Andrew Patton's research page
Research keywords: econometrics,
financial economics, forecasting, copulas, time series, dependence, volatility,
hedge funds.
BibTeX list of
these papers (text file)
Google Scholar: https://goo.gl/7JA7Kf
SoFiE Seminar Series: https://sofie.stern.nyu.edu/seminar
Dynamic Factor Copula Models with Estimated Cluster Assignments, with Dong Hwan Oh, working paper, November 2020.
Paper (PDF), Abstract (HTML),
Supplemental Appendix
(PDF)
Testing Forecast Rationality for Measures of Central Tendency, with Timo
Dimitriadis and Patrick
Schmidt, working paper, October 2019, revised
September 2020.
Paper (PDF), Abstract (HTML),
Supplemental Appendix
(PDF)
Bootstrapping Two-Stage Quasi-Maximum Likelihood Estimators of Time
Series Models, with Sílvia
Gonçalves, Ulrich Hounyo and Kevin Sheppard,
working paper, October 2019.
Paper (PDF), Abstract
(HTML)
Realized Semibetas: Signs of Things to Come, with Tim Bollerslev
and Rogier
Quaedvlieg, working paper, September 2019, revised
October 2020.
Paper (PDF), Abstract
(HTML), Supplemental Appendix (PDF)
Testing for Unobserved Heterogeneity via k-means Clustering, with Brian Weller, working paper, July 2019.
Paper (PDF), Abstract (HTML),
Supplemental Appendix
(PDF)
Comparing Predictive Accuracy in the Presence of a Loss Function Shape
Parameter, with Sander Barendse, working paper, May 2019, revised December 2020.
Paper (PDF), Abstract
(HTML), Supplemental Appendix (PDF)
Risk Price Variation: The Missing Half of Empirical Asset Pricing, with Brian Weller, working paper, September 2018, revised May
2019.
Paper (PDF), Abstract (HTML)
From Zero to Hero: Realized Partial (Co)Variances, with Tim Bollerslev, Marcelo C. Medeiros and Rogier Quaedvlieg,
working paper, July 2020.
Paper (PDF), Abstract
(HTML)
A Consistent Specification Test for Dynamic Quantile Models, with Peter Horvath, Jia Li and Zhipeng Liao, working paper,
July 2020, revised September 2020.
Paper (PDF), Abstract
(HTML), Supplemental Appendix (PDF)
Realized Semicovariances, with Tim
Bollerslev, Jia Li and Rogier Quaedvlieg,
2020, Econometrica, 88(4), 1515-1551.
Paper (PDF), Abstract
(HTML), Supplemental Appendix (PDF), Slides (PDF)
What You See is Not What You Get: The Costs of Trading Market
Anomalies, with Brian Weller,
2020, Journal of Financial Economics, 137, 515-549.
Paper (PDF), Abstract
(HTML), Slides (PDF)
Multivariate Leverage Effects and Realized Semicovariance
GARCH Models, with Tim Bollerslev
and Rogier
Quaedvlieg, 2020, Journal of Econometrics, 217, 411-430.
Paper (PDF), Abstract
(HTML)
Comparing Possibly Misspecified Forecasts, 2020, Journal of Business
& Economic Statistics, 38(4), 796-809.
Paper (PDF), Abstract
(HTML), Supplemental Appendix
(PDF), Slides (PDF)
Dynamic Semiparametric Models for Expected Shortfall (and
Value-at-Risk),
with Johanna F. Ziegel and Rui Chen,
2019, Journal of Econometrics, 211(2), 388-413.
Paper (PDF), Abstract (HTML),
Supplemental Appendix
(PDF), Slides (PDF), Code (MATLAB)
Modeling and Forecasting
(Un)Reliable Realized Covariances for More Reliable Financial Decisions, with Tim
Bollerslev and Rogier Quaedvlieg,
2018, Journal of Econometrics, 207(1), 71-91.
Paper (PDF), Abstract
(HTML), Web Appendix (PDF), Slides (PDF)
Time-Varying Systemic Risk: Evidence from a Dynamic Copula Model of CDS
Spreads, with Dong Hwan Oh, 2018, Journal
of Business & Economic Statistics, 36(2), 181-195.
Paper (PDF), Abstract
(HTML), Web Appendix (PDF), Code (MATLAB), Slides
(PDF)
Asymptotic Inference about Predictive Accuracy using High Frequency
Data, with Jia Li, 2018, Journal of Econometrics, 203(2), 223-240.
Paper (PDF), Abstract
(HTML), Supplemental Appendix (PDF), Slides (PDF)
Modelling Dependence in High Dimensions with Factor Copulas, with Dong Hwan Oh, 2017, Journal of Business
& Economic Statistics, 35(1), 139-154.
Paper (PDF), Abstract (HTML), Web Appendix (PDF), Slides (PDF)
Exploiting the Errors: A Simple Approach for Improved Volatility
Forecasting, with Tim Bollerslev
and Rogier
Quaedvlieg,
2016, Journal of Econometrics, 192, 1-18.
Paper (PDF), Abstract (HTML), Web Appendix (PDF), Code and data (MATLAB),
Slides (PDF)
Daily House Price Indexes: Construction, Modeling,
and Longer-Run Predictions, with Tim Bollerslev
and Wenjing Wang, 2016, Journal of Applied Econometrics, 31, 1005-1025.
Paper (PDF), Abstract
(HTML), Web
Appendix (PDF)
High-Dimensional Copula-Based Distributions with Mixed Frequency Data, with Dong Hwan Oh, 2016, Journal of Econometrics, 193, 349-366.
Paper (PDF), Abstract
(HTML), Web
Appendix (PDF), Slides (PDF)
The Impact of Hedge Funds on Asset Markets, with Mathias Kruttli and Tarun
Ramadorai,
2015, Review of Asset Pricing
Studies 5(2), 185-226.
Paper (PDF), Abstract (HTML), Web Appendix (PDF), Illiquidity measure time series (TXT), Slides (PDF)
Does Anything Beat 5-Minute RV?
A Comparison of Realized Measures Across Multiple Asset Classes, with Lily Liu and Kevin
Sheppard, 2015, Journal of Econometrics, 187(1), 293-311.
Paper (PDF), Abstract (HTML), Web Appendix (PDF), Slides (PDF)
Dynamic Copula Models and High Frequency Data, with Irving De Lira Salvatierra, 2015, Journal of Empirical Finance, 30(1), 120-135.
Paper (PDF), Abstract (HTML),
Web
Appendix (PDF)
Good Volatility, Bad Volatility: Signed
Jumps and the Persistence of Volatility, with Kevin
Sheppard,
2015, Review
of Economics and Statistics, 97(3), 683-697.
Paper (PDF), Abstract (HTML), Web Appendix (PDF)
Change You Can Believe In? Hedge Fund Data Revisions, with Tarun
Ramadorai and Michael Streatfield, 2015, Journal of Finance, 70(3), 963-999.
Paper
(PDF), Abstract (HTML), Web
Appendix (PDF), Slides
(PDF)
-- This paper was reviewed in The Telegraph
(Nov 2011), BBC News (June 2012), The Economist (April 2013).
--
Previously circulated as "The Reliability of Voluntary Disclosures:
Evidence from Hedge Funds"
Copulas in Econometrics, with Yanqin Fan, 2014. Annual Review
of Economics,
6, 179-200.
Paper (PDF), Abstract (HTML)
Simulated Method of Moments Estimation for Copula-Based Multivariate
Models, with Dong Hwan Oh, 2013, Journal of the American Statistical Association,
108(502), 689-700.
Paper (PDF), Abstract (HTML), Supplemental Appendix (PDF)
On the High Frequency Dynamics of
Hedge Fund Risk Exposures, with Tarun
Ramadorai,
2013, Journal of Finance, 68(2), 597-635.
Paper (PDF), Abstract
(HTML), Web Appendix
(PDF), Slides (PDF)
-- An earlier version of this paper was
circulated as On the High
Frequency Dynamics of Hedge Fund Risk Exposures, April 2010.
Does Beta Move with News?
Firm-Specific Information Flows and Learning about Profitability,
with Michela Verardo, 2012, Review of Financial Studies,
25(9), 2789-2839.
Paper (PDF), Abstract (HTML), Slides (PDF)
-- An early version of this paper was
circulated as Financial Markets Group
Discussion Paper 630, London School of Economics.
A Review of Copula Models for
Economic Time Series, 2012, Journal of Multivariate Analysis, 110, 4-18.
Paper (PDF), Abstract
(HTML)
-- A longer and more detailed version of this
review is my 2012 Handbook
of Economic Forecasting chapter.
Forecast Rationality Tests Based on
Multi-Horizon Bounds, with Allan Timmermann, 2012, Journal
of Business and Economic Statistics, 30(1), 1-17.
Paper (PDF), Abstract (HTML), Slides
(PDF)
-- This paper was the JBES Invited Address at the 2011 ASSA meetings.
Data-Based Ranking of Realised Volatility
Estimators, 2011,
Journal of Econometrics, 161(2), 284-303.
Paper (PDF), Abstract
(HTML), Slides (PDF)
Predictability of Output Growth and Inflation:
A Multi-Horizon Survey Approach, with Allan Timmermann, 2011, Journal of Business and
Economic Statistics, 29(3), 397-410.
Paper (PDF), Abstract (HTML), Slides (PDF)
-- Some
of the results in the above paper (and the JME paper below) were previously presented
in “Learning in Real Time: Theory and Empirical Evidence from the Term
Structure of Survey Forecasts”, Centre for Economic Policy Research
Discussion Paper DP6526. An early version of that paper was circulated as
"How Quickly is Macroeconomic Uncertainty Resolved? Theory and Evidence
from the Term Structure of Forecast Errors".
Volatility Forecast Comparison using Imperfect Volatility Proxies, 2011, Journal of Econometrics, 160(1), 246-256.
Paper (PDF), Abstract (HTML), Code (MATLAB),
Slides (PDF)
-- Longer
working paper version: “Volatility
Forecast Comparison using Imperfect Volatility Proxies”, April 2006, Quantitative Finance Research Centre,
University of Technology Sydney, Research Paper 175.
Why do Forecasters Disagree? Lessons from the Term Structure of
Cross-Sectional Dispersion, with Allan Timmermann, 2010, Journal of Monetary Economics, 57(7), 803-820.
Paper (PDF), Abstract (HTML), Technical
Appendix (PDF), Slides
(PDF)
Monotonicity in
Asset Returns: New Tests with Applications to the Term Structure, the CAPM and
Portfolios Sorts, with Allan Timmermann,
2010. Journal of Financial Economics,
98(3), 605-625.
Paper (PDF), Abstract (HTML), Code (MATLAB),
Slides (PDF)
-- An earlier version of this paper was circulated as Portfolio Sorts and Tests
of Cross-Sectional Patterns in Expected Returns, February 2008.
Optimal Combinations of Realised
Volatility Estimators,
with Kevin Sheppard , 2009, International Journal of Forecasting, 25(2), 218-238.
Paper (PDF), Abstract
(HTML), Slides (PDF)
Are "Market Neutral" Hedge
Funds Really Market Neutral?, 2009, Review of
Financial Studies, 22(7), 2495-2530.
Paper (PDF), Abstract (HTML), Slides (PDF)
-- This paper was reviewed in the Financial Times: 27 May 2005 (PDF), 9 May
2005 (PDF), 30 April 2004 (PDF)
-- This paper was awarded the Inquire UK best paper award, 2004.
Testing Forecast Optimality under
Unknown Loss, with Allan Timmermann, 2007, Journal of the American Statistical Association,
102(480), 1172-1184.
Paper (PDF), Abstract (HTML), Slides (PDF)
Properties of Optimal Forecasts
under Asymmetric Loss and Nonlinearity, with Allan Timmermann, 2007, Journal of Econometrics, 140(2),
884-918.
Paper (PDF), Abstract (HTML), Slides (PDF)
Modelling Asymmetric Exchange Rate
Dependence, 2006, International
Economic Review, 47(2), 527-556.
Paper (PDF), Abstract
(HTML), Code (MATLAB), Slides (PDF)
-- This paper was previously circulated as “Modelling Time-Varying Exchange Rate Dependence Using the Conditional
Copula”, University of California, San Diego, Discussion
Paper 01-09.
-- The Joe-Clayton and symmetrised Joe-Clayton copula density functions can be
found here (PDF).
Common Factors in Conditional
Distributions for Bivariate Time Series, with Clive
W. J. Granger and Timo Teräsvirta, 2006, Journal of Econometrics, 132(1), 43-57.
Paper (PDF), Abstract (HTML), Code (MATLAB)
Estimation of Multivariate Models
for Time Series of Possibly Different Lengths, 2006, Journal of Applied Econometrics, 21(2), 147-173.
Paper (PDF), Abstract (HTML), Code (MATLAB), Slides (PDF)
-- This paper was previously circulated as: “Estimation of Copula Models for Time Series of Possibly Different
Lengths”, University of California, San Diego, Discussion
Paper 01-17.
-- The full set of results for simulations in this paper are available here.
On the Out-of-Sample Importance of
Skewness and Asymmetric Dependence for Asset Allocation, 2004, Journal of Financial
Econometrics, 2(1),
130-168.
Paper (PDF), Abstract
(HTML), Code (MATLAB), Slides (PDF)
-- This paper received the Journal
of Financial Econometrics' Engle prize
-- This paper was reviewed in the Financial Times: June 2003 (PDF)
-- Two corrections of typos in Appendix B can be found here (PDF).
-- The Joe-Clayton and symmetrised Joe-Clayton copula density functions can be
found here (PDF). Matlab
functions for these can be found here (ZIP).
Impacts of Trades in an
Error-Correction Model of Quote Prices, with Robert F. Engle,
2004, Journal of
Financial Markets, 7(1), 1-25.
Paper (PDF), Abstract
(HTML)
What Good is a Volatility Model?, with Robert F. Engle,
2001, Quantitative
Finance, 1(2),
237-245.
Paper (PDF), Abstract
(HTML)
-- The data used in this paper (ASCII).
-- This paper was re-printed in: Forecasting
Volatility in the Financial Markets, Third Edition, 2007, J. Knight
and S.
Satchell (eds),
Butterworth-Heinemann.
-- And also in: Beyond Equilibrium and Efficiency, 2007, J.D. Farmer and J. Geanakoplos (eds), Oxford
University Press.
Multivariate GARCH Modeling of Exchange Rate Volatility Transmission in the
European Monetary System, with Colm Kearney, 2000, The Financial
Review, 35(1),
25-46.
Abstract (HTML).
Discussion of “Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings,” by Ehm, Gneiting, Jordan and Krüger,
Journal of the Royal Statistical
Society, 78(3), 505-562.
Discussion of “Comparing Predictive Accuracy, Twenty
Years Later: A Personal Perspective on the Use and Abuse of Diebold-Mariano
Tests” by F. X. Diebold, 2014, Journal of Business
& Economic Statistics, 33(1), 22-24.
Copula Methods for Forecasting Multivariate Time Series, 2013, in G. Elliott and A. Timmermann
(eds.) Handbook of Economic Forecasting, Volume 2, Springer Verlag.
Paper (PDF), Abstract (HTML), Code (MATLAB).
Generalized Forecast Errors, A Change of
Measure, and Forecast Optimality Conditions,
with Allan Timmermann, 2010, in Volatility and Time Series Econometrics:
Essays in Honor of Robert F. Engle, edited by T. Bollerslev, J.R.
Russell and M.W.
Watson, Oxford University Press.
Paper (PDF), Abstract (HTML)
-- This paper, along with my Journal of Econometrics and JASA papers with Allan
Timmermann, nests our earlier working paper: “Properties of
Optimal Forecasts”, August 2003, Centre for Economic Policy Research Discussion
Paper DP4037.
Correction to “Automatic
Block-Length Selection for the Dependent Bootstrap”, with Dimitris N. Politis and Halbert
White, 2009, Econometric
Reviews, 28(4), 372-375.
Paper (PDF), Code
(MATLAB), Original paper by Politis and White, 2004, Econometric Reviews, (PDF)
Copula-Based Models for Financial Time Series, 2009, in T.G. Andersen, R.A. Davis,
J.-P. Kreiss and T. Mikosch (eds.) Handbook of Financial Time Series, Springer Verlag.
Paper (PDF), Abstract (HTML), Code (MATLAB)
Evaluating Volatility and Correlation
Forecasts, with Kevin Sheppard, 2009, in T.G. Andersen, R.A. Davis,
J.-P. Kreiss and T. Mikosch (eds.) Handbook of Financial Time Series, Springer Verlag.
Paper (PDF), Abstract
(HTML)
Non-Linearities and Stress Testing, with Mathias Drehmann
and Steffen Sorensen, March 2006, forthcoming in the Proceedings of the
Fourth Joint Central Bank Research Conference on Risk Measurement and Systemic
Risk.
Paper (PDF), Abstract
(HTML)
Book
review: "Copula Methods in Finance", by U. Cherubini,
E. Luciano and W. Vecchiato, 2004, John Wiley &
Sons. In RISK, June 2005, 18(6).
Paper (PDF)
Applications of Copula Theory in
Financial Econometrics, June 2002.
Ph.D. dissertation
Department of Economics,
University of California, San
Diego.
Abstract (HTML).
Matlab code for some of the computations
in the above papers can be found here.
40th International Symposium on Forecasting, Rio de Janeiro/virtual (October 26-28, 2020)
Central European University, Department of Economics (November 6, 2020)
(EC)^2 conference: High Dimensional Modeling in Time Series, Paris/virtual (December 11-12, 2020)
UC – Riverside, Department of Economics (January 15, 2021)
Aarhus University, Department of Economics (March 25, 2021)
University of Geneva, Geneva Finance Research Institute (April 22, 2021)
The Econometrics of Macroeconomic and Financial Data: A Conference in Honor of Francis X. Diebold, Dallas (April 30 – May 1, 2021)
North American Summer Meeting of the Econometric Society, Montreal/virtual (10-13 June, 2021)
Society for Financial Econometrics annual meeting, San Diego (14-17 June, 2021)
__________________________________________
Multivariate
GARCH Modeling of Exchange Rate Volatility
Transmission in the European Monetary System
(co-authored with Colm
Kearney)
Abstract
We construct a series of 3-, 4- and 5-variable multivariate GARCH models of
exchange rate volatility transmission across some of the important European
Monetary System currencies, including the French franc, the German mark, the
Italian lira, the British pound and the European Currency Unit. The models are
estimated without imposing the common restriction of constant
correlation on both daily and weekly data from April 1979 to March 1997. Our
results indicate the importance of checking for specification robustness in
multi- variate GARCH modeling; we find that increased
temporal aggregation reduces observed volatility transmission, and that the
mark plays a dominant position in terms of volatility transmission.
Keywords: volatility, GARCH,
exchange rates, time-varying correlation.
J.E.L. Codes: C32, F31, G15.
__________________________________________
Impacts
of Trades in an Error-Correction Model of Quote Prices
(co-authored with Rob
Engle)
Abstract
In this paper we analyze and interpret the quote
price dynamics of 100 NYSE stocks with varying average trade frequencies. We
specify an error-correction model for the log-difference of the bid and the ask
price, with the spread acting as the error-correction term, and include as regressors the character- istics
of the trades occurring between quote observations, if any. We find that short
duration and medium to large volume trades have the largest impacts on quote
prices for one hundred stocks, and that buyer-initiated trades primarily move
the ask price while seller-initiated trades primarily move the bid price.
Trades have a greater impact on quotes in both the short and the long run for
the infrequently traded stocks than for the more actively traded stocks.
Finally, we find strong evidence that the spread is mean-reverting.
Keywords: market microstructure,
error correction, vector autoregression, price
dynamics.
J.E.L. Codes: C32, G0, G1.
__________________________________________
What
Good Is A Volatility Model?
(co-authored with Rob Engle)
Abstract
A volatility model must be able to forecast volatility; this is the central
requirement in almost all financial applications. In this paper we outline some
stylised facts about volatility that should be incorporated in a model;
pronounced persistence and mean-reversion, asymmetry such that the sign of an
innovation also affects volatility and the possibility of exogenous or pre-
determined variables influencing volatility. We use data on the Dow Jones
Industrial index to illustrate these stylised facts, and the ability of GARCH-
type models to capture these features. We conclude with some challenges for
future research in this area.
Keywords: volatility modeling, ARCH, GARCH, volatility forecasting.
J.E.L. Codes: C22.
__________________________________________
Modelling
Asymmetric Exchange Rate Dependence
previously circulated as: Modelling Time-Varying Exchange Rate
Dependence Using the Conditional Copula
Abstract
We test for asymmetry in a model of the dependence between the Deutsche mark
and the Yen, in the sense that a different degree of correlation is exhibited
during joint appreciations against the U.S. dollar versus during joint
depreciations. Such a dependence structure is not consistent with the commonly
employed normal or Student's t distribution assumptions. We verify that the
theory of copulas may be extended to conditional distributions, and employ it
to construct flexible models of the conditional dependence structure of these
exchange rates. We find evidence that the mark-dollar and Yen-dollar exchange
rates are more correlated when they are depreciating against the dollar than
when they are appreciating. We also find strong evidence of a structural break
in conditional density of these exchange rates upon the introduction of the
euro.
Keywords: exchange rates,
density forecasting, copulas, multivariate GARCH, asymmetry.
J.E.L. Codes: C32, C51, C52,
F31.
__________________________________________
Estimation
of Multivariate Models for Time Series of Possibly Different Lengths
Abstract
We consider the problem of estimating parametric multivariate density models
when unequal amounts of data are available on each variable. We focus in
particular on the case that the unknown parameter vector may be partitioned into
elements relating only to a marginal distribution and elements relating to the
copula. In such a case we propose using a multi-stage maximum likelihood
estimator (MSMLE) based on all available data rather than the usual one-stage
maximum likelihood estimator (1SMLE) based only on the overlapping data. We
provide conditions under which the MSMLE is not less asymptotically efficient
than the 1SMLE, and we examine the small sample efficiency of the estimators
via simulations. The analysis in this paper is motivated by a model of the
joint distribution of daily Japanese yen - U.S. dollar and euro - U.S. dollar
exchange rates. We find significant evidence of time variation in the
conditional copula of these exchange rates, and evidence of greater dependence during
extreme events than under the normal distribution.
Keywords: copulas, maximum
likelihood, two-stage estimation, exchange rates, missing data.
J.E.L. Codes: C13, C32, C51,
F31.
__________________________________________
On
the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset
Allocation
Abstract
Recent studies in the empirical finance literature have reported evidence of
two types of asymmetries in the joint distribution of stock returns. The first
is skewness in the distribution of individual stock returns. The second is an
asymmetry in the dependence between stocks: stock returns appear to be more
highly correlated during market downturns than during market upturns. In this
paper we examine the economic and statistical significance of these asymmetries
for asset allocation decisions in an out-of-sample setting. We consider the
problem of a CRRA investor allocating wealth between the risk-free asset, a
small-cap and a large-cap portfolio. We use models that can capture
time-varying moments up to the fourth order, and we use copula theory to
construct models of the time-varying dependence structure that allow for
different dependence during bear markets than bull markets. The importance of
these two asymmetries for asset allocation is assessed by comparing the
performance of a portfolio based on a normal distribution model with a
portfolio based on a more flexible distribution model. For investors with no
short sales constraints we find that knowledge of higher moments and asymmetric
dependence leads to gains that are economically significant, and statistically
significant in some cases. For short sales constrained investors the gains are
limited.
Keywords: stock returns,
forecasting, density forecasting, normality, asymmetry, copulas.
J.E.L. Codes: G11, C32, C51.
__________________________________________
Applications
of Copula Theory in Financial Econometrics
Ph.D. dissertation, Department of
Economics, University of California, San
Diego.
Abstract
The work presented in this dissertation was motivated by the widely accepted
observation that many economic variables are non-normally distributed. They
exhibit fat-tails, skewness, and recent work suggests that some also exhibit
'asymmetric dependence', where some pairs of variables are more highly
correlated during negative movements than positive movements.
This observation raises two important problems: the construction of alternative,
more palatable, density specifications, and the description and analysis of
dependence between these variables in a more general manner than linear
correlation, as when the joint distribution of the variables of interest is
non-elliptical the correlation coefficient is no longer sufficient to describe
the dependence structure.
The four chapters of this dissertation investigate applications of copula
theory to address these problems. The theory of copulas allows us to consider
the dependence between two random variables in a general way, and to construct
flexible parametric multivariate distributions.
Chapter One, titled Modelling
Time-Varying Exchange Rate Dependence Using the Conditional Copula, extends
the existing theory of copulas to allow for conditioning variables, and shows
how to construct and evaluate flexible parametric multivariate distributions
using copula theory through an application to a model of the joint distribution
of the Deutsche mark - U.S. dollar and Japanese yen - U.S. dollar exchange
rates.
Chapter Two, titled Estimation of Copula Models for Time
Series of Possibly Different Lengths, looks at the multi-stage maximum
likelihood estimation of parametric multivariate time series models constructed
using copula theory, allowing for the possibility that we have more data
available on one variable than another.
Chapter Three, titled Skewness, Asymmetric Dependence, and Portfolios, provides
a link between two findings in the empirical finance literature: those of
skewness in individual asset returns and asymmetric dependence between asset
returns. I show that the presence of asymmetric dependence between two assets
can lead to skewed portfolios even if the individual assets themselves are not
skewed.
Chapter Four, titled On
the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset
Allocation, investigates the importance of skewness and asymmetric
dependence for asset allocation in an out-of-sample study. The goal of this
chapter was to determine for a particular pair of assets whether flexible
density models lead to better portfolio decisions than a multivariate normal
distribution model. I find significant improvements, both economically and
statistically.
__________________________________________
Common
Factors in Conditional Distributions for Bivariate Time Series
(co-authored with Clive Granger
and Timo Teräsvirta)
Abstract
A definition for a common factor for bivariate time series is suggested by
considering the decomposition of the conditional density into the product of
the marginals and the copula, with the conditioning
variable being a common factor if it does not directly enter the copula. We
show the links between this definition and the idea of a common factor as a
dominant feature in standard linear representations. An application using a
business cycle indicator as the common factor in the relationship between U.S.
income and consumption found that both series held the factor in their marginals but not in the copula.
Keywords: common factors,
copulas, business cycles.
J.E.L. Codes: C32, C53.
__________________________________________
Properties
of Optimal Forecasts
(co-authored with Allan Timmermann)
Abstract
Evaluation of forecast optimality in economics and finance has almost
exclusively been conducted under the assumption of mean squared error loss. Under
this loss function optimal forecasts should be unbiased and forecast errors
serially uncorrelated at the single period horizon with increasing variance as
the forecast horizon grows. Using analytical results we show in this paper that
all the standard properties of optimal forecasts can be invalid under
asymmetric loss and nonlinear data generating processes and thus may be very
misleading as a benchmark for an optimal forecast. Our theoretical results
suggest that many of the conclusions in the empirical literature concerning suboptimality of forecasts could be premature. We extend
the properties that an optimal forecast should have to a more general setting
than previously considered in the literature. We also present new results on
forecast error properties that may be tested when the forecaster's loss
function is unknown but restrictions can be imposed on the data generating
process, and introduce a change of measure, following which the optimum
forecast errors for general loss functions have the same properties as optimum
errors under MSE loss.
Keywords: forecast evaluation,
loss function, rationality, efficient markets.
J.E.L. Codes: C53, C22, C52.
__________________________________________
Are "Market Neutral" Hedge Funds
Really Market Neutral?
Abstract
Using a variety of different definitions of "neutrality", this paper
presents significant evidence against the neutrality to market risk of hedge
funds in a range of style categories, including the "market neutral"
category. I suggest that the completeness of the neutrality of a fund to market
risks can be considered by generalizing standard definitions of "market
neutrality", and propose five different neutrality concepts: "Mean
neutrality" nests the standard correlation-based definition of neutrality,
"variance neutrality" and "tail neutrality" relate to the
neutrality of the risk of the hedge fund to market risks, and "complete
neutrality" corresponds to independence of the fund to market risks. I
suggest statistical tests for each neutrality concept, and apply the tests to a
combined database of monthly returns on 1,423 hedge funds from five fund style
categories. For the so-called "market neutral" style, I find that
around one-quarter of funds exhibit some significant exposure to market risk;
this proportion is statistically significantly different from zero, but less
than the proportion of significant exposures for other hedge fund styles.
Keywords: diversification,
alternative investments, correlation, portfolio decisions.
J.E.L. Codes: G23, G11.
__________________________________________
Properties
of Optimal Forecasts under Asymmetric Loss and Nonlinearity
(co-authored with Allan Timmermann)
Abstract
Evaluation of forecast optimality in economics and finance has almost
exclusively been conducted under the assumption of mean squared error loss.
Under this loss function optimal forecasts should be unbiased and forecast
errors serially uncorrelated at the single period horizon with increasing
variance as the forecast horizon grows. Using analytical results we show that
standard properties of optimal forecasts can be invalid under asymmetric loss
and nonlinear data generating processes and thus may be very misleading as a
benchmark for an optimal forecast. We establish instead that a suitable
transformation of the forecast error - known as the generalized forecast error
- possesses an equivalent set of properties. The paper also provides empirical
examples to illustrate the significance in practice of asymmetric loss and
nonlinearities and discusses the effect of parameter estimation error on
optimal forecasts.
Keywords: loss function,
nonlinear data generating process, rationality, market efficiency, prediction.
J.E.L. Codes: C53, C22, C52.
__________________________________________
Testing
Forecast Optimality under Unknown Loss
(co-authored with Allan Timmermann)
Abstract
Empirical tests of forecast optimality have traditionally been conducted under
the assumption of mean squared error loss or some other known loss function.
This paper establishes new testable properties that hold when the forecaster's
loss function is unknown but testable restrictions can be imposed on the data
generating process, trading off conditions on the data generating process
against conditions on the loss function. We propose flexible estimation of the
forecaster's loss function in situations where the loss depends not only on the
forecast error but also on other state variables such as the level of the
target variable. We apply our results to the problem of evaluating the Federal
Reserve's forecasts of output growth. Forecast optimality is rejected if the
Fed's loss only depends on the forecast error. However, the empirical findings
are consistent with forecast optimality provided that over-predictions of
output growth are costlier to the Fed than under-predictions, particularly
during periods of low economic growth.
Keywords: Federal Reserve,
output growth, forecast evaluation, loss function, forecast efficiency.
J.E.L. Codes: C53, C22, C52
__________________________________________
Non-Linearities and
Stress Testing
(co-authored with
Mathias Drehmann and Steffen Sorensen)
Abstract
We explore the impact of possible non-linearities
on aggregate credit risk in a vector autoregression
framework. By using aggregate data on corporate credit in the
Keywords: credit risk, impulse
response functions, stress testing, nonlinear time series, VAR models
J.E.L. Codes: G33, C32.
__________________________________________
Volatility
Forecast Comparison using Imperfect Volatility Proxies
Abstract
The use of a conditionally unbiased, but imperfect, volatility proxy can lead
to undesirable outcomes in standard methods for comparing conditional variance
forecasts. We derive necessary and sufficient conditions on functional form of
the loss function for the ranking of competing volatility forecasts to be
robust to the presence of noise in the volatility proxy, and derive some useful
special cases of this class of "robust" loss functions. We motivate
the theory with analytical results on the distortions caused by some
widely-used loss functions, when used with standard volatility proxies such as
squared returns, the intra-daily range or realised volatility. The methods are
illustrated with an application to the volatility of returns on IBM over the
period 1993 to 2003.
Keywords: forecast evaluation,
forecast comparison, loss functions, realised variance, range.
J.E.L. Codes: C53, C52, C22.
__________________________________________
Corporate Defaults and Macroeconomic Shocks:
Non-linearities and Uncertainty
(co-authored with
Mathias Drehmann and Steffen Sorensen)
Abstract
We propose a framework to explore the impact of non-linearities
in the transmission of macroeconomic shocks to corporate credit risk. A number
of models used in the literature assume a linear relation between credit risk
and the macroeconomic shocks. Using a rich database containing more than 30,000
public and private firms in the
Keywords: credit risk, impulse
response functions, nonlinear time series, VAR models.
J.E.L. Codes: G33, C32.
__________________________________________
Time-Varying Liquidity in Hedge Fund Returns
(co-authored with
Sheng Li)
Abstract
The liquidity of hedge funds' investments is of great
interest both to hedge fund investors and to market regulators. We propose a
method for determining the factors that affect the (unobservable) liquidity of
hedge fund investments. Our method exploits the link between illiquidity and
serial correlation in hedge fund returns established by Getmansky,
Lo and Makarov (2004), and does not require information on the actual positions
taken by the hedge fund, nor even the `style' of the hedge fund; we use only
the returns reported by the hedge fund and other easily observed information.
Using a panel of monthly returns on over 600 individual hedge funds, we find
significant evidence of time variation in the degree of liquidity of hedge fund
investments. Broadly stated, hedge funds in equity-based styles, such as equity
market neutral and equity hedge or non-hedge, exhibit decreases in liquidity
when stock market returns are low and bond market returns are high. In
contrast, hedge funds in fixed income styles, such as convertible arbitrage or
fixed income, exhibit lower liquidity when equity market volatility is high,
and when the fund experiences in-flows or out-flows of funds.
Keywords: liquidity, serial correlation, return smoothing, hedge funds
J.E.L. Codes: G23, G11, C22.
__________________________________________
Copula-Based Models for Financial Time Series
Abstract
The number of papers on copula theory in finance and economics has grown
enormously in recent years. One of the most influential of the 'early' papers
on copulas in finance is that of Embrechts, McNeil
and Straumann (2002). Since then, scores of papers
have been written, exploring the uses of copulas in finance, macroeconomics,
microeconomics, as well as developing the estimation and evaluation theory
required for these applications. Nelsen (2006) and Joe (1997) provide detailed
introductions to copulas and their statistical and mathematical foundations,
while Cherubini, et al. (2004) focus primarily on applications of copulas in
mathematical finance and derivatives pricing. In this survey I focus on
financial time series applications of copulas.
Keywords:
multivariate models, dependence, rank correlation, conditional copulas.
J.E.L. Codes: C32, C22, C13.
__________________________________________
Evaluating Volatility Forecasts
(co-authored with Kevin Sheppard)
Abstract
This chapter considers the problem of evaluation and
comparison of univariate and multivariate volatility forecasts, with explicit
attention paid to the fact that in such applications the object of interest is
unobservable, even ex post. Thus the evaluation and comparison of volatility
forecasts must rely on direct or indirect methods of overcoming this
difficulty. Direct methods use a "volatility proxy", i.e. some
observable variable that is related to the latent variable of interest.
Indirect methods of overcoming the latent nature of the variable of interest
include comparing forecasts via mean-variance portfolio decisions or
comparisons based on portfolio "tracking error". The main results of
this chapter can be summarised as follows. Firstly, we suggest a minor modification
of the widely-used Mincer-Zarnowitz regression for
testing volatility forecast optimality which exploits the additional structure
that holds under the null hypothesis. This "MZ-GLS" test has good
size and much better finite sample power than other MZ tests. Secondly, we find
that the use of loss functions that are "non-robust", in the sense of
Patton (2006) can yield perverse rankings of forecasts, even when accurate
volatility proxies are employed. Finally, consistent with the large and growing
literature on realised volatility, our simulations clearly demonstrated the
value of higher-precision volatility proxies, such as realised variance
Andersen, et al. (2003) or daily high-low range. Even simple estimators based
on 30-minute returns provide large gains in power and improvements in
finite-sample size.
Keywords: variance, covariance,
realized volatility, volatility proxies, Mincer-Zarnowitz.
J.E.L. Codes: C53, C12, C22.
__________________________________________
Predictability of Output Growth and Inflation: A
Multi-Horizon Survey Approach
(co-authored with Allan Timmermann)
Abstract
We develop an unobserved components approach to study surveys of forecasts
containing multiple forecast horizons. Under the assumption that forecasters
optimally update their beliefs about past, current and future state variables
as new information arrives, we use our model to extract information on the
degree of predictability of the state variable and the importance of measurement
errors on that variable. Empirical estimates of the model are obtained using
survey forecasts of annual GDP growth and inflation in the US with forecast
horizons ranging from 1 to 24 months, and the model is found to closely match
the joint realization of forecast errors at different horizons. Our empirical
results confirm several findings in the existing literature that were obtained
using very different data sets: professional forecasters face severe
measurement error problems for GDP growth in real time, while this is not an
problem for inflation; inflation exhibits greater persistence, and thus is
predictable at longer horizons, than GDP growth; the persistent component of
both of these variables is well-approximated by a low-order autoregressive specification.
Keywords: Fixed-event forecasts,
multiple forecast horizons, Kalman filtering, survey
data.
J.E.L. Codes: E37,
C53, C32.
__________________________________________
Monotonicity in Asset Returns: New Tests with Applications to the Term Structure,
the CAPM and Portfolios Sorts
(co-authored
with Allan Timmermann)
Abstract
Many theories in finance imply monotonic patterns in expected returns and other
financial variables: The liquidity preference hypothesis predicts higher
expected returns for bonds with longer times to maturity; the CAPM implies
higher expected returns for stocks with higher betas; and standard asset
pricing models imply that the pricing kernel is declining in market returns.
The full set of implications of monotonicity is generally not exploited in
empirical work, however. This paper proposes new and simple ways to test for
monotonicity in financial variables and compares the proposed tests with extant
alternatives such as t-tests, Bonferroni bounds and
multivariate inequality tests through empirical applications and simulations.
__________________________________________
Generalized Forecast Errors, A Change of
Measure, and Forecast Optimality Conditions
(co-authored with Allan Timmermann)
Abstract
This paper establishes properties of optimal forecasts under general loss
functions, extending existing results obtained under specific functional forms
and data generating processes. We propose a new method that changes the
probability measure under which the well-known properties of optimal forecasts
under mean squared error loss can be recovered. We illustrate the proposed
methods through an empirical application to U.S. inflation forecasting.
Keywords: forecast evaluation, loss function,
rationality tests.
J.E.L. Codes: C53, C22, C52.
__________________________________________
Data-Based Ranking of Realised
Volatility Estimators
Abstract
This paper presents new methods for formally comparing the accuracy of
estimators of the quadratic variation of a price process. I provide conditions
under which the relative average accuracy of competing estimators can be
consistently estimated (as T-> +inf) from
available data, and show that existing tests from the forecast evaluation
literature may be adapted to the problem of ranking these estimators. The
proposed methods eliminate the need for specific assumptions about the
properties of the microstructure noise, and the need to estimate quantities
such as integrated quarticity or the noise variance,
and facilitate comparisons of estimators that would be difficult using methods
from the extant literature, such as those based on different sampling schemes
(calendar-time vs. tick-time). In an application to high frequency IBM stock
price data between 1996 and 2007, I find that tick-time sampling is generally
preferable to calendar-time sampling, and that the optimal sampling frequency
is between 15 seconds and 5 minutes, when using standard realised variance.
Keywords: realised variance, volatility forecasting,
forecast comparison.
J.E.L. Codes: C52, C22, C53.
__________________________________________
Why do Forecasters Disagree? Lessons from the
Term Structure of Cross-Sectional Dispersion
(co-authored with Allan Timmermann)
Abstract
Using data on cross-sectional dispersion in forecasters' long- and short-run
predictions of macroeconomic variables, we identify key sources of disagreement.
Dispersion among forecasters is highest at long horizons where private
information is of limited value and lower at short forecast horizons. Moreover,
differences in views persist through time. Such differences in opinion cannot
be explained by differences in information sets; our results indicate they stem
from heterogeneity in priors or models. We also find evidence that differences
in opinion move countercyclically, with heterogeneity
being strongest during recessions where forecasters appear to place greater
weight on their prior beliefs.
Keywords: fixed-event forecasts,
Kalman filtering, optimal updating, dispersion in
beliefs.
J.E.L. Codes: E37, C53, C32.
__________________________________________
Optimal Combinations of Realised Volatility Estimators
(co-authored with Kevin Sheppard)
Abstract
Recent advances in financial econometrics have led to the development of new
estimators of asset price variability using frequently-sampled price data, known
as "realised volatility estimators" or simply "realised
measures". These estimators rely on a variety of different assumptions and
take many different functional forms. Motivated by the empirical success of
combination forecasts, this paper presents a novel approach for combining
individual realised measures to form new estimators of price variability. In an
application to high frequency IBM price data over the period 1996-2008, we
consider 32 different realised measures from 8 distinct classes of estimators.
We find that a simple equally-weighted average of these estimators cannot
generally be out-performed, in terms of accuracy, by any individual estimator.
Moreover, we find that none of the individual estimators encompasses the
information in all other estimators, providing further support for the use of
combination realised measures.
Keywords: realised variance, volatility forecasting,
forecast comparison, forecast combination.
J.E.L. Codes: C52, C22, C53.
__________________________________________
Does Beta Move with News? Firm-Specific Information Flows and Learning about
Profitability
(co-authored with Michela Verardo)
Abstract
We
investigate whether the betas of individual stocks vary with the release of
firm-specific news. Using daily firm-level betas estimated from intra-day
prices for all constituents of the S&P 500 index, we find that the betas of
individual stocks increase by an economically and statistically significant
amount on days of quarterly earnings announcements, and revert to their average
levels two to five days later. The increase in betas is greater for
announcements with larger positive or negative earnings surprises, with greater
analyst forecast dispersion, and occurring earlier in the earnings season.
Furthermore, the increase in betas is greater for stocks with higher turnover
and analyst coverage and for stocks whose fundamentals are more connected with
market-wide fundamentals. These findings are consistent with a framework of
information spillovers in which investors learn about
the profitability of a given firm by using information on other firms.
Keywords: Realized covariance, realized volatility,
earnings announcements, high-frequency data.
J.E.L. Codes: G14, G12, C32.
__________________________________________
On the Dynamics of Hedge Fund Risk Exposures
(co-authored with Tarun
Ramadorai)
Abstract
We propose a new method to capture changes in hedge funds' exposures to
risk factors, exploiting information from relatively high frequency
conditioning variables. In a large sample of funds, we find substantial
evidence that hedge fund risk exposures vary significantly across and within months, and that capturing
within-month variation is more important for hedge funds than mutual funds. We
consider different within-month functional forms, and uncover patterns such as
day-of-the-month variation in risk exposures. We also find that changes in
portfolio allocations, rather than changes in the risk exposures of the
underlying assets, are the main drivers of hedge funds' risk exposure
variation.
Keywords: beta, time-varying risk, performance
evaluation, window-dressing, hedge funds, mutual funds
J.E.L. Codes: G23, G11, C22
__________________________________________
Forecast Rationality
Tests Based on Multi-Horizon Bounds
(co-authored with Allan Timmermann)
Abstract
Forecast
rationality under squared error loss implies various bounds on second moments
of the data across forecast horizons. For example, the mean squared forecast
error should be increasing in the horizon, and the mean squared forecast should
be decreasing in the horizon. We propose rationality tests based on these
restrictions, including new ones that can be conducted without data on the
target variable, and implement them via tests of inequality constraints in a regression
framework. A new optimal revision test based on a regression of the target
variable on the long-horizon forecast and the sequence of interim forecast
revisions is also proposed. The size and power of the new tests are compared
with those of extant tests through Monte Carlo simulations. An empirical
application to the Federal Reserve's Greenbook
forecasts is presented.
Keywords:
Forecast optimality, real-time data, survey forecasts, forecast horizon
JEL Codes:
C53, C22, C52.
__________________________________________
Good Volatility, Bad
Volatility: Signed Jumps and the Persistence of Volatility
(co-authored with Kevin Sheppard)
Abstract
Using
recently proposed estimators of the variation of positive and negative returns
(“realized semivariances”), and high
frequency data for the S&P 500 index and 105 individual stocks, this paper
sheds new light on the predictability of equity price volatility. We show that
future volatility is much more strongly related to the volatility of past
negative returns than to that of positive returns, and this effect is stronger
than that implied by standard asymmetric GARCH models. We also find that the
impact of a jump on future volatility critically depends on the sign of the
jump, with negative (positive) jumps in prices leading to significantly higher
(lower) future volatility. A simple model exploiting these findings leads to
significantly better out-of-sample forecast performance, across forecast
horizons ranging from 1 day to 3 months.
Keywords:
Realized variance, semivariance, volatility
forecasting, jumps, leverage effect
J.E.L.
Codes: C58, C22, C53
__________________________________________
Modelling Dependence in High Dimensions with
Factor Copulas
(co-authored with Dong Hwan Oh)
Abstract
This paper presents flexible new models for the dependence structure, or
copula, of economic variables based on a latent factor structure. The proposed
models are particularly attractive for relatively high dimensional
applications, involving fifty or more variables, and can be combined with
semiparametric marginal distributions to obtain flexible multivariate
distributions. Factor copulas generally lack a closed-form density, but we
obtain analytical results for the implied tail dependence using extreme value
theory, and we verify that simulation-based estimation using rank statistics is
reliable even in high dimensions. We consider "scree" plots to aid
the choice of the number of factors in the model. The model is applied to daily
returns on all 100 constituents of the S&P 100 index, and we find
significant evidence of tail dependence, heterogeneous dependence, and
asymmetric dependence, with dependence being stronger in crashes than in booms.
We also show that factor copula models provide superior estimates of some
measures of systemic risk.
Keywords:
Correlation, dependence, copulas, tail risk.
JEL Codes:
C32, C51, C53.
__________________________________________
Change You Can Believe In? Hedge Fund Data
Revisions
(co-authored with Tarun Ramadorai and Michael
Streatfield)
Abstract
We analyze the reliability of voluntary
disclosures of financial information, focusing on widely-employed publicly
available hedge fund databases. Tracking changes to statements of historical
performance recorded at different points in time between 2007 and 2011, we find
that historical returns are routinely revised. These revisions are not merely
random or corrections of earlier mistakes; they are partly forecastable by fund
characteristics. Moreover, funds that revise their performance histories
significantly and predictably underperform those that have never revised,
suggesting that unreliable disclosures constitute a valuable source of
information for current and potential investors. These results speak to current
debates about mandatory disclosures by financial institutions to market
regulators.
__________________________________________
Simulated Method of
Moments Estimation for Copula-Based Multivariate Models
(co-authored with Dong
Hwan Oh)
Abstract
This paper considers the estimation of the parameters of a copula via a
simulated method of moments type approach. This approach is attractive when the
likelihood of the copula model is not known in closed form, or when the
researcher has a set of dependence measures or other functionals
of the copula that are of particular interest. The proposed approach naturally
also nests method of moments and generalized method of moments estimators.
Drawing on results for simulation based estimation and on recent work in
empirical copula process theory, we show the consistency and asymptotic
normality of the proposed estimator, and obtain a simple test of over-identifying
restrictions as a goodness-of-fit test. The results apply to both iid and time
series data. We analyze the finite-sample behavior of these estimators in an extensive simulation
study. We apply the model to a group of seven financial stock returns and find
evidence of statistically significant tail dependence, and mild evidence that
the dependence between these assets is stronger in crashes than booms.
__________________________________________
A Review of Copula Models for Economic Time Series
Abstract
This survey reviews the large and growing literature on copula-based
models for economic and financial time series. Copula-based multivariate models
allow the researcher to specify the models for the marginal distributions
separately from the dependence structure that links these distributions to form
a joint distribution. This allows for a much greater degree of flexibility in
specifying and estimating the model, freeing the researcher from considering
only existing multivariate distributions. The author surveys estimation and
inference methods and goodness-of-fit tests for such models, as well as
empirical applications of these copulas for economic and financial time series.
__________________________________________
Copula Methods for Forecasting Multivariate
Time Series
Abstract
Copula-based models provide a great deal of flexibility in modelling multivariate distributions, allowing
the researcher to specify the models for the marginal distributions separately
from the dependence structure (copula) that links them to form a joint
distribution. In addition to flexibility, this often
also facilitates estimation of the model in stages, reducing the computational
burden. This chapter reviews the growing literature on copula-based models for
economic and financial time series
data, and discusses in detail methods for estimation, inference, goodness-of-fit testing, and model selection that
are useful when working with these models. A representative data set of two
daily equity index returns is used to illustrate all of the main results.
__________________________________________
Does Anything Beat 5-Minute RV?
A Comparison of Realized Measures Across Multiple Asset Classes
(co-authored with Lily
Liu and Kevin
Sheppard)
Abstract
We study the accuracy of a wide variety of estimators of asset price
variation constructed from high-frequency data (so-called "realized
measures"), and compare them with a simple "realized variance"
(RV) estimator. In total, we consider over 400 different estimators, applied to
11 years of data on 31 different financial assets spanning five asset classes,
including equities, equity indices, exchange rates and interest rates. We apply
data-based ranking methods to the realized measures and to forecasts based on
these measures. When 5-minute RV is taken as the benchmark realized measure, we
find little evidence that it is outperformed by any of the other measures. When
using inference methods that do not require specifying a benchmark, we find
some evidence that more sophisticated realized measures significantly
outperform 5-minute RV. In forecasting applications, we find that a low
frequency "truncated" RV outperforms most other realized measures.
Overall, we conclude that it is difficult to significantly beat 5-minute RV for
these assets.
__________________________________________
Time-Varying
Systemic Risk: Evidence from a Dynamic Copula Model of CDS Spreads
(co-authored with Dong
Hwan Oh)
Abstract
This paper proposes a new class of copula-based dynamic models for high dimension
conditional distributions, facilitating the estimation of a wide variety of
measures of systemic risk. Our proposed models draw on successful ideas from
the literature on modeling high dimension covariance
matrices and on recent work on models for general time-varying distributions.
Our use of copula-based models enables the estimation of the joint model in
stages, greatly reducing the computational burden. We use the proposed new
models to study a collection of daily credit default swap (CDS) spreads on 100
U.S. firms over the period 2006 to 2012. We find that while the probability of
distress for individual firms has greatly reduced since the financial crisis of
2008-09, the joint probability of distress (a measure of systemic risk) is
substantially higher now than in the pre-crisis period.
__________________________________________
Daily House Price Indexes: Construction, Modeling, and Longer-Run Predictions
(co-authored with Tim Bollerslev and
Wenjing
Wang)
Abstract
We construct daily house price
indexes for ten major U.S. metropolitan areas. Our calculations are based on a
comprehensive database of several million residential property transactions and
a standard repeat-sales method that closely mimics the procedure used in the
construction of the popular monthly Case-Shiller house price indexes. Our new
daily house price indexes exhibit similar characteristics to other daily asset
prices, with mild autocorrelation and strong conditional heteroskedasticity,
which are well described by a relatively simple multivariate GARCH type model.
The sample and model-implied correlations across house price index returns are
low at the daily frequency, but rise monotonically with the return horizon, and
are all commensurate with existing empirical evidence for the existing monthly
and quarterly house price series. A simple model of daily house price index
returns produces forecasts of monthly house price changes that are superior to
various alternative forecast procedures based on lower frequency data,
underscoring the informational advantages of our new more finely sampled daily
price series.
__________________________________________
Dynamic Copula Models and High Frequency Data
(co-authored with Irving
De Lira Salvatierra)
Abstract
This paper proposes a new class of dynamic copula models for daily asset
returns that exploits information from high frequency (intra-daily) data. We
augment the generalized autoregressive score (GAS) model of Creal, et al.
(2012) with high frequency measures such as realized correlation to obtain a
"GRAS" model. We find that the inclusion of realized measures
significantly improves the in-sample fit of dynamic copula models across a
range of U.S. equity returns. Moreover, we find that out-of-sample density
forecasts from our GRAS models are superior to those from simpler models.
Finally, we consider a simple portfolio choice problem to illustrate the
economic gains from exploiting high frequency data for modeling
dynamic dependence.
__________________________________________
The Impact of Hedge Funds on Asset Markets
(co-authored with Mathias
Kruttli and Tarun
Ramadorai)
Abstract
This paper provides empirical evidence of the impact of hedge funds on
asset markets. We construct a simple measure of the aggregate illiquidity of
hedge fund portfolios, and show that it has strong in- and out-of-sample
forecasting power for 72 portfolios of international equities, corporate bonds,
and currencies over the 1994 to 2013 period. The forecasting ability of hedge
fund illiquidity for asset returns is in most cases greater than, and provides
independent information relative to, well-known predictive variables for each
of these asset classes. We construct a simple equilibrium model based on
liquidity provision by hedge funds to noise traders to rationalize our
findings, and empirically verify auxiliary predictions of the model.
__________________________________________
Asymptotic Inference about Predictive
Accuracy using High Frequency Data
(co-authored with Jia Li)
Abstract
This paper
provides a general framework that enables many existing inference methods for
predictive accuracy to be used in applications that involve forecasts of latent
target variables. Such applications include the forecasting of volatility,
correlation, beta, quadratic variation, jump variation, and other functionals of an underlying continuous-time process. We
provide primitive conditions under which a "negligibility" result
holds, and thus the asymptotic size of standard predictive accuracy tests,
implemented using a high-frequency proxy for the latent variable, is
controlled. An extensive simulation study verifies that the asymptotic results
apply in a range of empirically relevant applications, and an empirical
application to correlation forecasting is presented.
__________________________________________
Copulas in Economics
(co-authored with Yanqin Fan)
Abstract
Copulas are
functions that describe the dependence between two or more random variables.
This article provides a brief review of copula theory and two areas of
economics in which copulas have played important roles: multivariate modeling and partial identification of parameters that
depend on the joint distribution of two random variables with fixed or known
marginal distributions. We focus on bivariate copulas, but provide references
on recent advances in constructing higher dimensional copulas.
__________________________________________
High-Dimensional Copula-Based Distributions
with Mixed Frequency Data
(co-authored with Dong
Hwan Oh)
Abstract
This paper
proposes a new general model for high-dimensional distributions of asset
returns that utilizes mixed frequency data and copulas. The dependence between
returns is decomposed into linear and nonlinear components, which enables the
use of high frequency data to accurately measure and forecast linear
dependence, and the use of a new class of copulas designed to capture nonlinear
dependence among the resulting linearly uncorrelated, low frequency, residuals.
Estimation of the new class of copulas is conducted using composite likelihood,
making this approach feasible even for hundreds of variables. A realistic
simulation study verifies that multistage estimation with composite likelihood
results in small loss in efficiency and large gain in computation speed. In-
and out-of-sample tests confirm the statistical superiority of the proposed
models applied to daily returns on all constituents of the S&P 100 index.
__________________________________________
Comparing Possibly Misspecified Forecasts
Abstract
Recent work
has emphasized the importance of evaluating estimates of a statistical
functional (such as a mean, quantile, or distribution) using a loss function
that is consistent for the functional of interest, of which there are an
infinite number. If forecasters all use correctly specified models free from
estimation error, and if the information sets of the competing forecasters are
nested, then the ranking induced by a single consistent loss function is sufficent for the ranking by any consistent loss function.
This paper shows, via analytical results and realistic simulation-based
analyses, that the presence of misspecified models, parameter estimation error,
or nonnested information sets, leads generally to
sensitivity to the choice of (consistent) loss function. Thus, rather than
merely specifying the target functional, which narrows the set of relevant loss
functions only to the class of loss functions consistent for that functional,
forecast consumers or survey designers should specify the single specific loss
function that will be used to evaluate forecasts. An application to survey
forecasts of US inflation illustrates the results.
__________________________________________
Exploiting the Errors: A Simple Approach for
Improved Volatility Forecasting
(co-authored with Tim Bollerslev
and Rogier
Quaedvlieg)
Abstract
We propose
a new family of easy-to-implement realized volatility based forecasting models.
The models exploit the asymptotic theory for high-frequency realized volatility
estimation to improve the accuracy of the forecasts. By allowing the parameters
of the models to vary explicitly with the (estimated) degree of measurement
error, the models exhibit stronger persistence, and in turn generate more
responsive forecasts, when the measurement error is relatively low.
Implementing the new class of models for the S\&P500 equity index and the
individual constituents of the Dow Jones Industrial Average, we document
significant improvements in the accuracy of the resulting forecasts compared to
the forecasts from some of the most popular existing models that implicitly
ignore the temporal variation in the magnitude of the realized volatility
measurement errors.
__________________________________________
Modeling and Forecasting (Un)Reliable Realized Covariances for More Reliable
Financial Decisions
(co-authored with Tim Bollerslev and Rogier
Quaedvlieg)
Abstract
We propose
a new framework for modeling and forecasting common
financial risks based on (un)reliable realized covariance measures constructed
from high-frequency intraday data. Our new approach explicitly incorporates the
effect of measurement errors and time-varying attenuation biases into the
covariance forecasts, by allowing the ex-ante predictions to respond more
(less) aggressively to changes in the ex-post realized covariance measures when
they are more (less) reliable. Applying the new procedures in the construction
of minimum variance and minimum tracking error portfolios results in reduced
turnover and statistically superior positions compared to existing procedures.
Translating these statistical improvements into economic gains, we find that
under empirically realistic assumptions a risk-averse investor would be willing
to pay up to 170 basis points per year to shift to using the new class of
forecasting models.
__________________________________________
Dynamic Semiparametric Models for
Expected Shortfall (and Value-at-Risk)
(co-authored withJohanna
F. Ziegel and Rui Chen)
Abstract
Expected Shortfall
(ES) is the average return on a risky asset conditional on the return being
below some quantile of its distribution, namely its Value-at-Risk (VaR). The Basel III Accord, which will be implemented in
the years leading up to 2019, places new attention on ES, but unlike VaR, there is little existing work on modeling
ES. We use recent results from statistical decision theory to overcome the
problem of "elicitability" for ES by
jointly modelling ES and VaR, and propose new dynamic
models for these risk measures. We provide estimation and inference methods for
the proposed models, and confirm via simulation studies that the methods have
good finite-sample properties. We apply these models to daily returns on four
international equity indices, and find the proposed new ES-VaR
models outperform forecasts based on GARCH or rolling window models.
__________________________________________
(co-authored with Tim Bollerslev, Jia Li and Rogier Quaedvlieg)
Abstract
We propose a new decomposition of the realized
covariance matrix into components based on the signs of the underlying
high-frequency returns. Under an asymptotic setting in which the sampling
interval goes to zero, we derive the asymptotic properties of the resulting realized semicovariance
measures. The first-order asymptotic results highlight how the concordant
components and the mixed-sign component load differently on economic
information concerning stochastic correlation and jumps. The second-order asymptotics, taking the form of a novel non-central limit
theorem, further reveals the fine structure underlying the concordant semicovariances, as manifest in the form of co-drifting and
dynamic “leverage” type effects. In line with this anatomy, we
empirically document distinct dynamic dependencies in the different realized semicovariance components based on data for a large
cross-section of individual stocks. We further show that the accuracy of
portfolio return variance forecasts may be significantly improved by using the
realized semicovariance matrices to “look
inside” the realized covariance matrices for signs of direction.
__________________________________________
What You See is Not
What You Get: The Costs of Trading Market Anomalies
(co-authored with Brian Weller)
Abstract
Abstract Is there a gap between the profitability of a trading strategy
“on paper” and that which is achieved in practice? We answer this
question by developing a general technique to measure the real-world
implementation costs of financial market anomalies. Our method extends Fama-MacBeth regressions to compare the on-paper returns to
factor exposures with those achieved by mutual funds. Unlike existing
approaches, our approach delivers estimates of all-in implementation costs
without relying on parametric microstructure models or explicitly specified
factor trading strategies. After accounting for implementation costs, typical
mutual funds earn low returns to value and no returns to momentum.
__________________________________________
Multivariate
Leverage Effects and Realized Semicovariance GARCH
Models
(co-authored with Tim Bollerslev and Rogier Quaedvlieg)
Abstract
We propose a new decomposition of the realized covariance matrix into
four “realized semicovariance” components
based on the signs of the underlying high-frequency returns. We derive the asymptotic distribution
for the different components under the assumption of a continuous multivariate semimartingale and standard infill asymptotic arguments.
Based on high-frequency returns for a large cross-section of individual stocks,
we document distinctly different features and dynamic dependencies in the
different semicovariance components. We demonstrate that the accuracy of
portfolio return variance forecasts may be significantly improved by exploiting
these differences and “looking inside” the realized covariance
matrices for signs of direction.
__________________________________________
Risk Price
Variation: The Missing Half of the Cross-Section of Expected Returns
(co-authored with Brian Weller)
Abstract
Equal compensation across assets for the same risk exposures is a bedrock
of asset pricing theory and empirics. Yet real-world frictions can violate this
equality and create high-Sharpe ratio opportunities. We develop new methods for
asset pricing with cross-sectional heterogeneity in compensation for risk. We
extend k-means clustering to group assets by risk prices and introduce a formal
test for whether differences in risk premia across
market segments are too large to occur by chance. Using portfolios of US
stocks, international stocks, and assets from multiple classes, we find
significant evidence of cross-sectional variation in risk prices for all 159
combinations of test assets, factor models, and time periods. Variation in risk
prices is as important as variation in risk exposures for explaining the
cross-section of expected returns.
__________________________________________
Comparing Predictive
Accuracy in the Presence of a Loss Function Shape Parameter
(co-authored with Sander Barendse)
Abstract
We develop tests for out-of-sample forecast comparisons based on loss
functions that contain shape parameters. Examples include comparisons using
average utility across a range of values for the level of risk aversion,
comparisons of forecast accuracy using characteristics of a portfolio return
across a range of values for the portfolio weight vector, and comparisons using
recently-proposed \Murphy diagrams" for classes of consistent scoring rules.
An extensive Monte Carlo study verifies that our tests have good size and power
properties in realistic sample sizes, particularly when compared with existing
methods which break down when then number of values considered for the shape
parameter grows. We present three empirical illustrations of the new test.
__________________________________________
Testing for
Unobserved Heterogeneity via k-means Clustering
(co-authored with Brian Weller)
Abstract
Clustering methods such as k-means
have found widespread use in a variety of applications. This paper proposes a
formal testing procedure to determine whether a null hypothesis of a single
cluster, indicating homogeneity of the data, can be rejected in favor of multiple clusters. The test is simple to
implement, valid under relatively mild conditions (including non-normality, and
heterogeneity of the data in aspects beyond those in the clustering analysis),
and applicable in a range of contexts (including clustering when the time
series dimension is small, or clustering on parameters other than the mean). We
verify that the test has good size control in finite samples, and we illustrate
the test in applications to clustering vehicle manufacturers and U.S. mutual
funds.
__________________________________________
Realized Semibetas: Signs of Things to Come
(co-authored with Tim Bollerslev and Rogier Quaedvlieg)
Abstract
We propose a new decomposition of the traditional market beta into four semibetas
depending on the signed covariation between the market and individual asset
returns. Consistent with the
pricing implications from a mean-semivariance framework, we show that higher semibetas defined by negative market and negative
(positive) asset return covariation predict significantly higher (lower) future
returns, while the other two semibetas do not appear
to be priced. Our main empirical
findings rely on realized semibetas calculated from
two decades of high-frequency intraday data for the S&P 500 stocks with the
return predictability ranging from daily to monthly holding periods. The
results extend to similarly constructed monthly semibetas
calculated from daily data over a longer sample period. They also remain robust to the inclusion
of a long list of other controls, including up and downside betas. Rather than betting on or against beta,
we conclude that it is better to bet on and
against the “right” semibetas.
__________________________________________
Testing Forecast
Rationality for Measures of Central Tendency
(co-authored with Timo Dimitriadis and Patrick Schmidt)
Abstract
Rational respondents to economic surveys may report as a point forecast
any measure of the central tendency of their (possibly latent) predictive
distribution, for example the mean, median, mode, or any convex combination
thereof. We propose tests of forecast rationality when the measure of central
tendency used by the respondent is unknown. We overcome an identification
problem that arises when the measures of central tendency are equal or in a
local neighborhood of each other, as is the case for
(exactly or nearly) symmetric distributions. As a building block, we also
present novel tests for the rationality of mode forecasts. We apply our tests
to survey forecasts of individual income, Greenbook
forecasts of U.S. GDP, and random walk forecasts for exchange rates. We find
that the Greenbook and random walk forecasts are best
rationalized as mean, or near-mean forecasts, while the income survey forecasts
are best rationalized as mode forecasts.
__________________________________________
Bootstrapping
Two-Stage Quasi-Maximum Likelihood Estimators of Time Series Models
(co-authored with Sílvia Gonçalves, Ulrich Hounyo and Kevin Sheppard)
Abstract
This paper’s main contribution is to
theoretically justify the application of bootstrap methods in multistage
quasi-maximum likelihood estimation involving time series data. Two consistency
results are provided: consistency of the bootstrap distribution and consistency
of bootstrap variance estimators. These results justify constructing bootstrap
percentile intervals and computing bootstrap standard errors using multi-step
quasi-maximum likelihood estimation, avoiding the need to analytically quantify
the estimation uncertainty caused by the multistage estimation process. Our
results should be useful for inference in many models in finance and economics such as
multivariate copula models or large multivariate GARCH models, which are often
estimated in stages.
__________________________________________
From Zero to Hero:
Realized Partial (Co)Variances
(co-authored with Tim Bollerslev, Marcelo C. Medeiros and Rogier Quaedvlieg)
Abstract
This paper proposes a generalization of the class of realized semivariance and semicovariance
measures introduced by Barndorff-Nielsen, Kinnebrock
and Shephard (2010) and Bollerslev, Li, Patton and Quaedvlieg (2020a) to allow
for a finer decomposition of realized (co)variances. The new “realized
partial (co)variances” allow for multiple thresholds with various
locations, rather than the single fixed threshold of zero used in semi
(co)variances. We adopt methods from machine learning to choose the thresholds
to maximize the out-of-sample forecast performance of time series models based
on realized partial (co)variances. We find that in low dimensional settings it
is hard, but not impossible, to improve upon the simple fixed threshold of
zero. In large dimensions, however, the zero threshold embedded in realized
semi covariances emerges as a robust choice.
__________________________________________
A Consistent
Specification Test for Dynamic Quantile Models
(co-authored with Peter Horvath, Jia Li and Zhipeng Liao)
Abstract
Correct specification of a conditional quantile model implies that a
particular conditional moment is equal to zero. We nonparametrically
estimate the conditional moment function via series regression and test whether
it is identically zero using uniform functional inference. Our approach is
theoretically justified via a strong Gaussian approximation for statistics of
growing dimensions in a general time series setting. We propose a novel
bootstrap method in this nonstandard context and show that it significantly
outperforms the benchmark asymptotic approximation in finite samples,
especially for tail quantiles such as Value-at-Risk (VaR).
We use the proposed new test to study the VaR and CoVaR (Adrian and Brunnermeier
(2016)) of a collection of US financial institutions.
__________________________________________
Dynamic Factor
Copula Models with Estimated Cluster Assignments
(co-authored
with Dong Hwan Oh)
Abstract
This paper proposes
a dynamic multi-factor copula for use in high dimensional time series
applications. A novel feature of our model is that the assignment of individual
variables to groups is estimated from the data, rather than being pre-assigned
using SIC industry codes, market capitalization ranks, or other ad hoc methods. We adapt the k-means clustering
algorithm for use in our application and show that it has excellent
finite-sample properties. Applying the new model to returns on 110 US equities,
we find around 20 clusters to be optimal. In out-of-sample forecasts, we find
that a model with as few as five estimated clusters significantly outperforms
an otherwise identical model with 21 clusters formed using two-digit SIC codes.
__________________________________________
Andrew Patton
213
Social Sciences Building, Box 90097
Durham NC
27708-0097
USA
Email:
andrew.patton@duke.edu
Phone: +1 919 660 1849
Fax: +1 919 684
8974
Web: . http://econ.duke.edu/~ap172
__________________________________________
Last updated: December 2020.
Go to Andrew's main page.