Question

In: Finance

Consider the following information: Rate of Return if State Occurs State of Economy Probability of State...

Consider the following information: Rate of Return if State Occurs State of Economy Probability of State of Economy Stock A Stock B Recession 0.30 0.06 –0.20 Normal 0.30 0.11 0.11 Boom 0.40 0.15 0.28 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.) 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.)

Solutions

Expert Solution

Expected Return of A = 11.10%

Expected Return of B = 8.50%

Standard Deviation of A = 3.73%

Standard Deviation of B = 19.94%

Notes:

Stock A:

State of Economy Probability Expected Stock Return on Stock Expected Return ( Probability * Expected Stock Return)
Recession 0.30 0.06 0.0180
Normal 0.30 0.11 0.0330
Boom 0.40 0.15 0.0600
Expected Return   0.1110
Expected Return   % 11.10 %
State of Economy Probability Probable Return Deviation ( Probable Return- Expected Return) Deviation Squared Product ( Deviation Squared* Probability)
Recession 0.30 6.00 -5.100 26.010000 7.80300
Normal 0.30 11.00 -0.100 0.010000 0.00300
Boom 0.40 15.00 3.900 15.210000 6.08400
Variance ( Sum of Product) 13.89000
Standard Deviation (Square root of Variance) 3.73 %

Stock B:

State of Economy Probability Stock Return Expected Return   ( Probability * Expected Return
Recession 0.30 -0.20 -0.0600
Normal 0.30 0.11 0.0330
Boom 0.40 0.28 0.1120
Expected Return   0.0850
Expected Return % 8.50 %
State of Economy Probability Probable Return Deviation ( Probable Return- Expected Return) Deviation Squared Product ( Deviation Squared* Probability)
Recession 0.30 -20.00 -28.5 812.25 243.675
Normal 0.30 11.00 2.5 6.25 1.875
Boom 0.4 28.00 19.5 380.25 152.1
Variance 397.6500
Standard Deviation 19.94%

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