Asset turnover is a statistic that applies to any fund (i.e., a combination of assets) over a period of time. Asset turnover is a measurement of how much rebalancing was necessary over time to achieve the actual weightings of the assets in the fund.
To calculate the turnover from one period to the next, we first calculate the weight that each asset would have in the next period if no rebalancing had taken place. From that, we subtract the weight that the respective asset actually had in the next period. The total asset turnover is the sum of the absolute values of these differences divided by 2. The division by 2 is necessary because by adding the turnovers for all assets, we have actually counted every shifted dollar twice: once when it was taken from one asset and then again when it was added to another.
The annualized cumulative asset turnover is the sum of the turnovers for all periods as described above, divided by the number of years.
When calculated for a Style Benchmark, a high Turnover will denote a shift in style.
Asset turnover from period j to period j+1 =
m = number of assets that make up the fund
wij = weight of i-th asset for j-th period
rij = return on i-th asset in j-th period
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