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 £20,000 to invest. You have decided to invest £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 £20,000 to invest. You have decided to invest £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:

"ER(A) = -0.1\\times0.3 + 0\\times0.5 + 0.4\\times0.2 = 0.05 or 5%,"%

"ER(B) = -0.05\\times0.3 + 0.05\\times0.5 + 0.5\\times0.2 = 0.11 or 11%."%

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:

"s(A) = (0.3\\times(-0.1 - 0.1)^{2} + 0.5\\times(0 - 0.1)^{2} + 0.2\\times(0.4 - 0.1)^{2})^{0.5} = 0.187" or 18.7%.

"s(B) = (0.3\\times(-0.05 - 0.167)^{2} + 0.5\\times(0.05 - 0.167)^{2} + 0.2\\times(0.5 - 0.167)^{2})^{0.5} = 0.208" or 20.8%.

b) Assuming that you have £20,000 to invest. You have decided to invest £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.

"ER = 0.5\\times0.05 + 0.5\\times0.11 = 0.08" or 8%,

"s = (0.5^{2}\\times0.187^{2} + 0.5^{2}\\times0.208^{2} + 2\\times0.5\\times0.5\\times0.5\\times0.187\\times0.208)^{0.5} = 0.171" or 17.1%.

c) A fully diversified portfolio includes any risk too.

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