Lesson 9 of 25 · 7 min

Loss aversion, and why a decline is held rather than acted on

A round trip in price is not a round trip in position, because the balance kept moving while the price came back.

Loss aversion is the asymmetry by which a loss of a given size registers more heavily than a gain of the same size. Its most visible consequence is a boundary effect around zero: the state of not having lost anything is defended much harder than an equivalent amount of gain is pursued.

In a pledged account the boundary is drawn at the purchase price, and the purchase price is a fact about the past that appears in no clause and no calculation. Take 3,650 shares bought at $88.10, a position of $321,565, now trading at $71.40, a position of $260,610. The fall is ($88.10 − $71.40) ÷ $88.10 = 19.0 percent and the rise needed to undo it is $16.70 ÷ $71.40 = 23.4 percent.

Against a balance of $164,000 the loan-to-value is $164,000 ÷ $260,610 = 62.9 percent today. Suppose the price does return to $88.10, and suppose it takes nineteen months, with the balance capitalising at an illustrative 8.1 percent. The balance is then $164,000 × (1 + 0.081 ÷ 12)^19 = $186,361. The position is worth $321,565 again, and the loan-to-value is $186,361 ÷ $321,565 = 58.0 percent, against the 51.0 percent it was at that same price before the decline.

The price came back and the position did not. Seven points of loan-to-value were consumed by $22,361 of interest during the wait, and that consumption is a function of the duration rather than the depth of the drawdown. A deeper fall that recovers quickly costs less than a shallow one that takes years.

The word even is doing the work here. It refers to the price, which is one of the two terms in the ratio, and the boundary is felt as though it referred to the position.

Key terms

Loss aversion: Weighting a loss more heavily than a gain of equal size, which makes the point of zero loss a boundary rather than just another number.
Break-even price: The price at which a holding has returned to its purchase cost. It says nothing about the loan that has accrued in the meantime.
Duration of a drawdown: How long a decline lasts, as distinct from how deep it goes. Interest accrues on the first and is indifferent to the second.

Worked example

Back to the same price, not to the same position

3,650 shares bought at $88.10, falling to $71.40 and returning to $88.10 nineteen months later. Balance $164,000, capitalising at an illustrative 8.1%.

Position at the purchase price: $321,565
Loan-to-value at that price, before the fall: 51.0%
Position at $71.40: $260,610
Balance after nineteen months: $186,361
Loan-to-value back at $88.10: 58.0%

The chart returned to where it started and the loan-to-value was 7.0 points worse. $22,361 of interest is the difference between the two.

Check yourself

A holding falls from $88.10 to $71.40 and returns to $88.10 nineteen months later. The balance of $164,000 capitalised at 8.1 percent throughout. Is the position where it started?

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.