Correlation Dynamics

Project Description

• Our business is optimal trade execution in US cash equities. We wish to improve models of factor dynamics and correlation dynamics relevant in risk and fair price models.
• Background: stock returns are commonly modeled as linear regressions on factor returns; the coefficients reflect the correlation structure over the training dataset. Unfortunately the correlation structure changes - what is useful is not the past correlation structure but the future one. ADCC models use a GARCH-like approach to model correlation dynamics, but we are concerned they may fail to adequately capture the context-dependenxy of the correlation structure.
• The basic idea here is to develop an alternative way to model factor dynamics, that doesn't use daily returns but instead models the market as a Poset of "events". Each event is a significant change in one of the factors over a period of time from t1 to t2. We provide a simple algorithm to identify events, and provide a dataset of daily prices and volumes.
• The first stage of the project involves the following steps. This is a very deep problem and if the first stage is successful more will follow.
• (1) compute daily returns (close to close) using the data provided
• (2) Build the daily returns correlation matrix of 57 factors (see attachment) --> report #1
• (3) Build Lasso regressions to explain daily returns of each factor as a function of a subset of the others. Here the choice of Lasso is intended to provide natural feature selection; other feature selection methods may be suggested by the researcher.
• (4) Use the provided algorithm to construct the events history for each factor. Each event comprises an event type ("rise", "fall" or "equilibrium"), a start and end time, and 57 factor returns.
• (5) Build correlation matrix of event factor returns, and test vs the null hypothesis that it is the same as the daily returns correlation matrix --> report #2
• (6) Build Lasso regressions for event factor returns, use these to produce estimates and compute the R^2. Then compute the R^2 using the daily returns regressions saved from point (3) above --> report #3
• (7) Construct a chronology of the market activity through a sequence of non-overlapping "leading events". A leading event is an event for which the % unexpected factor return is greater than for all other events with overlapping start/end times. A simple algorithm will be provided to derive this from the events history --> report #4 
• The utility of step 7 will become apparent when we state the next phase of the project.
• If successful, the next stage of the project will address conditional correlations. Stage 3 will establish whether the event representation enables better forward correlation predictions than an ADCC model.
• The data consists in price and volume data, daily from 2008 to Oct. 2013. Subsequent dates are reserved for OOS testing
• We use mainly R and Mathematica here
• The deliverables will be the mentioned reports, enriched data tables produced, and the corresponding code
• Data shared for the duration of the project may not be used for any other purpose and must be destroyed upon termination. The project itself will remain confidential unless otherwise stated, the reports and all documentation related to the project will be considered confidential and must be destroyed upon termination
• Sample data, an Excel example of the events history logic and the data spec are attached below