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"Though I appreciate that, in my experience as a money manager few investors prefer to buy shares at ~$134000 rather than ~$130000 the same day."

Surely you are correct, but I doubt Mr. Buffet informed Mr. Tilson of the impending increase in price before he informed anybody else.

Before the buyback, without hindsight, Tilson's IV estimate realized over 5 years would have given him something like a 15% annual return expectation with some estimate of 3-month or 6-month or 12-month downside risk. After the buyback, without hindsight, his IV estimate would give him something like a 14% annual return (~92% of prior return estimate). The downside deviation was clearly reduced by more than 8% of its prior value. So I think it is a very reasonable decision to increase purchase activity on behalf of your clients in that scenario, if 3/6/12 month downside risk is important to them as it nearly universally is.

"The major change was an increased price and a firmer short term downside.
It appears to me that the major beneficiary from increasing allocation
after that, because of that, is the manager rather than the client."

But why does it benefit the manager at all? Asset retention, right? Asset retention is just another way to say that you didn't do something to make your client fire you. So is pursuit of asset retention all that different from pursuit of clients' objectives? The alignment is even more clear if you believe (as I'm sure Tilson does) that your management can generate more alpha than the competitors who would stand to absorb your clients' allocations.

But I'll let that be my last word on the issue, as I understand and respect your perspective as well. You can close the topic with your thoughts if you'd like.
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