Combining Alphas via Bounded Regression

Abstract

We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications typically there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted) regression over SCM principal components. Regression often produces alpha weights with insufficient diversification and/or skewed distribution against, e.g., turnover. This can be rectified by imposing bounds on alpha weights within the regression procedure. Bounded regression can also be applied to stock and other asset portfolio construction. We discuss illustrative examples.

Heterotic Risk Models

“…so not more than 1% of each stock's ADDV is bought or sold. We use the bounded regression algorithm and the R source code of (Kakushadze, 2015b) to run these simulations. Expectedly, the liquidity bounds (89) lower ROC and CPS while improving SR, but in the same fashion for all 3 weighted regression alphas i)-iii).…”

“…The 1-factor model gives almost the same results. 40 The source code for this algorithm is not included in (Kakushadze, 2015a), so we include it in Appendix C. It is similar to the source code of (Kakushadze, 2015b) for the bounded regression.…”

“…In this appendix we give the R source code for the optimization algorithm with linear homogeneous constraints and position bounds we use in Section 6.5. This code is similar to the code for the bounded regression algorithm discussed in detail in (Kakushadze, 2015b) with one important difference, so our discussion here will be brief. The entry function is bopt.calc.opt().…”

“…3 For a partial list of literature related to factor risk models, see, e.g., (Acharya and Pedersen, 2005), (Ang et al, 2006), (Anson, 2013/14), (Asness, 1995), (Asness and Stevens, 1995), (Asness et al, 2001), (Bai, 2003), (Bai and Li, 2012), (Bai and Ng, 2002), (Bansal and Viswanathan, 1993), (Banz, 1981), (Basu, 1977), (Black, 1972), , (Blume and Friend, 1973), (Brandt et al, 2010), (Briner and Connor, 2008), (Burmeister and Wall, 1986), (Campbell, 1987), (Campbell et al, 2001), (Campbell and Shiller, 1988), (Carhart, 1997), (Chamberlain and Rothschild, 1983), (Chan et al, 1985), (Chen et al, 1986(Chen et al, , 1990, (Chicheportiche and Bouchaud, 2014), (Cochrane, 2001), (Connor, 1984(Connor, , 1995, (Connor and Korajczyk, 1988, 1989, (Daniel and Titman, 1997), (DeBondt and Thaler, 1985), (Dhrymes et al, 1984), (Fama and French, 1992, 2015, (Fama and McBeth, 1973), Harvey, 1991, 1999), (Forni et al, 2000(Forni et al, , 2005, (Forni and Lippi 2001),…”

How to combine a billion alphas

“…A nice thing about our optimization reducing to a regression, which is computationally cheap, is that it can be readily modified to incorporate bounds on the alpha weights w i . Indeed, since w i are proportional to the regression residuals, we can simply use the bounded regression discussed in [Kakushadze, 2015b]. Similarly, we can incorporate trading costs via the method discussed in [Kakushadze, 2015a].…”