Final answer:
Karen's tax basis in the inherited stock portfolio is the fair market value at the time of her grandmother's death, which is $250,000. This determines potential capital gains or losses when Karen decides to sell the stocks.
Step-by-step explanation:
When inheriting a stock portfolio, the tax basis for the beneficiary (in this case, Karen) is generally the fair market value of the stock on the date of the decedent's death, not what the stock was originally purchased for. Because Karen's grandmother's stock portfolio was worth $250,000 at the time of her grandmother's passing, this value becomes Karen's tax basis in the stock portfolio.
The tax basis is important because it determines the capital gains tax Karen would potentially have to pay if she sells the stocks. Should she sell the stock at a price higher than $250,000, she would owe taxes on the gain above this basis. Conversely, if she sells the stock for less than her tax basis, she would have a capital loss which can offset other capital gains or up to $3,000 of ordinary income.