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

Question

Consider the following information: Probability of State Rate of Return if State Occurs Economy of Economy Stock A Stock B Recession .21 .040 – .41 Normal .61 .120 .31 Boom .18 .300 .54 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(RB) % 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 A % B %

Explanation / Answer

Expected Return of Stock A = Probability of economy state * Stock A return of economical state + Probability of normal state * Stock A return of normal state + Probability of boom state * Stock A return of boom state

Or, expected return of stock A = 0.21*0.04 + 0.61*0.12 + 0.3*0.18 = 0.1356 = 13.56%

Expected Return of Stock B = Probability of economy state * Stock B return of economical state + Probability of normal state * Stock B return of normal state + Probability of boom state * Stock B return of boom state

Or, expected return of stock B = 0.21*(-0.41) + 0.61*0.31+ 0.54*0.18 = 0.2002 = 20.02%

SD of Stock A = {(Stock A return of economical state – expected return of stock A) ^ 2 * Probability of economy state + (Stock A return of normal state – expected return of stock A) ^ 2 * Probability of normal state +

(Stock A return of boom state – expected return of stock A) ^ 2 * Probability of boom state} ^ (0.5)

Or, SD of stock A = {(0.040 – 0.1356) ^2*0.21 + (0.12-0.1356) ^2*0.61 + (0.3-0.1356) ^2*0.18} ^ (0.5)

Or, SD of stock A = {0.001919 + 0.0001484 + 0.004865} ^ (0.5) = 8.33%

SD of Stock B = {(Stock B return of economical state – expected return of stock B) ^ 2 * Probability of economy state + (Stock B return of normal state – expected return of stock B) ^ 2 * Probability of normal state +

(Stock B return of boom state – expected return of stock B) ^ 2 * Probability of boom state} ^ (0.5)

SD of Stock B = {(-0.41-0.2002)^2*0.21 + (0.31-0.2002)^2*0.61 + (0.54-0.2002)^2*0.18}^ (0.5)

Or, SD of stock B = {0.0782 + 0.007354 + 0.0208} ^ (0.5) = 32.61%

Stocks

Return

Standard Deviation

A

13.56%

8.33%

B

20.02%

32.61%

Stocks

Return

Standard Deviation

A

13.56%

8.33%

B

20.02%

32.61%

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