## Explanation

In this example, the goal is to calculate the required recovery rate (or gain) to complete offset a loss expressed as a negative percentage. This is not a difficult problem, but you must pay attention to the sign of the loss and be sure to format the result with the percentage number format.

### Background

One of the most important aspects of investing is the math of gains and losses. A 50% loss does not require a 50% gain to recover the loss, it actually requires a *100% gain*. Put simply, as a loss gets larger (as a percentage), the recovery rate (or gain), required to offset the loss *increases at an increasing rate*:

- A loss of 10% requires a gain of 11.1%
- A loss of 20% requires a gain of 25%
- A loss of 50% requires a gain of 100%
- A loss of 80% requires a gain of 400%

### Formula

With a loss expressed as a percentage, you can calculate the required gain or recovery rate with a formula like this:

`=1/(1-%loss)-1`

The formula above assumes the loss is given as a *positive* percentage. If the loss is given as a *negative* percentage (as in the worksheet shown), use the modified formula below:

`=1/(1+%loss)-1`

In the worksheet shown, the loss percentages are in column C. The formula in F5, copied down, is:

`=1/(1+C5)-1`

This formula evaluates like this:

```
=1/(1+-0.05)-1
=1/(0.95)-1
=1.0526-1
=0.0526
=5.3%
```

The result is a decimal value that should be formatted with the percentage number format.

### Formula check

To check the calculated recovery rate for each loss, the formula in G5, copied down, is:

`=D5*(1+F5)`

This formula simply multiples the result in column D by 1 plus the recovery rate. In all cases, it should return the initial value in column B, proving that the recovery rate will completely offset the loss.