Mathematical Finance
Department of Mathematics and Statistics
Texas Tech University
TBD -->Abstract: Using long-standing models for expected returns of US equities,
we show that firm environmental ratings interact with those forecasted returns and produce excess returns both unconditionally and conditionally.
Well-known factor models subsume neither environmental-related return differentials nor expected return premia from those scores and models.
In addition, combining information from both inputs—expected return models and economic, social, and governance (ESG) information—
may provide an advantage in selecting investments.
For financial fiduciaries, this notion shifts the conversation about ESG reflecting only constraints to one of an expanded information
and possibly investment opportunity set.
Brief Bio: Dr. Guerard is the Chairman of the Scientific Advisory Board of McKinley Capital.
He joined McKinley Capital in 2005 as the Director of Quantitative Research.
Prior to his tenure at McKinley Capital, John held a number of senior-level positions including Vice President for Daiwa Securities Trust Co.
where he co-managed the Japan Equity Fund with Nobel Prize winner Dr. Harry Markowitz.
Dr. Guerard is a winner of the Moskowitz Prize, a global award recognizing outstanding quantitative research in sustainable and responsible investing.
A brief bio for Dr. Guerard can be found here
Abstract: Two-way fixed -effects models are a popular tool for measuring the effect of policies using panel data. Recent methodological literature has emphasized two potential pitfalls of this technique. First, in the presence of treatment effect heterogeneity, two-way fixed-effects estimators may recover a weighted average of treatment effects in which some effects may receive negative weights. Second, the commonly employed cluster-robust standard error estimators may yield unreliable inference when clusters are heterogeneous. We review these recent advances and provide a guide for estimation and inference in two-way fixed-effects models.Abstract:
Accurate estimation and optimal control of tail risk is important for building portfolios with desirable properties,
especially when dealing with a large set of assets.
We consider optimal asset allocation strategies based on the minimization of two asymmetric deviation measures,
related to quantile and expectile regression, respectively.
Their properties are discussed in relation with the ‘risk quadrangle’ framework introduced by Rockafellar and Uryasev (2013),
and compared to traditional strategies, such as the mean-variance portfolio.
In order to control estimation error and improve the out-of-sample performances of the proposed models,
we include ridge and elastic-net regularization penalties.
We also propose an application of the framework to the enhanced index replication problem,
that aims to minimize the asymmetric risk measures related to the expectile,
while controlling for the distance from a benchmark by penalizing the deviation of the portfolio weights compared to the ones in an index.
Our approach aims to address the needs of investors interested in smart beta products (systematic strategies that
aim to maintain costs smaller than traditional active strategies) in a market context where cheap ETFs are available.
The analysis is supported by an empirical study on the real data.
Abstract: We introduce two new high-frequency volatility estimators that account
for possible breakpoints in the spot volatility process.
They are $\ell_1$-penalized versions of classical estimators - quadratic variation
and jump robust bipower variation.
We show that in the presence of a mean-square error of order $o_P(1)$ achieved
by these classical estimators, detecting breakpoints using the volatility estimator
is asymptotically equivalent to detecting them using the infeasible (latent)
volatility path.
The proposed estimators are evaluated in simulations and on real data.
They are computationally efficient, and they accurately detect breakpoints even close
to the end of the sample. Both properties are very desirable for algorithmic trading firms.
In terms of out-of-sample volatility prediction, the new estimators outperform all
competitors at various frequencies and forecasting horizons.
In the last part of the talk, we discuss multivariate extensions of the proposed
estimators and their application and empirical performance in portfolio optimization.
Abstract:
The Greenwood statistic Tn and its functions, including sample coefficient of variation, often arise
in testing exponentiality or detecting clustering or heterogeneity.
We provide a general result describing stochastic behavior of Tn in response to stochastic behavior
of the sample data.
Our result provides a rigorous base for con- structing tests and assuring that confidence regions are
actually intervals for the tail parameter of many power-tail distributions.
We also present a result explaining the connection between clustering and heaviness of tail for several
classes of distributions and its extension to general heavy tailed families.
Our results provide theoretical justification for Tn being an effective and commonly used statistic
discriminating between regularity/uniformity and clustering in presence of heavy tails in applied sciences.
We also note that the use of Greenwood statistic as a measure of heterogeneity or clustering is limited to
data with large outliers, as opposed to those close to zero.
Abstract: We extend the Markov Decision Process setup to the cases of MFG and MFC problems
and we generalize the optimality Bellman equation for Q-learning.
By introducing two learning rates, one for the Q-matrix and one for the population distribution,
we are able to design a single algorithm which learns the optimal policies for the MFG or for the MFC
depending on the ratio of these two rates.
Applications to problems in finance are also discussed.
This is joint work with Andrea Angiuli and Mathieu Laurière.
Brief Bio: Professor Fouque's research is in the domain of random media with applications
ranging from wave propagation phenomena to financial mathematics.
He has published over one hundred research articles and co-authored three books:
"Derivatives in Financial Markets with Stochastic Volatility" (Cambridge University Press, 2000),
"Wave Propagation and Time Reversal in Randomly Layered Media" (Springer, 2007), and
"Multiscale Stochastic Volatility for Equity, Interest-Rate and Credit Derivatives" (Cambridge University Press, 2011).
Jean-Pierre Fouque received his Ph.D. in Mathematics from the University Pierre et Marie Curie, Paris.
He held positions at the CNRS and at the Ecole Polytechique in France, before joining North Carolina State University
in 1998 where he started the Masters of Financial Mathematics.
In 2006, he joined the department of Statistics and Applied Probability at the University of California Santa Barbara
where he is a Distinguished Professor and Co-director of the Center for Financial Mathematics and Actuarial Research (CFMAR).
He is currently Editor-in-Chief of the SIAM Journal on Financial Mathematics and Past-President of the Bachelier Finance Society.
He is a Fellow of the Institute of Mathematical Statistics since 2009 and a SIAM Fellow since 2011.
We empirically examine the equity portfolio choices of investors with generalized disappointment aversion (GDA) preferences. Contrary to expected utility investors, GDA investors suffer, out-of-sample, large monetary utility losses from suboptimal portfolio choices such as equally weighted portfolios. These losses increase in the level of disappointment aversion and the number of stocks available for investment. A novel semi-parametric method based on L-moments enables us to study the impact of very high order moments on portfolio choice. Higher order moments, beyond four, are as important as lower order moments in explaining portfolio choice of investors.
Please virtually attend on Friday at 2 PM CDT (UT-5) via this Zoom link.
Abstract: We investigate whether fitting errors of equity-option-implied volatility surfaces are informative
about intermediary frictions.
Relating observed implied volatilities to a smoothed volatility surface,
we find that this error metric increases in idiosyncratic stock volatility and measures of option and stock illiquidity.
An aggregation across the stock universe adds valuable information and the resulting overarching measure of volatility
noise peaks during market distress, exhibits sensible correlations to economic state variables,
and reveals a close link to intermediary equity and debt constraints.
In line with intermediary asset pricing, we find that volatility noise is informative for the cross-sectional variation
in expected returns beyond the equity option market.
This is joint work with Michael Hofmann.
Brief Bio: Marliese Uhrig-Homburg is a professor of finance at the Karlsruhe Institute of Technology (KIT)
in Germany, holding the Endowed Chair (DZ BANK) of Financial Engineering and Derivates.
She obtained a doctoral degree from University of Mannheim and completed her habilitation on “The cost of debt,
credit risk, and optimal capital structure” in 2001.
Her research focuses on the pricing and the role of derivatives, credit risk, fixed income and energy markets,
and the interaction between investment and financing decisions.
She is the author of several recent papers on financial engineering in leading academic journals, among others in the
Journal of Finance, Journal of Corporate Finance, Journal of Banking and Finance, Review of Derivatives Research and
Journal of Environmental Economics and Management.
She is member of the Advisory Board of the German Finance Association (DGF),
co-organizes the triannual international Symposium on Finance, Banking and Insurance in Karlsruhe,
and is vice-speaker of the section Banking and Finance of the German Academic Association for Business Research (VHB).
Since 2008 she serves as vice-dean of the department of Economics and Business Engineering at KIT.
Abstract: We study equity return jump risk for a large sample of emerging and developed markets,
by using an analytical framework that endogenously differentiates between jumps and smooth variation.
Jump-size characteristics and jump risks are heterogeneous across equity markets.
Average jump size tends to be larger, while average jump intensity is typically lower for emerging than for developed markets.
We find that international jump risks exhibit strong commonality: The first principal component explains over 60% of
their variation. Its correlation with VIX exceeds 0.7.
Jumps' contribution to total return variability spikes at times of heightened volatility and is typically higher for emerging
than for developed markets.
Individual markets' jump risks have statistically- and economically-significant relationship with VIX,
while local variables do not seem to be uniformly important for jump risks' dynamics.
This is joint work with Mehmet Ozsoy.
Frank Fabozzi, Emeritus Professor of Finance, EDHEC Business School, Nice
will moderate an industry panel discussing the transition from a mathematics background to a career in asset management.
The panelists will be:
- Dr. Stoyan Stoyanov, Director of Equity Research, Charles Schwab
- Dr. Joseph Simonian, Founder and CIO of Autonomous Investment Technologies
- Dr. Wesley Phoa, Senior Vice President, Capital Group
Abstract: This talk will focus on the development and implementation of a systematic trading strategy.
It will cover the life cycle of systematic trading, the common pitfalls of backtesting,
and the out-of-sample stability of a systematic strategy.