(Expected rate of return and risk) Summerville Inc. is considering an investment

Question

(Expected rate of return and risk) Summerville Inc. is considering an investment in one of two common stocks. Given the information that follows, which investment is better, based on the risk (as measured by the standard deviation) and return of each?

Common Stock A                                             Common Stock B

Probability          Return                                  Probability          Return

0.30                        11%                                        0.20                        -.5%

0.40                        15%                                        0.30                        6%

0.30                        19%                                        0.30                        14%

                                                                                0.20                        22%

Explanation / Answer

Hi,

Please find the answer as follows:

Expectec Return (Stock A) = .30*11 + .40*15 + .30*19 = 15%

Expected Return (Stock B) = .20*-5 + .30*6 + .30*14 + .20*22 = 9.4%

Variance (Stock A) = .30*(11-15)^2 + .40*(15-15)^2 + .30*(19-15)^2 = 9.6%

Variance (Stock B) = .20*(-5-9.4)^2 + .30*(6-9.4)^2 + .30*(14-9.4)^2 + .20*(22-9.4)^2 = 83.04

Standard Deviation (Stock A) = (9.6)^.5 = 3.098 or 3.10%

Standard Deviation (Stock B) = (83.04)^.5 = 9.11%

Stock A is the better investment.

Thanks.

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