Statistical analysis of illiquidity risk and premium in financial price signals

Price is the most visible signal produced by competition and interaction among a complex ecology of entities in a system called financial markets. This thesis deals with statistical analysis and model identification based on such signals. We approach this problem at various levels of abstraction, with a particular emphasis on linking certain statistical anomalies identified to specific frictions that are only observable in a more microscopic view.We first give a brief review of the framework for the analysis of financial prices. We highlight the important role of information by introducing the concept of informational efficiency. The main body consists of two parts. Part A consists of Chapters 3, 4 and 5. We first link unpredictability of financial returns, a direct consequence of the informational efficiency, to the expected covariance structure of resulting return signals. We discuss a particular algorithm designed to detect the existence of weak mean-reverting component in the observed returns. Applying this detection scheme to US stock returns between 1995 and 2007, we detect a statistically significant but continually decreasing mean-reverting component in the returns. To explain this observation, we link the mean-reverting component to the arrival structure of buyers and sellers and their interactions. We discuss a particular model for this interaction and apply various tests to establish the validity of the proposed model. Part A concludes with an application of these tools in analyzing the sequence of events in August 2007 which resulted in a breakdown of normal behavior of the system.Part B, consisting of Chapters 6 and 7, also deals with the issue of predictability in financial returns, but at a different frequency and based on a different set of instruments. We first produce the evidence for an unusually high level of predictability among returns of certain classes of hedge funds. To explain this observation, we discuss a model built based on the notion of partially observed price signals. When prices are not observed, for example due to lack of trading, the most recent price is used to calculate the value of an investment, and this process results in perceived serial correlation in the calculated returns. We view this lack of trading as the second example of friction in this system, and set out to link this friction to the mean of the resulting returns signals. We find strong link between predictability and first moment in certain groups of returns used.