Question

Consider the following probability distribution for stocks A and B: State Probability Return on Stock A Return on Stock B 1 0.10 10 % 8 % 2 0.20 13 % 7 % 3 0.20 12 % 6 % 4 0.30 14 % 9 % 5 0.20 15 % 8 % The expected rate of return and standard deviation of the global minimum variance portfolio, G, are ________ and ________, respectively.

Answer 1

It can be deduced that the expected rates of return of stocks A and B are 13.2% and 7.7% respectively.

How to calculate the expected rates of return

E(RA) = 0.1 (10%) + 0.2 (13%) + 0.2 (12%) + 0.3 (14%) + 0.2 (15%)= 13.2%

E(RB) = 0.1 (8%) + 0.2 (7%) + 0.2 (6%) + 0.3 (9%) + 0.2 (8%)= 7.7%

Therefore, the expected rates of return of stocks A and B are 13.2% and 7.7% respectively.

The standard deviation will be calculated thus:

Var(RA) = [0.1 (10%-13.2%)² + 0.2 (13%-13.2%)² + 0.2 (12%-13.2%)² + 0.3 (14%-13.2%)² + 0.2 (15%-13.2%)2 ] 1/2

= 1.5%

Var(RB) = [0.1 (8%-7.7%)² + 0.2 (7%-7.7%)² + 0.2 (6%-7.7%)² + 0.3(9%-7.7%)² + 0.2 (8%-7.7%)² ] 1/2

= 1.1%

Therefore, the standard deviation of stocks A and B are 1.5% and 1.1% respectively.

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