Question

Portfolio Standard DeviationSuppose the expected returns and standard deviations of Stocks A and B are E(RA) = .11, E(RB) = .13, σA = .47, and σB = .81. a.Calculate the expected return and standard deviation of a portfolio that is composed of 40 percent A and 60 percent B when the correlation between the returns on A and B is .5. b.Calculate the standard deviation of a portfolio with the same portfolio weights as in part (a) when the correlation coefficient between the returns on A and B is −.5. c.How does the correlation between the returns on A and B affect the standard deviation of the portfolio?

Answer 1

Calculation of expected return of the portfolio:

Hence expected return of the portfolio is .122000.

Calculation of Standard Deviation of the Portfolio:

SD_A=.47

SD_B=.81

Weight(W_A)=.4

Weight(W_B)=.6

SD of Portfolio=

  

  

  

      

=.60242(approx)

If the correlation between the returns of A and B is -.5, SD of Portfolio shall be as follows:

=.4245(Approx)

Negative correlation between the returns of the securities of a portfolio reduces the risk because loss of one security shall be set off by profit of another securities.

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