.A portfolio has $200,000 invested in Asset X and $300,000 in Asset Y. Consider the summary measures in the following table. Measures Expected return (%) Standard deviation (%) Correlation coefficient 8 12 Asset X Asset Y 12 20 0.40 a. Calculate the portfolio weights for Asset X and Asset Y. b. Calculate the expected return for the portfolio. c. Calculate the standard deviation for the portfolio.
Question
.A portfolio has 300,000 in Asset Y. Consider the summary measures in the following table.
Measures
Expected return (%)
Standard deviation (%)
Correlation coefficient
8
12
Asset X Asset Y
12
20
0.40
a. Calculate the portfolio weights for Asset X and Asset Y.
b. Calculate the expected return for the portfolio.
c. Calculate the standard deviation for the portfolio.
Solution
a. Calculate the portfolio weights for Asset X and Asset Y.
The portfolio weight is calculated by dividing the amount invested in each asset by the total amount invested in the portfolio.
For Asset X: Weight of X = Amount invested in X / Total amount invested Weight of X = 200,000 + $300,000) Weight of X = 0.4 or 40%
For Asset Y: Weight of Y = Amount invested in Y / Total amount invested Weight of Y = 200,000 + $300,000) Weight of Y = 0.6 or 60%
b. Calculate the expected return for the portfolio.
The expected return of the portfolio is calculated by multiplying the weight of each asset by its expected return and then adding these values together.
Expected return = (Weight of X * Return of X) + (Weight of Y * Return of Y) Expected return = (0.4 * 8%) + (0.6 * 12%) Expected return = 3.2% + 7.2% = 10.4%
c. Calculate the standard deviation for the portfolio.
The standard deviation of the portfolio is calculated using the following formula:
Standard deviation = sqrt[(weight of X^2 * standard deviation of X^2) + (weight of Y^2 * standard deviation of Y^2) + (2 * weight of X * weight of Y * standard deviation of X * standard deviation of Y * correlation coefficient of X and Y)]
Standard deviation = sqrt[(0.4^2 * 12^2) + (0.6^2 * 20^2) + (2 * 0.4 * 0.6 * 12 * 20 * 0.40)] Standard deviation = sqrt[19.2 + 144 + 57.6] Standard deviation = sqrt[220.8] Standard deviation = 14.86%
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