Question

Consider the following information: Economy Economy Rate of Return If State Occurs State of Probability of - State of Stock A Stock B Recession 20 .05 - 20 Normal 57 Boom 23 26 08 .09 a. Calculate the expected return for Stocks A and B. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) b. Calculate the standard deviation for Stocks A and B. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) a. ſ Stock A expected return Stock B expected return Stock A standard deviation Stock B standard deviation 8.55% 7.11 2.691

Answer 1

State of Economy	Probability	Stock A return	Stock B return
Recession	0.2	0.05	-0.2
Normal	0.57	0.08	0.09
Boom	0.23	0.13	0.26

Expected Return

Expected Return when the probabilities of different state of economies are given is calculated using the formula:

Expected return = E[R] = p₁*R₁ + p₂*R₂ + p₃*R₃

Expected return for Stock A = E[R_A] = 0.2*0.05 + 0.57*0.08 + 0.23*0.13 = 0.01 + 0.0456 + 0.0299 = 0.0855 = 8.55%

Expected return for Stock B = E[R_B] = 0.2*(-0.20) + 0.57*0.09 + 0.23*0.26 = -0.04 + 0.0513 + 0.0598 = 0.0711 = 7.11%

Standard Deviation

Variance of the return, when different state of economies are given, can be calculated using the below formula:

Variance = σ² = p₁*( R₁ - E[R])² + p₂*( R₂ - E[R])² + p₃*( R₃ - E[R])²

For A

E[R_A] = 0.0855

Variance of stock A = σ_A² = 0.2*( 0.05-0.0855)² + 0.57*( 0.08-0.0855)² + 0.23*( 0.13-0.0855)² = 0.00072475

Stadard Deviation is square-root of varance

Standard Deviation of A = σ_A = (0.00072475)^1/2 = 0.0269211812519436 = 2.69211812519436% ~ 2.69%

For B

E[R_A] = 0.0711

Variance of stock B = σ_B² = 0.2*(-0.20-0.0711)² + 0.57*( 0.09-0.0711)² + 0.23*(0.26-0.0711)² = 0.02310979

Stadard Deviation is square-root of varance

Standard Deviation of B = σ_B = (0.02310979)^1/2 = 0.152019044859518 = 15.2019044859518% ~ 15.20%

Answer

Stock A expected return	8.55	%
Stock B expected return	7.11	%
Stock A standard deviation	2.69	%
Stock B standard deviation	15.20	%