Estimation of holding periods applied to the case of short and leveraged ETFs

The estimation of the holding periods of financial products has to be done in a dynamic process in which the size of the observation time interval influences the result. Small intervals will produce smaller average holding periods than bigger ones. The approach developed in this paper offers the possibility of estimating this average independently of the size of this time interval. This method is demonstrated on the example of two distributions, based on the exponential and the geometric probability functions. The estimation will be found by maximizing the likelihood function. The two examples will finally be applied to the financial instrument Exchange Traded Fund (ETF). The analysis contains ETFs with leverage factors of -2, -1, +1 and +2. Although different ETFs are treated, the majority of the data is concerned with the 'db x-tracker ShortDAX ETF', 'db x-trackers DAX ETF', 'iShares DAX (DE)' and the 'Lyxor ETF LevDAX'. By the application of the proposed estimation approaches, the average holding periods of ETFs increase by 4%-29%. This increase depends on the time interval T of observation, the leverage factor, and the average holding period.