How is the annualized return for an evaluation period calculated?

The annualized return for an evaluation period is correctly represented by the formula shown in the chosen answer. This approach accounts for the effect of compounding, which is essential when assessing returns over multiple periods.

The formula ([(1+r1) \times ... \times (1+rn)]^{\frac{1}{n}} - 1) effectively compounds each return over the evaluation period. By multiplying the growth factors ( (1 + ri) ) for each period and then taking the ( n )th root of the product, you derive the average compounded growth per period, which reflects how investments grow over time.

This is a critical aspect in financial analysis because investors are often more interested in understanding how their investments would perform if they are able to reinvest returns rather than just looking at arithmetic averages. Arithmetic averages can misrepresent the potential performance, especially when dealing with volatile returns, as they do not account for the effects of compounding.

The other choices do not appropriately capture the concept of annualized returns. For instance, simply averaging returns or dividing cumulative return by total years does not consider the compounding effect, and calculating return based on the final and initial value fails to reflect returns over an extended period accurately when there are multiple