A cost basis records a historical fact and nothing beyond it. One particular person, on one particular day, completed a transaction at one particular price. No causal relationship exists between that fact and the asset's subsequent performance. The market does not know anyone's cost, and its path is not altered by where any participant happens to have transacted. Considered as an input to valuation, the information content of a cost basis is approximately zero. It is a fact about the holder, and what the market prices is the holding.
In practice, however, it is displayed in the most prominent position available and colour-coded by sign. That design takes a continuous axis of prices and cuts it into two categories of entirely different character. A substantial body of behavioural research shows that people apply different decision rules within each of them. In the gain region they tend towards realising, and in the loss region they tend towards accepting additional risk in pursuit of recovery. The same investor, facing the same asset, becomes two different investors depending on which side of an arbitrary line they stand.
The most common expression of this is waiting to get back to even. Somebody knows perfectly well that a position no longer matches the judgement that established it. They resolve nonetheless to hold until the price returns to the original level. That resolution makes the timing of the sale depend upon the transaction price. The transaction price is the one variable in the entire situation with no bearing on the asset itself. An investment decision has, in effect, been handed over to a historical record.
Less remarked upon is the way a cost basis distorts decisions to add. Below the original price, adding is naturally described as averaging down. Above it, an identical action is described as chasing. Both descriptions refer to precisely the same behaviour, and the only thing separating them is where the reference point happens to sit. An investor may therefore reach opposite conclusions about two identical opportunities, for no better reason than the price at which the first transaction happened to occur.
One qualification deserves stating plainly, since the argument would otherwise be too tidy. A cost basis is not useless in every context, because it determines tax liability. Tax is a real cost, and a real cost legitimately enters a decision. The distinction lies between using the number to calculate a consequence and using it to settle a view. The first is arithmetic and belongs within the analysis, while the second is anchoring and does not. In practice the two are easily confused, because the tax argument is always available and always sounds rigorous.
The only question with any bearing on the present is a simple one. At today's price, and with what is known today, would this position be established at all? Answering it requires no reference to the cost basis whatever. Holding an asset one would not acquire today and acquiring an asset one would not hold today are economically the same act. The first merely feels like waiting, while the second feels like a mistake. The distinction is carried almost entirely by feeling, and the arithmetic contributes nothing to it.
Awareness alone does not remove the bias, because it is embedded in the interface, in the records, and in every act of checking a position. What can be done is to restate the question deliberately each time the portfolio is reviewed. Changing how a question is phrased does not change the asset in any respect. It changes which set of decision rules gets applied to it, and that is usually where the outcome was decided long before any transaction took place.