To calculate the arithmetic return and geometric return for the stock based on the given returns, let's go through the following steps:

1. Arithmetic Return:

   • The arithmetic return is simply the average of the returns over the period.
   • Formula: $\text{Arithmetic Return} = \frac{\sum \text{Returns}}{\text{Number of Returns}}$

   Given returns: $-19.2\%$, $29.2\%$, $26.4\%$, $-10.3\%$, $35\%$, and $27.2\%$.

   $\text{Arithmetic Return} = \frac{-19.2 + 29.2 + 26.4 - 10.3 + 35 + 27.2}{6}$

2. Geometric Return:

   • The geometric return is calculated using the compounded growth rate.
   • Formula: $\text{Geometric Return} = \left( \prod (1 + \text{Return}) \right)^{\frac{1}{\text{Number of Returns}}} - 1$

   Converting each percentage to a decimal: $\text{Returns as decimals} = -0.192, 0.292, 0.264, -0.103, 0.35, 0.272$ Then apply the formula:

   $\text{Geometric Return} = \left((1 - 0.192) \times (1 + 0.292) \times (1 + 0.264) \times (1 - 0.103) \times (1 + 0.35) \times (1 + 0.272)\right)^{\frac{1}{6}} - 1$

I’ll calculate these values for you now.The calculated returns for the stock are as follows:

• Arithmetic Return: $14.72\%$
• Geometric Return: $12.55\%$

Would you like further details on these calculations or have any questions?

Here are some related questions to explore further:

1. How would these returns impact the future value of an investment in this stock?
2. Why might the geometric return be lower than the arithmetic return?
3. How do arithmetic and geometric returns differ in assessing investment performance?
4. How would one calculate the compounded annual growth rate (CAGR) using these returns?
5. What role does volatility play in the difference between arithmetic and geometric returns?

Tip: The geometric return is often used for assessing actual investment growth over time as it accounts for compounding.