residual variance of the portfolio

Question set 1

Project description

Answer these questions:

3) Assume the following:

Residual variance

Stock x .02 cov (Ex, Ey) =.01

Stock Y .06

Also assume that a portfolio of x and y is constructed, with a 2/3 weight for x and a 1/3 weight for y.

a) What is the residual variance of the portfolio if the single-factor model is assumed?

b) What is the residual variance of the portfolio without the single factor model assumption?

Security Beta Residual variance ?^2 r

A .5 .04 .0625

B 1.5 .08 .2825

Suppose an equally weighted portfolio of A and B is formed.

5) what is the beta coefficient for the portfolio?

6) Compute the residual variance of the portfolio assuming the single-factor model.

7) Compute the variance of the portfolio assuming the single-factor model.

8)Fill in the missing columns in the following table. Assume the variance of the market factor (M) to be .0016.

Secutrity i Variance of i Correlation of i with M Beta Systematic Risk Unsystematic risk

i=1 .006 .9

i=2 .006 .3

i=3 .006 0

9) what is the meaning of unsystematic risk?

Use the following data for questions 10,11,12,13,14.

Correlation coefficient between stocks A and B =.50

Standard deviation of the market factor (M) =.10

Correlation of stock with M Standard Deviation

Stock A 0 .10

Stock B 0.5 .20

10) what are the beta values for A and B?

11) What is the covariance between A and B, assuming the single-factor model?

12) What is the True covariance between A and B?

13) Suppose a portfolio was constructed, with weights of .40 for A and .60 for B. What is the beta of this portfolio?

14) compute the variance of the portfolio in question 13, assuming the Markowitz model.

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