Final answer:
The arithmetic average return for the stock over the past four years is calculated to be 9.12%.
Step-by-step explanation:
The arithmetic average return for the stock over the past four years can be calculated by adding the returns for each year and then dividing by the number of years. To find the average return, we sum up 11.87%, -16.04%, 21.06%, and 19.59% and then divide the result by 4.
The calculation:
(11.87 + (-16.04) + 21.06 + 19.59) / 4 = 36.48 / 4 = 9.12%
Therefore, the arithmetic average return for the stock is 9.12%.
The arithmetic average return for a stock over a specified period is determined by summing the individual returns for each year and dividing the total by the number of years. For the past four years, with returns of 11.87%, -16.04%, 21.06%, and 19.59%, the calculation is as follows:
\[ \text{Average Return} = \frac{11.87 + (-16.04) + 21.06 + 19.59}{4} = \frac{36.48}{4} = 9.12\% \]
Hence, the arithmetic average return for the stock over the given four-year period is 9.12%. This metric provides a simplified measure of the stock's performance over the specified timeframe, offering a standardized representation of the annual returns. However, it's important to note that the arithmetic average return has limitations, especially in capturing the effects of compounding and fluctuations in the stock's value over the years.