As a risk averse investor, which of the following four otherwise identical investment would you prefer? Security W, which exhibits a standard deviation of 2% and offers an average return of 12%. Security Z, which exhibits a standard deviation of 2% and offers an average return of 8%. Security X, which exhibits a standard deviation of 4% and offers an average return of 12%. Security Y, which exhibits a standard deviation of 4% and offers an average return of 8%.

Step-by-step explanation:

Assuming normal distribution,

The right investment should be the one that gives a high probability or cover a larger area under the probability distribution curve assuming the same time of return. Subjecting the given statistics to

Area = x + 3 (sd)

Where x is the mean, SD = standard deviation

Given the mean

Xw = 12%, Sd = 2%. of Security W

Xz = 8%, Sd = 2% of Security Z

Xx = 12%, Sd = 4% of Security X

XY = 8%, Sd = 4% of Security Y

Area Xw = 0.12 + 3 (0.02)

= 0.12 + 0.06

= 0.18 unit square

Area Xz = 0.08 + 3 (0.02)

= 0.08 + 0.06

= 0.14 unit square

Area Xx = 0.12 + 3 (0.04)

= 0.12 + 0.12

= 0.24 unit square

Xy = 0.08 + 3 (0.04)

= 0.08 + 0.12

= 0.20 unit square

Now since the area under the represent probability. We assume this probability of return. Hence the investment Xx will give a higher return than all. The Security X is a good one