"Estimate the weights (wi) for assets in the three portfolios given the following information about the portfolio holdings:
"
Price Number of securities Market value Portfolio weights Percentages to one decimal place
a. Stock A $25 200 500 0.22522523 22.50%
Stock B $53 100 5300 0.23873874 23.90%
Stock C $119 100 11900 0.53603604 53.60%
Total Value 22200
Price Number of securities Market value Portfolio weights Percentages to one decimal place
b. Bond A $975 10 5000 22200 22.52%
Bond B $1,020 20 5300 22200 23.88%
Bond C $888 10 11900 22200 53.60%
Bond D $1,150 10
Total Value
Price Number of securities Market value Portfolio weights Percentages to one decimal place
c. Stock A $25 1,000
Stock C $119 500
Bond D $1,150 20
Total Value
Price Number of securities Market value Portfolio weights Percentages to one decimal place
d. Stock B $53 1,000
Stock C $119 100
Bond A $975 20
Bond B $1,020 10
Total Value
To estimate the weights (wi) for assets in the three portfolios, you need to calculate the portfolio weight for each individual asset.
a) For Portfolio a:
- Stock A has a market value of $500, so its portfolio weight is calculated as $500 divided by the total value of the portfolio, which is $22,200.
- Stock B has a market value of $5,300, so its portfolio weight is calculated as $5,300 divided by $22,200.
- Stock C has a market value of $11,900, so its portfolio weight is calculated as $11,900 divided by $22,200.
The portfolio weights for the assets in Portfolio a are:
- Stock A: 0.22522523 (22.50%)
- Stock B: 0.23873874 (23.90%)
- Stock C: 0.53603604 (53.60%)
b) For Portfolio b:
- Bond A has a market value of $5,000, so its portfolio weight is calculated as $5,000 divided by the total value of the portfolio, which is $22,200.
- Bond B has a market value of $5,300, so its portfolio weight is calculated as $5,300 divided by $22,200.
- Bond C has a market value of $11,900, so its portfolio weight is calculated as $11,900 divided by $22,200.
- Bond D has a market value that is not provided, so the portfolio weight for Bond D cannot be calculated without more information.
The portfolio weights for the assets in Portfolio b are:
- Bond A: 0.22522523 (22.52%)
- Bond B: 0.23873874 (23.88%)
- Bond C: 0.53603604 (53.60%)
c) For Portfolio c:
- Stock A has a market value of $1,000, so its portfolio weight is calculated as $1,000 divided by the total value of the portfolio.
- Stock C has a market value of $500, so its portfolio weight is calculated as $500 divided by the total value of the portfolio.
- Bond D has a market value of $20, so its portfolio weight is calculated as $20 divided by the total value of the portfolio.
The portfolio weights for the assets in Portfolio c cannot be calculated without knowing the total value of the portfolio.
d) For Portfolio d:
- Stock B has a market value of $1,000, so its portfolio weight is calculated as $1,000 divided by the total value of the portfolio.
- Stock C has a market value of $100, so its portfolio weight is calculated as $100 divided by the total value of the portfolio.
- Bond A has a market value of $20, so its portfolio weight is calculated as $20 divided by the total value of the portfolio.
- Bond B has a market value of $10, so its portfolio weight is calculated as $10 divided by the total value of the portfolio.
The portfolio weights for the assets in Portfolio d cannot be calculated without knowing the total value of the portfolio.
To estimate the weights (wi) for assets in the three portfolios, we need to divide the market value of each asset by the total value of the portfolio.
a) Portfolio A:
Stock A: Market value = $500, Total value = $22,200
Weight (wi) = Market value / Total value = $500 / $22,200 = 0.22522523 or 22.50%
Stock B: Market value = $5,300, Total value = $22,200
Weight (wi) = Market value / Total value = $5,300 / $22,200 = 0.23873874 or 23.90%
Stock C: Market value = $11,900, Total value = $22,200
Weight (wi) = Market value / Total value = $11,900 / $22,200 = 0.53603604 or 53.60%
b) Portfolio B:
Bond A: Market value = $5,000, Total value = $22,200
Weight (wi) = Market value / Total value = $5,000 / $22,200 = 0.22522523 or 22.52%
Bond B: Market value = $5,300, Total value = $22,200
Weight (wi) = Market value / Total value = $5,300 / $22,200 = 0.23873874 or 23.88%
Bond C: Market value = $11,900, Total value = $22,200
Weight (wi) = Market value / Total value = $11,900 / $22,200 = 0.53603604 or 53.60%
Bond D: Not provided, Total value not provided
c) Portfolio C:
Stock A: Market value = $n/a, Total value = $n/a
Weight (wi) = Market value / Total value = unavailable
Stock C: Market value = $n/a, Total value = $n/a
Weight (wi) = Market value / Total value = unavailable
Bond D: Not provided, Total value not provided
d) Portfolio D:
Stock B: Market value = $n/a, Total value = $n/a
Weight (wi) = Market value / Total value = unavailable
Stock C: Market value = $n/a, Total value = $n/a
Weight (wi) = Market value / Total value = unavailable
Bond A: Market value = $n/a, Total value = $n/a
Weight (wi) = Market value / Total value = unavailable
Bond B: Market value = $n/a, Total value = $n/a
Weight (wi) = Market value / Total value = unavailable
Please note that for portfolios c and d, the market values and total values are not given, so it is not possible to calculate the weights (wi) for the assets.