In R: Cross Sectional Volatility
Readers of Cross Sectional Volatility raised numerous questions on implementing the trading signal derived from cross sectional volatility. Towards exploring and visualizing these questions, an implementation in R is considered here.
People of Quant Research
Academia is an important participant in the quant world, contributing fundamental research across diverse fields: statistics, econometrics, information theory, signal processing, machine learning, dynamical systems, econophysics, optimization, information geometry, pattern recognition, data mining, and mathematical finance. Due to fragmentation and politics, there is no single place to monitor relevant research (both working papers and journal articles). While arXiv and SSRN are hubs, many papers are published directly to widely varying journals.
This post is a work in progress, enumerating key quant researchers who are actively publishing, along with their respective affiliated institutions (academic, investment, or both), who are followed by Quantivity. This list will be periodically updated, and thus may be worthy of revisiting.
Cross Sectional Volatility
Delay Embedding as Regime Signal prompted enough questions to warrant further commentary on the principal component space 
- Lineage: this model is stylistically representative of the statarb tradition, spanning from Computational Methodology for Modeling the Dynamics of Statistical Arbitrage (Burgess, 1999) to Statistical Arbitrage in the US Equities Market (Avellaneda and Lee, 2008); on the practical side, both Burgess and Neil Yelsey (acknowledged by Infantino and Itzhaki) are reputed to have run arbitrage desks
- Exemplary: this illustrates how to build models which are transformations of returns (commonly via dimensional reduction), rather than returns themselves—as Paul Grimoldi commented; this also speaks to Jeff’s question last year regarding the contrast of classic technical analysis with quantitative methods: visual pattern analysis of returns versus statistical analysis / ML on transformed returns
Intuition of this model is compelling, albeit obfuscated fairly heavily by its rough mathematical presentation: mean-reverting convergence can be predicted via a dimensionally-reduced (principal components) space of returns from an equity portfolio. The following seeks to explain this intuition, including use of more standard mathematical language than found in § 2.4 and § 3.1.
Delay Embedding as Regime Signal
Infantino and Itzhaki, in their 2010 thesis Developing High-Frequency Equities Trading Models, utilize a regime switching signal based upon time delay embedding. The intuition underlying this signal and use for regime discovery are unexpectedly interesting.
Why Log Returns
A reader recently asked an important question, one which often puzzles those new to quantitative finance (especially those coming from technical analysis, which relies upon price pattern analysis):
Why use the logarithm of returns, rather than price or raw returns?
The answer is several fold, each of whose individual importance varies by problem domain.
Curiosity of LPPL
Recent work building non-linear regime models has led Quantivity back into econophysics. In doing so, coincidentally bumped into the proposed Log-Periodic Power Law (LPPL), which is a log-periodic oscillation model for describing the characteristic behavior of a speculative bubble and predicting its subsequent crash. In other words: a macro regime discovery model.
This model was independently proposed by Sornette, Johansen and Bouchaud (J. Phys. I. France 6 pp. 167-175, 1996) and Feigenbaum and Freund, (Int. J. Moder Phys. B 10: 3737, 1996 and Modern Physics Letters B 12, 1998). Econophysics fans will recollect Bouchaud from Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management and Capital Fund Management.
Mathematically, LPPL proposes price 
Employee Stock Option (ESO) Hedging
Utility of quantitative finance often arises in unexpected places. An example is employee stock options (ESO). Specifically, a surprising number of ESO planning questions boil down to dynamic hedging and its relationship to financial, tax, and/or regulatory considerations.
As always, the two questions for ESOs are: when to exercise and when to sell (including potential for multiple partials of each), and what quantities for each.
CFTC / SEC Flash Report
Quantivity recommends reading Finding Regarding the Market Events of May 6, 2010, in detail. Four thoughts worth pondering during reading, given this lays HFT bare:
- Veracity: is this report correct and complete?
- Implications: given obvious front-running, what are the best second-order parasitic algos?
- Simulation: interesting exercise to simulate this market condition, given the trigger was a simple program order, and back out the aggregate HFT algos necessary to generate this market behavior
- Liquidity: what does liquidity mean in a HFT world, and how should theory be amended commensurately?
This event also demands a collective wish goodbye to orderly price discovery, as this is the ultimate proof by construction of the contrary.
Subsequent posts may comment further, particularly on parasitic algo design. Readers with more inside knowledge are encouraged to comment directly or contact Quantivity privately.
Combining Regression & Ranking
Many types of trading analysis problems boil down to a combination of regression and ranking, in one guise or another (e.g. classical or minimizing custom loss functions). Yet, the relationship between these two techniques is subtle and their interdependence subject to myriad practical difficulties. One familiar example is the lack of necessary performance equivalence, meaning excellent regression may result in poor ranking and vice versa.
KDD-2010 recently included a paper, Combined Ranking and Regression by Sculley, which describes an approach combining both techniques by simultaneously optimizing dual objective functions. Specifically, from p. 1:
HF Basket Prediction via RMT / PCA
What if robust principal components could be identified for arbitrary baskets in real-time and used for HF intra-day prediction? Such would be an essence of high-frequency market regimes.
Tanaka-Yamawaki posits the emerging existence of such a methodology in an abstract for upcoming KES2010 and Econophysics Colloquium 2010. This work builds upon Plerou et al., who pioneered applying random matrix theory (RMT, aka stochastic eigenanalysis) to analysis of cross-correlations of equity price changes in Random Matrix Approach to Cross Correlation in Financial Data.
While the concept of applying real-time PCA is hardly new, what may be new is: use of RMT for rigorously separating correlation signal from noise, doing so in real-time, and focus on intra-day prediction.
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