I want to calculate the Turnover of my scaled Momentumportfolio (Barroso und Santa-Clara 2015) They described Turnover Ratio with the following formula:
While i understand the general concept (without Lt):
Why does the weighting factor (Lt) impact the Turnoverratio in the shown way.
If i got a scaling factor (Lt) of 2, everything would be scaled by 2 but the percentage Turnover Ratio wouldn't be the same ?
So in this case a lower (higher) weighting would cause a lower (higher) Turnover Ratio.
Any one able to explain this ?
(the 0.5 is because its a Long-Short Portfolio, so the formula is for each leg)