Essays on Trading Costs and Securities Lending


Student thesis: Doctoral Thesis

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Award date14 May 2020


The following collection of essays are linked by one theme, uncertainty. The dynamic nature of financial markets and trading, as with the rest of social sciences where changes can be observed and decisions can be taken by participants to influence the system, means that along with better models and predictive technologies predictions need to be continuously revised; and yet unintended consequences set in.

A glimpse of what a journey towards the land of unintended consequences holds can be seen by reminding ourselves that all knowledge creation is but an unintended consequence. We start with an attempt to understand the papers written by others, (literature review of knowledge already created or summary of experiments performed and under what conditions), and end up with papers of our own (results that add what is missing or suggest improvements). Although, to be precise, as researchers we do want to intentionally create new knowledge, but the exact new knowledge we end up creating is unintentional; we stumble upon it as we wander around the knowledge that is already in place. This is simply because our intentions, or what we intend, can only be catered from what we already know or from existing knowledge; new knowledge, which is unknown, has to come from the realm of the unintentional.

A further glance in this direction might show that in the process of creating knowledge and trying to understanding the world better, we might just end up understanding one another better, perhaps becoming more tolerant in the process, an unintended yet very welcome consequence; making us wonder whether the true purpose of all knowledge creation might be to make us more tolerant. An unwelcome but unintended consequence of all this knowledge creation is that perhaps more knowledge is being lost than what is being (re?)-created. As someone has already said, everything might have already been said, but not by everyone and perhaps not to everyone (since we sometimes forget things that we ourselves might have said). Hoping that there is something here that is new for you or something that you have forgotten, which might make it seem new.

Each of the three topics below is presented as a separate part in itself and is meant to be self contained. Though at times we refer the reader to different sections for a more detailed exposition on a particular sub-topic. We regret any inconvenience that this loss of continuity might bring, but hope that this makes for a more concise presentation. There are several appendices for each part where additional relevant papers, graphical aids, mathematical proofs and other supplementary material are given and linked into the narrative.

Admittedly, our initial ambitions to produce a normative theory for the topics considered here, are undone by the present state of affairs in social science modeling. Though we consider many elements of financial (social) systems at face value, this cannot be termed a positive theory. For now, if these end up producing a useful theory, our work is done. While a detailed axiomatic approach to uncertainty and unintended consequences is postponed for another time (or perhaps another lifetime), the present assortment has the following three elements:

A Dynamic Programming Approach to Trading Costs: Separating Market Impact from Market Timing

We develop a fundamentally different stochastic dynamic programming model of trading costs. Built on a strong theoretical foundation, our model provides insights to market participants by splitting the overall move of the security price during the duration of an order into the Market Impact (price move caused by their actions) and Market Timing (price move caused by everyone else) components. We derive formulations of this model under different laws of motion of the security prices, starting with a simple benchmark scenario and extending this to include multiple sources of uncertainty, liquidity constraints due to volume curve shifts and relate trading costs to the spread. We develop a numerical framework that can be used to obtain optimal executions under any law of motion of prices and demonstrate the tremendous practical applicability of our theoretical methodology including the powerful numerical techniques to implement them. Our decomposition of trading costs into Market Impact and Market Timing allows us to deduce the zero sum game nature of trading costs. It holds numerous lessons for dealing with complex systems, wherein reducing the complexity by splitting the many sources of uncertainty can lead to better insights in the decision process.

Securities Lending Strategies: Exclusive Valuations and Auction Bids

We derive valuations of a portfolio of financial instruments from a securities lending perspective, under different assumptions, and show a weighting scheme that converges to the true valuation. We illustrate conditions under which our alternative weighting scheme converges faster to the true valuation when compared to the minimum variance weighting. This weighting scheme is applicable in any situation where multiple forecasts are made and we need a methodology to combine them. Our valuations can be useful either to derive a bidding strategy for an exclusive auction or to design an appropriate auction mechanism, depending on which side of the fence a participant sits (whether the interest is to procure the rights to use a portfolio for making stock loans such as for a lending desk, or, to obtain additional revenue from a portfolio such as from the point of view of a long only asset management firm). We run simulations to establish numerical examples for the set of valuations and for various bidding strategies corresponding to different auction settings.

Securities Lending Strategies: Valuation of Terms Loans using Option Theory

We develop models to price long term loans in the securities lending business. These longer horizon deals can be viewed as contracts with optionality embedded in them and can be priced using established methods from derivatives theory, becoming to our limited knowledge, the first application that can lead to greater synergies between the operations of derivative and delta-one trading desks, perhaps even being able to combine certain aspects of the day to day operations of these seemingly disparate entities. We run numerical simulations to demonstrate the practical applicability of these models. These models are part of one of the least explored yet profit laden areas of modern investment management. We develop a heuristic that can mitigate the loss of information that sets in when parameters are estimated first and then the valuation is performed by directly calculating the valuation using the historical time series. This can lead to reduced models errors, robust estimation systems and greater economic stability. We illustrate how the methodologies developed here could be useful for inventory management. All these techniques could have applications for dealing with other financial instruments, non-financial commodities and many forms of uncertainty.