https://file.aiquickdraw.com/mathbot/file/172536591676404lm2moi.jpg

Let's break down the problem step by step.

### Part a: Calculate the rate of return for each year

The rate of return for each year is calculated using the formula:
\[
\text{Rate of Return} = \frac{\text{End Price} - \text{Beginning Price}}{\text{Beginning Price}}
\]

#### 2009:
\[
\text{Rate of Return} = \frac{21.55 - 14.36}{14.36} = \frac{7.19}{14.36} \approx 0.5007 \text{ or } 50.07\%
\]

#### 2010:
\[
\text{Rate of Return} = \frac{64.78 - 21.55}{21.55} = \frac{43.23}{21.55} \approx 2.0056 \text{ or } 200.56\%
\]

#### 2011:
\[
\text{Rate of Return} = \frac{72.38 - 64.78}{64.78} = \frac{7.60}{64.78} \approx 0.1173 \text{ or } 11.73\%
\]

#### 2012:
\[
\text{Rate of Return} = \frac{91.80 - 72.38}{72.38} = \frac{19.42}{72.38} \approx 0.2683 \text{ or } 26.83\%
\]

### Part b: Calculate the average return

The average return (expected value) over these 4 years is calculated as:
\[
\text{Average Return} = \frac{\sum (\text{Rate of Return})}{\text{Number of Years}} = \frac{0.5007 + 2.0056 + 0.1173 + 0.2683}{4} = \frac{2.8919}{4} \approx 0.722975 \text{ or } 72.30\%
\]

### Part c: Calculate the standard deviation of returns

The standard deviation measures the variability of returns. First, calculate the squared deviations from the mean for each year, then find the variance, and finally take the square root of the variance to get the standard deviation.

1. \( (0.5007 - 0.7230)^2 \approx 0.04949 \)
2. \( (2.0056 - 0.7230)^2 \approx 1.64119 \)
3. \( (0.1173 - 0.7230)^2 \approx 0.36690 \)
4. \( (0.2683 - 0.7230)^2 \approx 0.20715 \)

Variance:
\[
\text{Variance} = \frac{0.04949 + 1.64119 + 0.36690 + 0.20715}{4} \approx \frac{2.26473}{4} \approx 0.56618
\]

Standard Deviation:
\[
\text{Standard Deviation} = \sqrt{0.56618} \approx 0.7525 \text{ or } 75.25\%
\]

### Part d: Coefficient of Variation

The coefficient of variation (CV) is calculated as:
\[
\text{Coefficient of Variation} = \frac{\text{Standard Deviation}}{\text{Average Return}} = \frac{0.7525}{0.7230} \approx 1.041
\]

### Part e: Decision regarding inclusion in the portfolio

Since Mike's rule is to only include securities with a coefficient of variation below 0.90, the Hi-Tech stock with a CV of 1.041 should **not** be included in his portfolio.

---

### Do you want details or have any questions? 

Here are some relative questions to consider:
1. How would different dividend payments affect the rate of return calculation?
2. What would happen if one of the years had a negative rate of return?
3. How can the coefficient of variation be useful in comparing different stocks?
4. How does the standard deviation impact the risk assessment of an investment?
5. Could this method be applied to other financial metrics besides stock returns?

**Tip:** When analyzing investment returns, always consider the risk associated with the standard deviation and coefficient of variation, as they can give you a clearer picture of the investment’s performance stability.

The query submitted by the user: Calculate the rate of return for each year and determine the average return, standard deviation of returns, coefficient of variation, and decision regarding inclusion in the portfolio.

Learn how to calculate the rate of return for stocks over multiple years, determine the average return, standard deviation, coefficient of variation, and make portfolio inclusion decisions based on financial metrics. Suitable for advanced high school students or anyone interested in finance and investment analysis.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation