Imagine that a financial advisor is talking with a client who asks the advisor two questions:
- How well has the S&P/TSX Composite Index performed on average over the last five years? and
- How well has the ABC Canadian equity mutual fund performed over the last five years?
While both questions appear to require a response based on a common return, what return to quotemakes the difference between a valid response and a misleading response?
When quoting an annual return it is important to know whether the returns each year are independent of each other, or whether the returns are dependent/linked together. If the returns are independent of each other, an arithmetic (mean) return can be quoted. If the returns are linked together, a geometric (mean) return should be quoted.
In the question, “What did the S&P/TSX Composite do on average over the last five years?”, the returns on average are independent. Assume the following hypothetical returns for the S&P/TSX composite: