This paper gives the derivation of the Bivariate Stochastic Functional Form (BSFF), which may be seen as the direct generalization of the linear regression model. The derivation does not involve complex mathematical tools such as stochastic calculus. It extends the derivation of the univariate...

The traditional active vs passive debate has been shaken up by the emergence of “smart beta” strategies. As the population of these products has exploded, the quest to differentiate among them has focused on portfolio construction techniques rather than what actually matters, namely...

Low-risk stocks have historically outperformed high-risk stocks, delivering better long-term returns with less volatility. This counter-intuitive effect has persisted since 1926, violating one of the basic tenets of Finance Theory. We investigate the role of country and sector effects in...

Factor attribution based on linear regression often fails to satisfactorily explain the performance of systematic investment strategies. A volatile or persistent residual suggests nonlinear interactions between factor returns and portfolio construction. We propose a nonparametric adjustment to...

We investigate whether structurally hedging the currency risk of global equity products benefits long-term investors. Based on a 35 year back-test of 3 smart beta strategies from 6 currency perspectives, our answer is a qualified “yes”. Currency hedging was effective in reducing risk and...