# How to calculate Turnover Ratio of a scaled Portfolio

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)

• How is $L_t$ defined? It seems to be the inverse of how I would define leverage. – Alex C Sep 20 at 1:41
• The Authors define the weighting of the strategy as : target volatility/estimated volatility) So the strategy is scaled up, if the estimated volatility is low. So a higher weighting (Lt) would result in a scaled up strategy – KDMS Sep 20 at 12:51