Final answer:
When the S&P500 index goes up by 10% and then down by 10%, you are not back where you started.
Step-by-step explanation:
When the S&P500 index goes up by 10% and then down by 10%, you are not back where you started.
To understand why, let's assume that you initially had $100 invested in the S&P500. When the index goes up by 10%, your investment would increase to $110. However, when the index goes down by 10%, your investment would decrease by 10% of $110, which is $11, leaving you with $99.
Therefore, you end up with $99, which is not the same as your initial investment of $100, indicating that you are not back where you started.