Consider the following information Rate of Return if State Occurs Probability of

Question

Consider the following information Rate of Return if State Occurs Probability of State of Economy 20 60 20 Stock A .035 115 190 Stock B 30 20 43 Boom a. Calculate the expected return for the two stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return E(RA E(Rg) 11.4 % 14.60 % b. Calculate the standard deviation for the two stocks. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) Standard deviation OB 24 %

Explanation / Answer

Answer a.

Stock A:

Expected Return = 0.20 * 0.035 + 0.60 * 0.115 + 0.20 * 0.190
Expected Return = 0.114 = 11.40%

Stock B:

Expected Return = 0.20 * (-0.30) + 0.60 * 0.20 + 0.20 * 0.43
Expected Return = 0.146 = 14.60%

Answer b.

Stock A:

Variance = 0.20 * (0.035 - 0.114)^2 + 0.60 * (0.115 - 0.114)^2 + 0.20 * (0.190 - 0.114)^2
Variance = 0.002404

Standard Deviation = (0.002404)^(1/2)
Standard Deviation = 0.0490 = 4.90%

Stock B:

Variance = 0.20 * (-0.30 - 0.146)^2 + 0.60 * (0.20 - 0.146)^2 + 0.20 * (0.43 - 0.146)^2
Variance = 0.057664

Standard Deviation = (0.057664)^(1/2)
Standard Deviation = 0.2401 = 24.01%

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