigan, J. Jensen, L. Kletzer, C. Mann, Peter K. Schott, Greg C. Wright
This report, prepared for the Committee on Economic Statistics of the American Economic Association, examines the state of available data for the study of international trade and foreign direct investment. Data on values of imports and exports of goods are of high quality and coverage, but price data suffer from insufficient detail. It would be desirable to have more data measuring value-added in trade as well as prices of comparable domestic and imported inputs. Value data for imports and exports of services are too aggregated and valuations are questionable, while price data for service exports and imports are almost non-existent. Foreign direct investment data are of high quality but quality has suffered from budget cuts. Data on trade in intellectual property are fragmentary. The intangibility of the trade makes measurement difficult, but budget cuts have added to the difficulties. Modest funding increases would result in data more useful for research and policy analysis.
{"title":"Report on the State of Available Data for the Study of International Trade and Foreign Direct Investment","authors":"R. Feenstra, R. Lipsey, Lee G. Branstetter, C. Foley, J. Harrigan, J. Jensen, L. Kletzer, C. Mann, Peter K. Schott, Greg C. Wright","doi":"10.3386/W16254","DOIUrl":"https://doi.org/10.3386/W16254","url":null,"abstract":"This report, prepared for the Committee on Economic Statistics of the American Economic Association, examines the state of available data for the study of international trade and foreign direct investment. Data on values of imports and exports of goods are of high quality and coverage, but price data suffer from insufficient detail. It would be desirable to have more data measuring value-added in trade as well as prices of comparable domestic and imported inputs. Value data for imports and exports of services are too aggregated and valuations are questionable, while price data for service exports and imports are almost non-existent. Foreign direct investment data are of high quality but quality has suffered from budget cuts. Data on trade in intellectual property are fragmentary. The intangibility of the trade makes measurement difficult, but budget cuts have added to the difficulties. Modest funding increases would result in data more useful for research and policy analysis.","PeriodicalId":384078,"journal":{"name":"ERN: Other Econometrics: Data Collection & Data Estimation Methodology (Topic)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127765373","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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