101 Formulaic Alphas
Quantigic Solutions LLC; Free University of Tbilisi
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December 9, 2015
We present explicit formulas – that are also computer code – for 101 real-life quantitative trading alphas. Their average holding period approximately ranges 0.6-6.4 days. The average pair-wise correlation of these alphas is low, 15.9%. The returns are strongly correlated with volatility, but have no significant dependence on turnover, directly confirming an earlier result by two of us based on a more indirect empirical analysis. We further find empirically that turnover has poor explanatory power for alpha correlations.
101 Formulaic Alphas – Introduction
There are two complementary – and in some sense even competing – trends in modern quantitative trading. On the one hand, more and more market participants (e.g., quantitative traders, inter alia) employ sophisticated quantitative techniques to mine alphas.6 This results in ever fainter and more ephemeral alphas. On the other hand, technological advances allow to essentially automate (much of) the alpha harvesting process. This yields an ever increasing number of alphas, whose count can be in hundreds of thousands and even millions, and with the exponentially increasing progress in this field will likely be in billions before we know it…
This proliferation of alphas – albeit mostly faint and ephemeral – allows combining them in a sophisticated fashion to arrive at a unified “mega-alpha”. It is then this “mega-alpha” that is actually traded – as opposed to trading individual alphas – with a bonus of automatic internal crossing of trades (and thereby crucial-for-profitability savings on trading costs, etc.), alpha portfolio diversification (which hedges against any subset of alphas going bust in any given time period), and so on. One of the challenges in combining alphas is the usual “too many variables, too few observations” dilemma. Thus, the alpha sample covariance matrix is badly singular.
Also, naturally, quantitative trading is a secretive field and data and other information from practitioners is not readily available. This inadvertently creates an enigma around modern quant trading. E.g., with such a large number of alphas, are they not highly correlated with each other? What do these alphas look like? Are they mostly based on price and volume data, mean-reversion, momentum, etc.? How do alpha returns depend on volatility, turnover, etc.?
In a previous paper two of us [Kakushadze and Tulchinsky, 2015] took a step in demystifying the realm of modern quantitative trading by studying some empirical properties of 4,000 reallife alphas. In this paper we take another step and present explicit formulas – that are also computer code – for 101 real-life quant trading alphas. Our formulaic alphas – albeit most are not necessarily all that “simple” – serve a purpose of giving the reader a glimpse into what some of the simpler real-life alphas look like.7 It also enables the reader to replicate and test these alphas on historical data and do new research and other empirical analyses. Hopefully, it further inspires (young) researchers to come up with new ideas and create their own alphas.
We discuss some general features of our formulaic alphas in Section 2. These alphas are mostly “price-volume” (daily close-to-close returns, open, close, high, low, volume and vwap) based, albeit “fundamental” input is used in some of the alphas, including one alpha utilizing market cap, and a number of alphas employing some kind of a binary industry classification such as GICS, BICS, NAICS, SIC, etc., which are used to industry-neutralize various quantities.
In this section we describe some general features of our 101 formulaic alphas. The alphas are proprietary to WorldQuant LLC and are used here with its express permission. We provide as many details as we possibly can within the constraints imposed by the proprietary nature of the alphas. The formulaic expressions – that are also computer code – are given in Appendix A.
Very coarsely, one can think of alpha signals as based on mean-reversion or momentum.12 A mean-reversion alpha has a sign opposite to the return on which it is based. E.g., a simple mean-reversion alpha is given by
?ln(today)s open / yesterday’s close)
See full PDF below.