H11 - (c): Work out the covariance and the correlation...

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H AAS S CHOOL OF B USINESS U NIVERSITY OF C ALIFORNIA AT B ERKELEY BA 103 A VINASH V ERMA H OMEWORK 11: D UE A UGUST 9, 2011 1. The economy of a given country consists of just three sectors. In terms of market capitalization, Sector 1 makes up 20% of the entire economy, (that is, 20% of the “ market portfolio ”), and the balance is accounted for by Sectors 2 and 3. The market capitalization of Sector 3 is four times as much as that of Sector 2 . The standard deviation of returns on investments is 35% per year for Sector 1, 50% per year for Sector 2, and 25% per year for Sector 3. Returns on Sector 2 are uncorrelated with those on the other two Sectors. The correlation between returns on Sectors 1 and 3 is 0.4325. (a): Work out the variance of the market portfolio. (b): Work out the covariance and the correlation between the returns on investments in Sector 1 and returns on the market portfolio.
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Unformatted text preview: (c): Work out the covariance and the correlation between the returns on investments in Sector 2 and returns on the market portfolio. (d): Work out the covariance and the correlation between the returns on investments in Sector 3 and returns on the market portfolio. (e): Work out the beta between the returns on investments in Sector 1 and returns on the market portfolio. (f): Work out the beta between the returns on investments in Sector 2 and returns on the market portfolio. (g): Work out the beta between the returns on investments in Sector 3 and returns on the market portfolio. (h): Show that the average beta of the three sectors, that is an average of the beta of the three sectors weighted with the fraction that each sector forms of the market portfolio, is one. Homework on Portfolio Theory 1...
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This note was uploaded on 09/11/2011 for the course UGBA 103 taught by Professor Berk during the Summer '07 term at Berkeley.

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