Andrew
Patton's research page
|
Research
keywords: econometrics,
financial economics, forecasting, copulas, time series, dependence,
volatility, hedge funds. |
|
Working
Papers
Time-Varying Systemic Risk: Evidence from a Dynamic Copula Model of CDS
Spreads, with Dong
Hwan Oh, working paper,
May 2013. 
Paper (PDF), Abstract (HTML),
Web Appendix
(PDF)
Does Anything Beat 5-Minute RV?
A Comparison of Realized Measures Across Multiple Asset Classes, with Lily
Liu and Kevin
Sheppard, December 2012.
Paper (PDF), Abstract
(HTML), Slides Oct12 (PDF)
Modelling Dependence in High Dimensions with Factor Copulas, with Dong
Hwan Oh, working paper,
May 2011. Revised
December 2012.
Paper (PDF), Abstract (HTML), Web Appendix (PDF), Slides Sep12 (PDF)
Change You Can Believe In? Hedge Fund Data Revisions, with Tarun Ramadorai and Michael
Streatfield,
working paper, September 2011. Revised March
2013.
Paper
(PDF), Abstract (HTML), Slides Mar12 (PDF), Web
Appendix (PDF)
-- Previously circulated as "The Reliability of Voluntary Disclosures: Evidence
from Hedge Funds"
Good Volatility, Bad Volatility:
Signed Jumps and the Persistence of Volatility , with Kevin Sheppard, working paper, February 2011. Revised
October 2011.
Paper (PDF), Abstract (HTML)
Time-Varying Liquidity in Hedge Fund Returns, with Sheng Li, May
2007. Oxford-Man Institute of
Quantitative Finance working paper
OMI03/07.
Paper
(PDF), Abstract (HTML), Slides Oct07 (PDF)
Publications
in academic journals
Simulated Method of Moments Estimation for Copula-Based Multivariate
Models, with Dong
Hwan Oh, working paper,
November 2011. Revised May 2012. Forthcoming in Journal
of the American Statistical Association.
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), Slides Jun11
(PDF), Web Appendix
(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 Sep09 (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
Nov10 (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 May08 (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 Nov07 (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), Slides
July06 (PDF), Code (MATLAB)
-- 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), Slides Nov07 (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), Slides Jun09 (PDF), Code (MATLAB)
-- 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 Mar09 (PDF)
Are "Market Neutral" Hedge
Funds Really Market Neutral?, 2009, Review of Financial Studies,
22(7), 2495-2530.
Paper (PDF), Abstract (HTML), Slides June05 (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 May06 (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 July03 (PDF)
Modelling Asymmetric Exchange Rate
Dependence, 2006, International
Economic Review, 47(2), 527-556.
Paper (PDF), Abstract
(HTML), Slides June01 (PDF), Code (MATLAB)
-- 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). Matlab functions
for these can be found here.
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), Slides Nov01 (PDF), Code (MATLAB)
-- 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), Slides Oct02 (PDF), Code (MATLAB)
-- 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).
Other
publications
Copula Methods for Forecasting Multivariate Time Series, May 2012, in G. Elliott and A.
Timmermann (eds.) Handbook of Economic
Forecasting, Volume 2, Springer Verlag, forthcoming.
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).
Computer
code
Matlab code for some of the computations in the
above papers can be found here.
Upcoming
seminars/conferences
Humboldt - Copenhagen Conference in Financial Econometrics, Berlin (14-16 March 2013)
Applied Time Series Econometrics Workshop, Federal Reserve Bank of St. Louis (12 April 2013)
Volatility Institute conference, NYU-Stern (26 April 2013)
New
York University, Stern School of
Business (29 April 2013)
CIREQ conference on Financial and Time Series Econometrics, Montreal (3-4 May 2013)
ITAM Finance Conference, Mexico City (7-8 June 2013)
International Symposium on Econometric Theory and Applications (SETA), Seoul (20-21 July 2013)
OMI-SoFiE Financial Econometrics Summer School, Oxford (29 July - 2 August 2013)
__________________________________________
Abstracts
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 new models for the dependence structure, or copula,
of economic variables based on a factor structure. The proposed models are
particularly attractive for high dimensional applications, involving fifty or more
variables. This class of models generally lacks a closed-form density, but
analytical results for the implied tail dependence can be obtained using
extreme value theory, and estimation via a simulation-based method using rank
statistics is simple and fast. We study the finite-sample properties of the
estimation method for applications involving up to 100 variables, and apply the
model to daily returns on all 100 constituents of the S&P 100 index. 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 the proposed factor copula model provides 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 350 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, for forecast horizons ranging from 1 to 50 trading days. 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 5-minute "truncated" RV
outperforms most other realized measures. Overall, we conclude that it is
difficult to significantly beat 5-minute RV.
__________________________________________
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 enable 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.
__________________________________________
Contact
Information
Andrew
Patton
213 Social
Sciences Building, Box 90097
Durham NC
27708-0097
USA
and
Oxford-Man Institute of Quantitative
Finance
Email:
andrew.patton@duke.edu
Phone: +1 919 660 1849
Fax: +1 919 684
8974
Web: . http://econ.duke.edu/~ap172
__________________________________________
Last updated: May 2013.
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