Sub: Finance Question:
Calculation of variance of portfolio.

Topic: Portfolio management

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Suppose there are three risky assets, A, B and C with the following expected returns, standard deviations of returns and correlation coefficients. E (rA)= 4% E (rB)=5% E (rC) =15% S.DEVA=5% S.DEVB=7% S.DEVC=10% A, B=0.7 A, C=-0.2 B,C=0.3

QUESTION 1: Solving for the Global Minimum Variance Portfolio Consider a world where there are no risk free assets, and just these three risky assets. Suppose short sales are permitted. Solve for the weights and variance of the global minimum variance portfolio. If short sales are not permitted is the solution affected?

Solution:

Global Minimum Variance Portfolio is that set of portfolios that will provide the minimum level of risk for a given level of expected return. Given a world with just the three given risk assets we can use the Solver function in Excel to ascertain the weights and variance of the global minimum variance portfolio. We have to calculate the Variance Covariance matrix for the given set of assets. While variance is given by the square of Standard Deviation and is thus entered as diagonal values in

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Sub: Finance

Topic: Portfolio management

the matrix, Covariance is given by the product of correlation between two assets and the product of their respective standard deviations (correlation a,b x SD a x SD b) We then have to calculate the Portfolio Variance and Portfolio standard deviation. Using the variance-covariance matrix and “sum product” function in Excel and...

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