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Interpreting Return on Investment for a Loss

Article Quant Q&A · Author: ddxv
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Summary

The document explains how to interpret return on investment when an investment loses money. It applies the standard formula, dividing the gain or loss by the initial cost, to an example in which an investment’s value falls from 24 to 2. The resulting ROI is negative because the investment lost value relative to the amount originally invested.

The questioner compares the loss with the small amount left and finds that comparison confusing. The answer clarifies that the loss percentage uses the original cost as its denominator: the loss of 22 is 91.67% of 24, so the ROI is a 91.67% loss. The comparison to the remaining value uses a different denominator and does not represent ROI under this definition. The treatment is limited to this simple example and does not cover other performance measures, cash flows, or conventions for calculating returns.

Key ideas

  • ROI measures gain or loss relative to the original investment cost.
  • A negative ROI represents a loss as a fraction of the initial cost.
  • The denominator matters: comparing a loss with the remaining value answers a different question.
  • The example illustrates a loss of 22 against an initial cost of 24.

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StatisticsRisk management
Full text
# How to Calculate a Negative ROI?


# How to Calculate a Negative ROI?












How to properly calculate negative ROIs?

I am just wanting to calculate very simple ROIs, which could be very negative, but it doesn't seem to work.

Wikipedia defines ROI as this formula:

> return on investment = (gain from investment – cost of investment) / cost of investment

This doesn't seem to work right for negative numbers, for exmaple:

If I spend 24.00 and make 2.00 my calculation would be:

> (2-24) / 24 = -91.67%

This doesn't make sense to me, seeing as the total amount I lost was 22 which is 1000% of 2.

I hope someone can help explain what I am misunderstanding, or if there is a better way to work with negative ROI.

## Answer by Chris Degnen (score 0, accepted)

https://quant.stackexchange.com/a/31076

You made a 91.67 % loss. 91.67 percent of 24 being 22.

ROI = -91.67 %

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.