The alpha discovery phase is where the fun really starts. This is when you start looking for alphas, but what are alphas exactly? An alpha is an expression applied to the cross-section over your universe of stocks which returns a vector of real numbers whose values are proportional to the size of the position you will take on each asset. You can think of the numerical output of an alpha as providing an indication, or metric of conviction about future returns which will ultimately inform a trading decision. When you have discovered a successful alpha, the value in that vector for each stock is directly proportional to the rank of its return at a future time across the universe of stocks. For example, in a cross-sectional momentum strategy, we rank the stocks according to how much momentum they have as measured by a momentum indicator. We use the ranks to decide which stocks to put in along portfolio and which stocks to put in a short portfolio at every time interval. In this scenario, you can think of the logic that produces the ranks as the alpha, and the ranks themselves as the alpha vector. Taken together, the ranks are a vector of numbers that help inform the trading decision of which docs to hold long and short, and in what amounts. An alpha is one type of trading signal. A trading signal is a general term for any numerical signal that can be used to inform a trade. It could just be a single number. Therefore, alphas which are vectors are a subset of trading signals. The alpha discovery phase can also be called the signal research phase. This stage is where you test your hypothesis and see if you can come up with evidence that your idea may lead to strong future returns. This will be an iterative process. However, in modern markets, it’s rare that a single alpha will provide sufficiently consistent positive returns to provide the sole basis of an investment strategy. Typically, several alphas will be combined together to generate an overall alpha that has better performance than the best individual alpha. This is akin to the ideas of model stacking and ensembling in traditional machine learning. Combining alphas that have diverse inputs and underlying hypotheses can lead to a high-quality combined alpha vector. For example, a price-driven alpha such as the momentum alpha may combined well with an alpha based on company fundamentals since the inputs are very different. In this phase, alphas may be combined using simple logic like adding ranks are averaging, or through more complicated waiting schemes like finding the weights that lead to the lowest possible variance for the combined alpha. Another possible method is to translate your alphas into features and use them as inputs to a machine learning classifier to capture the relationships between the alphas. The output of this stage is a single alpha vector that incorporates the information of many individual alphas.