First off thank you for the lucid explanation, it helped a lot and I think I get the intuitional idea behind it now.
The formula takes minimum of the two because the idea is to identify the replaced securities in that period. The difference between the total buys and total sells is actually the cash inflow/outflow into/from the fund. Adding up the total buys and sells is actually leading to double counting of the actual value of the replaced securities within the fund. Replacement is essentially selling asset(s) and buying another or vice-versa of equal value, any buying/selling over this value is actually cash inflow/outflow.
So the formula doesn’t include cash inflow/outflow in the calculation, if it did, turnover ratio for newly established funds would be 100% or more, which its not as you rightly pointed out.
And lastly I am planning to keep an eye out on this ratio (or some other form of it), since turnover comes with costs, which itself end up compounding in long term.
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