PLEASE LEAVE IN DECIMAL FORM & SHOW WORK THANK YOU AVERAGES -0.0069 0.0018 0.001

Question

PLEASE LEAVE IN DECIMAL FORM & SHOW WORK THANK YOU

AVERAGES

-0.0069

0.0018

0.0015

covariance matrix:

1. For a portfolio formed by 40% in the SP500 and 60% in A. Calculate the return on the portfolio.

2. Using the covariance matrix from question 7, calculate the variance of the portfolio formed by 40% in the SP500 and 60% in A.

3. Using the variance from question 8, calculate the standard deviation of the portfolio formed by 40% in the SP500 and 60% in A.

4. Using the averages from question 7, calculate the average of a portfolio formed by 30% in A and 70% in B.

5. Using the covariance matrix from question 7, calculate the variance of a portfolio formed by 30% in A and 70% in B.

6. Using the variance from question 12, calculate the standard deviation for the portfolio formed by 30% in A and 70% in B.

-0.0069

0.0018

0.0015

Explanation / Answer

1. Return of the portfolio = (weight of A)*Return of A + Weight of SP500* Return of SP500
= 0.6*0.0018 +0.4*-0.0069
= -0.00168

2. Variance of the portfolio = (weight of A)^2 * Variance of A +(weight of SP500)^2 *Variance of SP500 +2*weight of A*Weight of SP500*Covariance of A and SP500
= 0.003559

3. Standard deviation of portfolio = Square root of variancce
= 0.059659

4. Return of the portfolio = (weight of A)*Return of A + Weight of B* Return of B
= 0.3*0.0018 +0.7*0.0015
= 0.00159

5. Variance of the portfolio = (weight of A)^2 * Variance of A +(weight of B)^2 *Variance of B +2*weight of A*Weight of B*Covariance of A and B
= 0.3*0.3*0.0041+0.7*0.7*0.00824+2*0.3*0.7*0.00514
= 0.006565

6. Standard deviation of portfolio = Square root of variancce
= 0.081027

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