You have a portfolio of 4 stocks with equal shares invested in each stock. Variancesof individual stocks are the same and equal to σ2=16. Correlations between each pair of stocks isrho.a) What would be the covariances between each pair of stocks as function of rho.b) Find the variance of equally-portfolio of these 4 stocks (again as a function of rho)c) What happens to the variance of your portfolio when rho increases.d) What would be the variance of your portfolio when rho = 1. Would it be larger or smallerthan the variance of individual stocks σ2 = 16?

Essentials Of Investments
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ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
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Chapter1: Investments: Background And Issues
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You have a portfolio of 4 stocks with equal shares invested in each stock. Variances
of individual stocks are the same and equal to σ2
=16. Correlations between each pair of stocks is
rho.
a) What would be the covariances between each pair of stocks as function of rho.
b) Find the variance of equally-portfolio of these 4 stocks (again as a function of rho)
c) What happens to the variance of your portfolio when rho increases.
d) What would be the variance of your portfolio when rho = 1. Would it be larger or smaller
than the variance of individual stocks σ2 = 16?

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