Suppose that there are four risky assets whose expected returns E(r) and variance- covariance matrix (S) are shown in the spreadsheet below. We also consider the portfolio weights of two portfolios x and y of risky assets (see Cells B8:E9): 8 Portfoliox 9 Portfolio y 13 Variance, 14 Covariance() 15 Correlation P A FOUR-ASSET PORTFOLIO PROBLEM Variance-covariance, S 11 Portfolio x and y statistics: Mean, variance, covariance, correlation 12 Mean 20 Portfolio variance, 21 Portfolio standard deviation o 22 17 Calculating returns of combinations of Portfolio x and Portfolio y 18 Proportion of x 19 Mean portfolio return, 0.10 0.01 0.03 0.05 0.01 0.30 0.06 -0.04 0.20 0.20 10.50% 0.1216 0.0714 0.4540 ? ? ? 0.3 0.03 0.06 0.40 0.02 0.30 0.10 ? 0.05 -0.04 0.02 0.50 0.40 0.10 0.10 Mean, Variance, 0.2014 Question il Question i Mean returns E(r) 7% 9% 11% 20% Question i i. Write the Excel formula used to estimate the mean and variance of portfolio y in cells E12 and E13, respectively. Explain your answer in detail. ii. Write the Excel formula used to estimate the correlation of portfolios x and y in cell B15. iii. Let a portfolio Z which consists of portfolios x and y. The portfolio weight of portfolio x in this new portfolio is 0.3. Estimate portfolio's Z mean return, variance, and standard deviation in cells B19, B20, and B21, respectively. Show your calculations in detail.
Suppose that there are four risky assets whose expected returns E(r) and variance- covariance matrix (S) are shown in the spreadsheet below. We also consider the portfolio weights of two portfolios x and y of risky assets (see Cells B8:E9): 8 Portfoliox 9 Portfolio y 13 Variance, 14 Covariance() 15 Correlation P A FOUR-ASSET PORTFOLIO PROBLEM Variance-covariance, S 11 Portfolio x and y statistics: Mean, variance, covariance, correlation 12 Mean 20 Portfolio variance, 21 Portfolio standard deviation o 22 17 Calculating returns of combinations of Portfolio x and Portfolio y 18 Proportion of x 19 Mean portfolio return, 0.10 0.01 0.03 0.05 0.01 0.30 0.06 -0.04 0.20 0.20 10.50% 0.1216 0.0714 0.4540 ? ? ? 0.3 0.03 0.06 0.40 0.02 0.30 0.10 ? 0.05 -0.04 0.02 0.50 0.40 0.10 0.10 Mean, Variance, 0.2014 Question il Question i Mean returns E(r) 7% 9% 11% 20% Question i i. Write the Excel formula used to estimate the mean and variance of portfolio y in cells E12 and E13, respectively. Explain your answer in detail. ii. Write the Excel formula used to estimate the correlation of portfolios x and y in cell B15. iii. Let a portfolio Z which consists of portfolios x and y. The portfolio weight of portfolio x in this new portfolio is 0.3. Estimate portfolio's Z mean return, variance, and standard deviation in cells B19, B20, and B21, respectively. Show your calculations in detail.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
Transcribed Image Text:Suppose that there are four risky assets whose expected returns E(r) and variance-
covariance matrix (S) are shown in the spreadsheet below. We also consider the portfolio
weights of two portfolios x and y of risky assets (see Cells B8:E9):
1
8 Portfolio x
9 Portfolio y
A FOUR-ASSET PORTFOLIO PROBLEM
Variance-covariance, S
20 Portfolio variance,
21 Portfollo standard deviation o
0.10
0.01
0.03
0.05
11 Portfolio x and y statistics: Mean, variance, covariance, correlation
12 Mean, Ejr,
13 Variance,
14 Covariance()
15 Correlation P
16
17 Calculating returns of combinations of Portfolio x and Portfolio y
18 Proportion of x
19 Mean portfolio return, r
0.01
0.30
0.06
-0.04
0.20
0.20
10.50%
0.1216
0.0714
0.4540
?
?
?
0.3
0.03
0.06
0.40
0.02
0.30
0.10
?
0.05
0.02
0.50
0.40
0.10
0.10
0.60
Mean, Er
Variance, 0.2014
Question il
Question ili
Mean returns E(r)
?
7%
9%
11%
20%
Question i
i. Write the Excel formula used to estimate the mean and variance of portfolio y in cells
E12 and E13, respectively. Explain your answer in detail.
ii. Write the Excel formula used to estimate the correlation of portfolios x and y in cell
B15.
iii. Let a portfolio Z which consists of portfolios x and y. The portfolio weight of portfolio
x in this new portfolio is 0.3. Estimate portfolio's Z mean return, variance, and
standard deviation in cells B19, B20, and B21, respectively. Show your calculations
in detail.
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