## Monday, March 9, 2009

### Why do you need to earn a higher rate than the percentage of investment loss?

Overview
One thing that confuses many investors is the fact that any percentage loss must be recovered by earning a higher rate of return than the percentage of loss (will illustrate this with examples later in this article). Accredited investors are aware of this difference and understand the relationship between percentage loss and percentage required to gain back the loss. This article will provide the math behind the relationship in a easy to read format. I’ll first look at the mathematical equation used to calculate the percentage loss of an investment. Then I’ll look at the mathematical equation to calculate the percentage gain required to make up a loss. By the end, you will be able to understand what percentage of a gain is required to make up for any loss in your investment. This knowledge is required to accurately manage your investments while implementing your long term investment plan.

We now consider the equation for calculating the percentage of loss.

Equation to calculate the percentage of loss:
Percentage loss = (Initial value – current value)/initial value

If you lose money, the loss is based on the initial value of the investment. You consider what the value was initially and what it is currently. The difference between the two is the amount of loss. That is where the equation shows (Initial value – current value). Then to get the percentage of loss, you need to divide this amount of loss by the initial value of the investment. The idea is the find out how big this loss is when compared to the initial value of the investment. That is where you see this difference between the initial and current value being divided by the initial value in the equation. The result of this division tells you what percent of the initial investment was lost. Now consider an example to help understand the equation better.

An example of a 25% loss:
For this example, lets assume Joe had a retirement account with \$100,000. Now, some time later, the account is worth \$75,000. I will walk through the percentage of loss equation to calculate the percentage of loss.

Percentage loss = (\$100,000 - \$75,000)/\$100,000
Percentage loss = \$25,000/\$100,000
Percentage loss = 25%

So we calculate that a drop from \$100,000 to \$75,000 is a 25% loss.

You can’t get back your investment by earning the same percent that was lost
You may be tempted to think a 25% gain is needed to get back to \$100,000. However, the problem is Joe now only has \$75,000 to start with. The amount of gain required is against \$75,000, not against \$100,000. The 25% loss was against the initial \$100,000 account value and any percentage gain must now be against the remaining \$75,000. Before calculating the percentage gain required to get back to the initial \$100,000, consider the associate equation…

Equation to calculate the percentage of gain required to make up a loss:
Percentage gain required = (Initial value – current value)/current value

Did you notice the very slight difference in the equation? The only change was dividing the loss by the current value of the investment instead of dividing by the initial value. This is required since you are starting with the current value that remains after experiencing the loss. You need to know what percent of additional funds are required against the current value to get back to the initial value. Now use the equation against the above example to find out what gain is required to make up for the 25% loss.

Calculating the percentage gain required to make up for the 25% loss:
Using the above equation for calculating the percentage gain required,

Percentage gain required = (\$100,000 - \$75,000)/\$75,000
Percentage gain required = \$25,000/\$75,000
Percentage gain required = 33.3%

So, we need to earn 33.3% against the remaining \$75,000 in order to get back to the initial \$100,000. Now consider additional examples.

Example of a 50% loss and calculating the percentage gain required:
Here Joe’s \$100,000 initial account value drops to \$50,000. Calculate the percentage loss first…

Percentage loss = (\$100,000 - \$50,000)/\$100,000
Percentage loss = \$50,000/\$100,000
Percentage loss = 50%

Since the current value of the account is \$50,000, what percentage gain is required to get back to the initial \$100,000 value?

Percentage gain required = (\$100,000 - \$50,000)/\$50,000
Percentage gain required = \$50,000/\$50,000
Percentage gain required = 100%

Joe now needs to earn 100% against his remaining \$50,000 value to get back to the initial \$100,000 value of the account.

Example of a 75% loss and calculating the percentage gain required:
Here Joe’s \$100,000 initial account value drops to \$25,000. Calculate the percentage loss first…

Percentage loss = (\$100,000 - \$25,000)/\$100,000
Percentage loss = \$75,000/\$100,000
Percentage loss = 75%

Since the current value of the account is \$25,000, what percentage gain is required to get back to the initial \$100,000 value?

Percentage gain required = (\$100,000 - \$25,000)/\$25,000
Percentage gain required = \$75,000/\$25,000
Percentage gain required = 300%

Joe now needs to earn 300% against his remaining \$25,000 value to get back to the initial \$100,000 value of the account.

Recap of above examples:
If Joe has a 25% loss, he needs to invest in something that will provide a 33% gain against his remaining funds to get back the loss.

If Joe has a 50% loss, he will need a 100% gain against the remaining funds.

If Joe has a 75% loss, he will need a very high 300% gain.

Summary
As you can see, there is a very large difference between the percentage loss of an investment and the required percentage gain to get back to that initial value. The higher the loss, the dramatically higher the required gain will be to make up for the loss. As the amount of loss increases, the required gain to make up for the loss increases much more since the remaining funds get smaller to use for making back the much larger loss. Again, seasoned investors, such as active accredited investors, understand this relationship between percent loss and percent gain required to make up the loss. Understanding the relationship will allow you to consider which investment strategy to consider as you move forward toward your long term financial goal.

Copyright 2009 Ole Cram, President of Marcobe Investments, Inc.
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