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:

  1. Average Returns:

    • X: 8.40%8.40\%
    • Y: 14.60%14.60\%
  2. Variance:

    • X: 260.300000260.300000
    • Y: 535.800000535.800000
  3. Standard Deviation:

    • X: 16.13%16.13\%
    • Y: 23.15%23.15\%

Would you like further details or have any questions?

Here are some related questions you might consider:

  1. How do average returns affect portfolio performance over time?
  2. What does the variance indicate about the risk associated with X and Y?
  3. How does the standard deviation relate to the expected range of returns?
  4. Could you interpret the relative riskiness of X and Y based on their standard deviations?
  5. 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