residual variance of the portfolio

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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