How is annual return (annual r) calculated?

The calculation of annual return, represented as annual r, is derived from the total price change over a specific period, typically expressed as a percentage. The correct formula recognizes that returns compound over time, which is crucial for understanding investment performance.

Using the formula ( \text{Annual r} = (1 + \text{percent change in price})^{12} - 1 ) accurately reflects the compounded nature of returns by applying the compounding effect over a period of one year, assuming monthly data. By raising the result of (1 + \text{percent change in price}) to the power of 12, you account for the effects of compounding, which results in a more accurate representation of how much an investment would grow over a year if the same return were achieved each month.

In contrast, the other choices misrepresent the calculation either by not accounting for compounding or by incorrectly manipulating the return calculation. For example, multiplying by 12 does not properly address compounding, and merely dividing by 12 fails to provide a compounded annual growth rate necessary for proper estimations of financial returns over a year.