Question

(Expected rate of return and risk) Summerville Inc. is considering an investment in one of two common stocks. Given the which investment is better, based on the risk (as measured by the standard deviation) information in the popup window: E and return of each? 96 (Round to two decimal places) a. The expected rate of return for Stock A is ]%. (Round to two decimal places) The expected rate of return for Stock B is b. The standard deviation for Stock A is[]%. (Round to two decimal places) The standard deviation for Stock B is [ ]%. (Round to two decimal places) c. Based on the risk (as measured by the standard deviation) and return of each stock, which investment is better? (Select the best choice below.) 0 A. Stock A is better because it has a higher expected rate of return with less risk. O B. Stock B is better because it has a lower expected rate of return with more risk. COMMON STOCK B COMMON STOCK A PROBABILITY RETURN RETURN PROBABILITY -5% 0.20 0.30 11% 0.30 6% 0.40 15% 0.30 0.20 14% 0.30 19% 22% (Click on the icon located on the top-right corner of the data table above in order to copy its contents into a spreadsheet)

Answer 1

Expected Return ER = ΣP_iR_i, where P is the probability and R is the return for Probability state i

Standard deviation = [ΣP_i(R_i - ER)²]^1/2

(a) Expected Return of A = 0.30*0.11 + 0.40*0.15+0.30*0.19 = 0.15 or 15%

Standard Deviation of A = [0.30(0.11-0.15)² + 0.40(0.15-0.15)² + 0.30(0.19-0.15)²]^1/2 = 0.0310 or 3.10%

(b) Expected Return of B = 0.20*(-0.05) + 0.30*0.06 + 0.30*0.14 + 0.20*0.22 = 0.094 or 9.4%

Standard Deviation of B = [0.20(-0.05-0.094)² + 0.30(0.06-0.094)² + 0.30(0.14-0.094)² + 0.20(0.22-0.094)²]^1/2 = 0.0911 or 9.11%

(c) Investment A is better since it has Higher Expected return for lower risk

option (a)