Appendix C: Computing Holding Growth and Rebalancing Growth

By Jesse Livermore, Chris Meredith, and Patrick O’Shaughnessy
May 2018

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To calculate the holding growth and rebalancing growth of a strategy over a given period, we start by separating out all of the holding periods and associated rebalancing events. We then go through each holding period and each rebalancing event and compute the change in the fundamental. After we have those numbers, we then calculate the arithmetic average holding growth across all holding periods and the arithmetic average rebalancing growth across all rebalancing events. Finally, we scale those averages by an adjustment factor that brings their sum equal to the actual overall EPS growth. 

The table below provides an illustration: 

After separating out all of the holding periods and rebalancing events, we calculate the change in EPS that occurs in each. In this case, each holding period sees a 0% change in EPS and each rebalancing event sees a 50% change. We average all of the holding period changes together to get 0% average holding growth for the overall period. Similarly, we average all of the rebalancing event changes together to get 50% average rebalancing growth for the period. We then scale those numbers, 0% and 50%, so that they sum to the actual overall EPS growth for the period. Since that overall growth is also equal to 50% [(337.5/100)^(1/3)-1=50%], there is no need to scale the numbers in this case. 

Using the actual numbers from the decomposition of the top quintile of the Value factor, suppose that the overall EPS growth is 13.33% and the average rebalancing growth and average holding growth is 26.93% and -15.02%, respectively. These numbers--26.93% and -15.02%--do not sum to 13.33%. So we scale them to sum. We calculate the holding growth as -15.02%/(26.93%-15.02%)*13.33% = -16.80% and the rebalancing growth as 26.93%/(26.93%-15.02%)*13.33% = 30.13%. Notice that 30.13%-16.80% = 13.33%, which is the overall EPS growth for the period. 

This technique is not literally valid in the mathematical sense. EPS growth is a single compound process and cannot be split into separate compound processes that then add together. We use the technique only as a heuristic to generate numbers that are intuitive.

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