Going back to the question I asked earlier, based on whether the gain coefficient and the accelerate coefficient are positive or negative, can you decide which scenarios we would rather go long or short? We’ll take a look at how the coefficients of the stock price approximation formula can inform our decision as to which stock we should go long or short. This in turn allows us to create an alpha factor based on these two coefficients. Let’s take an example of two stocks, A and B. Stock A has a gain coefficient of 10 and an accelerate coefficient of two. Stock B also has a gain coefficient of 10 and accelerate coefficient of negative two. If you were going long both stocks, which one would you put more weight on? Since stock A has the trajectory of an accelerated gain, whereas stock B looks like a decelerated gain, we would put a larger long wait on stock A, the accelerated gain. Let’s look at another example with two downward trending stocks. Let’s say stock C has a gain coefficient of negative 10 and accelerate coefficient of two. Stock D has a gain coefficient of negative 10, as well as an accelerate coefficient of negative two. If you were to go short both stocks, which one would you put a larger short position on? In this case, stock C has the trajectory of a decelerated loss, and stock D has the look of an accelerated loss. So, you’d prefer to put a larger shortwave on stock D, the accelerated loss. Now, you may have noticed something interesting with the signs of the gain and the accelerate coefficients. When the product of gain times accelerate is positive and large, the signal generally means to take a larger long position. When both are negative, the signal means to take a larger short position. If we were to convert the gain and accelerate coefficients into ranks then multiply them together, the product of the gain times accelerate would represent an alpha factor. When the rank of gain and the rank of accelerate are both small, the product is small, and this is a signal to take a larger short position. If the rank of gain and the rank of accelerate are both large, then the product is also large, and this is a signal to take a larger long wait. This is our first conditional factor. The key idea is that when you see and think conditional. Here, we have momentum and convexity. So, to summarize, we can use a multiple regression where the independent variables are time and time squared, and the dependent variable is the stock price. This regression gives us estimates for the coefficients gain and accelerate. We create our factor by first converting gain and accelerate into ranks, and then multiplying the ranks together to create a joint factor.