You are going to invest all of your funds in one of three projects with the foll

Question

You are going to invest all of your funds in one of three projects with the following

distribution of possible returns:

Project 1                                   Project 2

Standard Deviation 12%            Standard Deviation 19.5%

Probability Return                      Probability Return

50% Chance 20%                      30% Chance 30%

50% Chance -4%                       40% Chance 10%

30% Chance -20%

Project 3

Standard Deviation 12%

Probability Return

10% Chance 30%

40% Chance 15%

40% Chance 10%

10% Chance -21%

Explanation / Answer

E(R) for Project 1 = (0.5) * (0.2) + (0.5) * (-0.04) + (0.3) * (-0.2)

                          = 0.1 - 0.02 - 0.06 = 0.02 or 2%

E(R) for Project 2 = (0.3) * (0.3) + (0.4) * (0.1)

                          = 0.09 + 0.04 = 0.13 or 13%

E(R) for Project 3 = (0.1) * (0.3) + (0.4) * (0.15) + (0.4) * (0.1) + (0.1) * (-0.21)

                          = 0.03 + 0.06 + 0.04 - 0.021 = 0.109 or 109%

Standard deviation for Project 1 = 12%

Standard deviation for Project 2 = 19.5%

Standard deviation for Project 3 = 12%

For risk averse investors, Project 3 is suitable since E(R) ie. expected return is more and standard deviation is less.

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