The paper titled, The Formation Process of Winners and Losers in Momentum Investing, discusses how the trajectory of a stock is an indicator for whether its momentum is accelerated or decelerated. When a stock is recently showing higher returns, this paper refers to these as accelerated gains. When a stock is recently showing minimal positive returns, the paper refers to these as decelerated gains. If you look at a stock price trajectory of an accelerated gain, the shape will be convex. In case you can’t remember what a convex curve looks like, the plot of y equals x squared is an example of a convex function. Essentially, the trajectory is showing an accelerated increase. On the other hand, a stock price trajectory of a decelerated gain will have a concave shape. As a reminder of what concave means, a plot of y equals the square root of x is an example of a concave function. The trajectory is showing a decelerated increase. We can also describe accelerated losses and decelerated losses as concave or convex. An accelerated loss has a concave shape. You can imagine the plot of y equals negative x squared as a concave function. A decelerated loss has a convex shape. You can imagine the plot of y equals negative square root of x as a convex shape. So far, we’ve described four general shapes. What we want to point out is which type of trajectory may be preferred for going long or going short. We’d say that an accelerated gain may have higher future returns compared to a decelerated gain, if the starting and end points are the same. So, we would prefer to go long the accelerated gain, a bit more than the decelerated gain. We would also say that an accelerated loss is predictive of more negative returns compared to a decelerated loss. So, all else being equal, we would prefer to short the accelerated loss more than the decelerated loss. An important point that might not be obvious to see in the paper is that we can view the convexity or concavity of a curve in a relative terms. In other words, compared to a convex curve, a straight line is relatively more concave. Likewise, compared to a concave curve, a straight line is relatively more convex. You may recall with the example of the tortoise stock and the rabbit stock. The tortoise stock trajectory look like a straight line, whereas the rabbits stock was concave. So, relative to the rabbit stocks trajectory, the tortoise stocks trajectory was more convex and also more predictive of higher future returns under this hypothesis.