🔺A 50% Gain Doesn’t Equate to Breaking-Even on a 50% Loss

One of the most important and often forgotton concepts is the percentage relationship between gains and losses. Why is it so important? Because the relationship is non-linear. Therefore, required gains to break-even grow exponentially as losses increase in percentage terms.

For example, if you bought a stock that is priced at $10 and it goes down to $5 that is a 50% loss. It might not seem like much as the decline in nominal terms is only $5, so it should not be all that difficult for there to be an incremental $5 increase to get back to $10 at which point you break-even, right? No. The required increase in percentage terms from $5-to-$10 is actually 100% and for the stock to increase from $10-to-$15 for a gain of $5 from the initial cost basis of $10, but at the current price of $5 is 200%. As you can can see, the gains that are required to break-even or generate a return are not proportional to the loss in percentage terms, although it seems simple in nominal terms. How is this knowledge helpful and applicable?

The above link demonstrates the required percentage gain required to break-even on percentage losses (5%-100%). For example, at a 5% loss, the required gain to break-even is 5.26%. At a 10% loss, the required gain to break-even is 11%. At a loss of 20%, the required gain to break-even is 25%. At a 30% loss, the required gain to break-even is 43%. The required incremental gain to break-even went from 0.26%-to-13%.

Based on this data, nobody should accept losses beyond 20% as the required percentage gains to break-even really begin to grow exponentially. Additionally, a person could easily look at their performance and set additional boundaries based on their maximum and average percentage gains. If the maximum percentage gain on any project has never been above 20%, then there should not be any reasonable expectation to believe that break-even could occur on losses of 20% or greater. If the average gain on projects has been 10%, then its also reasonable to set a boundary of automatically cutting your losses at 10%-15% on projects and move-on.
That is why it is better to cut losses sooner rather than later as the opportunity costs compound exponentially. Additionally, by setting such boundaries, it limits the ego, cognitive errors and human emotion.

It should be noted that the above example is universal and does not merely apply to stocks.

Please refer to the report on Intangible Costs: A Businesses’ Greatest Costs are Intangible in Nature https://internationalcapitalmarkets.org/2019/09/07/a-businesses-greatest-costs-are-intangible/

Published by Diamond1

I have an extensive background throughout the financial spectrum with high-level experience on the sell-side, high-net worth private banking, portfolio management, international finance, public pensions, VC, PE, and economics. I enjoy working and collaborating with people that I admire and trust.

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