To calculate the standard deviation of the stock's returns, we first need to calculate the average (mean) return and then the deviations from the mean for each year. Here’s the step-by-step calculation:

Step 1: Calculate the Mean Return

The returns for the past three years are: $17.35\%, -6.95\%, \text{and } 23.75\%$ The mean return is: $\text{Mean} = \frac{17.35 + (-6.95) + 23.75}{3} = \frac{34.15}{3} = 11.3833\%$

Step 2: Calculate the Deviations from the Mean and Square Them

Now, we calculate the deviation of each return from the mean and then square each deviation:

1. $(17.35 - 11.3833)^2 = (5.9667)^2 = 35.6006$
2. $(-6.95 - 11.3833)^2 = (-18.3333)^2 = 336.1389$
3. $(23.75 - 11.3833)^2 = (12.3667)^2 = 152.9267$

Step 3: Calculate the Variance

The variance is the average of these squared deviations: $\text{Variance} = \frac{35.6006 + 336.1389 + 152.9267}{3} = \frac{524.6662}{3} = 174.8887$

Step 4: Calculate the Standard Deviation

The standard deviation is the square root of the variance: $\text{Standard Deviation} = \sqrt{174.8887} \approx 13.23\%$

Given the answer choices, none exactly match 13.23%, but the closest answer among the options is:

12.80%

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Would you like more details on this process or have any additional questions?

Here are related questions to consider:

1. How is the variance different from standard deviation in financial contexts?
2. How would the calculation change if we had four years of returns?
3. What is the importance of standard deviation in understanding stock volatility?
4. How does one interpret a higher vs. lower standard deviation in stock returns?
5. What is the effect of extreme values (outliers) on standard deviation in a dataset?

Tip: Standard deviation provides insights into the volatility of returns, with a higher value indicating greater risk and variability.