The expected returns and standard deviation of returns for two securities are as

Question

The expected returns and standard deviation of returns for two securities are as follows:

Security Z Security Y

Expected Return 15% 35%

Standard Deviation 20% 40%

The correlation between the returns is +0.25.

a) Calculate the expected return and standard deviation for the following portfolios:

i) All in Z

ii) 0.75 in Z and 0.25 in Y

iii) 0.5 in Z and 0.5 in Y

iv) 0.25 in Z and 0.75 in Y

v) All in Y

b) Draw the mean-standard deviation frontier.

c) Which portfolios might not be held by an investor who likes high expected return and low standard deviation? (In other words, which portfolios are on the efficient frontier?)

Explanation / Answer

The expected returns and standard deviation of returns for two securities are as follows:

Security Z Security Y

Expected Return 15% 35%

Standard Deviation 20% 40%

The correlation between the returns is +0.25.

a) Calculate the expected return and standard deviation for the following portfolios:

i) All in Z

Expected Return =15%

Standard Deviation 20%

ii) 0.75 in Z and 0.25 in Y

Expected Return == (.75x15)+(.25x35)= 20%

Standard Deviation= (.75^2x.2^2)+(.25^2x.4^2)+(2x.75x.25x.2x.4x.25)= 4%

iii) 0.5 in Z and 0.5 in Y

Expected Return == (.5x15)+(.5x35)= 25%

Standard Deviation= (.5^2x.2^2)+(.5^2x.4^2)+(2x.5x.5x.2x.4x.25)=6%

iv) 0.25 in Z and 0.75 in Y

Expected Return = (.25x15)+(.75x35)= 30%

Standard Deviation= (.25^2x.2^2)+(.75^2x.4^2)+(2x.75x.25x.2x.4x.25)=10%

v) All in Y

Expected Return = 35%

Standard Deviation = 40%

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