Consider the following information: Your portfolio is invested 20 percent each i

Question

Consider the following information:

Your portfolio is invested 20 percent each in A and C, and 60 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

What is the standard deviation? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

   

Rate of Return if State Occurs State of Probability of Economy State of Economy Stock A Stock B Stock C   Boom .40 .18 .40 .29   Good .25 .15 .22 .11   Poor .30 .01 –.09 –.06   Bust .05 –.07 –.24 –.09

Explanation / Answer

(a) Your portfolio is invested 20 percent each in A and C, and 60 percent in B, then the expected return of the portfolio=

b. (1)  the variance of this portfolio = 0.018 + 0.0004 + 0.0513 = 0.0697 / 3

= 0.023233 or 2.3233 %

b. (2)  theStandard Deviation of this portfolio =

Standard Deviation = Squar Root [0.00600695 - (0.0697)2]

= Square Root (0.00114886)

= 0.0339 or 3.39 %

Probability Rate of Return Expected return A B C A B C 0.40 0.18 0.40 0.29 0.072 0.16 0.116 0.25 0.15 0.22 0.11 0.035 0.055 0.0275 0.30 0.01 -0.09 -0.06 0.003 -0.027 -0.018 0.05 -0.07 -0.24 -0.09 -0.20 -0.190 -0.040 TOTAL EXPECTED 0.09 0.002 0.0855 INVESTED % 20 20 60 0.018 0.0004 0.0513 EXPECTED RETURN OF THE PORTFOLIO = 0.0697 = 6.97%

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