# 13 – M4 L3a 12 Return Denominator Leverage And Factor Returns V3

Let’s get back to the interpretation of the factor return. When initially learning about alpha factors, the magnitude of the return can create some confusion. In the alphas we work with below the annual returns range from 1%-4% or so. Let’s be honest, that seems really small, is that what institutions really want from their researchers? The key to placing these returns and context is to understand the concept of the return denominator in research and the actual leverage likely to be used in production trading. Let’s first define return denominator, when we normalize an alpha vector one of the steps is to sum up the absolute values of the alpha values, then divide each value by the sum in order for the normalized vector to have the sum of absolute values equal to one. The sum of the absolute magnitudes of the alpha values is the denominator that I’m referring to. Leverage is the act of borrowing money in order to take positions in assets like stocks. The leverage ratio is the sum of the absolute value of all positions long and short divided by whatever capital we actually devote to supporting those positions. This concept will likely become more clear when we study backtesting in term two, until then, think about it this way, a trading strategy produces dollars of gains and losses, to convert those dollars in terms of returns or in return space, we need to divide by some denominator, which in this case is called the capital denominator. At the research stage, we ignore this and simply assume one dollar of capital to one dollar of longs and shorts. When we increase leverage by putting less than one dollar of capital against one dollar of positions, the leverage ratio increases. A leverage ratio of one means we apply one dollar of capital for one dollar of positions. A leverage ratio of four means, we apply 25 cents of capital for one dollar of positions. In research, we are looking at the return of the normalized alpha factor, the denominator is one, which implies a leverage ratio of one. In a real trading, we would combine several factors and then apply leverage, depending on the final portfolio, an institution might apply leverage of anywhere from two times to six times. In the context of that leverage the magnitude of the alpha factor returns start to make sense and likely look comparable to the published returns observable from hedge fund return indices. This insight should also help explain why I continually refer to implementing this style of trading as inside an asset management firm. It would be very unlikely that an individual, could obtain the necessary leverage and low-cost market access to allow him or her to trade in this style, in an individual brokerage account.