In a scenario where you invest $1,000 and your total return after two years is a 10.26% loss, what is your average annual loss?

To determine the average annual loss when you experience a total return of 10.26% loss over two years, you need to understand how losses compound over multiple periods. The average annual rate of return is calculated by dividing the total return by the number of years, but when dealing with a loss that compounds, the approach is slightly different.

In this situation, a total loss of 10.26% means that after two years, your investment's value reduced to 89.74% of its original amount. To find the average annual loss, you can use the formula for the average annual rate of return derived from the compound annual growth rate (CAGR) formula, which accounts for the compounding effect:

1. Convert the total percentage loss into a multiplier: 100% - 10.26% = 89.74%, or 0.8974.

2. Set this equal to (1 + average annual rate) raised to the power of the number of years. For this scenario:

   [ 0.8974 = (1 + r)^2 ]

3. To isolate ( r ), take the square root of both sides:

   [ \sqrt{0.897