Based on the following information, the expected return and standard deviation f

Question

Based on the following information, the expected return and standard deviation for Stock A are _____ percent and ______ percent, respectively. The expected return and standard deviation for Stock B are _____ percent and ______ percent, respectively. (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16))


Rate of Return if State Occurs

State of Economy Probability of State of Economy Stock A Stock B
Recession 0.2 0.03 -0.21
Normal 0.6 0.08 0.16
Boom 0.2 0.14 0.33

Explanation / Answer

Answer

The expected return of an asset is the sum of the probability of each return occurring times the probability of that return occurring. So, the expected return of each stock is:

E(RA) = 0.2(3.0%) + 0.6(8.0%) + 0.2(14.0%) = 8.20%
E(RB) = 0.2(-21.0%) + 0.6(16.0%) + 0.2(33.0%) = 12.00%

To calculate the standard deviation, we first need to calculate the variance.

Variance A^2 =  [0.2(0.03 – 0.082) + 0.6(0.08 – 0.082) + 0.2(0.14 – 0.082)] = 0.001216
Standard deviation A = 0.03487 = 3.49%
Variance B^2 = [0.2(-0.21 – 0.12) + 0.6(0.16 – 0.12) + 0.2(0.33 – 0.12)] = 0.03156
Standard deviation V =0 .17765 = 17.76 %

 

 the expected return and standard deviation for Stock A are 8.20 and 3.49 respectively

 

The expected return and standard deviation for Stock B are 12.00 and 17.76 respectively 

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