Mueller's case (Reading 8 Problem 11)

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In the answer part of unique circumstances, it is said the stock position can be reduced by at least 50% without reducing the asset base to pay a tax obligation.
If the stock position is reduced , won’t it reduce the asset base to pay taxes?
 
I guess the explanation here is Muellers are holding low basis stock. If they sell the stock, they will be liable for capital gain. But they could offset the capital gain with the tax loss carry forward. So they don’t have to pay any taxes, and their asset base will not be reduced.
 
When you reduce your asset base this triggers a tax event. So reducing asset base means paying more taxes. (liquidate your portfolio)
We are told the Mueller’s investment portfolio amounts to 600k, one third of which is invested in the stocks of Mueller’s employer and these stocks have very low cost basis. That’s 200k worth of low cost basis stocks in a“technology company with a highly uncertain future” .
To reduce this kind of risk exposure it is suggested to utilize the 100k tax losses by selling at least 50% and offsetting the capital gains with these losses.
If the above mentioned cost base is NIL then you can sell exactly 50% of 200K to achieve 100K capital gain. The answer also recognizes the fact the cost base is probably more than NIL so you can liquidate MORE than 50% without paying any tax using the below formula:
200k-cost base) * X=100k
So for example if cost base is 20K then X=55.5%
 
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