Notes on Uncertainty, Unintended Consequences and Everything Else

Abstract

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 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 seven topics below, classified into three main categories, is presented as a separate part in itself and is meant to be self-contained.

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 elements:

2.1 Microstructure Topics

1. A Dynamic Programming Approach to Separate the Impact and Timing of Trading Costs: David vs Goliath (You against the Markets)

• We develop a set of stochastic dynamic programming models that seek to separate the effect of one's actions in a financial market trading scenario from the actions of other players. Such a separation brings about a reduction in complexity since participants can better plan their course of action based on a greater focus on the set of controls and states that hold greater significance for their destiny while being cognizant of the implications of the actions of the rest of the participants.

2. A Tale of Two Consequences: Intended and Unintended Outcomes of the Japan TOPIX Tick Size Changes

• We apply the methodology from part I to a recent event in financial markets (TOPIX 100 tick size changes on the Tokyo Stock Exchange in 2014).

3. Hong Kong - Shanghai Connect / Hong Kong - Beijing Disconnect (?): Scaling the Great Wall of Chinese Securities Trading Costs

• We apply the methodology from part I to another recent event in financial markets (the opening of the Hong Kong Shanghai Connect, connecting the stock exchanges in the two cities in 2014) and illustrate a comparative approach at studying complex systems that perhaps can be one way to overcome a seemingly unsurmountable obstacle, that is, the lack of data.

2.2 Tools for Combating Uncertainty

1. Combining Dimension Reduction, Distance Measures and Covariance

• We develop a novel methodology based on the marriage between the Bhattacharyya distance, a measure of similarity across distributions of random variables, and the Johnson-Lindenstrauss Lemma, a technique for dimension reduction. The resulting technique is a simple yet powerful tool that allows comparisons between data-sets representing any two distributions. We consider an asset pricing application and then briefly discuss how this methodology lends itself to numerous market-structure studies and even applications outside the realm of finance / social sciences by illustrating a biological application.
2.3 Asset Pricing Topics

1. Securities Lending Strategies, Exclusive 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.

2. 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.
• 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. We run numerical simulations. We illustrate how the methodologies developed here could be useful for inventory management.

3. Solving the Equity Risk Premium Puzzle and Inching Towards a Theory of Everything

• We review a few attempts done over the years to explain the equity risk premium anomaly.

Keywords: Notes, Uncertainty, Unintended, Consequences, Everything Else