Multiple Perspectives on Crowding in Financial Markets

We present evidences of crowding on the Russell 3000 reconstitutions events.
The Russell US index have attracted the attention of practitioners and academics for their "index effects". It has been shown, see for example, that securities which are added to equity indexes, such as the Russell US index as well the S&P500, present positive returns shortly after their addition. Similarly, deletions receive sub-par returns after their deletions from the indexes.
We investigated the crowdedness of the Russell index strategies. As already discussed, the Russell US indexes have started receiving quarterly up- dates in order to add the most recently issued securities satisfying certain index eligibility criteria. Hence, we studied whether market participants implementing index strategies also update their strategies quarterly according to their quarter index additions or simply follow the Russell reconstitution on an annual basis. As discussed, the main factors contributing to the abnormal price impact measured on index additions and deletions are the corresponding buy and sell order of the market participants updating their index strategies and that push the prices up or down accordingly. Therefore, if a market participant were to follow the index rebalancings quarterly, during the annual reconstitution she would only have to buy shares of the security which she believes will be added to the index and which were not added to the index at any of the most recent Q3, Q4 and Q1 quarterly rebalancings. On the other end, if the majority of market participants were to follow the index annually then one would expect the securities added at the most recent Q3, Q4 and Q1 quarterly rebalancings to behave similarly to any other security added to the index, since both groups would feel a measurable buy presure genrated by the market participant updating their index portfolios.
In Section 5. We checked which of the hypothesis above is observed in the data. We compare the distributions of temporary and permanent price impacts, as defined in (1), of the quarterly additions which were added to the most recent Q3, Q4 and Q1 quarterly rebalances and which remained in the following annual reconstitutions and to those of all the other annual additions (see "Quarterly additions" and "New issues" . In order to investigate the similarity between the price impact of the aforementioned two groups we conduct a bootstrap two sample t-test assuming unequal variances and unequal sample sizes under the null hypothesis that the two groups are sampled from the same distribution, as well as for a brief review of the subject.
We also test the complementary hypothesis of whether the index quarterly additions present abnormal price impacts shortly after the corresponding quar- terly rebalancings. Therefore, we compare the price impacts of the quarterly additions with those of the securities which have not changed index member- ship in the most recent annual reconstitution. In fact, these latter is a group of securities which can be safely taken to be devoid of any index addition effect, which for example could also be observed in price a security being deleted from the Russell 2000 and being added to the Russell 1000 but still remaining in the Russell 3000 index.
To conclude, no compelling evidences were found supporting the hypothesis that the majority of market participants follow the index rebalancings on a quar- terly basis. Our results are compatible with the hypothesis that the majority of market participants follow the index strategies annually and that the annual rebalance strategies are more crowded that the quarter rebalancings ones.

Probabilistic modelling permeates the Financial services, healthcare, technology and other Service industries crucial to the UK's continuing social and economic prosperity, which are major users of stochastic algorithms for data analysis, simulation, systems design and optimisation. There is a major and growing skills shortage of experts in this area, and the success of the UK in addressing this shortage in cross-disciplinary research and industry expertise in computing, analytics and finance will directly impact the international competitiveness of UK companies and the quality of services delivered by government institutions.
By training highly skilled experts equipped to build, analyse and deploy probabilistic models, the CDT in Mathematics of Random Systems will contribute to
- sharpening the UK's research lead in this area and
- meeting the needs of industry across the technology, finance, government and healthcare sectors

MATHEMATICS, THEORETICAL PHYSICS and MATHEMATICAL BIOLOGY

The explosion of novel research areas in stochastic analysis requires the training of young researchers capable of facing the new scientific challenges and maintaining the UK's lead in this area. The partners are at the forefront of many recent developments and ideally positioned to successfully train the next generation of UK scientists for tackling these exciting challenges.
The theory of regularity structures, pioneered by Hairer (Imperial), has generated a ground-breaking approach to singular stochastic partial differential equations (SPDEs) and opened the way to solve longstanding problems in physics of random interface growth and quantum field theory, spearheaded by Hairer's group at Imperial. The theory of rough paths, initiated by TJ Lyons (Oxford), is undergoing a renewal spurred by applications in Data Science and systems control, led by the Oxford group in conjunction with Cass (Imperial). Pathwise methods and infinite dimensional methods in stochastic analysis with applications to robust modelling in finance and control have been developed by both groups.
Applications of probabilistic modelling in population genetics, mathematical ecology and precision healthcare, are active areas in which our groups have recognized expertise.

FINANCIAL SERVICES and GOVERNMENT

The large-scale computerisation of financial markets and retail finance and the advent of massive financial data sets are radically changing the landscape of financial services, requiring new profiles of experts with strong analytical and computing skills as well as familiarity with Big Data analysis and data-driven modelling, not matched by current MSc and PhD programs. Financial regulators (Bank of England, FCA, ECB) are investing in analytics and modelling to face this challenge. We will develop a novel training and research agenda adapted to these needs by leveraging the considerable expertise of our teams in quantitative modelling in finance and our extensive experience in partnerships with the financial institutions and regulators.

DATA SCIENCE:

Probabilistic algorithms, such as Stochastic gradient descent and Monte Carlo Tree Search, underlie the impressive achievements of Deep Learning methods. Stochastic control provides the theoretical framework for understanding and designing Reinforcement Learning algorithms. Deeper understanding of these algorithms can pave the way to designing improved algorithms with higher predictability and 'explainable' results, crucial for applications.
We will train experts who can blend a deeper understanding of algorithms with knowledge of the application at hand to go beyond pure data analysis and develop data-driven models and decision aid tools
There is a high demand for such expertise in technology, healthcare and finance sectors and great enthusiasm from our industry partners. Knowledge transfer will be enhanced through internships, co-funded studentships and paths to entrepreneurs