Question #87592

Consider the following information:

Bear Market Normal Market Bull Market

Probability 0.3 0.5 0.2

Return on Stock A -10% 0% 40%

Return on Stock B -5% 5% 50%

a) Calculate and comment upon the expected return and standard deviation of A and B.

b) Assuming that you have Â£20,000 to invest. You have decided to invest Â£10,000 in stock A and the remainder in stock B. Calculate and comment upon the expected return and standard deviation of your portfolio if the correlation between A and B is 0.5.

c) Does a fully diversified portfolio include any risk? Use and explain appropriate diagrams in your answer.

Bear Market Normal Market Bull Market

Probability 0.3 0.5 0.2

Return on Stock A -10% 0% 40%

Return on Stock B -5% 5% 50%

a) Calculate and comment upon the expected return and standard deviation of A and B.

b) Assuming that you have Â£20,000 to invest. You have decided to invest Â£10,000 in stock A and the remainder in stock B. Calculate and comment upon the expected return and standard deviation of your portfolio if the correlation between A and B is 0.5.

c) Does a fully diversified portfolio include any risk? Use and explain appropriate diagrams in your answer.

Expert's answer

a) The expected return is:

%

%

Means for A and B are:

x(A) = (-0.1 + 0 + 0.4)/3 = 0.1,

x(A) = (-0.05 + 0.05 + 0.5)/3 = 0.167,

Standard deviation of A and B is:

or 18.7%.

or 20.8%.

b) Assuming that you have Â£20,000 to invest. You have decided to invest Â£10,000 in stock A and the remainder in stock B. Calculate and comment upon the expected return and standard deviation of your portfolio if the correlation between A and B is 0.5.

or 8%,

or 17.1%.

c) A fully diversified portfolio includes any risk too.

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