Markov Seminars
Typical Spread Trading
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Use a multivariate method like PCA to identify constituent legs of a trade
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Select weights for each leg based on some exogenous criteria.
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Model the resulting spread as a univariate process
Problems
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A single spread is almost always insufficient to represent the state of a dynamic multivariate system
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Exogenous weights typically aren't chosen to optimize anything meaningful
A Better Aproach
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Use a multivariate method to identify constituent legs of a trade
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Select trade weights as the solution to a well-specified optimization problem involving the multivariate process
Benefits
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Make maximal use of available information
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Ensure consistent assumptions throughout the investment process
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Extract maximum expected return per unit of risk on each trade
Key Topics
Using maximum likelihood estimation to calibrate the Multivariate Ornstein-Uhlenbeck model
Using maximum likelihood estimation to calibrate the Multivariate Ornstein-Uhlenbeck model
When can a spread be modeled as a single univariate process?
Modeling symmetric and asymmetric interactions between variables
Parsimonious parameterization of the scatter matrix using Cholesky decomposition of the covariance matrix
Initialization of the scatter matrix with a fast estimate of the multivariate quadratic variation
When can a spread be modeled as a single univariate process?
Modeling symmetric and asymmetric interactions between variables
Parsimonious parameterization of the scatter matrix using Cholesky decomposition of the covariance matrix
Initialization of the scatter matrix with a fast estimate of the multivariate quadratic variation
Efficient computation of the matrix exponential via series expansion
Implications of complex eigenvalues in the transition matrix
Simulation of the Multivariate Ornstein-Uhlenbeck process to calculate path-dependent risk measures
Chossing spreads to maximize ex ante Sharpe ratios for fixed investment horizons
Similarities and differences with principal components analysis
Better Modeling Leads to Better Trading
Principal components analysis has been used in multivariate analysis of financial markets since at least 1988, with publication of the Goldman Sachs working paper, Common Factors Affecting Bonds Returns, by Litterman and Scheinkman.
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And the Ornstein-Uhlenbeck process has been used in financial markets to model mean reversion in continuous time since at least 1971, when Merton used it to model the short rate in Optimum Consumption and Portfolio Rules in a Continuous-Time Model.
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But while while multivariate analysis and univariate mean reversion are common in finance, the analysis of multivariate mean reversion is still not common in financial markets, despite the fact that it's a powerful and flexible tool for characterizing the uncertainty of asset prices.
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Modeling multivariate mean reversion in continuous time requires a fair bit of effort and care. For example, calculation of the conditional expected value requires calculation of the exponential of the transition matrix. And because the model is so flexible, parameters can proliferate quickly as the number of variables increases.
But the additional care and effort can provide significant advantages. For example, a simple spread between two instruments isn't guaranteed to follow a univariate Ornstein-Uhlenbeck process even when the two instruments together follow a multivariate Ornstein-Uhlenbeck process.
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In these cases, analysis of the spread using a univariate process leads to model mis-specification -- clearly a problem for anyone looking to maximize ex ante risk-adjusted returns.
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In this seminar, we show how a set of instruments can be modeled as a multivariate system, with each instrument reverting around its own mean -- and with each instrument potentially interacting with the others. And we show the way this multivariate characterization can be used directly to maximize the ex ante Share ratios of spread trades.
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Why trade sub-optimally when an optimal solution is available?
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Join us on November 19 to learn how better modeling can lead to better trading results, for you and your colleagues.
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Doug Huggins
Doug has worked for a variety of banks and hedge funds since 1987, including Drexel Burnham Lambert, Credit Suisse, ABN AMRO, Citadel, and Deutsche Bank.
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He's had a number of roles throughout his career, including Global Head of Fixed Income Relative Value Research and Global Head of Hedge Fund Sales. He started a Global Proprietary Trading desk for ABN AMRO in 2003.
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Doug co-authored Fixed Income Relative Value Analysis, with Christian Schaller, in 2013.
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He has a PhD in Finance & Statistics from the University of Chicago.
