Compounded Two-Period Return

Simple returns over multiple periods compound multiplicatively, not additively.

Compute the ratio of the final price to the initial price and subtract $1$.

1. 1. Multiply the gross returns

   The gross return over both periods is the product of each period's gross return.

   $$\frac{110}{100}\times \frac{99}{110}=\frac{99}{100}=0.99$$

2. 2. Convert to a simple return

   Subtracting $1$ from the gross return gives the total simple return.

   $$0.99-1=-1\%$$

Answer: -1%