P-Q Convergence
Numerous smart people are foreshadowing a sea change in quantitative finance. This change has big alpha potential for the mathematically inclined, and will result in a much higher technical bar for those trying to learn algorithmic trading. And, pity those buy and hold investors.
Different folks are converging on this change in different colloquial ways. Derman has an upcoming book criticizing financial over-modeling. Taleb has been writing books on imprudent mathematical assumptions for many years. Haug has debunked Black-Scholes in several papers. Bouchaud and Potters have spent a decade popularizing econophysics by questioning classic dogma. Meucci wrote a book and has been teaching it for several years. Sornette is inventing quant macro by tackling crash modeling and prediction. Even big bank folks are jumping in, such as recent papers by Petrelli et al.
Despite different words, all boil down to the same fundamental change: convergence of the 
Fund Structure Arbitrage
An amusing old Nuclear Phynance thread comparing money management styles of Kelly and Soros reminds Quantivity of the perverse incentives which plague the financial services industry—retail investors have nobody with whom their incentives are perfectly aligned; instead, everyone takes a piece. Yet, rather than bemoan this state of affairs, more interesting is to pose the following comparative advantage question:
What advantages do sophisticated tech-savvy quantitative traders, managing their own money (whether retail or prop), have over funds?
Understanding this question naturally leads to the concept of fund structure arbitrage, which refers to potential profit earned by exploiting idiosyncrasies arising from the organizational and regulatory constraints imposed on institutional funds. This concept is important, as many novice traders make the mistake of dreaming up strategies in a vacuum, forgetting that what moves markets is big institutional money—much of which behaves with fairly predictable behavioral and statistical biases. For those who enjoy biological analogies, this is the study of pilot fish.
Optimal Equity Monetization: Part 3
The previous post Optimal Equity Monetization introduced a mathematical model for optimizing equity monetization. In the follow-up post Optimal Equity Monetization: Part 2, solutions are considered which assume 
Despite this topic seeming pedestrian at first glance, it turns out to be unexpectedly beautiful in exemplifying quant techniques spanning finance, ML, and pure math: fitting empirical returns, monte carlo, global optimization, integer composition, MLE, genetic randomization, and portfolio theory.
Optimal Equity Monetization: Part 2
The previous post Optimal Equity Monetization introduced a mathematical model for optimizing equity monetization. In this follow-up post, we consider several solutions to that model under naïve assumptions about the dynamics of
Begin by making the (unrealistic) assumption that the distribution of values for
Optimal Equity Monetization
A reader recently asked an interesting question regarding equity monetization, most frequently associated with 10b5-1 (closely related to previous post on Employee Stock Option Hedging):
What is the right way to model the monetization of a large concentrated equity position, including tax considerations?
This is a fun topic to demystify, as many financial advisers struggle to explain the answer in rigorous terms, often use grossly oversimplified assumptions (e.g. linear price change on underlying), and almost never provide analytic or code models. Towards this end, this post builds such an analytic model and walks through some (but not all) of the corresponding considerations.
Curated Research Feed
Multiple active projects are heating up nicely, motivating Quantivity to invest more time in several fields of the quant literature. Primary topics bookend the spectrum: asset allocation and computationally-intensive intraday, including crash modeling across all frequencies. Focus includes both published literature, along with real-time preprints from arXiv, SSRN, and numerous Fed. Given volume of articles, effective organization and search have evolved to become a bit burdensome.
Mean Reversion Redux
Readers of Momentum Redux requested a similar post for the mean reversion literature, recognizing the ying-yang relationship of momentum and mean reversion.
One of the most interesting wrinkles is the conceptual “apples and oranges” problem induced by trading frequency; authors use the same words, but mean different things. This subtlety, confusion, and opportunity for obfuscation arises from reversion manifesting at many frequencies simultaneously:
- Intraday: market making, inter-exchange arbitrage, and various recent HFT amusement
- Days – Months: factor convergence, whether cointegration, PCA, or more modern dimensional reduction methods (such as manifold learning)
- Months – Years: “contrarian” strategies based on accounting, FF anomalies, or behavioral models
Due to this heterogeneity, reversion manifests in many statistical guises; or, in ML speak: if you can extract a stable time-series or cross-sectional feature, you can probably trade it.
Momentum Redux
Momentum is being discovered in the blogosphere, once again. Hazah.
The finance literature includes a tradition of momentum, going back to early 1990s. Preceding academic treatment, momentum has been a staple of technical analysis for many decades. Prominent academic authors include Jegadeesh, Titman, Asness (grad student of Fama and French), Rouwenhorst, Moskowitz, and Hong. An abridged review of this literature may be perhaps useful, as substantive econometric effort has been invested in analysis spanning both time and asset class.
Covariance, Correlation, and RMT
As previously exemplified by basket prediction, Quantivity is finding increasingly frequent use of random matrix theory (RMT), particularly in context of portfolio / basket covariance and correlation analysis across all trading frequencies. Although undoubtedly an exaggeration, RMT is beginning to feel like PCA did in the 1990s.
Below is a survey of RMT literature to whet readers’ appetite. Readers are requested to suggest additional relevant literature in comments. Subsequent posts may delve into more details on practical use of RMT, pending reader interest.
Avellaneda Lectures: Models and Risk
Quantivity recently stumbled upon the following two excellent lecture series by Marco Avellaneda (affiliated with Courant Institute), while researching a new trading strategy. The first series surveys quant strategies, with an emphasis on mean-reversion and factor models. The second surveys risk and portfolio management. All relevant for building quantitative trading strategies.
While this material is available elsewhere, self-contained lectures which coherently assemble important themes from the literature are a joy to read.
Quantivity 
