So far, we’ve been looking at simple individual alpha factors. But there are times when we can create factors that are conditioned on another factor. We can create a conditional factor by multiplying two factors together. For example, if factor A gives an alpha value for a single stock, and factor B gives a different alpha value for that same stock, then we can create a conditioned, alpha value for that stock by multiplying those two separate alpha values together. Early on in my career, it was the case that some fairly simple, at least as thought of in hindsight today, factors could be profitable in live trading. Markets though have become much more competitive as time has marched on and as data, tools, and knowledge have become more available. Today, it’s likely that you need to find conditionals to make really good alpha factors as such, this section is critical. So, how do we interpret what this multiplication is doing? We’ll first look at a common practice in academic papers, which we’ll refer to as quantiles of quantiles. If a research paper is looking at the effects of one factor condition on another, they would divide the data into quantiles for one factor. Let’s say we’re using 10 decile groups, then within each decile group they would split the stocks into another 10 decile groups based on the second factor. So, now we have 100 quantile groups conditioned on two factors. Because we have 10 deciles based on one factor and each decile group has 10 deciles based on the second factor. Now, let’s see what happens if we create a condition factor based on two factors. Let’s say we have a stock universe of 100 stocks and we’ll convert signal A and signal B into scores from one to 10 for each signal, then we’ll calculate the conditional factor as signal A times signal B. Let’s pause a moment to think what multiplication means visually. If you remember learning your multiplication tables as a kid, you might remember seeing a rectangular grid with a column of numbers 1-10 along the left edge and the numbers 1-10 above the top. Multiplying the two numbers for each row and column allows us to fill all the boxes inside the multiplication table. This is exactly what we’re doing with our two factors. As you can see, the product of A times B, ranges from a value of one to a value of a hundred. Notice that, not all the values in between one and 100 are represented, as there are some numbers that occur twice. However, overall, you can see that there is a range of values between one and a hundred. Does this look familiar to you? When we discuss the process of calculating deciles nested inside deciles, we also ended up with 100 groups. Even though multiplication of the two factors does not give the exact same groupings as we would get from nested quantiles, they have the same goal of creating a composite factor that is conditioned on the value of both the individual factors. We will seek some conditional factors in detail when we analyze some research papers to generate factor ideas. When you read ideas or hypotheses like, stocks that go up on high volume are likely to revert, or momentum is more pronounced on stocks with low volume, you need to use conditionals. Also, whenever you see the word or concept of end, it is likely that you need to use a conditional.