Math Problem Statement
Solution
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:
2009:
2010:
2011:
2012:
Part b: Calculate the average return
The average return (expected value) over these 4 years is calculated as:
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.
Variance:
Standard Deviation:
Part d: Coefficient of Variation
The coefficient of variation (CV) is calculated as:
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:
- How would different dividend payments affect the rate of return calculation?
- What would happen if one of the years had a negative rate of return?
- How can the coefficient of variation be useful in comparing different stocks?
- How does the standard deviation impact the risk assessment of an investment?
- 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.
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Math Problem Analysis
Mathematical Concepts
Finance
Statistics
Probability
Formulas
Rate of Return = (End Price - Beginning Price) / Beginning Price
Average Return = Sum of Rates of Return / Number of Years
Variance = Sum of Squared Deviations / Number of Years
Standard Deviation = Square Root of Variance
Coefficient of Variation = Standard Deviation / Average Return
Theorems
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Suitable Grade Level
Advanced High School
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