Question

Rate of Return if State Occurs Probability of State of State of Economy Recession Economy Stock A Stock B 0.20 0.06 -0.11 Normal 0.55 0.13 0.17 Вoom 0.25 0.18 0.37 a. Calculate the expected return for the two stocks. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Answer is complete but not entirely correct. Expected return for A Expected return for B % 12.85 0.95 b. Calculate the standard deviation for the two stocks. (Do not round your intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.) Standard deviation for A Standard deviation for B

Answer 1

a). Expected Return = [Probability(i) * Return(i)]

=1

Stock A's Expected Return = [0.20 * 6%] + [0.55 * 13%] + [0.25 * 18%]

= 1.2% + 7.15% + 4.5% = 12.85%

Stock B's Expected Return = [0.20 * -11%] + [0.55 * 17%] + [0.25 * 37%]

= -2.2% + 9.35% + 9.25% = 16.4%

b). Standard Deviation = [{Probability(i) * (Expected Return - Return(i))²}]^1/2

=1

Stock A's Standard Deviation = [{0.20 * (12.85% - 6%)²} + {0.55 * (12.85% - 13%)²} + {0.25 * (12.85% - 18%)²}]^1/2

= [9.3845%² + 0.012375%² + 6.630625%²]^1/2

= [16.0275%²]^1/2

= 4.00%

Stock B's Standard Deviation = [{0.20 * (16.4% + 11%)²} + {0.55 * (16.4% - 17%)²} + {0.25 * (16.4% - 37%)²}]^1/2

= [150.152%² + 0.198%² + 106.09%²]^1/2

= [256.44%²]^1/2

= 16.01%