To solve this, we will first define the given stock returns for four years:

• Year 1: -3.69%
• Year 2: 28.44%
• Year 3: 12.38%
• Year 4: 4.48%

Step-by-Step Breakdown

a. Average Annual Return

The average annual return ($\bar{r}$) is the arithmetic mean of the returns over the four years. We calculate it as:

$\bar{r} = \frac{r_1 + r_2 + r_3 + r_4}{4}$

Where:

• $r_1 = -3.69\%$
• $r_2 = 28.44\%$
• $r_3 = 12.38\%$
• $r_4 = 4.48\%$

b. Variance of Stock Returns

The variance ($\sigma^2$) measures how much the returns deviate from the average return. It is calculated as:

$\sigma^2 = \frac{(r_1 - \bar{r})^2 + (r_2 - \bar{r})^2 + (r_3 - \bar{r})^2 + (r_4 - \bar{r})^2}{4}$

c. Standard Deviation of Stock Returns

The standard deviation ($\sigma$) is the square root of the variance:

$\sigma = \sqrt{\sigma^2}$

Let me calculate the values for you.### a. Average Annual Return The average annual return is 10.40% (rounded to two decimal places).

b. Variance of the Stock's Returns

The variance of the stock's returns is 140.73412 (rounded to five decimal places).

c. Standard Deviation of the Stock's Returns

The standard deviation of the stock's returns is 11.86% (rounded to two decimal places).

Let me know if you would like further details or explanations. Here are five related questions to expand your understanding:

1. How does the average return differ from the geometric mean return?
2. How would an increase in stock volatility affect the standard deviation?
3. What are the implications of a high variance in stock returns?
4. How is the variance of returns different from the covariance between two stocks?
5. What other methods can be used to measure the risk of a stock's returns?

Tip: The standard deviation is a key measure of risk, helping investors understand the volatility of an investment.