Should you combine positions or signals? (Part I): Having your cake and eating it too

Let’s just assume we have 2 signals (Trend and Carry). How do we combine these signals together? Generally there are two broad ways of doing it:

1. Combining positions of the individual signals
2. Regress future returns against the signals to get expected returns of each asset

In this article, I will talk about another way of doing portfolio construction. The approach kinda lies somewhere in between the two, and kinda aims to retain most of the benefits of each approach. Sometimes we do not necessarily have expected returns for each asset, rather we have 1) positions of each signal, 2) expected returns of each signal. We can use those two information to extract expected returns from of each asset. Let's dive in.