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 singlefactor 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 singlefactor model.
7) Compute the variance of the portfolio assuming the singlefactor 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 singlefactor 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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