Math Problem Statement
Use the following returns for X and Y.
Year Returns X Y 1 22.5% 28.5% 2 −17.5 −4.5 3 10.5 30.5 4 21.0 −16.0 5 5.5 34.5 Calculate the average returns for X and Y.
Note: Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.
Calculate the variances for X and Y.
Note: Do not round intermediate calculations and round your answers to 6 decimal places, e.g., .161616.
Calculate the standard deviations for X and Y.
Note: Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.
Solution
Here are the results for the given returns of X and Y:
-
Average Returns:
- X:
- Y:
-
Variance:
- X:
- Y:
-
Standard Deviation:
- X:
- Y:
Would you like further details or have any questions?
Here are some related questions you might consider:
- How do average returns affect portfolio performance over time?
- What does the variance indicate about the risk associated with X and Y?
- How does the standard deviation relate to the expected range of returns?
- Could you interpret the relative riskiness of X and Y based on their standard deviations?
- How would adding these assets to a portfolio impact its overall volatility?
Tip: Standard deviation provides insight into the volatility of an investment, indicating the range in which returns are expected to fall.
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Math Problem Analysis
Mathematical Concepts
Statistics
Variance
Standard Deviation
Average/Mean
Formulas
Average Return: (X1 + X2 + X3 + X4 + X5) / 5
Variance: (Σ(Xi - μ)²) / n
Standard Deviation: √Variance
Theorems
Law of Large Numbers
Properties of Variance and Standard Deviation
Suitable Grade Level
Grades 10-12
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